From 22c8bd9c6a6cbf3cfef5db863ef6557dc2fafd35 Mon Sep 17 00:00:00 2001 From: James Long Date: Tue, 30 Jun 2026 23:52:08 -0400 Subject: [PATCH] docs: add simulation architecture spec --- .../architecture-synthesis.md | 270 + .../simulation-research/paper-analyses.md | 290 + .../simulation-research/papers/.gitattributes | 1 + .../papers/2016-mysteries-of-dropbox.pdf | Bin 0 -> 291060 bytes .../papers/2019-coverage-guided-pbt.pdf | Bin 0 -> 1367878 bytes .../2021-mbt-web-applications-practice.pdf | Bin 0 -> 1136916 bytes .../2022-pbt-for-metamorphic-testing.pdf | Bin 0 -> 224394 bytes .../papers/2022-stairway-to-verification.pdf | Bin 0 -> 947689 bytes .../papers/2023-quickercheck.pdf | Bin 0 -> 2462102 bytes .../papers/2024-llms-write-good-pbt.pdf | Bin 0 -> 864101 bytes .../papers/2024-pbt-in-practice.pdf | Bin 0 -> 496661 bytes .../papers/2026-agentic-pbt.pdf | Bin 0 -> 403894 bytes .../2026-evolution-python-tests-to-pbt.pdf | Bin 0 -> 231803 bytes 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b/packages/opencode/specs/simulation-research/architecture-synthesis.md @@ -0,0 +1,270 @@ +# Architecture Synthesis For Opencode Simulation + +## Core Direction + +The simulation system should be a real-app, TUI-driven, stateful model-based testing harness. It should not be a custom app command, a forked backend, or a broad reimplementation of opencode services. + +The production app should run normally with one required flag: + +```sh +OPENCODE_SIMULATION=1 bun run dev +``` + +That flag enables narrow foundational layer replacements and starts a frontend-owned simulation WebSocket server. The backend server remains the normal server; simulation-only backend controls are gated behind the flag and are only reached through the frontend control server. + +## Control Surface + +- Frontend TUI process owns the external control server. +- Protocol: JSON-RPC 2.0 over WebSocket. +- Bind loopback only. +- Start at port `40900`, scan upward if occupied, and log/display the actual URL. +- External drivers never talk directly to backend simulation routes. +- The frontend proxies backend simulation control over the same transport the TUI already uses. + +Initial JSON-RPC method families: + +- `ui.state`: screen, elements, focus, generated executable actions. +- `ui.action`: execute real user-level inputs through OpenTUI APIs. +- `ui.render`: force/wait for render and return state. +- `backend.filesystem.seed` / `backend.filesystem.write`. +- `backend.network.register`. +- `backend.llm.enqueue`. +- `backend.snapshot`. +- `trace.list` / `trace.clear` / `trace.export`. +- `run.stabilize`: wait for TUI/backend quiescence and return observations. + +## Action Model + +Actions must stay at real user-input level. The old branch's action vocabulary is the right starting point: + +```ts +type UIAction = + | { type: "typeText"; text: string } + | { type: "pressKey"; key: string; modifiers?: KeyModifiers } + | { type: "pressEnter" } + | { type: "pressArrow"; direction: "up" | "down" | "left" | "right" } + | { type: "focus"; target: number } + | { type: "click"; target: number; x: number; y: number } +``` + +`ui.state` should return both: + +- `elements`: focusable/clickable/editor renderables. +- `actions`: generated executable actions derived from those elements. + +Fake OpenTUI renderer and visible terminal renderer should both adapt to this same action protocol. + +## Foundational Layer Replacement + +Simulation should plug into current `AppNodeBuilder.build(...)` and `AppNodeBuilderV1.build(...)` replacement seams. + +Acceptable core boundaries to swap: + +- `FileSystem.FileSystem` / `FSUtil.Service` where needed. +- `HttpClient.HttpClient`. +- `RequestExecutor` / `LLMClient` or equivalent lowest LLM boundary. +- Process spawner. +- Global paths / env / temp paths. +- Clock/random later, if needed. +- Database path or in-memory DB when simulation requires isolation. + +Avoid replacing application services unless a core boundary is impossible: + +- Do not replace `SessionPrompt`, `SessionProcessor`, `ToolRegistry`, route trees, or app-level provider abstractions as the default approach. +- Do not add a custom `simulate` command as the primary execution path. +- Do not implement a parallel fake app. + +## Trace Model + +The frontend simulation server owns an in-memory append-only trace log by default. + +Trace records should include: + +- Run metadata: app version, seed, renderer mode, simulation URL. +- Initial world setup: filesystem, config, environment, backend state. +- UI observations: screen, elements, generated actions, focused item. +- UI actions: command sent, concrete OpenTUI action, timestamp/order. +- Backend events: session events, provider requests, tool calls/results, permission decisions, status transitions. +- LLM scripts consumed and provider stream chunks. +- Filesystem and network operations/diffs. +- Stabilization boundaries and idle checks. +- Property checks and failures. +- Driver/model prompts and decisions when a model is driving exploration. + +The trace must support: + +- `trace.list`: query recent records. +- `trace.clear`: reset in-memory log. +- `trace.export`: produce JSON suitable for replay or test generation. + +File writing is not required initially, but the trace schema should be JSONL-friendly. + +## Model-Based Core + +The architecture should distinguish five concepts: + +```ts +type Scenario = InitialWorld & { actions: readonly Action[] } +type Action = UIAction | BackendControlAction | DriverAction +type Observation = UIObservation | BackendObservation | TraceObservation +type Model = abstract state machine over observable domains +type Property = (model, observations) => pass | fail | inconclusive +``` + +The model should be an executable specification, not a copy of production implementation. + +Good model properties: + +- Abstract. +- Observable. +- Finite nondeterminism. +- Explicit preconditions and postconditions. +- Valid transition relation. +- Allows multiple valid outcomes where opencode behavior is intentionally nondeterministic. + +Bad model properties: + +- Reimplements `SessionRunner` or provider streaming. +- Mirrors database internals exactly. +- Uses the same branch logic as production code. +- Requires complete knowledge of implementation scheduling. + +## Quiescence + +Quiescence is a first-class command, not a timeout hidden in tests. + +`run.stabilize` should check, as far as possible: + +- TUI render is idle. +- No active runner for the target session. +- No eligible durable input remains unprocessed unless intentionally queued. +- No running tool calls remain. +- Session status is stable. +- Projected transcript is stable across repeated reads. +- Backend event stream has no immediate pending event burst. + +If quiescence cannot be proved, the command should return structured uncertainty instead of silently sleeping. + +## Properties And Oracles + +Initial built-in properties should be simple and high-signal: + +- No frontend/backend crash. +- No unknown external network unless explicitly registered. +- No host filesystem escape. +- No duplicated visible message IDs. +- No orphan tool results. +- Durable prompt admission is not lost. +- Exact prompt retry reconciles or fails according to identity rules. +- Queue/steer promotion preserves documented delivery semantics. +- Interrupt/resume does not duplicate promoted inputs. +- Stabilized sessions have coherent status and transcript. + +Use multiple oracle styles: + +- Invariant checks after every step. +- Model/refinement checks against allowed abstract outcomes. +- Metamorphic checks across related runs. +- Differential checks across app versions, renderers, or storage modes. + +## Generation Strategy + +Start deterministic and structured. + +Inputs to generate: + +- Workspace filesystem shapes. +- Config variants. +- Auth/provider/model states. +- Session histories. +- Prompt text and delivery modes. +- LLM scripts with text, tool calls, errors, chunk boundaries. +- Tool outcomes and permission decisions. +- UI action sequences chosen from `ui.state.actions`. +- Interrupt/restart/crash points. + +Use fast-check later for the external runner: + +- `asyncProperty` for E2E simulation. +- `commands` for model-based command sequences. +- Seed/path replay. +- Shrinking action sequences. + +Do not run huge property suites in CI by default. Use simulation to discover/minimize traces, then generate normal deterministic tests for CI. + +## Coverage Guidance + +The simulation server and runner should collect effectiveness signals from day one: + +- UI element/action coverage. +- App route/screen coverage. +- Backend event type coverage. +- Session state transition coverage. +- Tool/permission outcome coverage. +- Network route coverage. +- Filesystem operation coverage. +- Error/retry/recovery coverage. +- Discarded/precondition-failed cases. + +Later, preserve interesting traces as corpus seeds and mutate them structurally. + +## Shrinking And Test Generation + +Shrinking should operate on semantic trace structures: + +- Remove actions. +- Reduce prompt text. +- Reduce filesystem size. +- Remove unrelated files/config fields. +- Simplify LLM scripts. +- Remove chunks while preserving tool-call validity. +- Move or remove interrupt/restart points. +- Reduce UI navigation before the failing action. + +Generated normal tests should include: + +- Minimal initial world. +- Explicit UI action sequence. +- Explicit LLM/tool/network scripts. +- Stabilization calls. +- Deterministic assertions over semantic observations. + +## LLM/Agent Driver Feedback + +The same WebSocket observations should support model-driven exploration. + +Expose enough semantic context for a model to reason: + +- Screen text. +- TUI elements with roles, labels, selectors, positions, capabilities. +- Available actions. +- Backend snapshot summaries. +- Recent trace records. +- Filesystem summary/diff. +- Network log. +- Session/message/tool summary. +- Property failures and uncertainty. + +Generated properties from models should follow a lifecycle: + +- Proposed from evidence. +- Translated to executable checks. +- Validity checked. +- Soundness checked on normal behavior. +- Coverage/adversarial checked where possible. +- Accepted, refined, or rejected with reason. + +## First Implementation Milestone + +Minimal useful milestone: + +1. `OPENCODE_SIMULATION=1` activates simulation replacements and frontend control server. +2. Frontend starts JSON-RPC WebSocket on `127.0.0.1:40900+`. +3. `ui.state`, `ui.action`, `ui.render`, `trace.list`, `trace.clear`, `trace.export` work. +4. Fake and visible OpenTUI renderers share the same action protocol. +5. Backend simulation controls are proxied through frontend WebSocket. +6. Backend has gated control routes only when simulation flag is enabled. +7. In-memory trace records UI actions, observations, backend control calls, and backend snapshots. +8. Foundational replacements cover at least LLM and network denial/registration. +9. A simple driver can seed LLM response, type a prompt through the TUI, press enter, stabilize, and assert no crash plus response visible. +10. The resulting trace can be exported as deterministic JSON for later replay/test generation. diff --git a/packages/opencode/specs/simulation-research/paper-analyses.md b/packages/opencode/specs/simulation-research/paper-analyses.md new file mode 100644 index 00000000000..ab8537678be --- /dev/null +++ b/packages/opencode/specs/simulation-research/paper-analyses.md @@ -0,0 +1,290 @@ +# Paper Analyses For Simulation Architecture + +This document extracts implementation-relevant lessons from the local paper corpus. The focus is opencode's proposed simulation system: real TUI-driven execution, narrow foundational layer replacement, WebSocket control, trace recording, model-based/property-based exploration, and generated deterministic tests. + +## 2016: Mysteries of Dropbox + +**Main idea:** stateful PBT can find bugs in real, black-box, nondeterministic distributed systems by generating action sequences, recording observations, and checking whether the observation trace has some valid explanation under a small model. + +Useful techniques: + +- Generate commands separately from observed effects. +- Model hidden nondeterministic events explicitly, even when the SUT does not expose them. +- Accept traces if there exists a sequence of hidden events that makes observations valid. +- Maintain possible model states, not a single expected state. +- Make quiescence explicit with a `STABILIZE` command. +- Re-run flaky failures during shrinking when nondeterminism cannot be fully controlled. + +Pitfalls: + +- Quiescence detection can lie. +- A model that is too permissive can explain away real bugs. +- Timing-dependent failures need either scheduler control or repeated validation. +- Raw happens-before modeling can become elegant but impractical. + +Implications for opencode: + +- Do not compare raw transcripts only. Compare observed behavior against allowed abstract outcomes. +- Represent hidden runtime transitions like prompt promotion, session wake, provider turn continuation, tool completion, retries, interrupt delivery, and event projection. +- Add a `drainUntilIdle` or `stabilize` simulation command with strict checks. +- Record all generated commands, UI actions, backend events, provider scripts, tool results, and snapshots in an append-only trace. +- Shrinking should preserve semantic validity and revalidate nondeterministic failures. + +## 2019: Coverage Guided, Property Based Testing + +**Main idea:** plain random generators often fail when valid inputs have sparse semantic preconditions. Coverage-guided PBT keeps interesting inputs and mutates structured values to explore deeper states. + +Useful techniques: + +- Maintain a corpus of inputs that improve coverage. +- Mutate typed structures rather than raw bytes. +- Keep both successful seeds and promising discarded seeds. +- Fall back to random generation when mutation stalls. +- Use coverage and progress counters, not only binary edge coverage. + +Pitfalls: + +- Instrumenting irrelevant framework code hurts performance. +- Generic mutators can explode in search space. +- Expert handwritten generators still outperform generic mutation but are expensive. + +Implications for opencode: + +- Preserve interesting `Scenario` and `Trace` seeds. +- Add structured mutators for prompts, tool calls, provider chunks, permission decisions, filesystems, config, interrupt timing, crash/restart points, and scheduler actions. +- Track semantic novelty: event types, session states, tool outcomes, permission branches, replay/recovery paths, and UI routes. +- Avoid byte fuzzing as the core; use it only inside fields that are naturally bytes/text. + +## 2021: Model-Based Testing In Practice + +**Main idea:** MBT works in industrial E2E systems when models are pragmatic, visible, and integrated into normal automation. Graph-like models are useful because actions and assertions are explicit and coverage is understandable. + +Useful techniques: + +- Model nodes as states/checkpoints and edges as actions. +- Split large systems into small composable models. +- Use traversal strategies, weights, and stop conditions. +- Report paths, coverage, and model transitions. + +Pitfalls: + +- Heavy formal models reduce adoption. +- Auto-inferred models can be noisy and costly to clean up. +- Coverage metrics must be live and inspectable. + +Implications for opencode: + +- Start with a small simulation DSL, not a complete formal model. +- Model domains separately: session lifecycle, prompt admission, queue/steer, tool execution, permissions, interrupts, compaction, crash/restart. +- Track command coverage, transition coverage, property coverage, and failure-mode coverage. +- Keep generated failure output readable: model path, user inputs, app observations, violated invariant. + +## 2022: Property-Based Testing For Metamorphic Testing + +**Main idea:** metamorphic testing helps when exact expected outputs are unavailable. It checks relations between multiple executions or transformed inputs. + +Useful techniques: + +- Generate source cases, derive follow-up cases, and compare related outputs. +- Use generators and shrinkers that preserve relation validity. +- Combine multiple metamorphic relations. + +Pitfalls: + +- Weak metamorphic relations miss real faults. +- Naive shrinkers can break validity. +- Reimplementing production logic in the oracle makes the test useless. + +Implications for opencode: + +- Use metamorphic relations for nondeterministic model behavior. +- Examples: + - Same prompt ID and same delivery mode should reconcile exactly on retry. + - Queueing independent prompts should preserve durable admission order. + - Interrupt/resume should not duplicate promoted user messages or orphan tool results. + - Crash after durable admission should not invent provider work unless recovery explicitly permits it. + - Fake renderer and visible renderer should agree on semantic action results. + - Two app versions should satisfy the same semantic invariants for the same trace. + +## 2022: Climbing The Stairway To Verification + +**Main idea:** PBT becomes stronger when it mirrors a refinement/specification structure. The test asks whether implementation behavior refines an executable abstract model. + +Useful techniques: + +- Generate one canonical test case and project it into abstract and concrete worlds. +- Compare implementation output to a finite set of model-allowed outcomes. +- Keep models abstract and observable. +- Use executable specs as cheaper, incremental versions of formal proofs. + +Pitfalls: + +- The model can become a second implementation. +- Strong preconditions plus random generation cause excessive discarded tests. +- Overly abstract nondeterminism can explode. + +Implications for opencode: + +- Build simulation around `scenario -> model outcomes -> real app run -> relation check`. +- The model should represent visible session, message, tool, provider, permission, event, status, and filesystem effects. +- The model must not reimplement `SessionRunner`, provider streaming, tool registry, or Effect scheduling. +- Generate concrete scenarios and derive abstract model inputs from them. + +## 2023: QuickerCheck + +**Main idea:** PBT and shrinking can be parallelized, especially for expensive properties, if workers have isolated state and reproducible seeds. + +Useful techniques: + +- Give each worker its own PRNG seed and size schedule. +- Stop all workers after the first counterexample. +- Run cleanup/finalizers for interrupted effectful properties. +- Use greedy parallel shrinking when deterministic minimality is less important than speed. + +Pitfalls: + +- Shared filesystem/global state breaks parallel PBT. +- Cancellation can leave processes, files, sockets, or locks behind. +- Parallel shrinking can be slower for cheap properties. + +Implications for opencode: + +- Design simulation workers as isolated from the start: workspace, DB, ports, fake providers, random seeds, trace buffers. +- Use `(campaignSeed, workerID, caseIndex)` for reproducibility. +- Separate fast local runs from long parallel campaigns. +- Add cleanup boundaries for every case. + +## 2024: Can Large Language Models Write Good Property-Based Tests? + +**Main idea:** LLMs can synthesize useful PBTs, but generated tests must be validated for validity, soundness, and property coverage. Two-stage prompting outperforms monolithic generation. + +Useful techniques: + +- First extract properties, then generate tests for one property at a time. +- Classify failures as invalid test, unsound property, weak property, or real bug. +- Use mutation/property coverage to check whether a property actually detects violations. + +Pitfalls: + +- Passing generated tests can be weak. +- LLMs overgeneralize documentation and miss implicit preconditions. +- Mutation coverage can be noisy if mutants are invalid or equivalent. + +Implications for opencode: + +- Treat model-generated simulation properties as candidates. +- Store property lifecycle: proposed, executable, validity-checked, soundness-checked, coverage-scored, accepted, rejected. +- Generate small focused properties, not one huge “test opencode” property. +- Expose enough observations for a model to validate its own property assumptions. + +## 2024: Property-Based Testing In Practice + +**Main idea:** experienced developers use PBT in a small number of high-leverage patterns. The hardest parts are writing useful properties, writing generators, shrinking, and knowing whether passing tests mean anything. + +Useful techniques: + +- High-leverage patterns include differential testing, model-based tests, round trips, catastrophic failure properties, and invariants. +- Developers validate PBT effectiveness through mutation testing, example inspection, code coverage, property coverage, and supplementary example tests. +- Passing tests need inspectable generated examples and distribution feedback. + +Pitfalls: + +- Derived generators can create false confidence. +- Shrinkers can violate invariants. +- Slow PBTs get removed. + +Implications for opencode: + +- Provide built-in property families instead of requiring every contributor to invent properties. +- Show generator stats: action distribution, trace length, discarded cases, transition coverage, example traces. +- Make failure output a concise, reviewable artifact. +- Support “promote minimized trace to normal test.” + +## 2026: Agentic PBT + +**Main idea:** an agentic loop can generate better PBTs than one-shot prompting by inspecting code/docs, proposing evidence-backed properties, running tests, triaging failures, refining false alarms, and reporting only reproducible bugs. + +Useful techniques: + +- Use a structured loop: inspect, propose, execute, triage, refine, report. +- Prefer high-value property patterns: invariants, round trips, inverse operations, multiple implementations, laws, confluence, metamorphic relations, and no-crash parser entrypoints. +- Keep an evidence chain for every property. + +Pitfalls: + +- Intent ambiguity is the main false-positive source. +- Internal helpers often have implicit preconditions. +- Extreme generated inputs can be unrealistic. + +Implications for opencode: + +- The simulation system should be friendly to model-driven exploration, not just batch tests. +- Store prompts, observations, selected actions, available actions, traces, refinements, and final classifications. +- Add a triage workflow before surfacing model-generated failures as bugs. + +## 2026: Evolution Of Python Tests Into PBT + +**Main idea:** existing example and parameterized tests often evolve naturally into PBTs. Generated deterministic tests and PBTs should be connected, not treated as separate worlds. + +Useful techniques: + +- Convert constants/parameter tables into generators. +- Keep explicit examples for known edge cases. +- Adjust generators/settings over time as tests mature. + +Pitfalls: + +- Coverage can be inflated by harness/generator code. +- PBTs can fail early and cover fewer later assertions. +- Slow PBTs are removed. + +Implications for opencode: + +- Use existing tests as simulation corpus seeds. +- Convert minimized simulation traces into normal deterministic tests. +- Keep SUT coverage separate from simulation harness coverage. +- Store generated regressions as explicit fixtures. + +## 2026: Natural Language To Executable Properties For Mobile Apps + +**Main idea:** natural-language app properties can become executable UI properties if the system first performs semantic grounding of UI elements. + +Useful techniques: + +- Decompose property synthesis into UI semantic grounding and executable property synthesis. +- Represent properties as precondition, interaction scenario, postcondition. +- Enrich each widget with text, ID, type, semantic label, functionality, screenshot/crop, and provenance. + +Pitfalls: + +- Similar widgets cause grounding errors. +- Free-form natural language is less reliable than structured Given/When/Then descriptions. +- Incorrect preconditions/postconditions are more common than incorrect interactions. + +Implications for opencode: + +- Expose semantic TUI state, not just screen text and coordinates. +- Elements/actions should have stable IDs, roles, labels, capabilities, focus/click/edit metadata, visibility, and provenance. +- Generated properties should use a precondition/action/postcondition structure. + +## 2026: PropGen Mobile App Testing + +**Main idea:** properties can be generated from runtime behavioral evidence. The loop is exploration, evidence collection, property synthesis, executable translation, testing, feedback, and refinement. + +Useful techniques: + +- Record condition-action-outcome traces. +- Use functionality-guided exploration plus random exploration fallback. +- Refine imprecise properties by classifying whether the problem is precondition, interaction, or postcondition. + +Pitfalls: + +- Single traces cause overfitting. +- Generated properties can assert incidental UI details. +- Refinement can overfit unless anchored to original evidence. + +Implications for opencode: + +- Record rich traces with before-state, action intent, concrete action, model/provider/tool effects, after-state, state diff, and outcome label. +- Let models derive properties from observed behavior, then validate and refine them. +- Use both model-guided goals and stochastic action exploration. diff --git a/packages/opencode/specs/simulation-research/papers/.gitattributes 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/Info 2 0 R /Root 1 0 R /Size 568 /ID [] >> +startxref +2443781 +%%EOF diff --git a/packages/opencode/specs/simulation-research/sources.md b/packages/opencode/specs/simulation-research/sources.md new file mode 100644 index 00000000000..804dc7d75cb --- /dev/null +++ b/packages/opencode/specs/simulation-research/sources.md @@ -0,0 +1,24 @@ +# Simulation Research Sources + +Local research corpus for the opencode simulation architecture work. + +## Downloaded Papers + +| Year | Paper | Local PDF | Extracted Text | Source | +| --- | --- | --- | --- | --- | +| 2016 | Mysteries of Dropbox: Property-Based Testing of a Distributed Synchronization Service | `papers/2016-mysteries-of-dropbox.pdf` | `text/2016-mysteries-of-dropbox.txt` | https://publications.lib.chalmers.se/records/fulltext/232551/local_232551.pdf | +| 2019 | Coverage Guided, Property Based Testing | `papers/2019-coverage-guided-pbt.pdf` | `text/2019-coverage-guided-pbt.txt` | https://lemonidas.github.io/pdf/FuzzChick.pdf | +| 2021 | Model-Based Testing in Practice: An Experience Report from the Web Applications Domain | `papers/2021-mbt-web-applications-practice.pdf` | `text/2021-mbt-web-applications-practice.txt` | https://arxiv.org/pdf/2104.02152 | +| 2022 | Application of Property-Based Testing Tools for Metamorphic Testing | `papers/2022-pbt-for-metamorphic-testing.pdf` | `text/2022-pbt-for-metamorphic-testing.txt` | https://arxiv.org/pdf/2211.12003 | +| 2022 | Property-Based Testing: Climbing the Stairway to Verification | `papers/2022-stairway-to-verification.pdf` | `text/2022-stairway-to-verification.txt` | https://trustworthy.systems/publications/papers/Chen_ROSKHK_22.pdf | +| 2023 | QuickerCheck: Implementing and Evaluating a Parallel Run-Time for QuickCheck | `papers/2023-quickercheck.pdf` | `text/2023-quickercheck.txt` | https://arxiv.org/pdf/2404.16062 | +| 2024 | Can Large Language Models Write Good Property-Based Tests? | `papers/2024-llms-write-good-pbt.pdf` | `text/2024-llms-write-good-pbt.txt` | https://arxiv.org/pdf/2307.04346 | +| 2024 | Property-Based Testing in Practice | `papers/2024-pbt-in-practice.pdf` | `text/2024-pbt-in-practice.txt` | https://www.cis.upenn.edu/~bcpierce/papers/icse24-pbt-in-practice | +| 2026 | Finding bugs across the Python ecosystem with Claude and property-based testing / Agentic PBT | `papers/2026-agentic-pbt.pdf` | `text/2026-agentic-pbt.txt` | https://arxiv.org/pdf/2510.09907 | +| 2026 | On the Evolution of Python Test Cases into Property-based Tests | `papers/2026-evolution-python-tests-to-pbt.pdf` | `text/2026-evolution-python-tests-to-pbt.txt` | https://soft.vub.ac.be/Publications/2026/vub-tr-soft-26-02.pdf | +| 2026 | From Natural Language to Executable Properties for Property-based Testing of Mobile Apps | `papers/2026-nl-to-executable-properties-mobile.pdf` | `text/2026-nl-to-executable-properties-mobile.txt` | https://arxiv.org/pdf/2603.21263 | +| 2026 | From Exploration to Specification: LLM-Based Property Generation for Mobile App Testing | `papers/2026-propgen-mobile-app-testing.pdf` | `text/2026-propgen-mobile-app-testing.txt` | https://arxiv.org/pdf/2604.13463 | + +## Notes + +The ACM PDF endpoint for `Property-Based Testing in Practice` returned `403`; the author-hosted University of Pennsylvania copy was downloaded successfully. diff --git a/packages/opencode/specs/simulation-research/text/2016-mysteries-of-dropbox.txt b/packages/opencode/specs/simulation-research/text/2016-mysteries-of-dropbox.txt new file mode 100644 index 00000000000..b1d2e80623c --- /dev/null +++ b/packages/opencode/specs/simulation-research/text/2016-mysteries-of-dropbox.txt @@ -0,0 +1,714 @@ + Mysteries of Dropbox + Property-Based Testing of a Distributed Synchronization Service + John Hughes∗† , Benjamin C. Pierce‡ , Thomas Arts∗ , Ulf Norell∗† , + ∗ Quviq AB, Göteborg, Sweden + † Dept of Computer Science and Engineering, Chalmers University of Technology, Göteborg, Sweden + ‡ Dept of Computer and Information Science, University of Pennsylvania, PA, USA + + + + + Abstract—File synchronization services such as Dropbox are Our goal in this paper is to present a testable formal specifi- +used by hundreds of millions of people to replicate vital data. cation for the core behavior of a file synchronizer. We do so via +Yet rigorous models of their behavior are lacking. We present a model developed using Quviq QuickCheck [4]. Despite the +the first formal—and testable—model of the core behavior of a +modern file synchronizer, and we use it to discover surprising apparent simplicity of the problem, we encountered interesting +behavior in two widely deployed synchronizers. Our model is challenges regarding both specification and testing. We used +based on a technique for testing nondeterministic systems that the model to test Dropbox, Google Drive, and ownCloud (an +avoids requiring that the system’s internal choices be made visible open source alternative), exposing unexpected behavior in two +to the testing framework. out of three. + In Section II, we introduce our testing framework. Sec- + I. I NTRODUCTION tion III gives a high-level overview of the concepts used in our + model, in particular the operations performed by test cases, the + File synchronization services—distributed systems that + observations made when a test case is run on the system under +maintain consistency among multiple copies of a file or + test (SUT), and the explanations that we construct to determine +directory structure—are now ubiquitous. Dropbox claim 400 + whether the test has passed or failed. Section IV presents the +million users,1 while Google Drive and Microsoft OneDrive + formal specification itself, beginning with a naive version and +are reported to have over 240 million users each.2 In addition + refining it in light of failed tests that reveal subtleties in the +to these large-scale commercial offerings and many smaller + synchronizer’s handling of corner cases. Section V describes +ones, there are a plethora of open source synchronizers, + further failed tests that, rather than pinpointing inadequacies +enabling users to create their own ‘cloud storage.’ With so + in the specification, seem to us to exemplify unintended +many people trusting their data to synchronization services, + behaviors of both Dropbox and ownCloud, including situations +their correctness should be a high priority indeed. + where each system can lose data. In Section VI, we discuss the + Surprisingly, then, it seems that only one file synchronizer + pragmatics of our testing framework, in particular our methods +has been formally specified to date: Unison [1]–[3]. However, + for triggering timing-dependent behaviors, for observing when +even Unison’s specification is not directly useful for testing; + the system has reached quiescence, and for shrinking tests to +moreover, Unison works rather differently from contemporary + minimal failing cases in the presence of nondeterminism. In +synchronization services: it synchronizes two peers at a time, + Section VII, we sketch an initially promising attempt to formu- +rather than many clients with one server; synchronization is + late the specification in terms of Lamport’s “happens before” +invoked explicitly by the user, rather than taking place auto- + relation and explain why it ultimately proved unsuccessful. +matically in the background; and conflict resolution involves + Section VIII surveys related work, and Sections IX and X +user interaction, rather than being performed automatically. + present future directions and concluding remarks. + Synchronizers are challenging not only to specify but also Our main contributions are as follows: (1) We construct the +to test. They are large-scale, nondeterministic distributed sys- first formal model of the core behavior of modern file synchro- +tems, with timing-dependent behavior. They must cope with nizers. (2) To define the model, we develop a technique for +conflicts (when the same file is modified concurrently on two testing nondeterministic systems that does not require that the +or more clients). They work in the background, and their system’s internal choices be visible to the testing framework. +state is unobservable. Moreover, they are slow. They share Our technique is based on an explicit representation of hidden +these difficulties with a large class of critical systems; thus, system state plus “conjectured events” that mutate it. (3) We +techniques for addressing these problems are valuable, not validate our final model against two commercial synchronizers +only for testing file synchronizers, but in a broader context. and one open-source one, showing that their behavior agrees + with the model in most situations. (4) We demonstrate the + 1 techcrunch.com, “Dropbox now has more than 400 million registered + effectiveness of our model and testing framework by using it +users”, June 24th , 2015. + 2 fortune.com, “Who’s winning the consumer cloud storage wars?” to reveal a number of surprising behaviors, likely not intended +November 6th , 2014. by the developers of these systems. + II. T ESTING A S YNCHRONIZATION S ERVICE ones we have tested so far. In particular, we did not want to + assume any direct access to remote servers outside our control. + We begin by making a rather drastic simplifying assump- Therefore, we treat the synchronizer as a ‘black box’, which +tion: we consider only one file, with operations to read, we communicate with only through the file system; our tests +write, and delete it. We consider only operations that read just read and write files on the virtual machines and check the +and write the entire file; we do not specify or test how the results for validity. This allows us to write the specification +synchronizer interacts with open files as they are modified. without dependencies on synchronizer-specific APIs.3 +Restricting our attention to one file may seem extreme, but +even this simple setting forces us to confront essential issues III. OVERVIEW OF THE S PECIFICATION +of synchronization—in particular subtleties arising in the pres- Our strategy for test case generation is very simple: we +ence of conflicts—and it is enough to expose surprising be- generate test cases consisting of random sequences of calls to +haviors in real systems. A plan for extending the specification a small set of basic filesystem operations. The basic operations +to multiple files and directories is sketched in Section IX. we consider are + We developed our model using Quviq QuickCheck [4], • R EAD N , which reads the (one) file on node N (one of +a descendant of Haskell QuickCheck [5]. QuickCheck tests the VMs), and +properties—universally quantified boolean formulæ—by gen- • W RITE N V , which writes the value V (a string) to the +erating random values for the quantified variables and check- file on node N . +ing that the formula evaluates to true. When a test fails, We will introduce a few additional operations below. +QuickCheck “shrinks” it, searching for a similar but smaller We use QuickCheck’s state machine library to generate +test that also fails and ultimately reporting a failing test that tests, with a trivial model state—our tests are simply random +is ‘minimal’ in some sense. (This process is akin to delta- sequences of R EADs and W RITEs, with random arguments. +debugging [6], although the details are slightly different.) One might expect to track the file contents in the model state, +QuickCheck provides a domain-specific language for defining and check that R EAD returns the modeled contents—but this +test data generators and shrinking searches; using this DSL, could only work if synchronization were instantaneous, which +users can exert fine control over the random distribution of of course it is not. Instead of trying to express our specification +test cases. A part of this DSL is a notation for specifying in this synchronous style, we collect observed events as each +state machine models, which generate test cases consisting of operation is actually executed, and we use a separate state +sequences of calls to an API under test [7], [8]; this is how machine to validate the resulting sequence of events. +we generated test cases for synchronizers. Quviq QuickCheck The observed events corresponding to the READ and WRITE +is embedded in the Erlang programming language—that is, operations are as follows: +specifications are just Erlang programs that call libraries + • when R EAD N returns the value V , we observe the event +supplied by QuickCheck—and the generated tests invoke the + R EADN → V , and +SUT directly via Erlang function calls. As a result, there is + • when W RITE N V overwrites the value Vold , we observe +no distinction between ‘abstract’ and ‘concrete’ test cases, as + the event W RITEN V → Vold . +there often is in model-based testing, and there is no need for +a ‘system adapter’; instead, generated test cases are directly Notice that, when we write the file, we observe the previous +executable. contents as well as the new one (taking the ‘previous contents’ + We ran our tests on laptops running a host operating system of a newly created file to be the special value ⊥). The value +(Windows 8.1 or Mac OS) together with several virtual ma- that we overwrite matters, because of the way synchronizers +chines running Ubuntu Linux. The file synchronizer under test handle conflicts. (This observation is not actually atomic, but +was installed on each virtual machine and under the host op- it is very unlikely that the dropbox dæmon will overwrite the +erating system, so we could read and write files on any of the file between our read and write, and we have not observed it +virtual machines, or on the host, and expect the synchronizer to happen.) +to propagate changes to all of the others. We ran distributed A conflict occurs when two or more clients write the +Erlang on the virtual machines and the host, using the host file concurrently—that is, without having seen each other’s +to coordinate each test by making remote procedure calls updates. For example, if client 1 writes ‘a’ to the file, and +on the virtual machines. All machines were also connected client 2 then writes ‘b’ before ‘a’ has been delivered to client 2 +to the internet, allowing us to test synchronization servers by the synchronizer, a conflict is created. One of the two values +running either remotely (in the case of Dropbox and Google wins, and eventually all clients will see this value in the file if +Drive), or on another VM (in the case of ownCloud). The use there are no more writes, but conflicting values are also saved +of multiple VMs on a single physical machine was purely in special files in the same directory, with names derived from +a matter of convenience: Erlang’s support for transparent 3 For testing the specification, we found it convenient to use limited +distribution would make it straightforward to run the same communication with the local dæmon, where available; for example, the +setup on multiple nodes. We used 3 VMs for most tests. Dropbox client on Ubuntu provides a handy Python script for querying + whether the local dæmon thinks it is up to date, which we used to speed + We wanted a model that would apply (perhaps with minor up testing a bit. This adds <10 lines of code per synchronizer to the test +adjustments) to many file synchronizers, not just the specific harness. + the name of the original file, such as ‘paper.tex (John’s tests may well result in a stable state never being reached! +conflicted copy)’; these files are eventually replicated In practice we wait up to 30 seconds, long enough to allow +to other clients just like any other file. To avoid depending synchronization to finish if it is going to but short enough to +on implementation-chosen names, our model specifies just the enable us to ‘shrink’ test cases (which involves running many, +set of values expected to appear in conflict files, and our test many failing tests—see Section VI) in a reasonable amount of +harness assumes that any files that appear in the same directory time. After 30 seconds we record a “failed stabilization” ob- +as the main one are conflict files. servation of the form S TABILIZE → {(V1 , C1 ), . . . , (Vn , Cn )}, + One subtlety in the specification of conflicts is that, because where each (Vi , Ci ) records the the file contents and conflict +conflicts can only be detected using global information, there set on one of the nodes. Such an observation is regarded as +may be a delay in the creation of conflict files. Consider the invalid by the specification, so any test that generates it is +following sequence of observations. considered to fail. + Since stabilization is slow—and most interesting after sev- + Client 1 Client 2 + eral read and write operations—we include it only 1/10 as + W RITE1 ‘a’ → ⊥ + often as R EADs and W RITEs. We also add a S TABILIZE at + W RITE2 ‘b’ → ⊥ + the end of every test case, which improves the probability of + R EAD2 → ‘a’ + detecting that something went wrong and also reduces the risk +The two writes are in conflict, and the write of ‘a’ has ’won’, of one test influencing the outcome of the next one. +so the value ‘b’ should appear in a conflict file. However, How can we decide whether a sequence of observed events +client 2 cannot determine this locally (since a different client is valid? We use a separate state machine, which accepts or re- +could have overwritten ‘b’ with ‘a’ in the meantime). So we jects a sequence of observed events. However, the observations +must wait for pending communications with the server to finish we make do not tell the whole story: in the background, the +before checking for the existence of conflict files. synchronizer is also performing actions. This makes our tests + We therefore add another operation to our test cases, nondeterministic—we cannot tell, from the events we have +S TABILIZE, which waits for synchronization to complete on observed, what state the whole system is in. We address this by +all client nodes. At this point, the same value V should be adding conjectured events to the observed ones, representing +in the file on all clients, and all clients should have the same actions taken by the synchronization service (messages be- +set of conflict files. Once the system is stable, we observe the tween local dæmons and a central server, interactions between +event S TABILIZE → (V, C), where C is the set of values in the dæmons and local filesystems, etc.). In general, we can add +conflict files (i.e., both the value and the conflict files should conjectured events to a given sequence of observed events in +be eventually consistent; we will see later that our model can many different ways, each resulting in a different combined +always reach such a state). Note that this is a system wide sequence of observed and conjectured events, which we call an +event, not an event observed on just one client. To check that explanation. If any of the explanations is accepted by our state +the correct conflict file is created in the example above, we machine, we consider the test to have passed. If there is no +would add a S TABILIZE operation to the end of the test, which way to insert conjectured events so the resulting explanation +should result in the following observed events: is accepted, then we consider that the test has failed. + Client 1 Client 2 Our conjectured events are uploads to, and downloads from, + W RITE1 ‘a’ → ⊥ the server. We write these events as U PN and D OWNN , + W RITE2 ‘b’ → ⊥ where N is the node taking part in the up- or down-load. + R EAD2 → ‘a’ Thus, when we model the state of the whole system, we will + S TABILIZE → (‘a’, {‘b’}) need to include the server’s state in the model. (Of course, + in reality ’the Dropbox server’ may itself be a replicated +If ‘b’ were missing from the conflict set in the last observed service involving many hosts. Our model implicitly assumes +event, this would represent lost data and the test would fail. strong consistency among these hosts; weaker consistency in + But how can we implement S TABILIZE? That is, how can Dropbox’s implementation might in principle cause our tests +we tell that synchronization is complete, given that we treat to fail, but we have not observed this.) +the synchronizer as a black box? Our solution is a little ad +hoc. Certainly, the value in the file and the conflict files must To make all of the above more concrete, here is an example +be the same on each client. Also, under Ubuntu, Dropbox of a simple test case: +provides a handy Python script to check the local Dropbox + Client 1 Client 2 +dæmon’s status; the dæmons on each client must be reporting + W RITE1 ‘a’ +‘up to date’. We wait for these necessary conditions to become + W RITE2 ‘b’ +true—but they are not sufficient, since the server may still + R EAD1 +be holding data that will be sent to the clients. So if a + W RITE2 ‘c’ +S TABILIZE → (V, C) operation ever leads to an observation + S TABILIZE +that would cause test failure, then we wait a bit longer and +retry the operation. We cannot wait too long, because failed Here is an observation that might arise from this test: + Client 1 Client 2 ‘a’ as the previous value), so it cannot have been in conflict + W RITE1 ‘a’ → ⊥ with any of the other W RITEs. + W RITE2 ‘b’ → ‘a’ + R EAD1 → ‘b’ + W RITE2 ‘c’ → ‘b’ IV. F ORMALIZING THE S PECIFICATION + S TABILIZE → (‘c’, ∅) +And here is a valid explanation of this observation: Formally, we use a deterministic state machine to accept or + reject explanations. We define the state of the machine, the + Client 1 Client 2 system state, as follows: + W RITE1 ‘a’ → ⊥ + U P1 • a global stable value ServerVal (i.e., the value currently + D OWN2 held on the server) + W RITE2 ‘b’ → ‘a’ • a global conflict set Conflicts (a set of values) + + U P2 • for each node N , + + D OWN1 – a local value LocalVal N , + W RITE2 ‘c’ → ‘b’ – a local freshness, Fresh?N ∈ {FRESH, STALE}, and + U P2 – a local cleanliness, Clean?N ∈ {CLEAN, DIRTY}. + R EAD1 → ‘b’ Values (i.e., file contents) are just strings. (We define the result + D OWN1 of a R EAD or W RITE before the file has ever been written to + S TABILIZE → (‘c’, ∅) be the special value ⊥.) +Of course, the same test may give rise to different observations In the initial state Sinit , the stable value and all the local +(and the same observation may be explained by many possible values are ⊥, and all nodes are FRESH and CLEAN. +explanations). For example, here is another observation that There are three kinds of observed events (R EAD, W RITE, +might arise from running the test above: and S TABILIZE) and two kinds of conjectured events (U P + Client 1 Client 2 and D OWN). A sequence of observed events is called an + observation. A sequence of both kinds of events is called an + W RITE1 ‘a’ → ⊥ + explanation. An explanation E explains an observation O if + W RITE2 ‘b’ → ⊥ + deleting the conjectured events from E leaves just O. + R EAD1 → ‘a’ + W RITE2 ‘c’ → ‘b’ For every event (of either kind), we will define a transition + S TABILIZE → (‘a’, {‘c’}) consisting of a precondition (which tells us whether the event + can happen in a given system state) and an effect (which +A valid explanation of this observation is: defines the change to the system state after the event has + happened). Taken together, these preconditions and effects + Client 1 Client 2 + define a partial function Next mapping a system state plus + W RITE1 ‘a’ → ⊥ + an event to a new state (or failing, if the event’s precondition + W RITE2 ‘b’ → ⊥ + is not satisfied by the state). + R EAD1 → ‘a’ + W RITE2 ‘c’ → ‘b’ An explanation E is valid with respect to some starting state + U P1 S if either (1) E is the empty sequence of events, or else (2) E + U P2 is a non-empty sequence e : E 0 (where : is ’cons’), such that + S TABILIZE → (‘a’, {‘c’}) Next(S, e) yields a new state S 0 and E 0 is valid with respect + to S 0 . + Conversely, suppose the synchronizer under test were mis- An observation O is valid if it is explained by some +behaving. Then the same test case might lead to an observation explanation that is valid with respect to the initial state. There +with no valid explanations. For example: are only finitely many valid explanations for each observation, + Client 1 Client 2 as we explain below, so validity of observations is decidable. + W RITE1 ‘a’ → ⊥ A test is a sequence of operations. It fails if the observation + W RITE2 ‘b’ → ‘a’ that arises by running it has no valid explanation; otherwise it + R EAD1 → ‘b’ succeeds. + W RITE2 ‘c’ → ‘b’ It remains only to define the transitions themselves. The + S TABILIZE → (‘c’, {‘a’}) read and write transitions are straightforward: +Here, the final S TABILIZE observation shows that a conflict +file has been created for the file value ‘a’. But ‘a’ was the R EADN → V +first value written to the file, and it must have been the first Precondition: LocalVal N = V +value uploaded to the server (because the second W RITE saw Effect: none + W RITEN Vnew → Vold U PN + Precondition: LocalVal N = Vold Precondition: Clean?N = DIRTY + Effect: LocalVal N ← Vnew Effect: Clean?N ← CLEAN + Clean?N ← DIRTY if Fresh?N = FRESH then + Fresh?N 0 ← STALE for all N 0 6= N +A write event does have a precondition, because it observes ServerVal ← LocalVal N +the value that is overwritten. That is, a read or write event on else Conflicts ← Conflicts ∪ {LocalVal N } +client node N is valid with respect to some model state if the +value that the event observes in the filesystem agrees with the U PN is only allowed if node N is DIRTY (written since the last +model’s current value for that node. Observing a R EAD has no D OWN). Its effect is either to update the server’s value from +effect on the model state, while observing a W RITE changes node N ’s if N is currently FRESH—i.e., if it is not in conflict +the model’s local value for node N to the one that was written with a W RITE on another node that has already reached the +by the W RITE operation and marks node N as DIRTY. server—or otherwise to mark the local value as a conflict. In + The S TABILIZE → (V, C) event has no effects (it is like a either case, node N is marked as CLEAN. +R EAD in this respect), but it has a very strict precondition: To decide whether a test succeeded, we construct a valid + explanation for the observation we made; that is, we insert + a sequence of U P and D OWN events between each pair of + S TABILIZE → (V, C) observed events that makes the explanation valid. How many + Precondition: ServerVal = V conjectured events might we need to insert? First of all, note + Conflicts = C that each U P event makes a DIRTY node CLEAN (and neither + for all N, Fresh?N = FRESH U P nor D OWN can make a CLEAN node DIRTY). So, if there + Clean?N = CLEAN are a total of N nodes, then at most N U P events can appear + Effect: none between consecutive observed events. Secondly, note that each + D OWN event makes a STALE node FRESH. So there can be at +The intuition for this precondition is that this observed event is most N D OWN events in a row. Since an U P event makes +not considered valid unless the system model has also reached N − 1 nodes STALE, each U P can be followed by up to +a stable state. The precondition can be satisfied by adding N − 1 D OWN events before another U P or an observed event +conjectured upload and download actions to the explanation must occur. Thus we need to insert at most N + N · (N − 1) +until all nodes in the system state are FRESH and CLEAN. conjectured events between each pair of consecutive ordered + The transition for failed stabilization events has an even events; there are only finitely many possible explanations for +stricter precondition: such an event is never allowed! each observation, so it is decidable whether a test has passed. + In our implementation, we do not explore all possible + S TABILIZE → {(V1 , C1 ), . . . , (Vn , Cn )} explanations. We construct the set of possible states before and + after each observed event in an observation. Given the set of + Precondition: False possible states before such an event, we select those satisfying + Effect: none the event’s precondition and apply the event’s action to them, + resulting in the set of possible states after the event. If the set +This ensures that any observation including a failed stabiliza- + of possible states ever becomes empty, then the test fails. +tion will be identified as a failing test case. + Now, given the set S of possible states after an observed + These are all the observed events. But we also need transi- event, we construct the set of states before the following one +tions for the conjectured events U P and D OWN. Downloading by taking the image of S under the transitive closure of U P and +a value from the server to a client node stores the server’s D OWN . In any such state, (a) every node will have a LocalVal +value as the local value for that node in the system state; drawn from the set V of all LocalVals plus the ServerVal in +it also changes the node from STALE to FRESH. However, it the given state, (b) the ServerVal will also be an element of +can only be performed if the client node is currently CLEAN. V , (c) the Conflicts will be the union of the Conflicts in +(Otherwise, it must be preceded by an U P event, which will the given state, and a subset of V , and (d) each node will be +reconcile the local value with the server’s.) FRESH or STALE, CLEAN or DIRTY . Since the size of V is at + most N + 1, it follows that there can be at most (N + 1)N +1 · + D OWNN 2N +1 · 4N states reachable from S. + Precondition: Fresh?N = STALE Should this set become too large to deal with during testing, + Clean?N = CLEAN a pragmatic solution would be to abandon that test case and + Effect: LocalVal N ← ServerVal generate another. We conjecture that most bugs can be found + Fresh?N ← FRESH by a relatively deterministic test, so we would not expect this + solution to make many interesting bugs impossible to find. + The most interesting case is the U P transition. Here is a However, in our experiments, N was at most 3, giving a +simple first attempt (we will refine it below): bound of at most 262144 states reachable from each state— + a large but not unmanageable number. In practice, we have that no further changes would be required. But QuickCheck +almost never seen more than 1,000 different possible states soon finds this failing test case: +during a test. Synchronizers are so slow that there is plenty of Client 1 Client 2 Client 3 +time to compute 1,000 model states after each observed event! + W RITE1 ‘a’ → ⊥ +Refining the model: repeated values R EAD2 → ‘a’ + W RITE1 ⊥ → ‘a’ + Perhaps not surprisingly, with the first-draft model as + R EAD2 → ⊥ +presented above, testing against Dropbox fails immediately. + W RITE3 ‘b’ → ‘a’ +QuickCheck reports the following minimal counterexample: + R EAD1 → ‘b’ + Client 1 Client 2 + Why does this test fail? Because: at step 4, the server value + W RITE1 ‘a’ → ⊥ + must be ⊥, since client 2 saw ⊥ after client 1 wrote it (and + W RITE2 ‘a’ → ⊥ + client 2 previously read the value ‘a’, so client 2 is not simply + S TABILIZE → (‘a’, ∅) reading the initial ⊥); at step 5, because the value client 3 +The test fails because the two writes conflict—neither saw the overwrites is not the server value, a conflict is created; the +value written by the other. Our model says that both nodes value ‘b’ should thus only appear in conflict files on other +must upload their values before the S TABILIZE and that, on nodes, never as the value in the file itself—yet it does just +the second U P required to enable it, the value should be added that in the last step. Thus, there can be no explanation for this +to the set of conflicts. Yet the set of conflicts is observed to be observation. +empty at the end. The Next function as defined above admits (This test is, of course, quite sensitive to timing. For +no valid explanations of this observation. example, the second operation (R EAD2 → ‘a’) reads the + Evidently, Dropbox considers that there is no conflict if the value written by the first W RITE1 ‘a’ → ⊥. This is only +same value is written independently by two clients. This is a possible if enough time passes after the first W RITE to allow +sensible design decision, but it needs to be reflected in our the synchronizer to act. The actual test case includes S LEEP +specification. To make the implementation and specification operations recording the need for these pauses, but they are +agree, we need to refine the specification to add special cases not shown in the observations we present. We will return to +in the U P event when the local and global values are identical: the question of timing in more detail in Section VI.) + We have discovered another inconsistency with our model, + U PN but not yet a bug: in fact, the behavior we are seeing reflects + Precondition: Clean?N = DIRTY another sensible design decision—that when a delete and + Effect: Clean?N ← CLEAN a write conflict, the write should take precedence (and the + if Fresh?N = FRESH then deletion should be silently forgotten). We must amend our + if LocalVal N 6= ServerVal then model to reflect this too: + Fresh?N 0 ← STALE for all N 0 6= N + U PN + ServerVal ← LocalVal N + else Precondition: Clean?N = DIRTY + if LocalVal N 6= ServerVal then Effect: Clean?N ← CLEAN + Conflicts ← Conflicts ∪ {LocalVal N } if Fresh?N = FRESH then + if LocalVal N 6= ServerVal then +With this modification, the test case passes. Here is a (newly Fresh?N 0 ← STALE for all N 0 6= N +valid) explanation for the observation we made: ServerVal ← LocalVal N + Client 1 Client 2 else + W RITE1 ‘a’ → ⊥ if LocalVal N 6∈ {ServerVal , ⊥} then + U P1 Conflicts ← Conflicts ∪ {LocalVal N } + W RITE2 ‘a’ → ⊥ The change is in the second-to-last line, which now states that + U P2 neither uploading the same value as the stable value, nor a + S TABILIZE → (‘a’, ∅) deletion, ever generates a conflict. With this change, we believe +Adding deletion to the model our model reflects the intended behavior of the synchronizers + we have tested. + Since we already model reading from a missing file by the +special value ⊥, deletion can be modelled simply as writing ⊥ V. S URPRISES +back to the file. Of course, when executing tests we actually What about unintended behaviors? +implement this by performing a real file deletion, but the event +that we observe is just W RITEN ⊥ → Vold , where Vold is Dropbox Surprises +the contents of the file just before deletion. Since the model Up to this point, we were essentially debugging our model +already encompasses W RITE events, we might have expected using Dropbox as a reference implementation. However, con- + tinued testing revealed further inconsistencies between our Here the file is created on one client, synchronized to the other, +model and Dropbox. and overwritten there—but Dropbox does not copy the new + The first surprise was that Dropbox can (briefly) delete a value to the other client, and so the system never becomes +newly created file: stable. Further investigation shows that Client 1 behaves as + though it is still FRESH, rather than STALE, so Client 2 never + Client 1 Client 2 + sees the value that Client 1 wrote, and if Client 2 writes + W RITE1 ‘a’ → ⊥ + another value to the file then it is just copied onto Client 1— + W RITE1 ⊥ → ‘a’ + no conflict is detected, and the value ‘a’ is lost forever. + W RITE2 ‘b’ → ‘a’ + Again, the behavior is timing dependent, occuring when the + W RITE1 ‘c’ → ⊥ + second W RITE happens very soon after the value ‘b’ arrives + R EAD1 → ⊥ + on Client 1. +In this case, W RITE2 ‘b’ and W RITE1 ‘c’ are in conflict; Dropbox offered the following response to these surprises: +the final R EAD1 should see one of these values, with the Our engineers thoroughly investigated the file and data issues +other eventually appearing in a conflict file—but at the time and were able to reproduce them programatically. Fortunately, +we try to read the file, it is not there at all! In this case we don’t believe these issues have occurred outside of the lab +stabilization would restore a correct file contents, but the test due to the precise conditions necessary for any data loss to +fails because our model does not allow the file to be missing, occur–namely, the local edit occurring within the same second +even briefly. (Of course, observing this transient behavior as the remote change and the saved file having the identical +requires executing the operations at just the right times; the file size as the original. While that fact gives us comfort, +test case found by QuickCheck includes S LEEP operations that Dropbox takes any potential data issue, no matter how remote +make this more likely.) in possibility, extremely seriously and we are developing fixes + The second surprise was that Dropbox can re-create deleted for the issue. We are grateful to the researchers for their +files, even when only one client is modifying the file!4 efforts in testing the Dropbox service using property-based + testing and raising awareness of property-based testing within + Client 1 + Dropbox. + W RITE1 ‘b’ → ⊥ + W RITE1 ⊥ → ‘b’ + R EAD1 → ‘b’ ownCloud Surprises + +In this case Dropbox does not later ‘correct the mistake’ by While most of our effort has been spent testing Dropbox, we +deleting the file again: it remains there permanently. (Again, have also used our model (unchanged) to test ownCloud and +of course, Dropbox does not always restore files after they Google Drive. So far, Google Drive has behaved as expected, +have been deleted: to provoke this behavior, the test case must but we elicited some surprising behavior from ownCloud. +include a S LEEP operation of just the right length.) The first surprise was that ownCloud can delete newly + A similar test shows that deleted files can reappear even if created directories, instead of propagating them to other +the creation and deletion take place on different nodes: nodes. More surprising yet, we actually discovered this when + our test setup failed! To mitigate the risk of one test case + Client 1 Client 2 interfering with the next, we run each test in a new directory. + W RITE2 ‘b’ → ⊥ We create these directories in batches, to reduce the time + W RITE1 ⊥ → ‘b’ spent waiting for them to propagate to all the nodes. At the + R EAD1 → ⊥ start of a test run, we delete left-over test directories, then + S TABILIZE → (‘b’, ∅) recreate the ones we need. So, our preparation for a testing +The R EAD1 → ⊥ verifies that the file was properly deleted; run looks like this: (1) On the host, delete all the left-over +but, after waiting for the system to stabilize, it reappears. directories from previous tests. (2) On each virtual machine, + The most alarming behavior we observed shows that Drop- wait for the left-over directories to disappear. (3) On the +box can lose data completely: host, create several hundred ‘fresh’ directories for the first + few hundred test cases to use. (4) On each virtual machine, + Client 1 Client 2 wait for all these new directories to appear. To our surprise, + W RITE2 ‘b’ → ⊥ when using ownCloud as the synchronizer, step (4) often failed + W RITE1 ‘a’ → ‘b’ to terminate. On checking progress, we found that not only + R EAD1 → ‘a’ had the test directories not appeared on the virtual machines, + S TABILIZE → but they had been deleted from the host! We surmise that + { (‘a’, ∅), (‘b’, ∅) } ownCloud may arrange deletion followed by recreation of the + same directory in the wrong order, if they occur sufficiently + 4 There were other machines logged in to the same Dropbox account, so + close together in time. +Dropbox was synchronizing the file at the same time to these other machines. +However, they were not involved in the test, and were not modifying the files After we worked around this issue, QuickCheck found one +in question; they were simply passive observers. further discrepancy between the specification and ownCloud’s + actual behavior: ownCloud can lose changes. The following just to allow a fixed time for synchronization to complete, +observation illustrates what can happen: because the more file operations a test case performs, the + slower synchronization becomes. It appears that synchronizers + Client 1 Client 2 + ‘back off’ when files are changing rapidly, waiting for a + W RITE1 ‘a’ → ⊥ + more opportune moment to do their job. This was the original + W RITE2 ‘b’ → ‘a’ + reason for including stabilization operations in our test cases, + W RITE1 ‘c’ → ‘a’ + combining observations from all of the virtual machines to try + S TABILIZE → (‘b’, ∅) + to detect when the synchronizer has nothing left to do. +At the end, all clients have stabilized on the value ‘b’, while The examples we presented above are minimized test cases, +‘c’ has been completely forgotten even though it was written found by QuickCheck’s shrinking search. Shrinking tries to re- +independently from ‘b’ (both writes saw the previous value duce the size of test cases by dropping calls from the sequence, +‘a’) and, according to the specification, it should at least but also reducing the duration of SLEEP operations—shrunk +appear in the final conflict set. This time, we could confirm the test cases should wait no longer than necessary to provoke +reason by reading the ownCloud source code. The ownCloud a failure. We also noticed that counterexamples leading to +client uses a simple test for when a file has been changed and wrong file contents were found in two forms: ending in a +needs to be uploaded to the server: it checks whether either the READ operation, or ending in a deletion (a W RITE of ⊥), +file’s modification time or its length are different from their which also observes the contents. We configured shrinking so +last seen values. But modification times are recorded in the that deletions shrink to R EAD operations (provided the test +filesystem with a 1-second granularity. So if the file is written still fails, of course), so that the latter form would shrink to +twice in quick succession (i.e., during the same second) and the former. +the new contents is the same length as the old one, no change Because of the non-determinism inherent in the system, +will be detected. Thus, ‘b’ is recorded as the file’s stable value: failing test cases may not fail every time they are run. This is +no matter how long we wait, the value (‘c’) will never reach problematic both when searching for a failing test case, and +the server or Client 2. If the next write to the file occurs on when shrinking one. Our solution in both cases is to run each +Client 2, ‘c’ will be silently overwritten. test several times, and consider the test to have failed if any + of the runs fails—thus reducing the probability of a ‘false + VI. P RAGMATICS OF T ESTING negative’ result. While running random tests, we repeated + Many of the behaviors we encountered were timing depen- each test three times, but while shrinking test cases, we +dent (we have not included timings here, since their values will repeated each one twenty times. (We work harder to avoid false +vary with factors like connection speed). Our main technique negatives during shrinking, because they lead QuickCheck to +for provoking timing-dependent behaviors was to include report non-minimal failing tests, which can waste a great deal +S LEEP operations in our tests, which cause the whole testing of human debugging time. In consequence, shrinking a failed +framework to pause for a specific period (up to one second, test to a minimal one can take 10–20 minutes to finish, at 10– +randomly chosen during test generation). 15 seconds per test. Twenty repetitions was usually enough to + We found that timing-dependent tests often failed with minimize failing tests.) +fairly low probability, which we could increase manually— +once we’d identified a test case that sometimes failed—by VII. A N A LTERNATIVE S PECIFICATION ATTEMPT +‘triggering’ some of the W RITE operations on changes in the There is an appealing analogy between file synchronization +file. That is, we busy-wait on some node until a specified services and the memory subsystems of modern multiproces- +value appears in the file and then immediately execute an sors. Network hosts with copies of a replicated file correspond +operation. Triggering an operation makes unexpected behavior to individual processor cores, the local filesystems correspond +more likely, since it may create a race condition between to per-core caches, and the central synchronization server +the test code running on node N , and the synchronization corresponds to the main memory. This suggests that one might +dæmon on that node. For example, it allowed us to observe try to leverage ideas from the literature on specifications of +the last two Dropbox surprises quite repeatably. It would be memory-system behavior (see [9], [10] for surveys) to specify +interesting to go a step further and automatically generate the desired behavior of a synchronizer. In particular, perhaps a +triggered operations as part of test cases; this would require specification could be based on Lamport’s notion of happened +a slightly richer generation-time state so that we can predict before relations [11], which express the causal ordering of +what value(s) might appear in the file. events in a distributed system. Indeed, an early version of our + We found the slowness of file synchronizers to be quite QuickCheck specification was written in this style, rather than +a problem; also the unpredictability of synchronization time. the model-based style that we have described in this paper. +It is not easy to tell when synchronization is complete—in This early specification used the same notions of tests and +particular, the icons that synchronizers display to show their observed events as our current one. But instead of trying +status are often wrong: the local dæmon itself is confused to match the observed behavior against the transitions of +about what state things are in! Yet we must know, if we are a concrete model of the system (including the server), it +to detect synchronization failures reliably. It does not work directly specified which observations were legal by attempting + to construct a partial ordering ≺ on the observed events such directories—in particular, they spend considerable effort on +that (1) if an event e happened before e0 on the same client, the subtleties of conflicts in this setting. However, they address +then e ≺ e0 , and (2) if e is the W RITE event that writes the a different distribution scenario, in which the execution of +value observed by e0 , then e ≺ e0 . If such a relation exists, the synchronizer is a visible user-initiated action rather than +then it can be taken as an explanation for the observation. For a continuous background activity and in which there is no +example, the validity of the observation centralized “global value.” They have not been used for testing. + We have implicitly assumed that the local filesystem is + Client 1 Client 2 + behaving correctly (so that discrepancies between our model + e1 : W RITE1 ‘a’ → ⊥ + and actual observations are attributable to Dropbox). Ridge et + e2 : W RITE1 ‘b’ → ‘a’ + al. [13] show how this can be tested, using a specification with + e3 : W RITE2 ‘c’ → ‘b’ + significant similarities to ours. +is justified by this relation e1 ≺ e2 ≺ e3 . On the other hand, A distinct body of specification work deals with specifying +if no ≺ relation exists that is consistent with the observations, the behavior of operational transform services—middleware +then a bug (or at least a discrepancy between the system and layers that maintain consistency of replicated data structures +the spec) has been detected. For example, the observation (databases, documents, spreadsheets, etc.) under concurrent + Client 1 Client 2 updates. Operational transform algorithms are widely used— + W RITE1 ‘a’ → ⊥ for example, they underlie behind the collaboration features + W RITE1 ‘b’ → ‘a’ in Apache Wave and Google Docs—and their theory is well + R EAD2 → ‘b’ developed [14]–[16, etc.]. However, although it has been used + R EAD2 → ‘a’ for debugging replication algorithms using symbolic model- + checking [17], the theory has not, to our knowledge, been +cannot be partially ordered in a way that respects the two applied to testing of actual distributed implementations. In- +conditions above. To deal with conflicts, we specified that, deed, since these specifications are based on notions of causal +at stabilization points, all of the maximal values in the partial ordering, our experiences reported in Section VII suggest that +order (that is, the values written by every W RITE event e such it might be difficult to do so, at least in a black-box style. +that for no W RITE event e0 do we have e ≺ e0 ) must appear Fraser and Wotowa [18] present a model-based testing +either as the local value or in the conflict set on all nodes. method for non-deterministic systems, using a model-checker + Unfortunately, although this style of specification at first to generate test cases (sequences of transitions in the model) +appeared quite natural and elegant, we found it difficult to which fulfill selected structural coverage criteria. But when test +extend to encompass all the behaviors we cared about. In cases are run, the implementation may choose to make differ- +particular, the fact that the same value can be written many ent transitions, because of non-determinism. If the implemen- +times during the same test run (e.g., the value ⊥ is written tation diverges from the model at a deterministic point, then +every time a file is deleted), renders the second condition the test fails, but if divergence occurs at a non-deterministic +above—“if e is the W RITE event that writes the value observed choice point, then the test is considered inconclusive. Fraser +by e0 ...”—impossible to test with certainty. and Wotowa show how to take inconclusive tests and generate + We tried dealing with this indeterminacy by constructing new branches, again using the model checker, that fulfill +≺ relations for all possible ways of matching W RITES with the selected coverage goal, starting from the state that the +later observations (and accepting a test case if we succeeded implementation chose. The test is repeated, and if the imple- +for any one of them), but the result was tricky to implement mentation follows either the original or the newly generated +and slow because the set of possibilities quickly became path, then the coverage goal is reached. If the implementation +large. Fortunately, this failed attempt gave us the idea of diverges again, then the test is still inconclusive, and another +working with limited knowledge about what the system is branch can be added in the same way. Tests generated in +doing by explicitly maintaining sets of possibilities, leading this way are tree-structured, and hopefully eventually the +to the current model-based specification. implementation will follow one of the paths in the tree, and + the coverage goal will be reached. + VIII. R ELATED WORK Arcaini et al. [19] generate tests with a model checker in + As far as we know, this is the first work to address testing a similar way, but instead of introducing branches, they reuse +a distributed synchronization service. But the problems of the model as a run-time monitor, to check that even if the +specifying the behavior of synchronizers and of testing the system follows a different path from the test case, then its +behavior of nondterministic and distributed systems have both input-output behavior still conforms to the model. They do +received considerable attention. assume that the inputs in the generated test can be supplied to + A series of formal specifications of the Unison file syn- the SUT even though it is following an unexpected path, and +chronizer [12] by Pierce and Balasubramaiam [1], Pierce they assume that outputs from the SUT always provide enough +and Vouillon [2] and Ramsey and Csirmaz [3] were the information to uniquely identify the corresponding model state +starting point for the present work. Those specifications go (‘strong conformance’). They evaluate their approach using a +further than ours in that they deal with multiple files and Tic-Tac-Toe game, in which the model requires moves to be + valid, but does not specify which moves the computer player determinism in those papers is quite different to the one used +should make. The Java implementation must be annotated in here. +order to link it to the model. No errors were discovered in the +Tic-Tac-Toe implementation (but neither were any expected). IX. F UTURE W ORK + In comparison, we use two state machines, a trivial one We have considered just the case of a single file. Naturally, +for generating tests, and a more interesting one as a run-time there are interesting questions to ask about a synchronizer’s be- +monitor. Our monitoring state machine is deterministic, but havior in the presence of multiple files and directory structures, +includes unobservable transitions—eliding those transitions such as “what happens when a directory is deleted on one +makes it non-deterministic. We allow multiple possible model client, while a file is written into that directory on another?” +states during monitoring (‘weak conformance’ in the sense of Extending the testing framework to multiple files and di- +[19]), and we treat the SUT as a black box—there is no need rectories will require slightly richer model states at test case +for instrumentation of the implementation to connect it to our generation time, including the paths that have been created +model. Our examples are more complex real applications, and so far, so that operations can stay within this set with high +we found a number of unexpected behaviors. enough probability to provoke bugs. + Ulrich and König propose architectures for testing dis- One challenge that can be expected when we make this +tributed systems [20], but assume that all internal actions of the extension is that the set of possible system states given a +SUT are observable by the tester, and that software probes are sequence of observed events is likely to grow much more +inserted into the SUT to allow the tester to control the timing quickly (it will be exponential in the number of files), and +of communications between nodes, and ensure that test runs we will probably need to find clever representations for this +are deterministic. Neither assumption holds in our setting. set. Possibilities include representing the set as a cartesian + Boy et al. report on an approach to testing servers by product of smaller sets—we can overapproximate the set of +running random sequences of API calls from a number of possible states without introducing false positives, so ideas +clients, and checking that specified invariants hold over the from abstract interpretation [32] should be applicable here. +resulting traces [21]. The invariants are specified as patterns Another rich source of incorrect behaviors in distributed +that are matched against the traces, and assertions that must systems is network partitions. To provoke such behaviors, it +hold if a pattern matches. Boy et al. found a subtle timing bug might be useful to extend our test cases with operations to +in a lock server using this method. The approach does not disconnect and reconnect hosts from the network. +address ‘conjectured events’, however, and does not include +shrinking—the lock-server bug was minimized by hand. X. C ONCLUSIONS + A variety of work on testing nondeterministic systems can We have described an executable formal specification of +be phrased in terms of the theory of input-output conformance the core behavior of file synchronization services. Since it’s +(ioco) testing [22], [23]. Indeed, there are some suggestive written in a black-box style, avoiding synchronizer-specific +similarities between aspects of this theory and the structures APIs and communicating only via the filesystem, we were able +we used in specification and testing of synchronizers—e.g., to apply it to three popular synchronizers—two commercial, +the inclusion in its labeled transition systems of quiescence one open source—and found surprising behaviors in two of +transitions, which are reminescent of our stabilization events. them. This shows the effectiveness of the method. +It would be interesting to try to reframe our development in + Given that three different synchronizers appear to share the +terms of ioco concepts. + same core specification, we expect that our model should be + QuickCheck was originally developed in and for Haskell + applicable (perhaps with small changes to the testing frame- +[5], and it has become the most widely used testing tool + work) to many others—e.g., Microsoft OneDrive, Box.net, +in that community. The version we used was developed + SpiderOak, Sugarsync, Seafile, Pulse, Wuala, Teamdrive, +by Quviq and supports Quviq’s core business: specification- + Cloudme, Cx, etc. Given the surprising behaviors already +based testing tools and services. Quviq QuickCheck [24] + found, this should be a valuable exercise. +extends the original version with libraries tailored for testing +industrial software, such as the state machine library used ACKNOWLEDGMENTS +here. It has been used to test many large systems, including +telecoms products [4], a messaging gateway [25], refactoring We thank John Lai and other Dropbox engineers for their +tools [26], [27], and quadcopters [28]. Probably the largest feedback. This work is partially funded by the EU FP7 +application so far was to test AUTOSAR basic software (C project PROWESS (#317820), the Swedish Strategic Research +code which runs in cars), in which a million lines of C Foundation (RAWFP), and the National Science Foundation +was tested against 3,000 pages of the AUTOSAR standard, (CCF-1421243). +using 20,000 lines of QuickCheck code [29]. Most of these R EFERENCES +systems are deterministic, but QuickCheck has also been used +to test for race conditions in concurrent programs [30], finding [1] S. Balasubramaniam and B. C. 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Available: http://doc.utwente.nl/65463/1/Tre96-CTIT96- + 26.pdf + \ No newline at end of file diff --git a/packages/opencode/specs/simulation-research/text/2019-coverage-guided-pbt.txt b/packages/opencode/specs/simulation-research/text/2019-coverage-guided-pbt.txt new file mode 100644 index 00000000000..7f5f298b026 --- /dev/null +++ b/packages/opencode/specs/simulation-research/text/2019-coverage-guided-pbt.txt @@ -0,0 +1,1393 @@ + 1 + +Coverage Guided, Property Based Testing + +LEONIDAS LAMPROPOULOS, University of Maryland, USA and University of Pennsylvania, USA +MICHAEL HICKS, University of Maryland, USA +BENJAMIN C. PIERCE, University of Pennsylvania, USA +Property-based random testing, exemplified by frameworks such as Haskell’s QuickCheck, works by testing an +executable predicate (a property) on a stream of randomly generated inputs. Property testing works very well +in many cases, but not always. Some properties are conditioned on the input satisfying demanding semantic +invariants that are not consequences of its syntactic structure—e.g., that an input list must be sorted or have +no duplicates. Most randomly generated inputs fail to satisfy properties with such sparse preconditions, and so +are simply discarded. As a result, much of the target system may go untested. + We address this issue with a novel technique called coverage guided, property based testing (CGPT). Our +approach is inspired by the related area of coverage guided fuzzing, exemplified by tools like AFL. Rather +than just generating a fresh random input at each iteration, CGPT can also produce new inputs by mutating +previous ones using type-aware, generic mutation operators. The target program is instrumented to track +which control flow branches are executed during a run and inputs whose runs expand control-flow coverage +are retained for future mutations. This means that, when sparse conditions in the target are satisfied and new +coverage is observed, the input that triggered them will be retained and used as a springboard to go further. + We have implemented CGPT as an extension to the QuickChick property testing tool for Coq programs; we +call our implementation FuzzChick. We evaluate FuzzChick on two Coq developments for abstract machines +that aim to enforce flavors of noninterference, which has a (very) sparse precondition. We systematically +inject bugs in the machines’ checking rules and use FuzzChick to look for counterexamples to the claim +that they satisfy a standard noninterference property. We find that vanilla QuickChick almost always fails +to find any bugs after a long period of time, as does an earlier proposal for combining property testing and +fuzzing. In contrast, FuzzChick often finds them within seconds to minutes. Moreover, FuzzChick is almost +fully automatic; although highly tuned, hand-written generators can find the bugs faster than FuzzChick, they +require substantial amounts of insight and manual effort. +Additional Key Words and Phrases: random testing, property-based testing, fuzz testing, coverage, QuickChick, +AFL, FuzzChick + +1 INTRODUCTION +Random testing methods probe a system’s behavior using randomly generated inputs. In property- +based random testing, illustrated in Figure 1a, the system’s expected behavior is specified as a col- +lection of properties—executable boolean predicates over inputs. For example, in QuickChick [Dénès +et al. 2014; Lampropoulos and Pierce 2018; Paraskevopoulou et al. 2015a,b], a modern property- +based random tester for the Coq proof assistant, the following property states that the sort function +should always produce sorted lists: + Definition prop_sort_correct (l : list nat) : bool := is_sorted (sort l). +QuickChick will repeatedly generate random lists and apply prop_sort_correct to each one, +continuing until either the property returns false or the process times out. QuickChick produces +random values by invoking a generator function of the appropriate type. While generators can be +written by hand, doing so requires nontrivial time and expertise; therefore, most property-based +Authors’ addresses: Leonidas Lampropoulos, University of Maryland, USA , University of Pennsylvania, USA, llamp@seas. +upenn.edu; Michael Hicks, University of Maryland, USA, mwh@cs.umd.edu; Benjamin C. Pierce, University of Pennsylvania, +USA, bcpierce@cs.upenn.edu. + +2019. 2475-1421/2019/1-ART1 $15.00 +https://doi.org/ + + + Proc. ACM Program. Lang., Vol. 1, No. OOPSLA, Article 1. Publication date: January 2019. + 1:2 Leonidas Lampropoulos, Michael Hicks, and Benjamin C. Pierce + +testing tools provide mechanisms for synthesizing them automatically [Bulwahn 2012a; Claessen +and Hughes 2000; Papadakis and Sagonas 2011]. For example, QuickChick can use Coq’s typeclass +mechanism to synthesize an appropriately typed generator using a predefined library of generator +combinators [Lampropoulos et al. 2018]. + A weakness of synthesized generators is that they are less effective than hand-crafted ones at +finding bugs when properties have sparse preconditions. Here is an example of such a property: + + Definition prop_insert_correct (x : nat) (l : list nat) : bool := + is_sorted l ==> is_sorted (insert x l). + +This property says that if a list l is sorted, then so should the list produced by insert x l. The ==> +operator denotes a property with a precondition: if its left-hand side is true, then the right-hand +predicate is tested; otherwise the property holds vacuously. For this example, QuickChick will +generate many random lists, but insert will only be tested on those lists that happen to be sorted. +The vast majority of such lists will be very small, since the probability that a random list is sorted +decreases quickly with its length. Accordingly, most of the generated tests will succeed vacuously, +and the right-hand side of the implication will rarely be checked. + To make property testing with synthesized generators more effective in such cases we take +inspiration from research on fuzz testing (or fuzzing). This technique, first conceived by Miller et al. +[1990], works by repeatedly feeding random bytes to a target program and seeing whether it crashes +(with an OS-level fault). If the target program imposes structural constraints on its input then the +core program logic will only be tested when those constraints are satisfied. If the constraints are +sparse, then input bytes generated in a purely random fashion are unlikely to satisfy them, limiting +the power of random tests to find bugs. Sound familiar? + The fuzzing community has addressed this problem by developing a technique called coverage +guided fuzzing (CGF), exemplified in the popular fuzzer AFL [2019]. Rather than generate each +new input from scratch, an input is obtained by mutating a prior test’s input. The process starts +with a seed input provided by the test engineer. The target program is instrumented (e.g., during +compilation) to efficiently track which control-flow edges are traversed when executing a given +test. If this input causes the program to traverse a previously unvisited edge, then it is deemed +“interesting” and retained as an object of future mutations. Doing so allows the fuzzer to gradually +explore many of the program’s control paths, especially ones that are reached by relatively few +inputs. In particular, if the program carries out a test that is satisfied by few inputs, a CGF tool will +remember such an input when it arises and use it as a springboard to cover more paths. CGF easily +outperforms completely random input generation, and it has even been shown to automatically +“reverse engineer” fairly complicated input formats [lcamtuf 2019b]. + This paper introduces coverage guided, property based testing (CGPT), a novel combination +of property testing and CGF. We have implemented this technique in FuzzChick, a redesign of +QuickChick. FuzzChick is depicted in Figure 1b. As with ordinary fuzzing, the property and the +code it tests are instrumented to gather control-flow coverage information. This information is used +to determine whether the prior input is interesting, in which case it will be repeatedly mutated to +produce subsequent inputs. FuzzChick synthesizes a standard random generator, which it uses to +produce the initial seed input (the test engineer does not have to provide one). It also synthesizes a +collection of mutators, each inspired by the kinds of mutators used in traditional fuzzing. FuzzChick +mutators are type-aware: instead of mutating binary streams, they mutate inputs at the algebraic +datatype level while preserving their type, which allows the mutations to be more targeted and +effective. They are applied during the testing process on seeds that were considered interesting to +obtain new ones, which are then in turn checked for new paths and mutated. If mutation-based + +Proc. ACM Program. Lang., Vol. 1, No. OOPSLA, Article 1. Publication date: January 2019. + Coverage Guided, Property Based Testing 1:3 + + + + RNG + FuzzChick + Random + RNG bits + Generator Mutator + Random + bits Structured + Random Mutated data + Generator + structured structured + Random data data Seed Pool + structured + Instrumentation + data Yes + + SUT + Property New No + Success/ SUT + Property Throw away + Success/ Paths? + Failure Discard + Failure Discard + + Report to User + Report to User + Coverage info + + (a) QuickChick (b) FuzzChick + +Fig. 1. QuickChick vs FuzzChick workflows. QuickChick (left) uses a simple testing loop: a generator produces +random structured data from a standard source of pseudo-random bits, and this data is used to test the desired +property. On success, repeat; on failure, report the counterexample. FuzzChick (right) instead instruments +the property being tested (including the system under test (SUT), but not including the testing framework +itself). Coverage information is used to determine whether the input (a data structure) is interesting or not. +In addition, the tool decides between mutating an existing interesting input (if one exists) or generating new +inputs randomly to reset the process. Both the mutator and the generator operate at the level of algebraic +data types. + + + +input generation covers no new paths for a long time, FuzzChick will just call the normal generator. +This serves to “reset” the state space exploration process, escaping from local minima. + Revisiting the sorted list example, suppose the random generator has produced the list [1;3;2;4]. +In a pure random setting, this test would be immediately discarded because it is not sorted. In +FuzzChick, however, it can be mutated to yield a few “similar” lists. For instance, it might be +changed to either [1;3;0;4] or [1;3;5;4] by mutating its third element. In the first case, testing +with the mutated list would cover no new paths, and the mutated test would be thrown away. In +the latter case, we would be able to cover more branches of the is_sorted predicate, since the list +contains a larger sorted prefix and FuzzChick treats visiting a branch more times as an increase in +coverage. This new list could in turn be reused, bringing us one step closer to a sorted input! + We evaluated FuzzChick by using it to test two formalized developments of secure machines +(§ 4). The most complicated machine spans more than 10k lines of Coq code, including definitions +and specifications (∼ 2000 LoC), testing infrastructure (∼ 2000 LoC), and proofs (∼ 6000 LoC). +Both machines aim to enforce flavors of noninterference. Informally, noninterference states that an +external observer without access to secret information cannot distinguish between two runs of a +program that differ only in such secret information. As such, noninterference is a perfect example +of a very sparse property: it requires randomly generating pairs of states that are identical in all +of their “public” locations. Both machines have been proved correct [Azevedo de Amorim et al. +2014], so in their original state they do not have any bugs left to find. Therefore, we systematically +inject bugs in the machines’ security checks and then see whether random testing can produce + + Proc. ACM Program. Lang., Vol. 1, No. OOPSLA, Article 1. Publication date: January 2019. + 1:4 Leonidas Lampropoulos, Michael Hicks, and Benjamin C. Pierce + +programs that are evidence of a noninterference violation. We measure effectiveness as mean time +to failure—i.e., how long does it take to produce an example violation? + We compare the performance of FuzzChick against two alternative, fully automated property- +based random testers: QuickChick and an adaptation of Crowbar [2017], a previously proposed +integration of the AFL fuzzer and a property testing framework. Crowbar works by using AFL +to fuzz the source of randomness used by a property tester’s generator, rather than the inputs +directly as FuzzChick does. (Crowbar is described in detail in § 2.2.) As Crowbar was originally +developed for use with its own simplistic OCaml-based property tester, we could easily adapt it to +work with QuickChick. Both these two and FuzzChick use automatically synthesized generators, +while FuzzChick also uses automatically synthesized mutators. + On these challenging applications, FuzzChick significantly outperforms both QuickChick and +Crowbar. For the simpler of the two machines, FuzzChick discovers most bugs within seconds, +while the other two systems mostly time out after an hour. For the more complicated and realistic +one, FuzzChick requires a few minutes for most bugs, while the other systems didn’t find most of +the bugs within eight hours. We also compared the performance of FuzzChick against QuickChick +when using a collection of highly tuned, hand-written generators [Hriţcu et al. 2013b, 2016]. With +them, QuickChick finds most bugs extremely quickly, in less than one second. However, the human +cost of such generators is high: they took most of a person-year to develop and comprise almost +1000 LOC. In short, FuzzChick represents a strong advance in automated input generation, but +there is still opportunity to improve. + In summary, we offer the following contributions: + • We present coverage guided, property based testing (CGPT), a novel combination of property + testing and coverage guided fuzzing. We have implemented CGPT in FuzzChick, an extension + of the QuickChick property-based random testing tool for Coq (§ 3). FuzzChick synthesizes + type-specific mutation operators, drawing inspiration from and generalizing AFL’s bit-level + operators. It also synthesizes traditional input generators, which it uses both to produce an + initial seed and to restart when testing gets stuck in a local minimum. + • We evaluate FuzzChick by using it to test the formal development of two abstract machines, + one simple and one more realistic, which aim to enforce a non-interference property (§ 4). The + evaluation systematically modifies these machines so that they omit various security checks, + and measures how quickly randomly testing the noninterference property can uncover them. + Compared against QuickChick and Crowbar, FuzzChick is far more effective: it discovers + most injected bugs orders of magnitude faster. FuzzChick is still equally far away from the + efficiency of expertly hand-written generators, but incurs far less manual work (§ 5). +We discuss related work in § 6 and conclude in § 7. + +2 BACKGROUND +We begin by describing QuickChick, a property-based random tester for Coq that serves as our +starting point. We also describe Crowbar [2017], a prior approach to combining property testing +and fuzzing, and our reimplementation of it, which we use as a point of comparison in the evalua- +tion section. Our main contribution—the idea of coverage guided, property-based testing (CGPT) +implemented in the tool FuzzChick—builds on these foundations; it is presented in § 3. + +2.1 QuickChick +Coq is a widely used proof assistant that has been used to prove the correctness of numerous +complex software systems including the CompCert optimizing C compiler [Leroy 2009] and the +CertiKOS hypervisor [Gu et al. 2016]). QuickChick [Lampropoulos 2018; Lampropoulos and Pierce + +Proc. ACM Program. Lang., Vol. 1, No. OOPSLA, Article 1. Publication date: January 2019. + Coverage Guided, Property Based Testing 1:5 + +2018; Paraskevopoulou et al. 2015a] is a tool that integrates random testing into Coq; its goal is +to help proof engineers iron out most of the bugs in both their programs and their specifications +before spending the (often significant) energy required to prove correctness formally. It works +by attempting to automatically generate counterexamples to hypothesized theorems. If no such +counterexample can be found, the proof engineer can proceed with greater confidence. + QuickChick originally started as a straightforward clone of Haskell’s QuickCheck tool [Claessen +and Hughes 2000] and still shares the same overall architecture, shown in Figure 1a. To test a piece +of software, QuickChick requires four ingredients: + • an executable property that is repeatedly tested against inputs of some type t, + • a generator for producing random inputs of type t, + • a printer of type t → string for reporting any counterexamples that are found, and + • a shrinker of type t → list t to “minimize” counterexamples before reporting them. +In Figure 1a, we group printers and shrinkers together under “Report to user,” as they are not the +focus of this paper and are identical across the different variants that we study. + The main loop of QuickChick, shown in Algorithm 1, is extremely simple: given a property P, a +generator gen and an upper limit for the number of tests, QuickChick keeps generating random +inputs until one fails or the limit is reached. + +Algorithm 1 QuickChick Testing Loop + function testLoop(P, gen, maxTests) + i←0 + while i < maxTests do ▷ Loop until test limit + x ← gen ▷ Generate an input + result ← P (x) ▷ Run the property over the input + if !result then return Bug x ▷ Bug Found + end if + end while + return NoBug + end function + + As an example of how QuickChick might be used, suppose we want to use Coq to formalize +and ultimately prove a simple property involving binary trees (with payloads at both nodes and +leaves—this choice allows us to showcase several aspects of our mutation operators later). The Tree +type definition and a mirror function, which mirrors a tree by swapping its children recursively, +can be written as follows. 1 + Inductive Tree A := + | Leaf : A -> Tree A + | Node : A -> Tree A -> Tree A -> Tree A. + + Fixpoint mirror {A : Type} (t : Tree A) : Tree A := + match t with + | Leaf x => Leaf x + | Node x l r => Node x (mirror r) (mirror l) +1 In Coq, putting curly braces around a function parameter declaration, like {A} here, is a request to the typechecker to + +infer this parameter, allowing it to be omitted at use sites. The keyword Inductive introduces an algebraic datatype +declaration: in this case, the datatype has constructors Leaf and Node, each of which takes parameters of appropriate +type and yields a tree. The Fixpoint keyword introduces a recursive function. + + Proc. ACM Program. Lang., Vol. 1, No. OOPSLA, Article 1. Publication date: January 2019. + 1:6 Leonidas Lampropoulos, Michael Hicks, and Benjamin C. Pierce + + end. +For our property, suppose we want to show that mirror is an involution: i.e., mirroring a tree twice +yields the original tree. + Definition mirror_twice {A : Type} (t : Tree A) := + mirror (mirror t) == t. + Before trying to prove this property, we can use QuickChick to search for possible counterexam- +ples. To do so, we need to define a generator, printer, and shrinker for elements of type Tree A. We +can do this by invoking the command + Derive (GenSized, Show, Shrink) for Tree. +The Derive command uses the representation of the Tree type to automatically derive the three +needed components. QuickChick can then use these components (implicitly—they will be supplied +by Coq’s typeclass inference mechanism, e.g., in the following command) when invoking the +QuickChick command at the top level: + QuickChick mirror_twice. +This command implements the testing loop described above; it runs 10000 tests (by default) and +reports that all of them succeeded. It also reports that none were discarded because of precondition +failure (as expected, since mirror_twice doesn’t have a precondition). + QuickChecking mirror_twice... + +++ Passed 10000 tests (0 discards) +If we had made a mistake in our definition of mirror, say by mirroring the left subtree twice in the +Node branch... + Fixpoint mirror {A : Type} (t : Tree A) : Tree A := + match t with + | Leaf x => Leaf x + | Node x l r => Node x (mirror l) (mirror l) + end. +...QuickChick would complain, outputting a (minimal) counterexample. + QuickChecking mirror_prop + Node 0 (Leaf 1) (Leaf 0) + *** Failed after 4 tests and 5 shrinks. (0 discards) + Let’s now take a closer look at QuickChick’s implementation, and in particular, at its automatically +derived generators. Coq includes a built-in functional programming language, which we’ve used +above to write our program and property. To execute programs in this language efficiently, and to +get access to “non-logical” run-time facilities like IO and randomness, we extract Coq programs +to OCaml and link them with a run-time library that provides these features. For the rest of this +paper, we keep our use of Coq-specific features to a minimum, so that a reader unfamiliar with +Coq can think of QuickChick and the target program as if they were implemented in OCaml. + In essence,2 a QuickChick generator that produces inputs of some type A is just a function from +a random seed type (intuitively, an integer) to the output type. Its type G A is defined as follows: + Definition G A := RandomSeed -> A. +2 To streamline this discussion, we are eliding an additional parameter to real QuickChick generators that controls the size + +of generated structures. + + +Proc. ACM Program. Lang., Vol. 1, No. OOPSLA, Article 1. Publication date: January 2019. + Coverage Guided, Property Based Testing 1:7 + +The most basic block by which we build generators is ret (short for return). Given an element +x of type A, the expression ret x represents a singleton probability distribution: no matter what +random seed r it is given, (ret x) r will always produce x. + Definition ret {A : Type} (x : A) : G A := + (fun r => x). +(The fun keyword introduces an anonymous function.) We also need to compose generators: given +a generator for elements of type A and a function that, given an A produces a generator for Bs, we +can bind them together to form a generator for Bs.3 + Definition bind {A B : Type} (g : G A) (k : A -> G B) : G B := + (fun r => + let (r1,r2) := randomSplit r in + let a := g r1 in (k a) r2). +To compose generators, we need to first run g to obtain an element a of type A, and then run (k a) to +obtain a B. One subtlety is that these two generators should be given independent random seeds to +avoid introducing bias in the resulting distribution. We use randomSplit for this: given an input seed +r it produces a pair of statistically independent seeds r1 and r2 [Claessen and Pałka 2013]. To make +programs easier to read, we use the notation x <- e1 ;; e2 to mean bind e1 (fun x => e2). + QuickChick provides a useful library of generator combinators, inspired by the ones in Haskell’s +QuickCheck. These combinators can be used if desired to write generators by hand; more im- +portantly for present purposes, they are also used by the Derive command when synthesizing +generators for arbitrary algebraic data types. The most common and expressive one is freq (short +for frequency): + Definition freq {A : Type} : list (nat * G A) -> G A. +As its type says, freq takes a list of generators, each associated with a natural number that is +interpreted as a weight. It picks one of these generators at random, based on the discrete distribution +induced by the weights. + As mentioned earlier, QuickChick can automatically derive a generator for a type based on the +structure of its definition. We need not dig into the details of the derivation algorithm here, but +let’s look at generator it produces for Tree A (modulo a bit of prettification). The derived generator +produces Trees up to some size limit. Since Trees are parametric it also needs an argument, +arbitrary, that can produce random instances of the inner type.4 + Fixpoint genSizedTree {A : Type} (arbitrary : G A) (size : nat) : G (Tree A) := + match size with + | O => + x <- arbitrary;; + ret (Leaf x) + | S size' => + freq [ (1, x <- arbitrary;; + ret (Leaf x)) + ; (size, x <- arbitrary;; + l <- genSizedTree size';; + r <- genSizedTree size';; +3 Haskell-inclined readers will recognize that G is similar to the Reader monad. +4 In the real implementation of QuickChick, the arbitrary parameter is provided automatically by Coq’s typeclass + +mechanism. We’ve converted it to an ordinary parameter here to make the presentation more accessible. + + + Proc. ACM Program. Lang., Vol. 1, No. OOPSLA, Article 1. Publication date: January 2019. + 1:8 Leonidas Lampropoulos, Michael Hicks, and Benjamin C. Pierce + + ret (Node x l r)) + ] + end. + +This generator begins by matching on its size parameter: if size is zero, then it can only create a +Leaf; if non-zero, it has a choice. To produce a Leaf it needs to also create an element of type A to +use as the payload. This is done using the arbitrary function. The O branch of the match generates +an arbitrary value for x and returns it wrapped in a Leaf constructor. To produce a Node, we +need to generate an element x of type A using arbitrary, and we need to generate its left and +right subtrees. We do this by recursively calling genSizedTree, but with a smaller size parameter. +In the S branch of the match, we can either produce a Leaf or a Node. We make the choice using +freq, skewing the distribution more heaving towards Nodes when the size parameter is large: The + 1 +weights given to freq will result in a Leaf size size of + of the time and a Node the remaining size + +1 +1 +the time. + +2.2 Crowbar and QcCrowbar +While automatically derived generators are useful, they do not work well when testing properties +with sparse preconditions. Consider for example binary search trees, which satisfy a property +similar to prop_insert_correct from the introduction: inserting an element in a binary search +tree yields a binary search tree. + Definition bst_insert_correct (x : nat) (t : Tree nat) := + is_bst t ==> is_bst (bst_insert x t). + +If we attempt to test that property with the derived generator, QuickChick gives up: + QuickChecking bst_insert_correct... + *** Gave up! Passed only 1281 tests + Discarded: 20000 + +Only roughly 6% out of all trees randomly generated by genSizedTree turn out to be valid according +to is_bst, so the is_bst (bst_insert x t) portion of the property is rarely tested. + Fuzz testing tools face a similar problem when testing programs operating on structured inputs: +since valid inputs are rarely produced randomly, most randomly generated inputs will be quickly +discarded by the target program, and little of its code will be tested. Modern tools like AFL [2019] +address this problem by using coverage-guided fuzzing (CGF). The idea is to track which portions of +the target program’s code are executed (“covered”) during a test, and to retain inputs that cover new +parts of the code. Future inputs are generated by mutating these retained, “interesting” inputs. Can +we employ a similar idea to improve the efficacy of testing properties with sparse preconditions? + A very clever recent attempt at doing so appeared in Crowbar [2017], which performs property +testing on OCaml programs. It is depicted in Figure 2. At a high level, Crowbar uses AFL to fuzz the +stream of random bits that controls the generators used by property-based testing. To achieve this +effect, Crowbar simply replaces the random number generator by a stream of bytes that it reads +from a file. The testing framework raises an exception when the property under test is invalidated, +so the whole program can be fuzzed using an out-of-the box fuzzer such as AFL. Crowbar uses an +OCaml compilation switch that adds AFL instrumentation, and gives this program to AFL. + The testing loop for Crowbar is exactly that of AFL—a sketch is shown in Algorithm 2. Given a +property P and an input seed corpus S, Crowbar keeps picking a seed from S, deciding how many +times to mutate it (in the fuzzing literature, this amount is often called the energy of a seed and +different ways of calculating this energy are called power schedules), mutating it and then either + +Proc. ACM Program. Lang., Vol. 1, No. OOPSLA, Article 1. Publication date: January 2019. + Coverage Guided, Property Based Testing 1:9 + + + + + AFL + Mutated + bits + “Random” API Mutator + “Random” + bits + + Generator Seed Pool + Structured + Yes + data + New No + SUT + Property Throw away + Paths? + Success/ + Instrumentation + + + + + Failure Discard + + + Report to User + Coverage info + + + Fig. 2. QcCrowbar Workflow + + +reporting a crash (violations of the property),5 or updating the seed corpus with new seeds that +were deemed interesting (because they explored new branches). This process is repeated until a +predefined time limit is reached. + +Algorithm 2 Crowbar Fuzzing Loop + function testLoop(P, S) + repeat + s ← nextSeed(S) ▷ Pick the next seed to mutate + p ← calcEnergy(s) ▷ Power Schedule + for i = 1 to p do + s ′ ← mutate(s) ▷ Mutate the input + if !P(s ′) then return Bug s ′ ▷ Bug Found + else if isInteresting (s ′) then + S ← S ∪ {s ′ } ▷ Add to queue + end if + end for + until Timeout + return NoBug + end function + + As QuickChick also targets OCaml via extraction from Coq, it is not too difficult to adapt the +Crowbar approach for QuickChick; we call the result QcCrowbar. We retargeted the extraction of +RandomSeed to type rnd and implemented a few wrappers for the rest of the randomness primitives +that QuickChick uses. The entire executable produced is then a valid target for AFL. + As we will see in § 5, QcCrowbar is roughly as effective as plain QuickChick with completely +random test case generation—i.e., not very effective, when the properties involved become more +5 The actual AFL implementation, rather than returning the first counter-example, will continue fuzzing to try to uncover + +more bugs until a given time limit is reached. Here, for ease of comparison with the other systems, we focus on the generation +aspect of the AFL fuzzing loop. + + + Proc. ACM Program. Lang., Vol. 1, No. OOPSLA, Article 1. Publication date: January 2019. + 1:10 Leonidas Lampropoulos, Michael Hicks, and Benjamin C. Pierce + +complex. The reason is that the binary input that is used as a source of randomness can only be +modified by AFL at the bit level; such bit-level manipulations of the input don’t have any obvious +correspondence to changes in the distribution of the structured data that is eventually fed into the +target program. AFL’s cleverly crafted mutations normally fiddle with the bits of a data structure; in +the Crowbar approach, they fiddle with the randomness used to generate a data structure. Therefore, +the changes that it makes can have much larger and less predictable effects on the structure that +gets generated. + Crowbar has other drawbacks, too. The way the testing infrastructure is set up, whenever we +want to test a command using QcCrowbar, a single OCaml file is produced that contains, in addition +to the property under test, all of the operational logic of QuickChick, including generation, printing +and shrinking. For concreteness, a standard size of an extracted file is roughly 4000-6000 lines. +Ideally, we would prefer to instrument only the property itself: we want to cover the precondition, in +order to guide generation towards non-discarded inputs, and the property itself, to guide generation +towards non-explored paths—we do not care if the printing code or other parts of QuickChick itself +are covered. This means that a large part of the coverage information provided is unnecessary, while +incurring significant instrumentation overhead. This, together with the expensive decision-making +logic and the repeated memory accesses for seed manipulation, result in a significant overhead +compared to pure random execution. On our more complex case study (§ 4), QuickChick using +hand-written random generators variants is able to execute roughly 40× more tests per second! + These somewhat disappointing observations are not criticisms of AFL, which was built and +optimized for a different use case. (Indeed, the fact that AFL works at all in this unusual setup is a +testament to its amazing engineering!) Still, they leave open the question of whether the general +techniques developed for advanced fuzzing tools can be applied to effective property-based testing. + We answer this question in the affirmative. To do so, the main idea that we need is that, rather than +relying on bit-level manipulations to mutate the source of randomness coming into the generator, +we should mutate the high-level outputs coming out of it. Enter CGPT. + +3 COVERAGE GUIDED, PROPERTY-BASED TESTING IN FUZZCHICK +In this section we introduce coverage guided, property-based testing (CGPT), an integration of +property testing with coverage guided fuzzing (CGF). We do so via FuzzChick, an extension of +QuickChick that uses CGPT. We discuss FuzzChick’s testing loop first (§ 3.1), and then discuss our +approach to automatically deriving the mutation operations that it uses (§ 3.2). We will keep using +the binary trees of the previous section as our running example. + +3.1 CGPT Testing Loop +The main idea behind CGPT is that testing inputs should only be rarely produced by generators; +more often they should be produced by mutators operating on seeds chosen by a coverage guided +fuzzing process. This is shown in Figure 1b. In FuzzChick, both generators and mutators are +synthesized automatically based on the input type. The generator synthesis is standard; we discuss +our algorithm for synthesizing mutators in the next subsection. + The CGPT testing loop is given in Algorithm 3. We generate an input x using (mostly) mutation +operators, run the property, and check the result. If the property fails, we report the counterexample +to the user. If not, we check whether the input is interesting or not (i.e., whether it exercises new +paths based on coverage information), assign it some energy, and add it to the appropriate queue. +At a high level, this loop is fairly similar to the one in AFL and the one shown for Crowbar in the +previous section (Algorithm 2). + The devil, of course, is in the details. The two main differences from Crowbar are the search +strategy (how CBPT picks the next seed to mutate) and the generation of inputs (whether we use + +Proc. ACM Program. Lang., Vol. 1, No. OOPSLA, Article 1. Publication date: January 2019. + Coverage Guided, Property Based Testing 1:11 + +Algorithm 3 CGPT Testing Loop + function testLoop(P, gen, mut, maxTests) + QSucc, QDisc ← ∅ ▷ Initialize queues + while i < maxTests do ▷ Loop until test limit + д ← pick(QSucc, QDisc, gen, mut) ▷ Pick how to generate next input + x ←g ▷ Run the generator/mutator + result ← P (x) ▷ Run the property over the input + if !result then return Bug x ▷ Bug Found + else if isInteresting (x) then + e ← calcEnergy (x) ▷ Power Schedule + if !discarded result then + enqueue(QSucc, (x, e)) ▷ If not discarded and interesting add to QSucc + else enqueue(QDisc, (x, e)) ▷ If discarded and interesting add to QDisc + end if + end if + end while + return NoBug + end function + + function pick(QSucc, QDisc, gen, mut) + if !isEmpty(QSucc) then + (x, e) ←dequeue(QSucc) ▷ Return top, decrease energy by one + if e > 0 then return mut(x) ▷ If there is energy left, mutate + else return pick(QSucc, QDisc, gen, mut) ▷ Otherwise, look for another seed + end if + else if !isEmpty(QDisc) then + (x, e) ←dequeue(QDisc) ▷ Return top, decrease energy by one + if e > 0 then return mut(x) ▷ If there is energy left, mutate + else return gen ▷ Otherwise generate randomly + end if + else return gen ▷ If no seeds exists, generate randomly + end if + end function + + +mutators or generators). Instead of having a single seed corpus like Crowbar, we take advantage of +the fact that we can differentiate between successful and discarded runs. We maintain two queues: +one for interesting seeds that succeed in satisfying the precondition (QSucc) and one for seeds +that were discarded (QDisc). While we prioritize seeds that pass the precondition, as nearby inputs +will also tend to satisfy it, we do remember discarded inputs that revealed new paths. The idea is +that, just like in the sorted example of the introduction, non-discarded inputs can sometimes be +discovered by following a sequence of inputs that, though they are discarded themselves, move +closer to satisfying the precondition. + The other difference is how the next input will be generated. Notice that CGPT mutations operate +at a higher level of abstraction than their lower-level counterparts in CGF tools, or Crowbar. Rather +than simply flipping bits in a semantically blind fashion, CGPT mutators operate at a higher level, +directly manipulating and constructing values of the desired type. This means there is a more +direct relationship between the original value and the mutated one, which should assist the search + + Proc. ACM Program. Lang., Vol. 1, No. OOPSLA, Article 1. Publication date: January 2019. + 1:12 Leonidas Lampropoulos, Michael Hicks, and Benjamin C. Pierce + +process. In addition, inputs need not only be produced by mutation, as in CGF. Instead, CGPT can +switch between mutation and generation. If there is a seed in the interesting queue that still has +energy left, we mutate that one. If not, we alternate between mutating a seed in the discarded +queue (if available) and generating completely random inputs. Initially, since the queues are empty, +we obtain seeds randomly. As we explore more paths, the queues get populated by seeds and we +switch to mutation-based generation. If, at any point, fuzzing appears to become stuck, we fall +back to random generation. Thus, the test engineer need not provide an initial seed for the fuzzing +process, which is good, as Klees et al. [2018] have shown that a poor choice of initial seed (which +can often be hard to judge) can harm overall performance. + Finally, there is a more minor difference in terms of the power schedule: how much we mutate +each seed. For the most part, to keep the comparison fair, the energy assigned to each seed is similar +to the one that AFL would assign it (that is, more energy for seeds that lead to short executions, or +for seeds that exercise a lot of new paths). However, using the same rationale as above, we assign +discards proportionally less energy than seeds that lead to successful runs. + +3.2 Deriving Mutators +A key element of CGPT is the use of mutation operators for producing new inputs. In FuzzChick, a +mutator has type T -> G T: given an input seed of some type T, a mutator is a random generator +for other values of type T. Rather than require the programmer to write mutators by hand, we have +developed an algorithm for deriving them automatically. We target simple algebraic data types, +possibly with type parameters, such as might be found in any functional language (omitting the +fancier data types made possible by Coq’s dependent type system). Formally, we consider several +ways of automatically deriving mutators for a datatype T with constructors Ci , each of type Ti → +T. The type Tree, for example, has constructors C 0 = Leaf, of type A → Tree A, and C 1 = Node, of +type A → Tree A → Tree A → Tree A. + The first way of deriving mutators is recursive mutation. That is, we obtain a mutator for an +element of T by mutating one of its subterms using an appropriate mutator mutateTk , where Tk is +the type of the subterm. Given an element of T beginning with constructor Ci , we can recursively +mutate any one of its arguments and keep the rest unchanged. We call this mutation operator +mutater .6 + + mutaterT (Ci x 1 . . . x n ) = {Ci x 1′ . . . x n′ | k ∈ {1 . . . n}, x k′ ∈ mutateTk x k , x j′ = x j for j , k} + +For the binary tree example, both constructors contain subexpressions that can be fuzzed. Since +trees are parametric, we need to assume that its parameter type A can also be mutated using some +function mutateA . Concretely, applying mutaterTree A to a Leaf x yields the following set of mutants: + mutaterTree A (Leaf a) = Leaf a' | a' ∈ mutateA a +  + +Similarly, applying mutater to Node a l r yields + mutaterTree A (Node a l r) = {Node a' l r | a' ∈ mutateA a} + ∪ {Node a l' r | l' ∈ mutateTree A l'} + ∪ {Node a l r' | r' ∈ mutateTree A r'} , +where mutateTree A is the mutator for Tree A (a combination of mutaterTree A with the other mutators +discussed below). +6 To lighten the notation, the mathematical definitions of the mutators in this section are slightly imprecise: Strictly speaking, + +in order to produce results of type G A, they should all take a random seed as a second argument. We consistently elide this +argument, in effect changing the type of mutators from A -> G A to A -> Set A. + + +Proc. ACM Program. Lang., Vol. 1, No. OOPSLA, Article 1. Publication date: January 2019. + Coverage Guided, Property Based Testing 1:13 + + The second kind of mutation operators correspond to bit-level mutations in AFL that result in +the deletion of bits. At the algebraic datatype level, we can mutate a term to a subterm with the +same type. We call this operator mutates .7 + + mutatesT (Ci x 1 . . . x n ) = {x k | k ∈ {1 . . . n}, Tk = T} + + In the particular case of binary trees, for example, this operator can only be applied to the Node +constructor, since a Leaf term has no subterms that are trees. + + mutatesTree A (Node a l r) = {l, r} + + Another way to mutate a term that also roughly translates to deleting bits is to mutate it to one +with a different constructor, subject to the requirement that that constructor’s type is a subsequence +of the one we’re trying to mutate. We call this operator mutated . That is, given two constructors, Ci +and Ci ′ , of types Ti → T and Ti′ → T, where Ci expects n arguments and Ci ′ expects n ′, we require +a mapping π : {1 . . . n ′ } → {1 . . . n}, such that the type of each argument of Ci ′ can be mapped to +the type of some argument in the Ci constructor: ∀k ∈ {1 . . . n ′ },Tk = Tπ (k ) . Then we can mutate a +term by switching the top-level constructor from Ci to Ci ′ and dropping some of the arguments: + + mutatedT (Ci x 1 . . . x n ) + = {Ci′ x π (1) . . . x π′ (n′ ) | i ′ , i, π : {1 . . . n ′ } → {1 . . . n}, ∀k ∈ {1 . . . n ′ }. Tk′ = Tπ (k ) } + +In the binary tree example, the Leaf constructor expects a single argument of type A. Since a Node +also includes such an argument, we can mutate Node a l r to Leaf a. + + mutatedTree A (Node a l r) = {Leaf a} + +Note that while the intuition behind mutated was that it results in “deleting bits”, it can also be +applied to change between constructors with identical signatures: for example mutating a true +boolean to false. + More generally, we can change from one constructor Ci ′ of T to any other constructor (or indeed +the same constructor) Ci ′ by applying any function π from argument positions of one to argument +positions of the other. Missing arguments to Ci ′ can be filled in simply by generating a random +element of the appropriate type (using arbitrary). + + mutateдT (Ci x 1 . . . x n ) = {Ci′ y1 . . . yn ′ | π : {1 . . . n} → {1 . . . n ′ } ∪ {⊥}, + ∀k ∈ {1 . . . n ′ }. + (π (k) = j ∧ Tj′ = Tk ∧ yj = xk )} + ′ + ∨ (π (k) =⊥ ∧yj = arbitraryTj ) + + For example, we can mutate a Leaf x to Node x l r, where the left and right subtrees are +generated arbitrarily. + + mutateдTree A (Leaf a) = {Node a l r | l, r ∈ arbitraryTree A } + +Interestingly, this does not have an exact equivalent at the AFL level; AFL mutations cannot generate +random bitstrings out of thin air. + Putting everything together, where the different mutation operators constitute different freq +choices, yields the derived mutator for trees shown in Figure 3—now written out in actual Coq + +7 Readers familiar with QuickCheck may notice a striking similarity to its shrinking operations. + + + + Proc. ACM Program. Lang., Vol. 1, No. OOPSLA, Article 1. Publication date: January 2019. + 1:14 Leonidas Lampropoulos, Michael Hicks, and Benjamin C. Pierce + +Fixpoint mutate_tree {A : Type} + (mutate : A -> G A) (arbitrary : G A) (t : Tree A) + : G (Tree A) := + match t with + | Leaf x => + freq [ (* Recursively mutate subterms *) + (1, x' <- mutate x ;; ret (Leaf x')) + (* Mutate to a larger constructor by generating subterms *) + ; (1, l <- arbitrary ;; r <- arbitrary ;; ret (Node x l r)) + ] + | Node x l r => + freq [ (* Recursively mutate subterms *) + (1, x' <- mutate x;; ret (Node x' l r)) + ; (1, l' <- mutate_tree l;; ret (Node x l' r)) + ; (1, r' <- mutate_tree r;; ret (Node x l r')) + (* Mutate to a subterm of the same type *) + ; (1, ret l) + ; (1, ret r) + (* Mutate to a smaller constructor, dropping subterms *) + ; (1, ret (Leaf x)) + ] + end. + + Fig. 3. A binary tree mutator, in Coq + + +notation.8 The arbitrary function provides a way of generating elements of type A, just like in the +previous section. Similarly, the mutate function provides a way of mutating values of type A. (Both +of these functions are implicitly parameterized on the type that they should return, using Coq’s +typeclass mechanism. The details of how this works are not too important; the effect is that Coq’s +type inference mechanism fills in appropriate type superscripts everywhere.) + Our chosen type A -> G A for mutation operators precludes a particular category of AFL muta- +tions: splicing using multiple seeds. That is, we can’t other existing seeds (or parts of other existing +seeds) in our mutators. This was a deliberate design decision to keep mutators lightweight and +avoid the overhead of keeping and traversing seeds during the mutation process; however, splicing +may well be a useful operator for FuzzChick, as it is for AFL. We leave exploring this bit of the +design space for future work. + +4 CASE STUDIES +To evaluate FuzzChick, we measured its bug-finding performance on two existing Coq developments, +both formalizing abstract machines that aim to enforce noninterference [Goguen and Meseguer +1982; Sabelfeld and Myers 2003] using run-time checks. Informally, noninterference states that +an external observer without access to secret information cannot distinguish between two runs +8 The code in the figure follows our current implementation in omitting some of the mutations generated by the mutate + д +operator: we always choose mutants with a different constructor and such that the arguments to the mutant are either a +subset or a superset of the arguments to the original (not a mixture of the two). The fully general mutator will sometimes +produce many more mutants of a given value, and we have not experimented with it enough yet to understand whether or +not this yields more effective testing overall. + + +Proc. ACM Program. Lang., Vol. 1, No. OOPSLA, Article 1. Publication date: January 2019. + Coverage Guided, Property Based Testing 1:15 + +of a program that differ only in such secret information. Noninterference is a good property on +which to evaluate CGPT, since it has a sparse precondition, as we will see. We describe the two +machines in this section and present our measurements and comparisons in § 5. This section serves +two purposes: to provide more background on noninterference, explaining the particularities of +this setting that make random testing hard; and to explain in detail the systematic fault injection +mechanism. + The first Coq development (§ 4.1) is a simple, stack-based machine with a handful of instructions +that employ simple data labeling policies. The second (§ 4.2) is more featureful—including, among +other things, registers, a richer label lattice, dynamic memory allocation, and a larger instruction +set. Both machines are borrowed from published papers [Hriţcu et al. 2013b, 2016], and they +have already been proved correct in Coq [Paraskevopoulou et al. 2015b]. Thus, by using explicit +fault injection, we can maintain perfect control over the ground truth of our experiments, unlike +prior fuzzing evaluations [Klees et al. 2018]. In particular, the dynamic IFC checks performed by +each of the machines are isolated into a separate “rule table,” which makes it straightforward to +systematically inject bugs and see whether testing can detect them. Finally, we also have access to +highly tuned, hand-written generators for the inputs to these machines; these serve as a point of +comparison in the evaluation in § 5. + +4.1 The IFC Stack Machine +The stack machine consists of a program counter, a stack, and separate data and instruction +memories. At the core of dynamic IFC enforcement lies the notion of labels [Montagu et al. 2013]. +Each runtime value is associated with such a label, representing a security level, which is propagated +throughout the execution of the program to represent the secrecy of each piece of data. The basic +values in the stack machine are labeled integers, called atoms, where each label can be either L +(“low,” denoting public information) or H (“high,” denoting secret information). These labels form a +trivial 2-element lattice where L ⊑ H ; we write ℓ1 ∨ ℓ2 for the join (least upper bound) of ℓ1 and +ℓ2 in this lattice. Memories are just lists of such atoms, while stacks can contain either atoms or +specially marked return addresses, which capture the program counter at the time a call was made. +Finally, the stack machine has a minimal set of instructions: + Instr ::= Push n | Load | Store | Add | Noop | Call n | Return | Halt +The argument to Push is an integer that gets pushed on the stack with label L, while the argument +to Call is the number of stack elements that are treated as arguments to the call. + Putting all this together, a machine state S is formally a 4-tuple, written pc s m i , consisting +of a program counter pc (an integer), a stack s (atoms or return addresses), a memory m (a list of +atoms), and an instruction memory i (a list of instructions). +4.1.1 Noninterference. The security property our machine enforces, noninterference, is based on a +notion of “indistinguishability.” Intuitively, two machine states are indistinguishable if they only +differ in secret data. We build up the notion formally from the machine parts. +Definition 1. + • Two atoms n 1 @ℓ1 and n 2 @ℓ2 are indistinguishable, written n 1 @ℓ1 ≈ n 2 @ℓ2 , if either ℓ1 = + ℓ2 = H or else n 1 = n 2 and ℓ1 = ℓ2 = L. + • Two instructions i 1 and i 2 are indistinguishable if they are the same. + • Two return addresses R(n 1 @ℓ1 ) and R(n 2 @ℓ2 ) are indistinguishable if either ℓ1 = ℓ2 = H or + else n 1 = n 2 and ℓ1 = ℓ2 = L. + • Two lists (memories, stacks, or instruction memories) xs and ys are indistinguishable if they + have the same length and their elements are pairwise indistinguishable. + + Proc. ACM Program. Lang., Vol. 1, No. OOPSLA, Article 1. Publication date: January 2019. + 1:16 Leonidas Lampropoulos, Michael Hicks, and Benjamin C. Pierce + +Definition 2. Machine states S 1 = pc 1 s 1 m 1 i 1 and S 2 = pc 2 s 2 m 2 i 2 are indistinguishable +if their corresponding components are indistinguishable: pc 1 ≈ pc 2 , s 1 ≈ s 2 , m 1 ≈ m 2 , and i 1 ≈ i 2 . + The particular variant of noninterference we are interested in is termination-insensitive nonin- +terference [Sabelfeld and Myers 2003]. We write S ⇓ S ′ to denote that if we repeatedly step the +machine S we will reach the halting state S ′ (its pc points to a Halt instruction). +Definition 3. A machine semantics is end-to-end noninterfering if, for any indistinguishable states +S 1 ≈ S 2 that execute to completion successfully, S 1 ⇓ S 1′ and S 2 ⇓ S 2′ , we have S 1′ ≈ S 2′ . + As Hriţcu et al. [2013b] realized, this end-to-end property, while intuitively simple, is quite hard +to falsify through random testing. Indeed, to discover a counterexample a testing tool needs to (a) +generate indistinguishable starting states, with programs that (b) run for long enough to reach +an interesting configuration where the bug might occur, and then (c) return to a low-pc state and +terminate successfully. + Instead, Hriţcu et al. found that testing a stronger property, the inductive one that is needed +to actually prove the correctness of the design, is much easier. This property, called single-step +noninterference (SSNI), comprises three cases, often called unwinding conditions [Goguen and +Meseguer 1982] in the literature: +Definition 4. A machine semantics is single-step noninterfering if: + (1) for all S 1 , S 2 ∈ Low, if S 1 ≈ S 2 , S 1 ⇒ S 1′ , and S 2 ⇒ S 2′ , then S 1′ ≈ S 2′ ; + (2) for all S < Low if S ⇒ S ′ and S ′ < Low, then S ≈ S ′; + (3) for all S 1 , S 2 < Low, if S 1 ≈ S 2 , S 1 ⇒ S 1′ , S 2 ⇒ S 2′ , and S 1′ , S 2′ ∈ Low, then S 1′ ≈ S 2′ . + Single-step noninterference as a property to test imposes a particularly challenging, sparse +precondition: the pair of states generated, S 1 and S 2 , must be low-equivalent and the machines +need to be able to execute (the same) single instruction successfully. A naive generator for states +(like QuickChick’s derived one) will have great difficulty satisfying this precondition. +4.1.2 IFC Rules and Systematic Mutations. Noninterference is enforced by propagating the labels +of values within the machine as it executes instructions and checking whether information ever +“leaks” from secret locations to public ones. For example, the rule for Store, which stores a pointer +in the stack, first checks that the join of the pc label and the pointer’s label is allowed to “flow” to +the label of the memory cell (this is often called the “no-sensitive-upgrades” check [Austin and +Flanagan 2009; Zdancewic 2002]). Then, it overwrites the cell’s contents, updating the label of the +element stored with the two labels. Such mechanisms are usually baked into the semantics: + + i(pc) = Store m(p) = n ′@ℓn′ + ℓp ∨ℓpc ⊑ ℓn′ m ′ = m[p := n@(ℓn ∨ℓp ∨ℓpc )] + (Store) + pc @ℓpc p @ℓp : n @ℓn : s m i ⇒ (pc+1)@ℓpc s m ′ i + + One abstraction that proves very handy in our experiments is to extract the IFC content of such +rules into a separate rule table that the operational semantics consult. For instance, the Store rule +now looks as follows: + i(pc) = Store m(p) = n ′@ℓn′ + (ℓpc , ℓr es ) = lookup(STORE, ℓp , ℓn , ℓn′ , ℓpc ) + ′ + + m ′ = m[p := n @ℓr es ] + (Store’) + pc @ℓpc p @ℓp : n @ℓn : s m i ⇒ (pc+1)@ℓpc + ′ s m′ i + + +Proc. ACM Program. Lang., Vol. 1, No. OOPSLA, Article 1. Publication date: January 2019. + Coverage Guided, Property Based Testing 1:17 + + The rule table contains the following entry associated with Store, where ℓp ,ℓn ,ℓn′ and ℓpc are the +corresponding arguments to lookup. + Check Final pc Label Result Label + ℓp ∨ℓpc ⊑ ℓn′ ℓpc ℓn ∨ℓp ∨ℓpc +Each rule contains a Check portion, which causes the machine to halt if executing the current +instruction would cause an IFC violation. It also gives the new pc label (which, for non-control-flow +instructions, is equal to the old one), as well as the label of the result of whatever operation we are +performing (here, the label of the element to be stored in the memory cell). + This factorization of IFC rules permits a systematic approach to evaluating our generators. Every +check performed and every join between labels when constructing the results is there to enforce a +particular noninterference policy. This means that if we remove any such check or taint we are +guaranteed to introduce a bug (or perhaps reveal that our IFC system is too restrictive, which would +also be a useful outcome of testing). Thus, we can systematically construct all possible variations +of a candidate rule in the rule table, using the lattice structure of the labels. For example, each row +of the following table represents a distinct mutant of the Store’ rule’s check: + Check Final pc Label Result Label + ℓpc ⊑ ℓn′ ℓpc ℓn ∨ℓp ∨ℓpc + ℓp ⊑ ℓn′ ℓpc ℓn ∨ℓp ∨ℓpc + ℓp ∨ℓpc ⊑ ℓn′ ⊥ ℓn ∨ℓp ∨ℓpc + ℓp ∨ℓpc ⊑ ℓn′ ℓpc ℓp ∨ℓpc + ℓp ∨ℓpc ⊑ ℓn′ ℓpc ℓn ∨ℓpc + ℓp ∨ℓpc ⊑ ℓn′ ℓpc ℓn ∨ℓp + +4.2 The IFC Register Machine +The register machine is a more realistic, scaled up version of the stack machine. It was first +presented in Hriţcu et al. [2016], where it was also proved in Coq to be noninterfering. The register +machine contains a plethora of features, originally intended to model an experimental processor +architecture [Chiricescu et al. 2013], that make generating well-distributed inputs much harder +and executing tests much slower. We briefly describe the delta between this machine and the stack +machine; for the interested reader, the machine is defined formally in Hriţcu et al. + The first difference that makes this machine more realistic is that uses registers instead of just a +stack. All instructions take registers as arguments and targets for their results. The instructions are: + Instr ::= Put n rd | Mov r s rd | Load rp rd | Store rp r s | Add r 1 r 2 rd | Mult r 1 r 2 rd | Eq r 1 r 2 rd | + Noop | Halt | Jump r | BranchNZ n r | Call r 1 r 2 r 3 | Return | Alloc r 1 r 2 r 3 + The IFC infrastructure for this machine is also beefed up by generalizing the label lattice. The +hard-coded 2-element lattice of the stack machine is replaced by an arbitrary lattice, which we +instantiate in our experiments with a sets-of-principles lattice [Stefan et al. 2012] or a four-element +diamond lattice. In addition, we encode observable, first-class labels, a feature used in a number of +modern IFC systems [Giffin et al. 2012; Hriţcu et al. 2013a; Stefan et al. 2011]. That is, the “attacker” +observing the system can detect discrepancies between labels, and the machine itself contains +instructions for comparing labels, joining them, etc. + Instr ::= Lab r s rd | PcLab rd | PutLab l rd | Join r 1 r 2 rd | FlowsTo r 1 r 2 rd +In addition, integer data, labels, data pointers, and instruction pointers are strongly typed in this +machine: they belong to different syntactic categories. + + Proc. ACM Program. Lang., Vol. 1, No. OOPSLA, Article 1. Publication date: January 2019. + 1:18 Leonidas Lampropoulos, Michael Hicks, and Benjamin C. Pierce + + Finally, this machine has a labeled memory model and dynamic memory allocation. The memory +is separated into 4 distinct regions, one for each label. When performing an Alloc r 1 r 2 r 3 instruction, +we specify the size of the memory block to be allocated (in r 1 ), as well as the label of the block (in +r 2 ). The machine then allocates a fresh block of memory at the region associated with the label in r 2 +and returns a pointer to it (in r 3 ). This pointer is stamped with the label of the context at the point +of allocation (program counter plus the labels of r 1 and r 2 ). A key invariant of the machine that +turned out to be necessary for the noninterference proof is that when we are accessing a block of +memory stamped with some label l, then we are accessing it through a sequence of pointers whose +labels are at least as secure as l. This invariant is an additional precondition that our generators +must satisfy: if we generate a pair of machine states that don’t have this property, then we can +trigger noninterference violations that would actually be false negatives! + All these features make the indistinguishability precondition for noninterference much harder +to satisfy. While it was (occasionally) possible to generate two equal instructions for the stack +machine, a naive generator has virtually zero chance of generating indistinguishable register +machine instructions, let alone whole machine states, as each instruction is chosen from a pool of +20, with each including one or more references to registers. Moreover, the added features make it +hard to generate instructions that can actually be executed: for that, most instructions’ arguments +need to be correctly typed (e.g., one can’t execute a load with a register that is not a pointer). +Moreover, having any sequence of pointers that can reach a memory block that is insufficiently +label-protected violates the reachability precondition. As a result, smart manual generators are +necessary for successful random testing in QuickChick. These generators comprise roughly 650 lines +of Coq code, capturing which registers contain what type of data, computing meets of reachable +pointer labels to produce valid stamps, and ensuring that the pair of machines are low-equivalent. + + + +5 EXPERIMENTAL EVALUATION +In this section we describe the experiments we carried out to evaluate the effectiveness of FuzzChick. +The performance metric we are interested in is mean time to failure (MTTF), which measures how +quickly a bug can be found (in wall-clock time). To measure it, we first systematically inject all +possible rule-table variants, such as the ones shown for the Store rule in the previous section, one at +a time. For the stack machine, this results in 20 different ways of getting the security enforcement +policy wrong; for the register machine, 33. For each of these variants, we test the (broken) artifact +independently and log the time until failure (or timeout) across multiple (5) runs. Despite the +relatively small number of runs, our results show that FuzzChick’s performance lies in the middle +of the other approaches with statistical significance (p = 0.05), mostly because of the order of +magnitude difference. The stack machine experiments were run in a machine with eight 2.30GHz +Intel i7 CPUS and 16GB of ram, while the register machine experiments in a twenty-four 2.4GHz +CPUs and 110GB RAM running Red Hat Enterprise Linux Server 7.4. + Comparing the MTTF of FuzzChick against QuickChick and QcCrowbar with automatically syn- +thesized generators and against QuickChick with hand-written generators, we find that FuzzChick’s +bug-finding performance falls in the (large) middle ground between the previously available fully +automatic approaches and the fully manual one—much better than prior automatic approaches, +but not as good as highly tuned manual testing. In particular, despite requiring very little manual +setup, FuzzChick is able to find most of the injected bugs within seconds or minutes, even for the +more challenging register machine, while the plain QuickChick and QcCrowbar are unable to find +most bugs even for the simpler stack machine after an hour or more of testing. + + +Proc. ACM Program. Lang., Vol. 1, No. OOPSLA, Article 1. Publication date: January 2019. + Coverage Guided, Property Based Testing 1:19 + + QuickChick + Injected Fault # QuickChick QcCrowbar FuzzChick + (hand-written) + 1 66.3 1h (t/o) 2.481 0.000 + 2 273.2 1h (t/o) 3.039 0.001 + 3 492.1 1h (t/o) 3.037 0.001 + 4 1h (t/o) 1h (t/o) 149.9 0.003 + 5 1h (t/o) 1h (t/o) 3.793 0.001 + 6 2452.7 1h (t/o) 2.030 0.001 + 7 1.115 3380.5 0.687 0.001 + 8 3.292 717.0 0.490 0.000 + 9 1h (t/o) 1h (t/o) 2283.0 0.003 + 10 1h (t/o) 1h (t/o) 1h (t/o) 0.003 + 11 1h (t/o) 1h (t/o) 153.4 0.000 + 12 351.4 1h (t/o) 388.5 0.002 + 13 1h (t/o) 1h (t/o) 414.3 0.001 + 14 349.4 1h (t/o) 1.341 0.000 + 15 1h (t/o) 1h (t/o) 382.8 0.002 + 16 1h (t/o) 1h (t/o) 2.900 0.002 + 17 1h (t/o) 1h (t/o) 3.201 0.003 + 18 1h (t/o) 1h (t/o) 1055.6 0.010 + 19 1h (t/o) 1h (t/o) 19.2 0.003 + 20 1h (t/o) 1h (t/o) 2.537 0.001 + + Fig. 4. MTTF (in seconds) across different bugs for the stack machine + + QuickChick + QuickChick QcCrowbar FuzzChick + (hand-written) + 81905.3 16510.5 25192.7 69634.2 + + Fig. 5. Number of tests executed per second across different methods + + +5.1 Stack machine +The results for the stack machine can be found in Figure 4. The first two columns are our baseline: +plain QuickChick and QcCrowbar with automatically derived generators. The third column shows +the performance of FuzzChick with a mostly automatic generator described below. The last column +shows QuickChick with the hand-written “smart generators” of Hriţcu et al. [2013b, 2016]. + Using derived generators alone (column QuickChick) fails to uncover most bugs within an hour +of testing. The reason quickly becomes apparent if we gather some simple statistics from the runs: +out of 200 million tests (for each bug), only about 5000 on average are not rejected! To see why +the rest are rejected, recall the property we’re testing, noninterference. To check noninterference, +first, the input machines must be indistinguishable and, second, both machines need to take a step +without crashing. Either of these checks cause many generated inputs to be discarded. For one +thing, generating pairs of machines randomly and then checking for indistinguishability will very +rarely succeed. But the default derived generators for pairs of machines does exactly that: + Definition gen_pair_state : G (state * state) := + st1 <- arbitrary ;; + st2 <- arbitrary ;; + + Proc. ACM Program. Lang., Vol. 1, No. OOPSLA, Article 1. Publication date: January 2019. + 1:20 Leonidas Lampropoulos, Michael Hicks, and Benjamin C. Pierce + + ret (st1, st2). +Worse, there are many configurations that can cause the machine to crash—for example, attempting +to execute an Add instruction while the stack is empty, or Return when there is no return stack +frame available. But the automatically generated instruction generator does not take that into +account either; it simply generates instructions uniformly at random: + Definition gen_instruction : G instruction := + freq [ (1, ret Nop) + ; (1, z <- arbitrary;; ret (Push z)) + ; (1, z <- arbitrary;; ret (BCall z)) + ; (1, ret BRet) + ; (1, ret Add) + ; (1, ret Load) + ; (1, ret Store)]. + The QcCrowbar implementation (column QcCrowbar) fares even worse. It does manage to +discover two out of the twenty IFC violations in some of the runs, but the AFL backend is unable +to overcome the deficiencies of the generator, in part because its instrumentation overhead leads +to executing many fewer tests (Figure 5). With naive random testing we were executing roughly +82,000 tests per second. QcCrowbar executes tests almost five times slower (∼ 16, 500 tests/sec). + The generator used for FuzzChick has a slight manual twist: we write one small manual generator +that uses the automatically synthesized generator for states to return a pair of identical states. + Definition gen_pair_state : G (state * state) := + st <- arbitrary ;; + ret (st, st). +This generator could obviously reveal no bugs if we used it with QuickChick or QcCrowbar, since +the initial machines are always identical. However, the FuzzChick mutators, by employing coverage +information, are able to massage the results of this overly rigid generator towards counterexamples. +The result is shown in the FuzzChick column. We can see that it can find 12 bugs within a few +seconds and 7 more within minutes (MTTF shown across 5 runs). One particularly hard bug is not +found within the one-hour time limit. + On the other end of the spectrum we have the smart manual generators of Hriţcu et al.. These +give excellent performance: all bugs are found within 10 milliseconds of testing. However, they +are significantly more expensive to write: these generators themselves are 271 lines (even for this +simple stack machine), and they constituted a publishable research contribution on their own. By +contrast, the manual effort needed to obtain the generator used for FuzzChick above is literally +writing the three lines of code above plus ten lines of Derive commands for the different datatypes. + +5.2 The Register Machine +The results for the register machine are similarly organized and appear in Figure 6. The basic +story here is the same as with the stack machine. The optimized hand-written generators are still +blazingly fast at finding bugs (in under a second), while using derived generators with QuickChick +or QcCrowbar leads to multi-hour timeouts almost across all bugs. The FuzzChick column offers +once again an attractive middle ground: it finds most of the bugs within minutes and five more +within hours, while timing out on three. + The number of tests run per second for each of the four approaches is shown in Figure 7. +Interestingly, FuzzChick executes slightly more tests per second than the naive random generators. +Apparently, when machine states are complex enough, mutating existing pairs of machines is faster + +Proc. ACM Program. Lang., Vol. 1, No. OOPSLA, Article 1. Publication date: January 2019. + Coverage Guided, Property Based Testing 1:21 + + QuickChick + Injected Fault # QuickChick QcCrowbar FuzzChick + (hand-written) + 1 4h (t/o) 8h (t/o) 36.8 0.056 + 2 4h (t/o) 8h (t/o) 351.6 0.292 + 3 4h (t/o) 8h (t/o) 5969.6 0.154 + 4 4h (t/o) 8h (t/o) 8h (t/o) 0.452 + 5 4h (t/o) 8h (t/o) 17361.6 0.017 + 6 4h (t/o) 8h (t/o) 407.7 0.015 + 7 4h (t/o) 8h (t/o) 939.1 0.052 + 8 4h (t/o) 8h (t/o) 653.1 0.057 + 9 4h (t/o) 8h (t/o) 8h (t/o) 0.073 + 10 4h (t/o) 8h (t/o) 2320.2 0.083 + 11 4h (t/o) 8h (t/o) 137.6 0.009 + 12 4h (t/o) 8h (t/o) 112.9 0.613 + 13 4h (t/o) 8h (t/o) 482.4 0.658 + 14 208.0 8h (t/o) 9.501 0.157 + 15 3h (t/o) 8h (t/o) 30.8 0.326 + 16 4h (t/o) 8h (t/o) 1174.4 0.080 + 17 4h (t/o) 8h (t/o) 115.3 0.141 + 18 4h (t/o) 8h (t/o) 31.1 0.312 + 19 4h (t/o) 8h (t/o) 141.1 0.073 + 20 4h (t/o) 8h (t/o) 46.5 0.047 + 21 4h (t/o) 8h (t/o) 84.7 0.087 + 22 12781.9 8h (t/o) 40.4 0.072 + 23 12902.6 8h (t/o) 41.5 0.137 + 24 12822.7 8h (t/o) 29.0 0.021 + 25 4275.6 8h (t/o) 29.3 0.006 + 26 4h (t/o) 8h (t/o) 50.3 0.002 + 27 4h (t/o) 8h (t/o) 61.6 0.002 + 28 4h (t/o) 8h (t/o) 9976.1 0.094 + 29 4h (t/o) 8h (t/o) 53.1 0.223 + 30 4h (t/o) 8h (t/o) 8h (t/o) 0.159 + 31 4h (t/o) 8h (t/o) 8h (t/o) 0.214 + 32 4h (t/o) 8h (t/o) 8497.9 0.365 + 33 4h (t/o) 8h (t/o) 30749.3 0.129 + + Fig. 6. Register machine results + + + QuickChick + QuickChick QcCrowbar FuzzChick + (hand-written) + 3906.6 96.0 4991.2 7660.2 + + Fig. 7. Number of tests executed per second across different methods + + +than generating everything from scratch! Also interestingly (and, to us, somewhat puzzlingly), the +performance of QcCrowbar, when testing the register machine compared to the stack machine, +seems to deteriorate significantly more than the performance of the randomized testers does. + + Proc. ACM Program. Lang., Vol. 1, No. OOPSLA, Article 1. Publication date: January 2019. + 1:22 Leonidas Lampropoulos, Michael Hicks, and Benjamin C. Pierce + + These results show that CGPT has promise. In particular, FuzzChick, while not a panacea, is far +better than QuickChick or QcCrowbar with automatic generators. Further exploring the remaining +gap between FuzzChick and handwritten generators offers an exciting avenue for future work. + +6 RELATED WORK +The random testing literature is vast; we concentrate here on two main threads: synthesizing +property-based random generators from preconditions, and innovations in fuzz testing that aim to +satisfy (sparse) constraints. + +6.1 Property-based generators +The “precondition problem” was identified almost at the same time as property-based random +testing was invented [Claessen and Hughes 2000]. In the years since then, many attempts have been +made to automatically produce generators for constrained inputs. Gligoric et al. [2010] develop +UDITA, a Java-based probabilistic language for generating linked structures efficiently. Bulwahn +[2012b] introduces the notion of smart enumerators in Isabelle’s QuickCheck, which only enumerate +inputs satisfying some precondition. On the random testing side, Claessen et al. [2014] develop an +algorithm for generating constrained inputs with a uniform (or near-uniform) distribution. Fetscher +et al. [2015] build upon this work to implement a similar approach in PLT Redex and demonstrate +excellent results in practice. Lampropoulos et al. [2017] further extend this approach by adding +a restricted form of constraint solving under user control. Finally, Lampropoulos et al. [2018] +synthesize correct-by-construction QuickChick generators, given preconditions expressed in the +form of (restricted) inductive relations in Coq. All of these automatic approaches yield generators +that are slower by an order of magnitude than their hand-written counterparts. They also may be +complementary to CGPT: a better generator could be used by CGPT directly (and produce more +interesting seeds faster), while the same techniques that produce generators for constrained inputs +could be adapted to produce mutators instead. + +6.2 Coverage-guided Fuzzing +Coverage-guided fuzzing (CGF) is the de facto standard, with AFL [2019], honggfuzz [2019], and +libFuzzer [2019] as prominent examples. We discuss several threads of research aimed at improving +the effectiveness of fuzzing in the presence of hard-to-satisfy constraints in the target program. + Improving Code Coverage. Much research in this area aims to improve on the basic idea of +maximizing code coverage. AFLFast [Böhme et al. 2016] updates AFL’s scheduling algorithm to +mutate seeds it deems more likely to lead to interesting new paths. CollAFL [Gan et al. 2018] +gathers path-based, rather than edge-based, coverage information. Fairfuzz [Lemieux and Sen 2018] +and Vuzzer [Rawat et al. 2017] use static analysis and instrumentation to prioritize rarely covered +parts of the program, and they try to mutate parts of an input that drive a program further down +rare paths. Angora [Chen and Chen 2018] and T-Fuzz [Peng et al. 2018] likewise use a variety of +techniques to reach and move past paths guarded by sparse constraints. Driller [Stephens et al. +2016] and QSym [Yun et al. 2018] combine ideas from fuzzing and symbolic execution (exemplified +by KLEE [Cadar et al. 2008] and Sage [Godefroid et al. 2008b]) to more reliably explore new code +paths. Many of these ideas could be adapted to the main CGPT fuzzing loop, and we would expect +to see corresponding benefits. + Zest [Padhye et al. 2018] is a recent system that combines generator-based testing (similar +to QuickCheck-style property-based random testers) and AFL-style fuzzing for Java programs. +Like Crowbar [2017], Zest fuzzes the set of random choices made by the generator. Like CGPT, +it distinguishes “discarded” runs that terminate due to the inputs being invalid from those that + +Proc. ACM Program. Lang., Vol. 1, No. OOPSLA, Article 1. Publication date: January 2019. + Coverage Guided, Property Based Testing 1:23 + +succeed or fail. It then may prefer valid inputs as targets for subsequent mutations. On a variety of +benchmarks, Zest achieves far greater coverage than AFL fuzzing or property testing alone. Since +Zest does not integrate input generation with mutation (the latter is indirect, as in Crowbar), its +fuzzing loop is different in important ways from that of CGPT, and it may suffer the drawbacks +mentioned in § 2.2. It would be interesting to modify Crowbar to see if its performance improves +when using Zest’s scheduling algorithm. + Grammar-based fuzzing. Property-based testing tools work by synthesizing well-formed inputs +directly, and CGPT is no different. Researchers in the fuzzing community have also examined +the benefits of producing inputs that are well-formed, or nearly so. Skyfire [Wang et al. 2017] +and Orthrus [Shastry et al. 2017] do this by generating well-formed initial seeds, according to a +probabilistic context-sensitive grammar inferred from real-world examples. QuickFuzz [Grieco +et al. 2016, 2017] allows seed generation through the use of grammars that specify the structure of +valid, or interesting, inputs (mainly file formats). DIFUZE [Corina et al. 2017] performs an up-front +static analysis to identify the structure of inputs to device drivers prior to fuzzing. + Other fuzzers generate grammar-compliant inputs during the fuzzing campaign. Grammar- +based whitebox fuzzing [Godefroid et al. 2008a] biases the scheduling of a whitebox fuzzer toward +grammar-compliant inputs. Glade [Bastani et al. 2017] synthesizes inputs from a learned grammar; +Learn&Fuzz [Godefroid et al. 2017] does likewise but mutates the example afterward. Godefroid +et al. suggest that well-formed inputs should be preferred two-to-one over malformed ones to +optimize bug finding. + Structure-guided mutation. Some fuzzing work has considered application-specific mutation +strategies. AFL can be configured to use a dictionary [lcamtuf 2019a] of useful bit patterns (e.g., +file format “magic numbers”) to be inserted, duplicated, or removed. Type-based mutation [Jain +et al. 2018] works by inferring the type of bytes—e.g., as ranges, offsets, or magic numbers—in an +input based on how the program uses them. Mutators are selected that may break assumed but +unenforced invariants (e.g., overflowing an integer or buffer) based on the type. + Smart Greybox Fuzzing [Pham et al. 2018] (SGF) develops structural mutation operators according +to a virtual file structure that it infers from valid (file-based) inputs. Like FuzzChick’s synthesized +mutators, these are based on high-level ideas of deletion, addition, and splicing. However, the input +format is learned imperfectly from examples, so the mutations are heuristic. SGF also employs a +power schedule that assigns more energy to seeds with a higher degree of grammar compliance. +Grammar-aware Greybox fuzzing [Wang et al. 2018] employs similar mutations, deriving them +from a provided grammar rather than a learned one. + +7 CONCLUSIONS +We have presented coverage guided, property based testing (CGPT), adapting key ideas from +coverage guided fuzzing (CGF), exemplified by tools like AFL, to the setting of property testing. +In particular, rather than always generating a distinct input from scratch for each test, CGPT +can mutate prior inputs, favoring those that result in more code coverage during testing. Indeed, +its scheduling algorithm is able to switch between mutation and generation to better optimize +increases in coverage. Unlike CGF, mutations in CGPT are at the level of high-level input types, +rather low-level bit-twiddling operations. Our FuzzChick implementation of CGPT, which extends +the QuickCheck property tester for the Coq proof assistant, synthesizes mutators for a type T +automatically, based on T’s algebraic structure. We evaluated the performance of FuzzChick against +both QuickChick and Crowbar, a previous (and more direct) attempt to combine CGF and property +testing. We found that FuzzChick gives orders of magnitude better performance using simple, mostly +automatically derived generators, though it is still significantly slower than expertly hand-written + + Proc. ACM Program. Lang., Vol. 1, No. OOPSLA, Article 1. Publication date: January 2019. + 1:24 Leonidas Lampropoulos, Michael Hicks, and Benjamin C. Pierce + +ones. 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Publication date: January 2019. + \ No newline at end of file diff --git a/packages/opencode/specs/simulation-research/text/2021-mbt-web-applications-practice.txt b/packages/opencode/specs/simulation-research/text/2021-mbt-web-applications-practice.txt new file mode 100644 index 00000000000..0c91da66c7a --- /dev/null +++ b/packages/opencode/specs/simulation-research/text/2021-mbt-web-applications-practice.txt @@ -0,0 +1,1334 @@ + Model-based testing in practice: An experience report from + the web applications domain + Vahid Garousi Alper Buğra Keleş, Yunus Balaman, Andrea Arcuri + Queen’s University Belfast, UK Zeynep Özdemir Güler Kristiania University College, Norway + Bahar Software Engineering Consulting Testinium A.Ş., Istanbul, Turkey Oslo Metropolitan University, Norway + Corporation, UK {alper.keles, yunus.balaman, andrea.arcuri@kristiania.no + v.garousi@qub.ac.uk zeynep.ozdemir}@ testinium.com + + + +Abstract: In the context of a software testing company, we have deployed the model-based testing (MBT) approach to take the company’s +test automation practices to higher levels of maturity and capability. We have chosen, from a set of open-source/commercial MBT tools, +an open-source tool named GraphWalker, and have pragmatically used MBT for end-to-end test automation of several large web and +mobile applications under test. The MBT approach has provided, so far in our project, various tangible and intangible benefits in terms of +improved test coverage (number of paths tested), improved test-design practices, and also improved real-fault detection effectiveness. +The goal of this experience report (applied research report), done based on “action research”, is to share our experience of applying and +evaluating MBT as a software technology (technique and tool) in a real industrial setting. We aim at contributing to the body of empirical +evidence in industrial application of MBT by sharing our industry-academia project on applying MBT in practice, the insights that we have +gained, and the challenges and questions that we have faced and tackled so far. We discuss an overview of the industrial setting, provide +motivation, explain the events leading to the outcomes, discuss the challenges faced, summarize the outcomes, and conclude with +lessons learned, take-away messages, and practical advices based on the described experience. By learning from the best practices in +this paper, other test engineers could conduct more mature MBT in their test projects. +Keywords: Software testing; test automation; model-based testing; web applications; experience report; applied research report +TABLE OF CONTENTS + + +1 INTRODUCTION ....................................................................................................................................................................... 2 +2 INDUSTRIAL CONTEXT, NEEDS AND MOTIVATIONS FOR THE PROJECT ......................................................................................... 3 +3 PROJECT PROCESS AND ACTION-RESEARCH QUESTIONS .......................................................................................................... 3 +4 BACKGROUND AND RELATED WORK ........................................................................................................................................ 4 + 4.1 An overview of how MBT works .......................................................................................................................................................4 + 4.2 State of the -art and -practice of MBT tools in general, tools for web applications, and types of test models...................................5 + 4.3 MBT literature in practice and industrial contexts .............................................................................................................................5 + 4.4 MBT body of knowledge in the Formal Methods community ............................................................................................................6 +5 PHASES AND ACTIVITIES OF THE MBT TEST-AUTOMATION PROJECT .......................................................................................... 7 + 5.1 Test-automation strategy ..................................................................................................................................................................7 + 5.1.1 Choosing the right test automation approach and tool (ARQ1) ........................................................................................................................... 7 + 5.1.2 How the test models were designed .................................................................................................................................................................... 9 + 5.1.3 Development of nodes/edges’ behavior in Java using the Selenium framework ............................................................................................... 12 + 5.2 Requirements coverage and requirements traceability ..................................................................................................................13 + 5.3 Video demos and the project artifacts ............................................................................................................................................14 + 5.4 Execution of MBT test suites ..........................................................................................................................................................14 + 5.5 Development of an MBT coverage tool ..........................................................................................................................................16 +6 EMPIRICAL FINDINGS GATHERED SO FAR IN THE PROJECT ....................................................................................................... 19 + 6.1 Evaluating the benefits of the MBT approach (ARQ2) ....................................................................................................................19 + 6.1.1 Increased test effectiveness in detection of real faults ...................................................................................................................................... 20 + 6.1.2 Improved test-case design practices, due to MBT ............................................................................................................................................. 20 + 6.1.3 Ability to systematically assess requirements coverage by using MBT ............................................................................................................. 22 + 6.1.4 Intangible but important benefits ........................................................................................................................................................................ 22 + 6.2 Challenges and open questions observed so far (ARQ3)...............................................................................................................23 +7 DISCUSSION: LESSONS LEARNED, LIMITATIONS AND TAKE-AWAY MESSAGES........................................................................... 23 + 7.1 Increase in maturity and capability of test automation using MBT ..................................................................................................23 + 7.2 Lessons learned and Take-away messages ..................................................................................................................................24 + 7.3 Limitations ......................................................................................................................................................................................25 +8 CONCLUSIONS AND ONGOING/FUTURE WORKS ....................................................................................................................... 25 +ACKNOWLEDGEMENTS ............................................................................................................................................................ 25 +REFERENCES .......................................................................................................................................................................... 25 + + + 1 + 1 INTRODUCTION +Systematic and adequate testing of software systems is a costly activity, but so do the costs caused by software defects due +to inadequate testing. In a quest to increase effectiveness and efficiency of testing, software engineers have used test +automation [1] for several decades now. While most practitioners use automation for the test execution phase, test +automation is “not just for test execution” [2], i.e., it can be used in other test activities such as test-case design. +Model-based testing (MBT) [3] is an established black-box testing approach for generation of test cases. In MBT, specific +types of models, often called test models, are developed or are reused from earlier software lifecycle phases (e.g., +requirements or design) for generation of test cases. When MBT is integrated with test execution tools such as Selenium for +web applications, it can also automate execution of test cases derived from test models, thus further increasing effectiveness +and efficiency of testing. +MBT has been around for at least 50 years now. An IBM technical report [4], published in 1970, is often referred to as one +of the first known reported applications of MBT. The modeling semantic (type of test models) followed in that first paper +was Cause-Effect Graphs, and a prototype tool, named TELDAP (TEst Library Design Automation Program), for generating +test cases was presented. A very large number of papers and reports have been published in MBT since then, by following +different approaches to MBT, e.g., from the standpoints of model semantics (UML models, BPMN or other model types), +level of modeling abstractions, test execution modes (offline or online), and test selection criteria (model coverage, fault- +based, etc.) [5-7]. However, many studies report that: “most developers [still] don’t view MBT as a mainstream [testing] approach” +[8]. +Specific domains have historically used and taken more advantage of MBT, e.g., embedded software, aerospace, railway +and telecommunications [5]. While test teams in the above specific domains often have the resources to adopt/build +domain-purpose (and often heavy-weight) MBT approaches, adopting MBT in the enterprise software domains, e.g., web +and mobile applications, has not been successful with heavy-weight approaches and, instead, needs lean, highly usable, +lightweight and cost-effective methods and tools [9]. +In the context of a software testing company (Testinium A.Ş.) with offices in several European countries, we have +pragmatically used MBT, since January 2019, to improve the company’s test-automation practices. The work is the result of +an industry-academia collaboration [10], and has been conducted in the context and using the funding of an international +large European R&D project named “TESTOMAT – The Next Level of Test Automation” (testomatproject.eu), in which 34 +industrial / academic partners across six countries are collaborating. The TESTOMAT project ran from 2018 to the end of +2020. To provide the larger context of the work reported in this paper, let us note that MBT is only one of the work-packages +of the TESTOMAT project, and in the industrial context of the subject company (Testinium A.Ş.), several other test +automation innovation have also been conducted and published as recent papers, e.g., experience reports and a set of +innovative best practices for executable natural-language test specifications using a test tool called Gauge (gauge.org) were +published in [11, 12]. +Given the very large number of MBT approaches and tools [6, 7], our goal in the TESTOMAT project has been not to develop +a yet new MBT approach, but rather to select and apply the “right” MBT approach(es) in the context of the subject company +(Testinium A.Ş.), to identify the practical challenges/questions that a typical company or test team would face when +deploying MBT in practice in the context of web and mobile applications, and to take the company’s test automation +practices using MBT to higher levels of maturity and capability. +In this paper, we report on the experience of a project on choosing and applying a practical MBT approach in practice, the +insights that we have gained, and the questions and challenges that we have faced so far, e.g., which MBT approach/tool +should we choose? How to deploy a lightweight MBT approach in our context? +Since this is mainly an industrial project and had to deliver improvements in practice, our approach has been “pragmatic”. +In discussion with company’s management, from the beginning of the project, it was clear that we could not use +“heavyweight” MBT and Model-Driven Engineering (MDE) approaches that would require extensive modelling without +considering their cost-benefits in practice [13]. For example, we had to ensure that the chosen modeling is as simple as +possible, to ensure ease of adaption in test teams. Our project’s philosophy has been similar to that of another experience +report on applying MBT in industry [13], in which the author argued that “it is important to always state where the models [to +be used in MBT] come from: are they artificial or did they already exist before the experiments” and that “one has to argue and evaluate +if the time and effort in developing and maintaining such models for a given system does pay off in the end”. + + + + 2 + The remainder of this paper is structured as follows. Since we used Gorschek et al.‘s process model [14] in our project +(details in Section 3), sections of this paper are structured based on that process. Section 2 reviews the industrial context, +needs and the motivations for the project. We discuss the research approach, design and questions of the project in Section +3. In Section 4, we review the related work. As the core of our work, our test automation strategy and test-artifact +development are discussed in Section 5. We report in Section 6 the empirical findings that we have gathered so far in the +project, for assessing the (positive) impacts and the benefits that MBT had in our project, and also the challenges and +questions that we have observed so far. In Section 7, we discuss the lessons learned, take-away messages, and practical +advice based on the described experience. Finally, Section 8 concludes the paper and discusses our current and future work +directions. + +2 INDUSTRIAL CONTEXT, NEEDS AND MOTIVATIONS FOR THE PROJECT +Testinium A.Ş. is officially classified as a Small/Medium-sized Enterprise (SMEs). The company employs more than 200 +software test engineers. Almost all test engineers have received different certificates types of the ISTQB (International +Software Testing Qualifications Board), e.g., the “Foundation Level” certificate. +The company has been proactive in adapting novel approaches to increase effectiveness and efficiency of its test activities, +and joining the European TESTOMAT project has been one of those initiatives. Almost all of the Systems Under Test (SUTs) +tested by test engineers are the clients’ web or mobile applications, e.g., the online ticket sales website of several major +airlines in Turkey. +Two major system GUI-level automated testing technologies used in the company are Selenium (selenium.dev) and Gauge +(gauge.org). System GUI-level testing is to conduct system testing on a SUT via its Graphical User Interface (GUI). While +such tools are effective for automated execution of the developed test scripts, based on our many test automation projects, +we and many others [15] have found those test tools alone are not enough for a successful test automation outcome. A critical +issue is that the automated test artifacts should be designed and developed properly, e.g., should be free from “test smells” +[16] and should be modular, since as test code grows, it becomes a code-base of its own. Furthermore, the test cases +underlying the test scripts should be systematically designed to have the most cost-effective test suites, i.e., the most-size- +optimal test suites having the highest fault detection effectiveness. Furthermore, test scripts have to be maintainable, since +the requirements, code-base and/or the GUI of the SUT often change. Doing all these aspects in a disciplined manner was +referred to as “software test-code engineering” (STCE) in our previous work [17]. An industry expert, named Hans +Buwalda, also summarizes this point clearly as: “Success in automation is not as much a technical challenge as it is a test design +challenge” (bit.ly/TestDesignForAutomation). +In our industrial context (Testinium A.Ş.), various black-box test design approaches have been in use since the company +was founded in 2010, e.g., category-partition testing and boundary-value testing. However, since such techniques can be +interpreted and applied in different ways by different test engineers, the automated test suites were designed in different +ways and we have been seeing the need for a “better” test-design approach. Furthermore, although there has been a very +large research literature on test-design in academia (like those discussed above, e.g., category-partition testing), systematic +test-case design practices do not seem to be in wide use in many industrial contexts [18]. This has mainly been attributed to +low applicability of textbook-based test-design approaches in practice [18]. +Based on the above exploratory phase and needs analysis in Testinium A.Ş., and by reviewing the experience report and +success stories of MBT in practice, e.g., [8], we selected MBT to improve the test-case design and test automation practices, +which was also raised as one of the work-packages of the TESTOMAT project (testomatproject.eu). + +3 PROJECT PROCESS AND ACTION-RESEARCH QUESTIONS +In terms of research process for the project and our industry-academia collaboration [10], we used the widely-cited process +model proposed by Gorschek et al. for action-research and technology transfer in SE [14], which consists of seven steps: (1) +Identify the industrial need(s), through assessment and observation activities; (2) Formulate a research agenda by reviewing +the state-of-the-art (literature) and -practice to find the research focus; (3) Formulate a candidate solution in cooperation +with industry; (4) Conduct lab validation (for example, through lab experiments); (5) Perform static validation in the +industrial context (for example, via interviews and seminars); (6) Perform dynamic validation (for example, pilot projects); +and (7) Release the solution in the industrial context step by step, while remaining open to smaller changes and +improvements. That process model [14] has been used widely cited in the literature and has been used in a large number +of industry-academia collaborations, e.g., our past projects with a large number of partners, e.g., [10, 19]. For our research +process, we also benefitted from other papers and guidelines for action research, e.g., [20-23]. + + + 3 + Our project goal was to assess practical applicability and cost-effectiveness of MBT in the industrial context by applying it +to several large testing projects, with the hope of making MBT a common test-automation approach in the company. We +believe that sharing our success story would motivate practitioners for using MBT. +Given the very large spectrum of MBT approaches and tools [6, 7], we had to choose and adapt the right MBT approach +and tool, by taking advice from an insightful voice-of-evidence paper [8] which mentioned: "Developers must obviously take +care to select an MBT approach that matches their project’s specific needs". +Furthermore, using any software engineering (SE) approach in practice by any SE team has non-trivial costs, and the +associated cost-benefits should be carefully analyzed, a topic referred to as "value-based" software engineering [24]. Only +if benefits of a given SE approach outweigh its costs, a given SE team will decide or continue using it. A paper by Neto et +al. [8] confirmed this issue by stating that: "it’s risky to choose an MBT approach without having a clear view about its complexity, +cost, effort, and skill required to create [develop] the necessary models" and that: "Evidence on these topics could be a useful step in +determining whether wider deployment of MBT approaches to different domains is worthwhile". We aimed at assessing these issues +and to contribute evidence to the state of practice in this area, since studies have reported "a serious lack in evidence" [25] in +MBT. +In the planning phase of our project, we derived the following three Action-Research Questions (ARQ), and we will address +them in this paper: +  ARQ1: How can we choose the "right" MBT test tool for our purpose? (discussed in Section 5.2) +  ARQ2: What benefits does the MBT approach provide in the industrial context? (discussed in Section 6.1) +  ARQ3: Which challenges and questions did we face in the MBT project (so far) and how can they be addressed? + (discussed in Section 6.2) + +4 BACKGROUND AND RELATED WORK +By a literature search, one can find out that, since the first known MBT paper, published in 1970 as an IBM technical report, +a few thousand papers have been published in various topics of MBT. Several survey and systematic review papers have +summarized such a large body of knowledge, e.g., [6, 7, 25]. +In the very large research literature and many books on MBT, we found that various MBT books and papers differ in terms +of how applied and practical they are. We found the book by Kramer and Legeard [26] especially useful during our work, +since it provides concrete, practical and pragmatic experience-based heuristics and guidelines for MBT. +In the rest of this section, we present: +  An overview of how MBT works +  State of the -art and -practice of MBT tools in general, tools for web applications, and types of test models +  MBT literature in practice and industrial contexts (since our work falls in this category) +  MBT body of knowledge in the Formal Methods community + +4.1 An overview of how MBT works +Model-based testing (MBT) [3] is an established black-box testing approach for generation of test cases. In MBT, specific +types of models, often called test models, are developed or are reused from earlier software lifecycle phases (e.g., +requirements or design) for generation of test cases. When MBT is integrated with test execution tools such as Selenium for +web applications, it can also automate execution of test cases derived from test models, thus further increasing effectiveness +and efficiency of testing. +A UML activity diagram showing the general context and general process of MBT (taken from [27]) is shown in Figure 1. +As discussed above, specific types of software models, often called test models, e.g., UML state-charts, are developed or are +reused from earlier software lifecycle phases, e.g., requirements or design (forward engineering). There have been also +many studies which have offered approaches for reverse engineering of (inferring) MBT models from code or other software +artifacts, e.g., [28-30]. Those test models specify the expected behavior of the SUT. Once test models are ready and have +been verified and validated, they can be used to derive test cases, which can then be executed on the SUT. + + + + + 4 + Forward Engineering Reverse Engineering + + Requirements Design Implementation + Requirements (SUT) + Analysis modeling + + + Reverse + Test Test Test Generation + Models Engineering of + Evaluation Execution (Test-case Design) + Models + + “Exercise” + (test) Model + Validation + Logs, System + outputs Under Test + (SUT) + + + Figure 1- A UML activity diagram showing the general context and general process of MBT [27] + +4.2 State of the -art and -practice of MBT tools in general, tools for web applications, and types of test models +There are perhaps hundreds of MBT tools, each specific to a certain domain and types of SUT’s, e.g., mobile and web +application, automotive software, etc. Even, surveys and systematic review on MBT tools and comparing their features +have been published, e.g., [6, 7, 31]. MBT tools are often classified and compared by their supported type(s) of test models, +test-generation criteria, and their test scripting capabilities [32]. Classification of several example (randomly-chosen) MBT +tools, as presented in [32], is shown in Table 1. + Table 1- Classification of several example (randomly-chosen) MBT tools, as presented in [32] + Tool name URL Target Type of Test-generation Test scripting + domain test criteria capabilities + model + Conformiq www.conformiq.com Web, desktop State Requirements-driven Textual test + Creator applications charts test generation, black- plans and + or web box test design executable test + services heuristics cases in Java, + and so on + Spec Explorer https://research.microsoft.com/en- Generic State Transition coverage Executable test + 2010 us/projects/specexplorer (applicable to charts cases in C# or + all software (Spec#) on-the-fly + domains) testing + MaTeLo www.all4tec.net Embedded Enhanced Probabilities for Textual test + software Markov transitions and inputs plans and + chains executable test + cases in TTCN-3 + +A subset of MBT tools are applicable to web applications. Given the nature of web applications, they are event-based +systems, e.g., any mouse click on a hyperlink or HTML button in a given web page will change the page, and also the “state” +of the web app under test. +By reviewing “survey” papers in this area [6, 7, 31] and also some exploratory Google searching, one can find a large list of +MBT tools which can be used to test web applications. The following list of tools is a partial randomly-chosen subset: + Commercial tools: TestModeller (testmodeller.io), TestOptimal (testoptimal.com), Tricentis Tosca (tricentis.com), etc. + Open-source/free tools, made in industry: fMBT (github.com/intel/fMBT), GraphWalker (graphwalker.github.io), + SpecExplorer [33], TCases (github.com/Cornutum/tcases), etc. + Academic prototype tools: ModBat [34], MoMuT [35], VERA [36], JTorX [37], Torxakis [38], TESTAR [39], etc. + +4.3 MBT literature in practice and industrial contexts +While it seems that most of MBT literature have been studies which conducted in academic and lab settings, a subset of the +literature are studies conducted in practice and industrial contexts. We review a few selected studies below. +An author with affiliation in both industry and academia reported his view of the state of the art and challenges of +“industrial-strength” MBT [40]. The reported experience and opinions are based on a MBT tool named RT-Tester, developed +by the author’s team. The paper highlights the importance of selecting the right modelling “formalism” for the testing +problem at hand, and the fact that development of models, properly, can prove to be a major hurdle for the success of MBT +in practice. As a related factor, the required skills for test engineers developing test models are significantly higher than for + + 5 + test engineers writing conventional test procedures. Other key factors for successful industrial-scale application of MBT as +reported in the paper were: tracing requirements to the model, and automated compilation of traceability data. +An experience report of introducing MBT in the context of a system named European Train Control System (ETCS), +developed by a large European company, named Thales was reported in [41]. The authors argued that MBT is not applicable +“out-of-the-box”, and application of MBT in a given environment (industrial context) requires specific adaptations. The +selected test model formalism was UML/OCL. Certain toolchain-specific model revisions had to be made, e.g., timed +triggers had to revised in the UML semantics (meta-model). The team used Borland Together for formalizing and +concretizing system models. The last sentence of the paper was: “it seems like the industry may already be aware of the possible +benefits of MBT but fears the issues and costs of its integration”. +Microsoft has been one of the companies from which many MBT papers have been published, e.g., [42-44]. A 2003 paper +[42] authored by a test architect at Microsoft reported the obstacles and opportunities for MBT in Microsoft. The author +reported that: “Model-based testing can provide a tremendous increase in testing capability, but modeling technology must be +integrated into everyday software testing. Small-scale pilot projects, readily available tools and tester education have made the migration +to test generation easier at Microsoft”. The author and his team used five characteristics of innovations that can accelerate or +impede adoption, from a well cited book on the topic: +  Relative advantage: is your innovation better than the existing method? +  Compatibility: does your innovation integrate with the existing method? +  Complexity: is your innovation difficult to understand? +  Trialability: is it easy for people to experiment with your innovation? +  Observability: are the benefits of your innovation easily visible? +The author then reviewed how each of those characteristics affected the promotion of MBT at Microsoft. According to the +paper [42], as of 2003, more than 600 of Microsoft 5000 testers were involved in some form of MBT. +Several papers from Microsoft have also presented their success story with MBT of documentation and quality assurance +of client–server and server–server protocols of Microsoft Windows [43, 44]. A Microsoft MBT tool named SpecExplorer was +used in those studies. The project was a large-scale undertaking in MBT: More than 25 000 pages of documentation for over +250 protocols had to be thoroughly verified to ensure that they are accurate, so that developers can implement protocols +from the information they contain. Application of MBT reflected an investment of over 50 person-years. In addition, a +substantial time investment was made in tool development, based on a continuous feedback loop from the test-suite +development process into the SpecExplorer development team. According to statistical analysis, MBT resulted in a 42% +productivity gain when compared with traditional test suites in a site where similar numbers of requirements were verified. +An interesting “voice of evidence” paper about MBT was published in IEEE Software in 2008 [8], which was based on +systematic literature review (SLR). The authors argued that a rich body of experiences has not yet been published on all the +SE techniques that researchers have proposed, including MBT. In fact, by some estimates, the techniques for which we do +have substantial experience are few and far between. Thus, our current paper is a suitable evidence/experience paper +aiming to address that gap. Based on their experience, the authors reported that: “most developers [still] don’t view MBT as a +mainstream [testing] approach” [8]. The study reported a "serious lack of evidence" in usefulness of different MBT approaches +[25], and that many publications on MBT provide only toy examples without proper comparison with other approaches. The +SLR divided the MBT studies into five categories: speculation, example, proof of concept, experience/industrial reports, +and experimentation. UML-based MBT models were by far the most widely used formalisms. Furthermore, since applying +MBT has non-trivial costs, the associated cost-benefits should be carefully analyzed when considering MBT, a topic referred +to as "value-based" SE [24]. The study discussed this issue by stating: "it’s risky to choose an MBT approach without having a +clear view about its complexity, cost, effort, and skill required to create [develop] the necessary models" and that: "Evidence on these +topics could be a useful step in determining whether wider deployment of MBT approaches to different domains is worthwhile". + +4.4 MBT body of knowledge in the Formal Methods community +Researchers in the Formal Methods community have also done a large number of works on MBT since a few decades ago, +e.g., see a short survey paper [45]. For example, a MBT approach using Labelled Transition Systems (LTS), which is a formal +method notation, was presented in [46]. An approach for inferring finite-state machines (FSM’s) was presented in [30], and +those FSM’s can later be used in MBT. Some fundamental work was done by Nicola and colleagues on testing +“equivalences” [47] which have been highly cited in follow-up MBT studies. Various MBT tools have also been proposed +by the Formal Methods community, e.g., [37, 38]. + + + + 6 + 5 PHASES AND ACTIVITIES OF THE MBT TEST-AUTOMATION PROJECT +As the “core” of our work, we present the phases and activities of our MBT test-automation project, which include the +followings. We first present our MBT test-automation strategy [15], which itself consists of: (1) how we selected the “right” +test automation tool; (2) how the test models were designed; and (3) To enable full automated execution of MBT models, +there is a need to development some type of “glue” code. +One of our goals in the project was to measure requirements coverage and ensure requirements traceability, which we will +also present next. We will also report some results from execution of MBT test suites. Last but not the least, we will discuss +briefly about development of an MBT coverage tool, that we saw the need for, during the project. + +5.1 Test-automation strategy +For any test automation project, having a proper strategy is vital [15]. Such a strategy should include the following aspects: +choosing the right test automation tool(s) [48], and how to develop the test scripts to ensure their quality (e.g., +maintainability) [17]. We discuss next how we approached each of those issues in our MBT project. + +5.1.1 Choosing the right test automation approach and tool (ARQ1) +"Selecting the right tool for the right purpose [in MBT] is a key to success" [25]. A large number of MBT tools exist, either as +commercial tools, open-source or academic prototype tools. As it has been reported in other areas of software testing, e.g., +[49, 50], the choice of test tools often play an important role in success or failure of test automation endeavors. +A Google search for “model-based testing tool” would return the names and links to at least a few hundred such tools. For +any test engineer, including us, choosing the “right” MBT tool is thus not trivial. For making such a choice, one would also +experience the “paradox of choice”, a phenomenon referred to as "the agony of choice", in an MBT book [26]. This +phenomenon has also been reported in other areas of SE (bit.ly/SoftwareEngPOC). While there are comparative studies +such as [7], we felt there was a lack of practical / pragmatic / "in-depth" studies comparing MBT tools, a need which we +believe should be addressed by future studies. +To choose the right tool, we did not have the time resources to consider and exhaustively compare “all” the MBT tools out +there, since there are simply too many tools. As discussed in Section 4.2, we relied on survey papers in this area [6, 7, 31] +and also our exploratory Google search (relying on Google’s PageRank) to hand-pick a manageable list of tools. The +following tools were those that appeared in our candidate list: + Commercial tools: TestModeller (testmodeller.io), TestOptimal (testoptimal.com), Tricentis Tosca (tricentis.com) + Open-source/free tools, made in industry: SpecExplorer [33], GraphWalker (graphwalker.github.io), NModel [51], + TCases (github.com/Cornutum/tcases) + Academic prototype tools: ModBat [34], MoMuT [35], CrawlJax [52] +For choosing the right testing tools in general, many practitioners have offered experience-based heuristics. A Grey- +Literature Review (GLR) done in 2017 [48] synthesized the heuristics reported in 53 blogs and white papers. The study +presented 17 different criteria for choosing the right tool under three categories: (1) test-requirements and test-environment +factors, (2) test-tool technical factors; and (3) test-tool non-technical factors. The five top criteria (of those 17) were: (1) the +tool matching the test requirements, e.g., type of SUT (for us, this was web/mobile apps), (2) tool being fit to the operating +environment, e.g., “right level” of model abstraction, test team’s expertise; (3) tool’s cost, (4) usability, and (5) availability +of support for the tool. +We conducted a pilot phase in which we reviewed each tool’s website to get familiar with its features and its modeling +semantic. We also downloaded and tried the tool on one of the company’s web applications (Testinium, testinium.com) to +be able to assess it w.r.t. the above five criteria. To make the evaluation of the above criterion #2 (tool being fit to the +operating environment) precise, we divided it into two parts: (2a) “right level” of model abstraction, and (2b) learnability +of the tool, given our test team’s expertise. Furthermore, in discussion with test engineers in the company (Testinium A.Ş.), +we identified two of the criteria (1 and 2a) as “essential”, i.e., if a tool fails any of them, it is out of the consideration. Results +of our evaluation of the 10 above MBT tools w.r.t. our evaluation criteria are shown in Table 2. + Table 2- Assessing a set of 10 MBT tools w.r.t. our evaluation criteria + Criteria + Tools + 1‐Matching test requirements‐ 2a‐Right level of model 2b‐ 3‐Tool cost 4‐Usability‐ 5‐Support + Essential abstraction‐ Essential Learnability Essential + + + + + 7 + TestModeller Exhaustive activity diagram, + resulting in repetition of nodes + (youtu.be/nctAQHsmjpI) Failed + TestOptimal Has a free + Community Reasonable (our Has a Q/A + version. Paid own usage, and page, with + Supports web/mobile apps, but not professional youtu.be/ very few + specific for them Web page UI flow diagram Reasonable version.  cVlyV7eYbq8) activities  + Tricentis Seems like a test‐data management tool + Tosca (youtu.be/f6aBpa95kLc). While the + introduction on its website mentions + MBT, support for MBT is very limited. + Not possible to design cycles and + complex flow/edge structures + Failed + SpecExplorer Support for MBT of web/mobile apps + seems very limited. Most of focus is on + API and unit testing. Failed + GraphWalker Specific for web/mobile apps Web page UI flow diagram Reasonable Free open‐ High ability to Has a Wiki + source  monitor the model and Forum + during execution (active + live (elements discussions)  + highlighted)  + NModel Test model is in a + programmatic format, instead + of visual diagrams + (doi.org/10.1007/978‐3‐642‐ + 05031‐2_14) Failed + TCases + Support for MBT of web/mobile apps + seems very limited. Most of focus is on + test‐case design for input space + exploration. Failed + ModBat Focus is on API testing. No support for + MBT of web/mobile apps. + (fmv.jku.at/modbat) Failed + MoMuT Focus is on embedded system testing. + No support for MBT of web/mobile + apps. (momut.org) Failed + CrawlJax + It produces as output a state‐flow + graph of the dynamic DOM states and + the event‐based transitions between + them. Focus is not on GUI testing of + web apps Failed + +As we can see in Table 2, only two tools (TestOptimal and GraphWalker) have pasted the filtering. After a careful +investigation, and as the assessments of these two tools in in Table 2 show, we selected GraphWalker, due to the following +rationale: (1) it fit our needs, and was open-source, thus we could also modify it to meet our purpose, if we wanted to; (2) +its modeling semantic was simple, light-weight and pragmatic; and (3) since it is open-source, we did not have to worry +about availability of support for the tool. Furthermore, many of the academic tools were mostly prototypes, thus were not +production-ready for our purpose, and most were based on heavyweight modeling formalisms. Furthermore, we found that +several case studies using GraphWalker have been shared by other test engineers, e.g., testing an information kiosk (panel) +software in New York’s subway (bit.ly/MBTGuidingTestingDecisions) and also for testing games +(bit.ly/MBTofAGameEngine), thus showing its applicability and usefulness in practice. + Lesson learned: We empirically observed that choosing the “right” MBT tool from amongst the very large pool of + available MBT tools, for a given industrial testing context and project, is challenging and not trivial. This validates the + empirical evidence reported in many academic and grey literature sources, e.g., [25, 48]. We found that, as also reported + in many other resources, selecting the “right” tool for the “right” purpose in MBT is a key to success. Even if a team has + the expertise and knows which MBT technique to use, but if the tool is not “right”, succeeding in MBT will be less likely. + We found the guidelines of a Grey-Literature Review (GLR) [48] in this topic useful as they helped us choose the right + tool. + +Based on how GraphWalker works, we designed our MBT approach as shown in Figure 2. Test engineers uses the system +requirements to design the test models, a form of activity diagrams showing the UI flow across different pages of a web +application under test. Test engineers should also develop the Selenium Java code to “implement” the action of each + + 8 + node/edge in the MBT test models. MBT test models are then executed using the chosen test tool (GraphWalker), which uses +the developed Selenium Java code to exercise (call) the front-end of the web application under test, and that communicates +with the back-end. Test outputs are recorded, logged and returned to test engineers by the chosen test tool (GraphWalker). +We discuss each of the steps of Figure 2 in more detail in the next sections. + + + + + Figure 2- An overview of our MBT approach + Lesson learned: When introducing MBT to a company for the first time, a lightweight MBT tool/approach is advisable, + especially when there exist success stories from other practitioners that have successfully used a given MBT tool in other + industrial contexts (companies). + +5.1.2 How the test models were designed +Among important issues in conducting MBT are levels of abstractions and granularity in test models [26]. They directly +impact how engineers should design the test models. Generally, one has to choose the “right” level of abstraction and this +impacts the choice of MBT tool and approach. The modeling formalism, abstraction level and granularity, followed by our +chosen MBT tool, showed to be practical and appropriate, for the context and domain at hand (web applications). +Let us continue with concrete examples from one of our actual SUTs: Testinium (testinium.com), the flagship test tool of the +company, which is a web-application gateway (wrapper) on the Selenium test framework and provides test-management +features and testing on the cloud. Figure 3 shows two screenshots from the SUT: the login screen and the “dashboard” +(main page) shown just after login. Essentially, we used the MBT approach to test this test tool. Our goal was to deploy MBT +extensively for this large SUT and use the knowledge and expertise that we and our test engineers would learn in the +process to increase the capacities of the test team in testing of the many SUTs provided by the company’s clients. + + + + + 9 + Figure 3- Screenshots from the SUT: Testinium +We show in Figure 4 two test models designed for testing the above two pages. In the modeling semantic of the tool, each +edge corresponds to an action (stimulus), e.g., e_click_signin, and each node corresponds to one or more verifications +(to be developed using “assert” functions in Selenium Java code), e.g., n_verify_in_forgot_password_page in Figure 4. +In this MBT approach, test models are lightweight UML activity diagrams, and are essentially the webpage flow-graphs of +the web application under test. The formalism supports definition of certain nodes as “shared” nodes (shown with orange +color in Figure 4), which allow breaking down the entire system to several models. When visiting a shared node, the tool +jumps to any node that has the same tag (they are like function calls). For the web applications domain, this lightweight +notation can be considered a domain-specific test modeling language. + + + + + 10 + Figure 4- Two MBT test models for the SUT: the MBT models of the login and dashboard pages (shown in Figure 3) +The MBT models could be, in principle, developed either manually or automatically, i.e., reverse-engineering of the web +GUI, also called GUI "ripping" [53]. While we have had some prior experience using some of GUI ripping tools [54], and +we actually tried the possibility of using that approach, we soon noticed that one disadvantage is getting very large models +with many details (clicking on every possible link in web pages), that later would require test engineers to spend a lot of +effort to prune ("clean") them to make them executable in MBT tools. +After some evaluations with our team-members, and since we found that developing test models manually did not take too +much effort and, in fact, did provide various “side” benefits (discussed next), we decided to develop the test models +manually. Test engineers actually benefitted from and liked the effort put into developing test models, since it was quite a + 11 + valuable learning experience for them to better understand the SUT and their test approach, an observation also reported +elsewhere [26]. Also like other studies [25], we observed that "testers working with MBT have increased motivations and are eager +to learn". + Lesson learned: Even if the MBT models may be developed semi-automatically by reverse-engineering them from the + web SUT, we however found that manual development of MBT models by test engineers provided various “side” + benefits, e.g., valuable learning experience, increasing motivations and interest of test engineers in test automation. Also + note that, if we use tools to reverse-engineer the MBT models, the huge effort to prune (clean) them to make them + executable in MBT tools often overweighs the cost of developing them from scratch manually. + +One important point is about design best-practices for models. When developing the test models, we used GraphWalker’s +online guidelines (graphwalker.github.io) and the chapter “Good MBT modeling practices” in an MBT book [26] to ensure +high-quality design for test models, which could be called “model design patterns”, similar to object-oriented (OO) design +patterns. For example, test models should be designed in a way to be understandable and maintainable. Aside from the +above sources, we found only a few sources in peer-reviewed and grey literature on this topic, and thus we think there is a +need for more research on this topic in future. + Challenge: We observed a general shortage of knowledge and resources on best practice and “design patterns” for + designing MBT models. We thus recommend more research and investigations on this very important topic by + researchers and practitioners in future. + +Last but not the least in this section, we discuss the size metrics of the MBT test suite. Since the SUT (Testinium) had 18 +distinct UI pages, our MBT test suites for the SUT resulted in 18 test models (two of them are shown in Figure 4). Altogether, +those 18 test models had 177 nodes and 260 edges. We have made all the MBT models and artifacts of this SUT available as +open-source in: github.com/vgarousi/MBTofTestinium. + +5.1.3 Development of nodes/edges’ behavior in Java using the Selenium framework +As shown in Figure 2 (our MBT approach), testers need to provide the behavior of nodes/edges in Java using the Selenium +framework. Once we ensured that our test models are properly designed (we did a few round of peer reviews), we +developed the Java test-code. For example, for the edge e_valid_login in Figure 4, we developed the Java test code shown +in Table 3. In this example Selenium Java code, to conduct a valid login, the username and password fields are first located. +Then, a correct combination of username and password values are entered in those fields. To find the HTML button for the +“Sign in”, a CSS selector path is given. The sign-in button is finally clicked programmatically. +As per our observations, the relatively-short Java methods implementing nodes/edges’ behavior were quite trivial to +develop and we did not notice any noticeable challenges. + Table 3- Java Selenium code implementing the behavior for edge e_valid_login in Figure 4 + public void e_valid_login() { + WebElement userNameElement = + methodsPage.findElement(By.id("username")); + userNameElement.clear(); + userNameElement.sendKeys(email); + WebElement passwordElement = + methodsPage.findElement(By.id("password")); + passwordElement.clear(); + passwordElement.sendKeys(password); + methodsPage.findEleminrent(By.cssSelector( + "input[class$=\"login-page__submit-btn\"][value=\"Sign In\"]")).click(); + } + +We observed that, the chosen modeling semantic provided (in a sense, "enforced") a suitable “separation of concerns” (SoC) +(design pattern) [55] in a way to make the test code modular and helped test engineers clearly know what to develop for +each Java method (for example the above method). Also, each method was only a few lines of code, which we think is a +best-practice on its own, conceptually similar to the following OO recommendation: "Small methods are a hallmark of OO +thinking" (bit.ly/OOPrinciples). +Test-code development was incremental and test engineers would run the model after developing several methods to test +the test suites, and make corrections if necessary. We used other test patterns when developing test code, e.g., “Page Object” +pattern as seen as methodsPage in the code listing above. To ensure quality of test code, we also conducted peer reviewing. + + + 12 + Thus, chances of having defects in the test suites were slim, and in case of observing issues, the team was able to quickly +find and resolve them. + Lesson learned: The modeling semantic of the chosen MBT tool provided (in a sense, "enforced") a suitable “separation + of concerns” (SoC) (design pattern) in a way to make the test code modular and helped test engineers clearly know what + to develop for each Java method. Also, each method was only a few lines of code, which we think is a best-practice on its + own, conceptually similar to the following OO recommendation: "Small methods are a hallmark of OO thinking”. + + + Advice: Even when using a lightweight MBT tool/approach, there is work that needs to be done manually by test + engineers. However, such work was not more difficult or time consuming than writing test cases by hand, nor it required + any special in-depth training to learn to use a tool like GraphWalker. + +5.2 Requirements coverage and requirements traceability +One of the work packages in our original project plan (testomatproject.eu) necessitated measuring requirement coverage in +design and also execution of test suites and also incorporating test-requirement traceability. Since our context is an agile +context, there were no formal pre-written requirements documents for any of the SUTs, including the SUT discussed in this +paper (Testinium). We did lightweight reverse engineering of use cases for the SUT (Testinium) based on the actual +implemented system, as shown in Figure 5. +The MBT tool has a simple but effective feature for requirements coverage and traceability, as shown in Figure 6. Using the +step labels in the description of each use-case (such as R1.1), we labeled each node of the test model accordingly, and in this +way, at end of each test execution, the MBT tool provides the ratio of requirements coverage, as a percentage value. + + + + + 13 + Figure 5- The SUT use-case diagram, and an example use-case description + + + + + Figure 6- Assigning a given node to a requirements item in the chosen MBT tool + +5.3 Video demos and the project artifacts +For interested readers, we have recorded several video screencasts of the MBT test executions and have posted them on +YouTube (bit.ly/VideosMBTTestinium). Also, to help other practitioners review and learn from our MBT project, we +provide the entire test artifacts (test models and Java codes) of the Testinium SUT, open source, in a GitHub repository +(github.com/vgarousi/MBTofTestinium). We have also posted the archived version of the MBT test-suite code and one of +the videos in a permanent location with a Digital Object Identifier (DOI) [56]. + +5.4 Execution of MBT test suites +Once we utilized best practices to iteratively design and develop the MBT test models and the required test artifacts (test +code to implement nodes/edges’ behavior in Java using Selenium), we could then start running the full MBT test suite on +the production SUT (Testinium). We soon decided to embed the MBT execution in the company’s Continuous Integration +(CI) pipeline, which would run at least once every night and report the results. We show in Figure 7 an email screenshot +from the nightly auto-scheduled MBT executions in the CI pipeline. The two attached TXT and Excel files are detailed logs +of test executions, i.e., paths, nodes and edges covered in the test run. Later in the paper, in Figure 9, we show a partial +snapshot from the output test log, an Excel file automatically generated by the extended reporting engine that we have +added to the MBT tool (GraphWalker), and emailed automatically, as shown in Figure 7. + + + + + 14 + Figure 7- An email screenshot from the nightly auto-scheduled MBT executions in the Continuous Integration (CI) + pipeline + Lesson learned: We found the practice of including the MBT execution in the Continuous Integration (CI) pipeline to be + a good approach, as it would execute automatically every night and report the results. + +For execution of MBT test suites, the other important aspect was setting the MBT tool parameters and configurations. The +chosen test tool (GraphWalker) provides a large number of parameters for designing and running a given MBT Test suite +(all details can be found in the tool’s website and online documentation). Two main parameters, worth mentioning, are the +level of model coverage that the test engineers want to cover the models for test-case generation and execution and the type +of graph traversal strategy. GraphWalker documentation phrases this as follows: ‘Path [test-case] generation consists of two +parts: “how to cover?” (generators) and “what to cover?” (stop conditions)’. A generator is an algorithm that decides how to +traverse a model. Four graph traversal algorithms (“generators”) are supported by GraphWalker, as of this writing1: + Random: Navigate through the model in a completely random manner, also called "Drunkard’s walk", or "Random + walk". This algorithm selects an out-edge from a vertex by random, and repeats the process in the next vertex. + Weighted random: Same as the random path generator, but will use the weight keyword when generating a path. The + weight is assigned to edges only, and it represents the probability of an edge getting chosen. + Quick random: Tries to run the shortest path through a model, but in a fast way. This is how the algorithm works: + o Choose an edge not yet visited by random. + o Select the shortest path to that edge using Dijkstra's algorithm + o Walk that path, and mark all the executed edges as visited. + o When reaching the selected edge in step 1, start all over, repeating the above four steps + o The algorithm works well for very large models, and generates reasonably short sequences. The downside is + when used in conjunction with extended finite-state machine, the algorithm can choose a path which is blocked + by a guard. + A* (A-star): Will generate the shortest path to a specific vertex or edge. +We should remind that the above four algorithms are among the classical graph traversal algorithms and further details +about them can be found in a typical graph theory textbook [57]. We have done some initial experimentation with some of +the above, but to keep the complexity of our work in a manageable level, we have configured the daily MBT run to use the +“Random” option. We plan to conduct in-depth studies by varying the choice of generators. +Open question: Any given MBT tool and approach (including the one that we selected), has various parameters and +configurations to be set, like the ones above. An important open question is which sets of parameters are the best, or would +provide better test outcomes, coverage, execution time, fault detection effectiveness, etc.? This raises the need for empirical +studies on the choice of those parameters and configurations and also possibly some new Search-based Software +Engineering (SBSE) [58] approaches to select the best options. +Another important aspect for MBT test execution is stopping conditions (criteria), a condition that decides when MBT test +execution stops. The generator will generate a new step in the path until the stop condition is fulfilled. Nine different +stopping conditions are supported by GraphWalker: + + + + +1 https://github.com/GraphWalker/graphwalker-project/wiki/Generators-and-stop-conditions + + + 15 + 1. Edge coverage: When, during execution, the percentage of traversed edges is reached, the test is stopped. If an edge + is traversed more than once, it still counts as 1 when calculating the percentage coverage. + 2. Vertex (node) coverage: When, during execution, the percentage of traversed states is reached, the test is stopped. + If a vertex is traversed more than once, it still counts as 1 when calculating the percentage coverage. + 3. Requirement coverage: When, during execution, the percentage of traversed requirements is reached, the test is + stopped. If a requirement is traversed more than once, it still counts as 1 when calculating the percentage coverage. + 4. Dependency edge coverage: When, during execution, all of the traversed edges with dependency higher or equal + to the dependency threshold are reached, the test is stopped. If an edge is traversed more than once, it still counts + as 1, when calculating the percentage coverage. The concept of “dependency edge” is actually more like operational + profiles [59], i.e., putting weight values on edges. + 5. Reached vertex: The stop condition is a named vertex. When, during execution, the vertex is reached, the test is + stopped. + 6. Reached edge: The stop condition is a named edge. When, during execution, the edge is reached, the test is stopped. + 7. Time duration: The stop condition is a time, representing the number of seconds that the test generator is allowed + to execute. + 8. Length: The stop condition is a number, representing the total numbers of edge-vertex pairs generated by a + generator. + 9. Never: This special stop condition will never halt the generator. +Again, we would have liked to put more resources and experiment with various parameters, but for the time being, we +decided used the Edge coverage=100% as the stopping condition, which we believe is a reasonable (and acceptable) +stopping condition, at least for all the test engineers that were involved in this project. +With the above parameters, each full execution of the MBT test suite would take about 6 hours. As discussed in Section 5.6, +we provide a glimpse of test execution in several YouTube videos (bit.ly/VideosMBTTestinium). + +5.5 Development of an MBT coverage tool +Two classical approaches for assessing effectiveness and efficiency of any testing technique are: (1) its ability to detect +defects (real or artificially injected defects, via mutation testing), (2) how much coverage is achieved during test execution; +and test coverage can have many different forms, e.g., requirements coverage, code coverage and MBT model coverage. +As we were preparing and planning to evaluate the benefits and effectiveness of the MBT approach w.r.t. the second +important aspect above (coverage), we searched for available coverage tools to apply in our context. +For measuring code coverage for web applications, one needs to measure both front-end (client-side) JavaScript (JS) and +also back-end (server-side) coverage values. In our search for JS coverage tools, we came across many tools, e.g., the Istanbul +tool (istanbul.js.org), the “Developer tools” (DevTools) protocol of Google Chrome (developers.google.com/ +web/tools/chrome-devtools). For assessing back-end (server-side) coverage, there are also various tools, depending on the +server-side technology, e.g., the JaCoCo code coverage library (jacoco.org) for server applications developed in Java, +xDebug (www.xdebug.org) and PVOC (github.com/krakjoe/pcov) for server applications developed in PHP. While all +these tools are quite stable and popular for their purposes, our code-coverage need in our context was to gather and present +both client-side and server-side coverage values in one user- (tester-) friendly output (e.g., in line charts), in a “live” manner +(as a given MBT test suite was running), and would “connect” to our selected MBT tool (GraphWalker) seamlessly (without +hassle). For such a requirement, we did not find any readily-applicable tool to work in conjunction with MBT for web +applications. +On the other hand, in terms of showing the MBT “model” coverage, our selected MBT tool (GraphWalker) would only +show the coverage values (how many edges and nodes have been covered) at the “end” of MBT test execution and not +“during” test execution. In discussions with the test engineers in the company (Testinium A.Ş.), they mentioned to us that, +for a test engineer, it is much useful to observe code and model coverage during MBT test execution, especially since such +a test execution for a medium size SUT (e.g., Testinium itself) would take about 6 hours (as discussed in Section 5.4), and it +is important get continuous regular feedback about test coverage which a test suite is running, not just at the end. +To meet all the above requirements, we decided to develop an MBT coverage tool to measure both model coverage as well +as code coverage at front-end (client-side) JavaScript (JS) and also back-end (server-side) of the web application under test. +To develop such a tool, we had to choose a client-side and server-side coverage tools and “integrate” their outputs and +show the results live visually. For model coverage, we used the API of our selected MBT tool (GraphWalker) to query the +model coverage in regular intervals (e.g., every 5 seconds). + + 16 + We named our new developed MBT coverage tool MBTCover. We have already made MBTCover open-source at: +github.com/vgarousi/ MBTCover. Already, the tool has started to be downloaded by developers in the community. +We explain next some technical details about how we developed MBTCover. To get front-end (client-side) JS coverage +values at runtime, we used the Chrome “Developer tools” (DevTools) protocol. To programmatically extract coverage live +from DevTools at runtime, we use a library called Puppeteer (www.pptr.dev) which provides an Application Programming +Interface (API) to the DevTools protocol. +To get back-end (server-side) coverage live at runtime, we used the JaCoCo code coverage library (jacoco.org). This was a +suitable choice since the implementation language of the SUT in our running case (Testinium) was Java. Of course, for other +SUTs which have been developed in other programming languages (such as .Net), other server-side code coverage +technologies should be used. +Further details about our implementation of MBTCover can be found directly in its open-source code-base at: github.com/ +vgarousi/MBTCover. +Two screenshots from the MBTCover tool are shown in Figure 8, in which the SUT is Testinium and the MBT suite is +running. Two charts, developed in JavaScript (JS), are updating live every few seconds, which is an option chosen by the +user, showing the front-end (client-side JS) coverage: (1) One chart shows the cumulative front-end (JS) coverage, meaning +that the coverage calculation has been done based on the combined lines of JS covered in all the web pages of the SUT, +reached so far, divided by the sum of all JS code lines; (2) The other front-end coverage shows the JS coverage % of the +current web page, being tested by the MBT suite. +In the current implementation, MBTCover measures the coverage of all the JS files: all third-party JS libraries imported in a +web page and also the customized JS files developed for the SUT. We plan to develop in near future a feature to select which +JS files to instrument and measure the coverage for. In the screenshots, we can see that the cumulative front-end (JS) +coverage has increased from mid-0% to above 50% and then back to mid-20% as the MBT suite continues execution and +visits different pages of the web app SUT. The reason for the fluctuation (up and downs) is that different web pages of the +SUT use (reference) different JS files with different Line-of-Code (LOC) sizes and also those different web pages use (call) +different amounts of JS LOC. Thus, the cumulative JS coverage would fluctuate as we can see in the screenshot. +In Figure 8, the other front-end coverage chart showing the JS coverage % of the current web page also provides valuable +information, as we can see the extent of JS code coverage in the current page, as being tested by the MBT suite. For example, +the MBT execution of Testinium starts with the Login page (Figure 3) and then moves to the Dashboard page (the first +orange and the second yellow chart lines correspond to hose two pages). As expected, the current web-page coverage chart +resets to the value of 0% in each page and then grows up to a certain level, until the web page changes as the MBT suite is +commanding the SUT. The test engineer can see live the extent of coverage in the current page and take actions if they +decides to, e.g., if the coverage is low, they can investigate why most parts of the included JS files have not been covered, +and they may decides to add more test paths to the MBT models, etc. +As shown in Figure 8, another chart shows the back-end (server-side) coverage of the web application under test. In the +current version of MBTCover, we are only showing one chart for server-side coverage, i.e., the cumulative code coverage. +Of course, server-side coverage would depend on the technology and programming language of the SUT files developed +to run in the server. For Testinium, this was the Java language. As we see in Figure 8, the server-side coverage value starts +from about 10% as the MBT suite starts execution and of course, since it is a cumulative percentage value, it will either stay +constant or go up. The server-side coverage value then slowly goes higher up to about 12% and then there is a quick jump +to about 27% and then higher. That jump was due to the SUT going to a certain page (“Create Page” feature of Testinium) +which exercises a large amount of the Java code-base on the server, thus leading to sudden increase in server-side coverage. +Furthermore, in discussions with the test engineers in the company (Testinium A.Ş.), they have mentioned to us that it +would be useful/interesting to observe “cumulative” coverage values while testing. We have developed the MBTCover +tool to work in this way, e.g., part (1) of Figure 8 shows the “cumulative” server-side coverage. Also, part (4) of Figure 8 +also shows the “cumulative” client-side coverage. The reason why the coverage values in part (4) drop down almost mid- +way in the shown chart is that new JS files (libraries, to be precise) have been imported in the HTML / JS files of client-side +code of Testinium in the new pages of the SUT that is being tested by the MBT suite. Therefore, the JS coverage calculation +(which is based on the formula: num_of_covered_JS_lines / total_JS_lines) would give a lower value since the “divisor” +value in the formula increases suddenly. +Just like other aspects of our work in this project (designing the MBT models and the Selenium code), our software +development process has been iterative and Agile. In iterative development of MBTCover, we saw the need to also show, +in the GUI of the tool, several important informative (useful) statistics, as shown in Figure 8, which include: (1) number of + 17 + test models reached so far, (2) number of nodes covered so far, and (3) number of nodes executed so far. Note that there is +a difference between the last two mentioned items since the form is the node coverage of MBT models, while the latter is +the number of nodes which have been executed and a given node could be counted more than once. Without these live +metrics, the tester has to wait until the end of MBT execution (and that could take up to 6 hours for our test suite), to see +the outcomes. + Lesson learned: While there are numerous coverage tools for conventional test automation, e.g., for xUnit frameworks, + to our surprise, there were no off-the-shelf readily-applicable coverage tools to work in conjunction with MBT for web + applications. Thus, practitioners should be aware of this, if they plan to measure coverage in conjunction with MBT. The + MBTCover tool, that we have developed, works with the chosen MBT tool (GraphWalker), thus it can be helpful. + + + + + 18 + Figure 8- Screenshots from the MBT coverage tool (MBTCover) that we have developed, as part of the project. (1) + MBTCover: Server-side coverage; (2) SUT: Testinium; (3) MBT execution tool: GraphWalker; (4): MBTCover: Client- + side coverage + +6 EMPIRICAL FINDINGS GATHERED SO FAR IN THE PROJECT +As discussed in Section 3, we derived in the planning phase of our project three Action-Research Questions (ARQ), two of +which were: +  ARQ2: What benefits does the MBT approach provide in the industrial context? +  ARQ3: Which challenges and questions did we face in the MBT project (so far) and how can they be addressed? +During the phases and activities of the MBT test-automation project (Section 5), we conducted the measurements to be able +to assess these two ARQs, and we report the empirical findings next. + +6.1 Evaluating the benefits of the MBT approach (ARQ2) +To assess the benefits of MBT in our project, we identified its benefits and (positive) impacts compared to the previous test +approach used in the company in the past years. As discussed in Section 2, various black-box test design approaches have +been in use since the company was founded in 2010, e.g., category-partition testing and boundary-value testing. However, +since such techniques can be interpreted and applied in different ways by different test engineers, the automated test suites +were designed in different ways, and we have been observing imperfections in terms of test-case design (e.g., test +duplications, and missing certain test cases or parts). +Based on our assessments (both qualitative and quantitate) during the project, since January 2019 up to this writing (Fall +2020), the key benefits of MBT have been as follows, which we discuss in detail next: +  Increased test effectiveness in detection of real faults +  Improved test-case design practices, due to MBT +  Ability to systematically assess requirements coverage by using MBT +  Intangible but important benefits + + + + + 19 + 6.1.1 Increased test effectiveness in detection of real faults +While the SUT reported in this paper (Testinium, testinium.com) is a major product of the company with a few hundred +clients, and that has been thoroughly tested throughout the years, we were still able to detect several major and minor +issues in the SUT, via MBT. This was especially the case in the context of “regression” MBT, i.e., running the MBT suite +every time that the SUT changes. In the last few months of the project (in 2020), there were a few updates to the SUT, and +thus we re-executed the large MBT suite with no additional cost. +Since we have embedded the MBT execution in the company’s Continuous Integration (CI) pipeline, in each revision of the +SUT, the MBT test suite automatically runs at night, and it has detected 11 defects in the SUT in the duration of four months +(June-September 2020, inclusive), e.g., system asking for login again after a long test execution, and certain test reports +which were supposed to be shown by Testinium, not being displayed. The first above defect showed the value of endurance +testing which was possible using MBT (each execution took more than 6 hours). Endurance testing (also known as soak +testing) is a type of non-functional software testing. Endurance testing involves testing a system over a significant period +of time, to discover how the system behaves under sustained use. + +6.1.2 Improved test-case design practices, due to MBT +Test-case design before MBT was mostly ad-hoc. Although black-box test design approaches were slightly in use, as per +inspections of the first author (an expert in software testing), many deficiencies were identified, e.g., duplications among +different test suites (could lead to test integrity problems, etc.), and many missing test paths and test cases. +We wanted to compare objectively the improvement test-case design practices, due to MBT. Before introducing MBT, the +SUT (Testinium) was tested automatically using a BDD test framework named Gauge (gauge.org), in which test scrips were +written in natural language (mostly Turkish, but English would also be possible), and then Selenium code was developed +to map those test scripts to Java commands to exercise the SUT. We have reported details of that other project in another +recent paper [11]. For the interested reader, we show an example of a Gauge test-script for the same SUT (Testinium) in +Table 4. + Table 4-An example Gauge test-script for the Testinium as the SUT + Level of 1 test “scenarios”. + Tags:LoginPage_InputControls + abstraction: * In the Login page, do the controls for the Email field + Calling 2 test + High * In the Login page, do the controls for the Password Call + “concepts” field + # In the Login page, do the controls for the Email field + * Go to "http://www.testinium.com" address + * Check if the "tbEmailOfLogin" element is visible + * Login using "testinium" and "passwd**" + 2 test “concepts”. Call + # Login using and + 3+4 test “steps” * Inside the field "tbEmailOfLogin", write + * Inside the field "tbPasswordOfLogin", write + * Check if the "btnSignInOfLogin" element exists + * "btnSignInOfLogin" elementine tıkla Call + @Step("Inside the field , write ") the + SUT + public void sendKey(String key, String text){ + ElementInfo elementInfo = Stor + A step Helper.INSTANCE.findElementInfoByKey(key); + “implementation” + Level of sendKeyBy(ElementHelper.getElementInfoToBy(elementInfo), + abstraction: elementInfo.getIndex(), text); + Low } + +We wanted to compare the two test-case design approaches: (1) Before: manual test design loosely following black-box +testing approaches and test scripting / execution using Gauge, in which our test engineers loosely followed the black-box +test design approaches, and (2) After: MBT (both test-case design and execution), as presented in this paper. Our metrics of +comparison were: (1) number of real faults detected by each test suite, (2) the number of test steps generated in each +approach, and (3) the time resource spent in each method to develop the test suites. The measured data for comparison are +shown in Table 5. The values for the number of real faults detected have been gathered in the same settings, i.e., executing +both test suites in a period of four months of the changed versions of the SUT (6 different versions). +As we can see in Table 5, manual test design using Gauge took about 4 engineer-months: one of the authors were developing +the test suites. The MBT test suite development took 2 engineer-months. We can see that with less overall time resources, +devoted to develop the test suites, MBT has provided more real-fault detection effectiveness. Also, in terms of test steps +(comprehensiveness), MBT has enabled us to generate more than 10 fold more test steps (38,460 versus 2,658). + + + 20 + … + Table 5-Comparing the two test-case design approaches + Test-design approach Number of real faults Number of test steps Time resource spent to + detected generated develop the test suites + Manual test design loosely 3 2,658 4 engineer-months + following black-box testing, and test + scripting / execution using Gauge + MBT (both test-case design and 11 38,460 2 engineer-months + execution) + +As an example of what the MBT test suites and steps look like, we show in Figure 9 a partial snapshot from the output test +log, an Excel file automatically generated by the extended reporting engine that we have added to the MBT tool +(GraphWalker). We can see the start and the end of the very long sequence of 38,460 test steps in this log. As we can see, +MBT test execution has taken more than 9 and half hours: starting on 22.34 PM and ending on 8:09 AM the next morning. +In Figure 9, the “model visit sequence number” column shows the sequence of visiting a given test model. As a reminder, +the entire MBT suite of the SUT has been broken into multiple models (18 test models), as discussed in Section 5.3. The +“Entity visit sequence number” column shows the sequence of visiting a given model entity (node or an edge of the state +diagram). For example, some nodes and edges towards the end of the test log in Figure 9 have been visited more than 500 +or 600 times. + + + + + 21 + Figure 9- Partial snapshot from the output test log, generated by the extended reporting engine that we have added to + the MBT tool +Thus, it is clear that MBT has led to major improvements in test-case design practices. Furthermore, we were able to gather +several expert opinions from senior testers who confirmed that test-case design practices have indeed been improved, +thanks to MBT. As a qualitative feedback, one test manager mentioned that: "The new MBT approach is very promising and we +are excited to use it more widely in as many test projects across the company as possible. MBT has increased effectiveness and efficiency +of our test design activities and will continue to do so in future." + +6.1.3 Ability to systematically assess requirements coverage by using MBT +As discussed in Section 5.5, one of the work packages of the R&D project (testomatproject.eu) was to measure requirement +coverage in design and also execution of test suites and also incorporating test-requirement traceability. We used the MBT +tool’s simple but effective feature for requirements coverage and traceability (as shown in Figure 6). That pragmatic and +lean feature helped us and our test engineers to design the MBT models while tracing certain elements of test models (nodes +and edges) back to requirements. Upon finishing execution of MBT test suites, since we had chosen edge-coverage of models += 100% as the test termination criteria, the tool would also provide 100% requirement coverage as the outcome. That test- +requirement traceability approach was welcomed by our test engineers and managers, and indeed was seen as a benefit +and (positive) impact of MBT. + +6.1.4 Intangible but important benefits +According to the informal feedback of the engineers involved in this project, MBT made the work of test engineers more +“interesting”, and more organized. Many in the company have told us that, thanks to MBT models, they can now see the +“big picture” of test-case design much more easily with having the test models in front of them, and the model being directly +executable. Attention to intangible benefits of any Software Engineering (SE) approach in practice is widely discussed +(bit.ly/Intangible BenefitsInSE) [26, 60]. While such benefits are difficult to measure, they should be considered when +assessing usefulness of any SE approach in practice. We were curious to know what made MBT and MBT test development +more “interesting” to our engineers and when, we asked them, we were told that development of MBT models looks like +an innovative and joyful design development task (see the model examples in Figure 4), and engineers would learn more +about test automation and the SUT in the process. It was clear to us and our test engineers that such intangible benefits +were indeed very important. + + Challenge: Systematic (quantitative) assessment and comparison of improvements in test-case design practices in our + industrial setting has not been trivial, due to issues such as measurements in work practices seen as “extra work” and + also to sensitivity of such measurements (outcome of measurements could harm practitioners’ prestige and position), as + reported in other studies too [61]. In other words, from an academic standpoint, formally quantify the benefits of MBT + in industry is a challenge, as controlled experiments are often not feasible in this context (not easy from an industrial + standpoint to “justify” the time and effort to do such experiments). We are exploring ways of doing such comparisons in + a quantitative but still viable ways. + + Lesson learned: MBT provides various intangible benefits which are as important as if not more as its tangible + (measurable) benefits. It is important to recognize, analyze and discuss them in test teams. As Albert Einstein said: “Not + everything that counts can be counted” [62]. + +We were also keen and careful of the cost-effectiveness of MBT throughout the MBT project so far. We are also aware of +several other studies which have touched on this issue, e.g., an experience report [13] by a researcher who had worked in +industry for several years and had used MBT, mentioned three points in this regard: (1) "it’s risky to choose an MBT approach +without having a clear view about its complexity, cost, effort, and skill required to create [develop] the necessary models" [8]; (2) “it is +important to always state where the models [to be used in model-based testing] come from: are they artificial or did they already exist +before the experiments” and (3) “one has to argue and evaluate if the time and effort in developing and maintaining such models for a +given system does pay off in the end”. For this purpose, we had group and individual discussions with test engineers in our +MBT project in several iterations. All the involved team members agreed that costs invested into MBT have been well worth +it, and everyone is eager to see a wider adoption of MBT in many client projects in the company. + Lesson learned: The action-research project (and the case study) of introducing MBT at Testinium A.Ş. has been a success + so far, as all involved engineers and managers found it useful, and want to continue to use it, and want to apply it to + other products as well. + + + 22 + 6.2 Challenges and open questions observed so far (ARQ3) +During the entire project, we have gathered the challenges and the open questions that we have observed so far, as reported +throughout the paper in the previous section. We provide some further discussions on each of them. +Challenges: +  While there are some studies which have proposed design patterns for UML models in general [63], we observed + a general shortage of knowledge and resources on best practices and design patterns for designing MBT models + (as discussed in Section 5.3). We thus recommend more research and investigations on this very important topic by + researchers and practitioners in future. Our approach for quality assurance of MBT models was regular peer review + and inspection by experience team members, but there is need for design patterns for this purpose to help test + engineers new to MBT design to design high-quality MBT models. +  Systematic quantitative assessment and comparison of improvements in test-case design practices in our industrial + setting has not been trivial (Section 6.1), due to issues such as measurements in work practices seen as “extra work” + from industrial side and also due to sensitivity of such measurements (outcome of measurements could harm + practitioners’ prestige and position), as reported in other studies too [61]. In other words, from an academic + standpoint, formally quantifying the benefits of MBT in industry is a challenge, as controlled experiments are often + not feasible in this context (not easy form industrial standpoint to “justify” the time and effort to do such + experiments). We are still exploring ways of doing such comparisons in a quantitative but still viable cost-effective + ways, so that we could get the buy-in of the practitioners. +Open questions: +  Any given MBT tool and approach (including the one that we selected: GraphWalker), has various parameters and + configurations to be set, such as the choice of graph traversal algorithms to generate test paths (Section 5.7). An + important open question is which sets of parameters are the best, or would provide better test outcomes, coverage, + execution time, fault detection effectiveness, etc. This raises the need for empirical studies on the choice of those + parameters and configurations and also possibly some new Search-based Software Engineering (SBSE) [58] + approaches to select the best options. + +7 DISCUSSION: LESSONS LEARNED, LIMITATIONS AND TAKE-AWAY MESSAGES +We discuss the lessons learned, limitations and take-away messages in this section. + +7.1 Increase in maturity and capability of test automation using MBT +In software engineering and software testing, maturity and capability of teams and organizations are widely discussed +issues. Usually, maturity relates to how well a team or a organization performs all processes of a software engineering topic, +e.g., testing [64]. Capability, on the other hand, relates to and is the level of a team or an organization’s ability and +improvement achievement in specific technical area, e.g., MBT testing. +In our context, test automation maturity was the high-level “umbrella” notion, under which we wanted to improve various +automation “capabilities”. Higher capabilities in MBT has been one of the approaches to increase the company’s overall test +automation maturity. As we discussed in the paper’s abstract and Section 1, in the planning phase of this project, we were +keen to improve both maturity and capability of test automation using MBT in the subject company. +There are systematic maturity and capability improvement models such as Test Maturity Model integration (TMMi) [65- +67]. We also have some past experience in applying TMMi in other industrial contexts, e.g., see the case study section of +[68]. +For the current paper and the current MBT project that we have conducted in the specific industrial context (Testinium +A.Ş.), we did not decide to use such systematic maturity improvement models in this first phase of the project, but instead +we decided to focus on the “technical” aspects of the MBT (as discussed in Section 5), and also evaluating the benefits and +challenges of the MBT approach (Section 6). Certainly, as a by-product, as both the tangible and intangible benefits of MBT +showed (Section 6.1), it is certain that maturity and capability of test automation in the subject company have improved +using MBT. We have plans to utilize one or more of the systematic maturity and capability improvement models, from the +literature, in this industrial context in future, and to assess whether they would provide extra benefits and improvement +recommendations. + + + + + 23 + 7.2 Lessons learned and Take-away messages +We summarize below the main lessons that we have learned so far in our MBT project, and also the practical advice based +on our described experience. Let us clarify that these lessons learned shall not be interpreted as facts or general rules, but +they are only several main lessons learned, experience and beliefs from our particular project and context. +Lesson learned 1: We empirically observed that choosing the “right” MBT tool from amongst the very large pool of +available MBT tools is not trivial (Section 5.2). We found that, as also reported in many other resources, selecting the “right” +tool for the “right” purpose in MBT is a key to success. We found the guidelines of a Grey-Literature Review (GLR) [2] in +this topic useful as they helped us choose the right tool. When introducing MBT to a company for the first time, a lightweight +MBT tool/approach is advisable, especially when there exist success stories from other practitioners that have successfully +used a given MBT tool in other industrial contexts (companies). +Lesson learned 2: Even if the MBT models may be developed automatically by reverse-engineering them from the web +SUT, we found that manual development of MBT models by test engineers provided various “side” benefits, e.g., valuable +learning experience, increasing motivations and interest of test engineers in test automation (Section 5.3). There were indeed +some of the intangible benefits of MBT (Section 6.1). +Lesson learned 3: The modeling semantic of the chosen MBT tool provided (in a sense, "enforced") a suitable “separation +of concerns” (SoC) (design pattern) in a way to make the test code modular and helped test engineers clearly know what to +develop for each Java method. This shows the importance of choosing the right MBT approach and tool (Section 5.2). +Lesson learned 4: Including the MBT execution in the Continuous Integration (CI) pipeline was shown to be a good practice +(Section 5.7), as it would execute automatically regularly (every night) and report the results. +Lesson learned 5: While there are numerous coverage tools for conventional test automation, e.g., for xUnit frameworks, +to our surprise, there were no off-the-shelf readily-applicable coverage tools to work in conjunction with MBT for web +applications, which would derive and show both front-end (client-side) JavaScript (JS) and also back-end (server-side) +coverage values, “live”, as a given MBT test suite is running. Thus, practitioners should be aware of this, if they plan to +measure coverage in conjunction with MBT. The MBTCover tool (Section 5.8), that we have developed, works with the +chosen MBT tool (GraphWalker), and thus it can be helpful. +Lesson learned 6: The action-research project of introducing MBT at Testinium A.Ş. has been successful so far, as all +involved engineers and managers found it useful, and want to continue to use it, and want to apply it to other test projects +as well (Section 6.1). +Furthermore, as discussed in Section 1, several motivators for this experience reports were the following phrases from the +literature, and for each of them we provide how this experience report relates or contributes to: + “…a serious lack in evidence" in MBT [25]: We have first-hand observed the evidence that MBT can work well in practice + if planned and conducted carefully, as we have done in our project. We thus believe this paper contributes to the body + of empirical evidence in industrial application of MBT by sharing our industry-academia project on applying MBT in + practice. + “most developers [still] don’t view MBT as a mainstream [testing] approach” [8] (a paper in 2008): Although as per review of + the industry and grey literature of MBT, industrial adoption of MBT still seems limited as of 2020, sharing positive + evidence of MBT in practice can help change the situation in the position direction, one success story at a time, and + gradually bring MBT to “mainstream”. In addition to sharing our experience in academic papers like this, we actively + disseminate our experience and findings to practitioners via industrial talks, e.g., [69]. We have been able to “influence”, + in a good way, at least five test engineers in our company to start using MBT in an active mode to develop test suites. + "Developers must obviously take care to select an MBT approach that matches their project’s specific needs" [8]: By carefully + considering our industrial context and project needs (Section 2), we selected the right test automation approach and + tool (Section 5.2), and we invite all practitioners to use our example approach in their projects. + “it is important to always state where the models [to be used in MBT] come from: are they artificial or did they already exist before + the experiments” and “one has to argue and evaluate if the time and effort in developing and maintaining such models for a given + system does pay off in the end” [13]: For this issue, it is true that we developed the MBT models from scratch since they + did not exist from before in our project, but with a pragmatic / lean MBT model formalism and good usability, the MBT + tool has minimized our MBT model development efforts (Section 5.3),and all team members believe that efforts put into + MBT model development are well worth it, especially since manual development of MBT models by test engineers + provided various “side” benefits, e.g., valuable learning experience, increasing motivations and interest of test + engineers in test automation. We believe this is in quite a contrast to many MBT approaches, proposed in academia + + + 24 + which are often not cost-effective in industry, e.g., the PhD work of the first author [70]. We discussed in some recent + works [19, 71] why such “heavy-weight” MBT approaches are hard to be applied in practice (industry). + +7.3 Limitations +The action-research project of introducing MBT at Testinium A.Ş. has been successful so far. However, no project in industry +or academia can be “perfect”. We have been aware of the limitations of our project so far, and in fact, we are working on +them. These limitations are: +Limitation 1: As the first paper of the MBT project, the current paper is an “experience report” based on action-research +[20-23], in which we have synthesized and presented the project, and empirical benefits of MBT in practice. To increase the +rigor of our assessment, we plan to conduct controlled experiments and rigorous case studies in our ongoing R&D project +in future. +Limitation 2: Choice of graph traversal algorithms in the GraphWalker tool to generate test paths (Section 5.7): To keep the +complexity of our work in a manageable level so far, we have configured the MBT runs to use the “Random” option. We +plan to conduct in-depth studies by using the other graph traversal algorithms (choice of generators). +Limitation 3: In this paper, we presented our experience of MBT in the context of one single SUT (Testinium, Figure 3). +Work has already started in the company to apply MBT on more large-scale SUTs, and we plan to share more findings from +those efforts as they become available in future. +Limitation 4: By seeing the lack of proper MBT coverage tools, development of our MBT coverage tool (MBTCover), as +discussed in Section 5.8, has been a good step in the project. While we have used that tool in an “exploratory” manner to +assess coverage and improve MBT test suites as needed, we plan to conduct more systematic studies on MBT coverage. +Limitation 5: We should also highlight that we applied MBT in one particular setting and thus every practitioner should +carefully review the literature (at the end of this paper), and do a proper planning to prevent disappointment with MBT. +Based on our experience, we can recommend the use of lightweight tools such as GraphWalker as a first step to introduce +MBT in companies dealing with web and enterprise applications. As there are a very few reported research and success stories +in this domain, this experience report provides a valuable contribution to inspire practitioners to try out MBT on their +projects. +Limitation 6: The opinion bias of the authors and the interviewed employees on the results can be a factor and threats to +validity. + +8 CONCLUSIONS AND ONGOING/FUTURE WORKS +We are glad to share that MBT has fully fulfilled the expectations in our industrial context. We believe that a good strategy +and a pragmatic approach has enabled us to achieve this. 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Oivo, ʺPractical relevance of software engineering research: synthesizing the community’s voice,ʺ Empirical Software + Engineering, vol. 25, pp. 1687–1754, 2020. + + + + + 28 + \ No newline at end of file diff --git a/packages/opencode/specs/simulation-research/text/2022-pbt-for-metamorphic-testing.txt b/packages/opencode/specs/simulation-research/text/2022-pbt-for-metamorphic-testing.txt new file mode 100644 index 00000000000..7e69e5aaf84 --- /dev/null +++ b/packages/opencode/specs/simulation-research/text/2022-pbt-for-metamorphic-testing.txt @@ -0,0 +1,508 @@ + Application of property-based testing tools + for metamorphic testing + + Nasser Alzahrani, Maria Spichkova, James Harland + School of Computing Technologies, RMIT University, Melbourne, Australia + s3297335@student.rmit.edu.au, {maria.spichkova,james.harland}@rmit.edu.au + + + + + Keywords: Software Testing, Metamorphic Testing, Property-Based Testing, Formal Specification + + Abstract: Metamorphic testing (MT) is a general approach for the testing of a specific kind of software systems – +arXiv:2211.12003v1 [cs.SE] 22 Nov 2022 + + + + + so-called “non-testable”, where the “classical” testing approaches are difficult to apply. MT is an effective + approach for addressing the test oracle problem and test case generation problem. The test oracle problem is + when it is difficult to determine the correct expected output of a particular test case or to determine whether + the actual outputs agree with the expected outcomes. The core concept in MT is metamorphic relations + (MRs) which provide formal specification of the system under test. One of the challenges in MT is effective + test generation. Property-based testing (PBT) is a testing methodology in which test cases are generated + according to desired properties of the software. In some sense, MT can be seen as a very specific kind of PBT. + In this paper, we show how to use PBT tools to automate test generation and verification of MT. In addition to + automation benefit, the proposed method shows how to combine general PBT with MT under the same testing + framework. + + Preprint. Accepted to the 17th International Conference on Evaluation of Novel Approaches to Soft- + ware Engineering (ENASE 2022). Final version published by SCITEPRESS, http://www.scitepress.org + + + + 1 INTRODUCTION on actual code which help in finding subtle faults on + live running systems [15]. One of the main attributes + Formal specification is an essential tool for managing of PBT is that it can automatically generate tests to + the complexity of specifying and verifying the design cover edge cases that are not so obvious to identify + and the development of critical software systems. The manually. Two main elements of PBT approach make + formal approach removes ambiguity, improves preci- this possible: (1) a random test generator, responsible + sion, and used to verify that the requirements are ful- for generating random values in a controlled way, and + filled. Appel et al. summarised a number of desired (2) a so-called shrinker, minimizing the number of the + qualities that the specification should have in order generated tests cases to allow for easier debugging. + to be effective, see [3]. Firstly, the specification has Metamorphic Testing (MT) is a special PBT tech- + to be formal, where the specification should be math- nique elaborated for the cases where it’s complicated + ematically precise. It should be rich, i.e. precisely to specify “classical” test cases having input and out- + expressing the intended behaviour of the system (we put data flows - in some cases, it’s difficult to iden- + could reformulate this quality as completeness). The tify what could be the correct output for each partic- + specification has to be two-sided where the specifica- ular input. For “classical” testing we need to have a + tion is exercised by both implementations and clients. so-called an oracle that can determine whether or not + Finally, the specification has to be live where it is au- the output is correct wrt. the provided input and this + tomatically checked against actual code rather than decision should be taken in a reasonable amount of + some abstract model. time, see [30]. In the case an oracle cannot be cre- + Formal languages like TLA+ [18], or Alloy [16] ated, the system are typically called non-testable (or + are generally concerned with specifying systems untestable), but MT can provide an effective solution + against some models rather than the actual code under to the oracle problem using Metamorphic Relations + development. On the other hand, property-based test- (MR), see e.g., [24]. MT was initially introduced in + ing (PBT) facilitates the use of formal specifications [5] in the domain of numerical analysis. Since then, it + has developed and been applied in many application phic testing. +areas, such as compilers, medical systems, embedded In validity checks, one writes functions to check +applications, search engines, service computing, sim- some invariants of the system under test or the +ulation software, image processing systems, machine datatypes used in the system. This process also in- +learning software and optimizing software [6]. cludes writing properties to check test-case generator + PBT tools for testing functional programs were and test-case shrinker both produce valid results. The +first introduced in the Haskell programming language last step is to write property for the functions under +by [11], where QuickCheck, a library for random test- test which performs a single random call and checks +ing of program properties, was implemented. Since that the return value is valid. For instance, when test- +then, many libraries have been developed following ing the functionality of inserting a value into a tree +this approach for different programming languages. datatype, we demand that all the keys in a left subtree +The main components of QuickCheck are the gener- must be less than the key in the node, and all the keys +ator of random values, the shrinker, and the checker in the right subtree must be greater. +which runs these random values with pre-selected A postcondition is a property that should be true +functions. In our work, we extend the generator and after a call. One can come up with such property by +the shrinker in order to automate MT test generation asking what would be the expected state of the system +and verification. after calling some function. A postcondition usually + The idea of generating random tests is not new, tests one function after calling this function with some +see for example [8]. However, using PBT tools such random argument and then checking an expected re- +QuickCheck has many advantages. First of all, PBT lationship between the result and its argument. For +has many tools for automating and controlling the Instance, after calling insert (which inserts a value in +generation of random test cases. Secondly, these tools some tree datatype), we should be able to find the key +allow controlled strategies for generating random data inserted without changing previously inserted keys. +of complicated data types, i.e., it is possible to config- A model-based property is used to test some func- +ure how the random values distribute over the input tion by making a single call and comparing its result +domain. Although [7] argues that one of MT’s main with the result of some abstract operation. The model +advantages is the ease of test case automation, the MT refers to the abstraction functions which map the real +automation is a complex task, when using PBT tools arguments and results to abstract values. +such as QuickCheck as a tool to test MR relations. Inductive properties are the properties that one can + Contributions: The main contribution of this pa- use induction to assert that the only function that can +per is a systematic approach in which we utilize the pass the tests is the correct one. This is usually done +random generation of test cases and automatic test- by relating a call of the function under test to calls +ing capabilities of PBT tools to automate some steps with smaller arguments. The set of inductive prop- +of metamorphic testing: More precisely, we auto- erties covering all possible cases allows the testing +mate test case generation and test case verification by of the base case and induction steps of an inductive +extending QuickCheck’s shrinker and generator with proof-of-correctness. +our customized shrinker and generator. These variants The canonical example in the literature to explain +are simpler and more amendable to customization in property based testing is the reversing a list. One +the context of MT. property that should hold for all lists is that reversing + a list x twice returns the original list: + reverse (reverse x) = x +2 BACKGROUND: In the case of functional oracle-based testing, we + PROPERTY-BASED TESTING would need to identify the equivalence partitions (the + sets of inputs that have to be handled equivalently as +Property-based testing (PBT) is an approach to test- they have to provide the same type of output but with +ing software by defining general specifications and possibly different values), and then specify at least +properties that must hold for all the executions of ran- one test case for each partition, or use boundary val- +domly generated test cases. The inputs to these test ues in partitions that are ranges. Thus, for reverse +cases are random. If these properties do not hold, function this could be an empty list [] and some non- +a minimized failing tests are reported. In PBT, test empty list, e.g, [1, 2, 3], i.e., our test cases would be +cases are generated randomly according to universally reverse (reverse []) = [] +quantified properties. Examples of quantified proper- reverse (reverse [1, 2, 3]) = [1, 2, 3] +ties include; validity checks, postconditions, model- In contrast to this approach, in PBT the checks take +based properties, inductive properties, and metamor- place on the return value of the function under test, + instead of checking values “hard-coded” in the test outputs. When implementing MT, we first generate +cases such as [] and [1, 2, 3]. That is, the input to source test cases. Then use the MR to generate new +the function under test would be automatically gener- input. This new input is then used to compare the +ated and the library chooses random values for testing output from the first set of the tests with the last ones. +rather than the tester specifying particular values. For In our proposed method, we show how to auto- +example, for the reverse function, one could call the mate the test case generation and verification of MT +reverse function twice and expect the original list to using QuickCheck. Our method can be generalized to +be returned. The library generates many random test work with other PBT tools other than QuickCheck as +cases and reports a failure if it finds a counterexample. our method extends features of QuickCheck that are + In the case of QuickCheck, the property to be common in other PBT tools. +passed to the library is reverse (reverse x) = x, the Figure 1 illustrates MT in the context of testing +library will generate the random values for x, and will a compiler. There are two paths that are expected to +report a failure if it finds a counterexample. lead to the same output: + It is worth noting that there are some anti-patterns (1) We start with Program 1, it is compiled to obtain +that could emerge while writing property-based tests. the corresponding executable code Executable 1. +Because it is sometimes difficult to think about a Then, we run Executable 1 with some input data +property, practitioners usually fall into the trap of du- x to get an output. +plicating the implementation of the code in tests. The +literature on PBT has many other examples of such (2) We modify Program 1 to a semantically equiv- +anti-patterns and how to avoid them. One solution to alent but syntactically different Program 2 (e.g., +avoid this problem is MT. by unrolling a loop or removing a comment etc.), + MT is a successful method in solving the oracle then apply the same compilation method to get the +problem in software testing. The core idea is this: in corresponding executable code Executable 2. Af- +the cases when it’s hard to specify in advance what ter that, we run Executable 2 with the same input +exactly should be the output of a function, we may be data x to get an output. +able to observe the change to the output when chang- When both outputs are obtained, we compare them: if +ing the input. That is, valuable information about the they are not exactly the same, the compiler is faulty. +function would be whether and how its input changes One of the benefits of using PBT for MT is the +when we change its input. For instance, even if the rich sets of tools available. For instance, PBT tools +expected result of a function such as inserting a key allow the creation of strategies for generating random +into a tree is difficult to predict, we may still be able data for complicated data types with minimal setup. +to express an expected relationship between this re- In MT, the operations and data types are usually more +sult and the result of some other call. In this case, if complicated than simple data types such as integers +we insert an additional key into t before calling insert or lists. Existing approaches for creating these data +k v, then we expect the additional key to appear in the types are ad-hoc [9]. In these other approaches, one +result also. has to do almost the same setup work for every kind + of data type in order to generate the random values. + PBT tools, on the other hand, are more general and + cover more data types without the need to duplicate + the code for every kind of data type or model. In ad- + dition, PBT requires less code than these other ap- + proaches with more control over the distribution of + the test cases space. These approaches evenly dis- + tribute the test cases over the input space. + Creating a random BST using any PBT library re- + quires less setup work. One only required to define + the data type and pass it to the library. However, since + Figure 1: Testing compilers using Metamorphic testing we are using these PBT tools for MT, some more + setup and customization are required. + +Metamorphic Relations (MRs) are a central element +of MT. The MRs are properties of the function under +test. An important (and usually missed) attribute of +MR is that they relate multiple inputs to their expected + 3 RELATED WORK 4 PROPOSED APPROACH +The effectiveness of MT in alleviating the oracle In this section, we present a systemic method to +problem has allowed it to appear in many different use PBT tools to test MRs. We specifically choose +application domains. However, many of these appli- QuickCheck to illustrate the proposed approach. Our +cations do not provide a systematic way to automate method is general and can be implemented using +some parts MT. other PBT libraries as well. Our proposed method + The automation of MT was first introduced in consists of three aspects. First, we develop a new gen- +[13] where they proposed a framework that utilizes erator for generating test cases for MT. Second, we +Constraint Logic Programming techniques to find test develop a new test case shrinker. Finally, we use the +data that violate a given metamorphic relation. How- newly designed generator and the shrinker instead of +ever, they require the usage of special metamorphic- QuickCheck’s default generator and shrinker. In the +relations, such as permutation-based relations, to rest of the section, we present the core features and +speed up the search among the possible test data. steps of our approach, and then discuss the advantages + There are few other efforts to automate MT steps. of this approach. +For instance, Zhu created a tool for automating meta- QuickCheck is a library for random testing of pro- +morphic testing for Java unit tests, see [32]. This gram properties. The programmer provides a spec- +method is specific to Java unit tests. Our method is ification of the program, in the form of properties +more general and can be applied in any programming that functions should satisfy. The library then gener- +language which has library support for PBT. ates a large number of random test cases and checks + An automatic MT framework for compilers is pro- that the property holds. Specifications are expressed +posed in [29]. Their approach in generating the test in Haskell. The Haskell programming language also +cases is similar to the approach presented in this pa- provides functions to define properties, observe the +per. However, their approach is tailored to the domain distribution of test data, and define test data genera- +of testing compilers, where we propose a generally tors, which is an important advantage for system spec- +applicable solution. ification. + In [20], the authors propose a method that allows When using PBT tools such as QuickCheck there +the composition of new metamorphic relations based is some expected setup that needs to be done before +on previously defined ones, their case study showed defining the properties. One such setup is shrinking. +that new metamorphic relations can be constructed The main objective of shrinking is to produce a mini- +by compositing some existing metamorphic relations. mum failing test cases which facilitate the debugging +They assert that the new derived metamorphic relation of the program. Another required setup is the random +delivers better metamorphic testing than the original values generator which can be configured depending +metamorphic relation as well as reduces the number on the scenario. More importantly, the generator and +of test cases. shrinker need to be designed to work together when + Work related to verifying authenticated data struc- testing MRs. Otherwise, if we use the default test +tures (ADS) is presented in [23]. The approach of case generator and shrinker, the checkers might miss +Miller provides a semantics for a programming lan- some test cases or generate invalid tests. The pro- +guage LambdaAuth, which supports ADS. This ap- posed method ensures that does not happen. +proach provides many benefits, however, it might be The steps needed to systematically test MR rela- +hard to convince practitioners to use it which is less tions using PBT tools are as follows: +likely to be widely spread among engineers and is dif- (1) Specify an MR property +ficult to have an impact. In [4], the authors used Is- +abelle proof assistant to formally verify LambdaAuth. (2) Customize the test case generator +They also assert that they found several mistakes in (3) Customize the test case shrinker +the semantics of lambdaAuth. In our work, we use (4) Run the checker +a mainstream programming language (Haskell) to de- +sign such ADS and verify our implementation of these Our main contributions are in Steps 2 and 3. Let us +ADS using PBT and MT. now discuss these steps and our solution in more de- + tail. + Step 1: Specify an MR property. Specifying + suitable MRs is key in MT. Although identifying MRs + is not a difficult task, this is typically a manual pro- + cedure, see [21], and we don’t intend to automate + it within our approach. However, there have been + some approaches intending to automate this step [10], is it uses partially defined test values. If a prop- +and in our future work, we consider combining our erty returns a Boolean result for a partially defined +method with these approaches. value, the shrinker does not enumerate more ver- + Step 2: Customize the test case generator. The sions of this value. The benefit is that the checker +first thing that all PBT libraries do is to generate ran- will stop as soon it encounters the first failing test +dom inputs for the functions under test. In the PBT which improves the speed of the checker. +literature, this is known as generation. For every type, One of the differences between QuickCheck +there is an associated random test generator. shrinker and our shrinker is that our method of shrink- + For example, to generate a list of values, one has ing is integrated into generation. It is worth noting +to use the generator together with two parameters. that almost all PBT tools in many different program- +The first parameter is the number of elements in the ming languages use a similar shrinking methodology +list. The second parameter is the size which depends as the one used in QuickCheck. The main problem +on the type of values being generated and the con- with this approach is that shrinking is defined based +text. For example, the size can be the maximum value on datatypes. This constraints the ways in which val- +of Integer type, the maximum length of a list, or the ues are shrinked. That is, there is only one way to de- +depth of a binary search tree. fine shrinking for the same data type without taking + For MT, the generator has to be customized to pro- into consideration the way it was generated. On the +duce valid test cases. In Section 5 we will present an other hand, our shrinker is composed with the gener- +example of BST, where the values should not be gen- ator and the generator controls how the values it pro- +erated uniformly. duces shrinks. + Step 3: Customize the test case shrinker. Al- Our approach to shrinking has many benefits. For +most all PBT libraries and frameworks have a mech- example, shrinking happens even if there is no defined +anism to reduce the set of generated test cases that shrinker on the datatype. This allows the shrinker +fails a property to a minimum number of failing test to share the same variants as the generator and, at +cases that is necessary for the debugging process, as the same time, reduce the effort needed to write a +an unnecessary large number of the failed tests cases separate shrinker for each datatype involved in the +(where many cases might refer to the same error) will test. Another benefit of our shrinker is that failure +make debugging process more complicated and time- reported is more revealing than the shrinker defined +consuming. This mechanism is known in the litera- as datatype. For instance, in QuickCheck, errors are +ture as shrinking. sometimes shrinked to different errors, which is un- + Step 4: Run the checker. In this step, we pass desirable since the error we expect is being reduced +the MR property, which was specified in Step 1 to the to another error we do not care about. To mitigate +checker. If the function under test does not satisfy the this problem, one has to duplicate the constraint logic +MR, the PBT library will report the failing test case both in the generator and in the shrinker. In our im- +that violated the MR property. plemented shrinker, the main idea is that we shrink the + outputs by shrinking the inputs. This help in finding +As mentioned in Step 3, we cannot use the de- possible more shrinks based on that representation. +fault QuickCheck’s shrinker for testing MR proper- Our designed shrinker covers the range between +ties. Thus, we modify QuickCheck generator with our the smallest value of some type and increases the +designed generator. The default QuickCheck’s gener- value until the test fails. It repeats this process until +ator is based on [12] which is found to require some the test passes. In this case, it reports the largest value +efforts to use in MT. On this basis, we design a mod- from the previous step as the smallest test case that +ified generator and instruct QuickCheck to use it in- fails the property, i.e., the boundary values. For exam- +stead of its default one. The advantage of the pro- ple, suppose that we are testing whether the value of +posed approach is that the testing of MT can together variable x of type Integer is less than 77 (x < 77). Sup- +with other properties under the same testing frame- pose that the first random value that is generated (by +work. Thus, the same shrinker and verifier can be the generator) is 90 which will cause the test to fail. +used for both MT and general properties to test. Then, the shrinker will generate new random values + Our version of shrinker has the following features: and in random steps ranging from zero to 89. Now, + • The values are enumerated by depth instead of maybe the new failing value is 89. The shrinker will + size and for this reason, the number of values repeat the same process again for the values between + tends to grow quickly as our shrinker explores fur- zero and 88. The shrinking repeats until the random + ther test cases. value is 78 after which the smallest failing test value + • The modified shrinker exploits laziness [14]. That is 77. After which the shrinker stops. + The way we ensure the validity of the generated ues into a BST. Starting with the Tree at the top, we +(then shrinked) test cases is by adding a precondition. insert some key k1 and some value v1 to get some +The main objective of a precondition is to inform the modified tree. Then, another key k2 and value v2 is +generator not to generate invalid test cases using the inserted into the modified tree to get the out put tree +valid function that we have to implement. The valid (whatever it is). We repeat the same operation to the +function checks the property before passing it to the original tree but we change the inputs to insert. That +generator. The generator will still generate random is, we insert k2 and v2 followed by inserting k1 and v1 +test cases but they will not be executed. The valid to get the out put tree. The metamorphic relation as- +function depends on the context. For instance, in the serts that the two out put trees should be the same oth- +context of Binary Search Trees, the valid function erwise insert is faulty. The notion of quality between +checks that the keys in the left subtree are less than two trees depends on the operations under test. For +the key at the root node and all the keys on the right insert, we can just assert that if the keys and values +subtree is greater than the key at the root node. in both trees are the same the trees are semantically + equivalent. + +5 EXAMPLE: BINARY SEARCH + TREE +As a running example to explain the proposed method +of applying the PBT tool QuickCheck for MT, we +consider the operations of inserting into and deleting +from a binary search tree (BST). This example not +trivial but is simple enough to explain the proposed +method. Another reason for choosing BST is that the +same approach can be used for testing more elaborate Figure 2: MR property: Tree 1 and Tree 2 are semantically + equivalent +kinds of trees such as Merkle trees [22], see also our +discussion future works in Section 6. To evaluate the +proposed approach, we also introduce faulty variants To test the effectiveness of the proposed method, we +of the operations under test, insert and delete. intentionally introduce faulty variants of insert and + A BST is a type of data structure for storing val- delete and test them in a similar way. The faulty vari- +ues such as integers in an organized way. The internal ants are: +nodes of BST store a key greater than all the keys in + Fault 1 insert removes the original tree and re- +the node’s left subtree and less than those in its right + turns just the newly inserted value in a single +subtree. BST are usually used for fast lookup, in- + node. +sert and delete of value items. Testing insert function +which inserts a key and value in a binary search tree Fault 2 delete does not build the tree above the +is difficult. Using MT approach, we can change the key being deleted. That is, it only returns the rest +input using a new key and value and then observe the of the tree instead. +relationship to the original call to insert function. MT +allows more numbers of properties to be tested. Us- Starting with the declaration of the data type, a BST +ing the example of trees, we can use insert with delete for some key k and value v, is either a Lea f or a +and test the output. Inversely, we can use delete with Branch containing left subtree, key k, value v and the +insert and test the output. This is true for any combi- right subtree, respectively. +nation of the operations under test. Step 1: Specify an MR property. This is the + One possible mistake when testing properties of property that we wish the PBT tool to check. Before +the insertion and deletion of BST, is that the test code we can choose the MR, we need to pick the functions +is the same as the implementation. Therefore, if there that we want to test. For this example we choose in- +is a bug in the implementation, it will also be in the sert and delete. insert takes key k, value v and the tree +tests which renders the tests useless. One solution to and returns the modified tree after the insertion. The +this problem is to get an appropriate metamorphic re- delete function takes key k and value v and returns the +lation to test the intended behaviour. This way we can modified tree after the deletion. +verify the correctness of the implementation without Since we want to test two distinct functions (in- +a expecting concrete output. sert and delete), there are, at least, two MRs that we + Figure 2 shows the MT of inserting keys and val- + identify. The MRs that we want to check are the fol- and generate the minimum failing examples for both +lowing: of the introduced faults. However, one interesting ob- + • MR 1: Inserting into the tree after modifying it servation is that fault 1 is missed by the checker when + with a delete operation should be the same as do- we don’t check both MR at the same time. There- + ing the deleting before inserting fore, it is recommended to include as many MRs as + necessary in a single test to specify properties of the + • MR 2: Deleting from the tree after modifying it function under test. + with inserting, should be the same as doing the One misconception of MT is that any property can + inserting before deleting be considered as an MR, see [7]. It is true that MR + Table 1 shows the precise Metamorphic Relations is a property but the inverse is not true. Therefore, +(properties) for inserting and deleting in the context when using PBT tools to test MR properties, we al- +of a binary search tree. The first set shows the inser- most always use two operations, at least, in a single +tion of key k and value v into the tree modified by the metamorphic test. More precisely, when using PBT +deletion of key k0 from the original tree. The MR as- tools to test metamorphic relations, we should either +serts this should be equivalent to deleting k from the change the input to same function as shown in Figure +tree modified by insertion key k and value v into the 2 or use two distinct operations as shown in Table 1. +same tree. The second is set of operations shows the +deletion of key k into the tree t modified by the inser- +tion of key k0 and value v0 . Again, the MR asserts this +should be equivalent to doing the deletion of k first, + 6 CONCLUSIONS +then, inserting k0 and v0 . + In this paper, we presented a systemic method for + This demonstrates how effective MT can be for + using PBT tools to automate the test generation and +generating properties. That is, if the number of opera- + verification of metamorphic relations. Many existing +tions is n, the number of derived operations is O(n2 ), + efforts for automating MT are domain-specific, i.e. +see also [19]. + the automation of the MT steps is elaborated to work + Step 2: Customize the test case generator. We + only for specific application domains such as web ser- +use the generator defined in section 4 which generate + vices and specific programming languages. The work +random trees by creating a random list of keys and + presented in this paper is more general and can be +a random list of values and inserting them into the + used in many different scenarios where MT is needed. +empty tree using insert function. We also have to de- + Its advantage is in using authenticated data structures +fine valid function which ensures the following: + (ADS) to solve the issue. + • All the keys in the left subtree is less than the key PBT tools are generally used for testing univer- + at the root node sal properties other than MR such as postconditions, + • All the keys in the right subtree is greater than the inductive properties, and model-based properties. In + key at the root node this paper, we have shown a method to created a spe- + Step 3: Customize the test case shrinker. Using cialized test-case generator and test-case shrinker to +the default shrink function, shrink might include in- automate some parts of MT steps. We showed that +valid trees. The library may shrink the test case before The default shrinker is not ideal for testing some kinds +reporting it. Or It may produce a valid tree with an in- of MR as it is difficult to compose previously de- +valid shrinking. Therefore, we must add the precon- fined MR to create new MRs. In addition, the default +dition discussed in 4 to ensure only valid trees partic- shrinker may report confusing failure cases since it is +ipates the shrinking process. This precondition holds based on defining shrinking on datatypes which forces +for any randomly generated test. The precondition is the user to add additional duplicated code. However, +just the valid function defined in Step 2. this workaround is not needed with our shrinker since + Step 4: Run the checker. The checker is just a it does not have to be defined on the datatypes and +function that takes any property and returns a Boolean there would no need to encode the invariants into the +value. We pass the MRs relations to the checker func- shrinkers, which requires more effort and could be +tion then the library will generate many test cases. difficult if the scenario is more complicated. We have +The number can be set when configuring the checker. implemented our method using one particular PBT + For the correct variants of insert and delete, the tool QuickCheck. However, our method is general and +PBT library reports a 100 passing tests. The number can be implemented using any other PBT tool. +of the generated test case can also be configured to We presented our method using the Binary search +increase the assurance of the test. For the faulty vari- tree example. The two operations we selected were +ants, the tests report failing of tests after 100 test cases insert and delete and we introduced faulty versions of + Table 1: Some MR properties for a BST insert and delete + op 1 op 2 Metamorphic properties + insert delete insert k v (delete k’ t)= delete k’ (insert k v t) + delete insert delete k (insert k’ v’ t) = insert k’ v’ (delete k t) + + +these two operations. We showed it is recommended [8] Tsong Yueh Chen, Fei-Ching Kuo, Robert G +to use as many MRs as necessary to specify the oper- Merkel, and TH Tse. Adaptive random testing: +ations under test otherwise the test might miss some The art of test case diversity. Journal of Systems +subtle faults. and Software, 83(1):60–66, 2010. + For future work, we plan to combine the proposed [9] Tsong Yueh Chen, Fei-Ching Kuo, Dave Towey, +approach to our earlier works presented in [1, 2], and Zhi Quan Zhou. A revisit of three studies +where we used PBT tools to test models generated related to random testing. Science China Infor- +by formal methods tools such as TLA+ [17]. Another mation Sciences, 58(5):1–9, 2015. +direction of the future work is to consider the human- + [10] Tsong Yueh Chen, Pak-Lok Poon, and Xiaoyuan +centered aspects to enhance the proposed framework, + Xie. 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In Proceed- + ings of the 11th International Conference on + \ No newline at end of file diff --git a/packages/opencode/specs/simulation-research/text/2022-stairway-to-verification.txt b/packages/opencode/specs/simulation-research/text/2022-stairway-to-verification.txt new file mode 100644 index 00000000000..09a79ab6be2 --- /dev/null +++ b/packages/opencode/specs/simulation-research/text/2022-stairway-to-verification.txt @@ -0,0 +1,982 @@ + Property-Based Testing: Climbing the Stairway to + Verification + Zilin Chen Christine Rizkallah Liam O’Connor + UNSW Sydney University of Melbourne University of Edinburgh + Sydney, Australia Melbourne, Australia Edinburgh, UK + zilin.chen@student.unsw.edu.au christine.rizkallah@unimelb.edu.au l.oconnor@ed.ac.uk + + Partha Susarla Gerwin Klein Gernot Heiser + Melbourne, Australia Proofcraft and UNSW Sydney UNSW Sydney + partha@spartha.org Sydney, Australia Sydney, Australia + kleing@unsw.edu.au gernot@unsw.edu.au + + Gabriele Keller + Utrecht University + Utrecht, Netherlands + g.k.keller@uu.nl + +Abstract Keywords: QuickCheck, functional programming, formal +Property-based testing (PBT) is a powerful tool that is widely verification, systems programming +available in modern programming languages. It has been ACM Reference Format: +used to reduce formal software verification effort. We demon- Zilin Chen, Christine Rizkallah, Liam O’Connor, Partha Susarla, +strate how PBT can be used in conjunction with formal ver- Gerwin Klein, Gernot Heiser, and Gabriele Keller. 2022. Property- +ification to incrementally gain greater assurance in code Based Testing: Climbing the Stairway to Verification. In Proceedings +correctness by integrating PBT into the verification frame- of the 15th ACM SIGPLAN International Conference on Software +work of Cogent—a programming language equipped with Language Engineering (SLE ’22), December 06–07, 2022, Auckland, +a certifying compiler for developing high-assurance systems New Zealand. ACM, New York, NY, USA, 14 pages. https://doi.org/ +components. Specifically, for PBT and formal verification to 10.1145/3567512.3567520 +work in tandem, we structure the tests to mirror the refine- +ment proof that we used in Cogent’s verification framework: 1 Introduction +The expected behaviour of the system under test is captured Property-based testing (PBT), in the style of QuickCheck [20], +by a functional correctness specification, which mimics the is a popular testing methodology and is supported in many +formal specification of the system, and we test the refinement modern programming languages [50]. In PBT, tests are spec- +relation between the implementation and the specification. ified using logical properties, which are automatically exe- +We exhibit the additional benefits that this mutualism brings cuted on randomly generated inputs in search of counter- +to developers and demonstrate the techniques we used in examples. PBT is not only useful in finding bugs in programs, +this style of PBT, by studying two concrete examples. it has also been leveraged to reduce the effort in formal verifi- + cation [15, 29, 37, 47]. Subjecting code to extensive PBT prior +CCS Concepts: • Software and its engineering Software to verification reduces the number of defects and specifica- +testing and debugging; Functionality; Formal software tion inconsistencies, thus reducing verification cost. Proof +verification; Designing software. engineers can first test a property and only attempt to prove + it after having gained reasonable confidence in its validity. + In program verification, it is common practice to prove +Permission to make digital or hard copies of all or part of this work for the correctness of a program against a formal specification. +personal or classroom use is granted without fee provided that copies are not +made or distributed for profit or commercial advantage and that copies bear The specification can be given in various forms (e.g. state +this notice and the full citation on the first page. Copyrights for components machines, process calculi, modal logics), depending on the +of this work owned by others than ACM must be honored. Abstracting with application domain. To show that the implementation con- +credit is permitted. To copy otherwise, or republish, to post on servers or to forms to the specification, the notion of refinement [7, 24, 52] +redistribute to lists, requires prior specific permission and/or a fee. Request is frequently used to establish the formal connection. +permissions from permissions@acm.org. +SLE ’22, December 06–07, 2022, Auckland, New Zealand + In this work, we explore the combination of PBT and +© 2022 Association for Computing Machinery. refinement-based formal verification. We borrow from veri- +ACM ISBN 978-1-4503-9919-7/22/12. . . $15.00 fication the functional correctness specification that is used to +https://doi.org/10.1145/3567512.3567520 dictate the behaviour of the system in question, and give it + + + + 84 + SLE ’22, December 06–07, 2022, Auckland, New Zealand Z. Chen, C. Rizkallah, L. O’Connor, P. Susarla, G. Klein, G.Heiser, and G. Keller + + +to PBT. Instead of testing logical properties about the sys- We examine these benefits by integrating PBT into the +tem, which is what PBT is typically designed for, we test Cogent framework. The BilbyFs file system [3], developed +the refinement relation between the implementation and in Cogent, provides an example of this effect. The entire Bil- +the specification. Using logical properties to describe the byFs had been formally specified but only partially verified. +behaviour of a system has been criticised for its practicabil- By applying PBT, we uncovered bugs in the specification and +ity [43], especially if the full functional correctness of the the implementation of BilbyFs. PBT has therefore already +system is desired. Instead, high-level properties of a system reduced the cost of verifying the remainder of the system by +can be proved on top of its functional specification. uncovering mistakes early on. + We introduce PBT to our development cycle, parallel to This work builds on top of a preliminary investigation [18]. +the refinement-based verification framework. Specifically, To summarise, we make the following contributions: +we formulate the refinement between the implementation • We demonstrate how to integrate PBT into a refine- +and the functional specification as the property to be tested, ment verification framework by using Cogent as the +which is an under-explored application of PBT. Employing target platform. Unlike previous use of PBT, our test +PBT in the formal verification context brings additional ben- specification is defined in terms of refinement proper- +efits beyond detecting bugs in the implementation of the ties (Section 3). +systems. • We argue why PBT is suitable to be employed in paral- + In contrast to the high-effort all-or-nothing of a full func- lel with formal verification, and explain the important +tional correctness proof, PBT provides a continuum ranging role that PBT plays in the design and implementation +from no assurance (no tests), to some assurance (good test of the systems (Section 4). +coverage), to better assurance (some properties proved, some • We provide two concrete examples from the testing of +tested), and all the way to high assurance (all properties components of the BilbyFs file system to demonstrate +proved). This allows users to make trade-offs between cost techniques that we used for specifying refinement re- +and assurance according to the criticality of a component. lations, modularising the tests, using mocks, handling + Tests are more immune to program evolution than formal non-determinism, and efficiently generating test data +proofs. A proof may require significant changes whenever (Section 5 and Section 6). +the code changes, even in scenarios where the specifica- • We discuss the engineering implications of our ap- +tion remains the same (e.g. optimisation). On the contrary, proach and lessons learnt and proposals resulting from +PBT only requires developers’ input when the specification them (Section 7). +changes. Therefore, PBT can provide quicker feedback on +the correctness of the change, reducing code maintenance + 2 Background +cost. Furthermore, all proofs depend on assumptions such as +the correctness of the hardware or the external software in- 2.1 Cogent +volved. Some of these assumptions can be tested to increase From the experience of formally verifying the seL4 microker- +the correctness of the overall system. nel, Klein et al. [41] have observed that the proofs connecting + It is usually challenging to verify software that was not the high-level specifications with the low-level C systems +designed for verification, as the code has to be structured in code are time consuming and tedious to develop, but are +a modular fashion, around clearly stated correctness prop- not particularly involved. As such they are good candidates +erties. This means that it is vital to have an effective means for automation. The Cogent verification framework was +for developers to express their design requirements in order conceived to partly automate these proofs. +to experiment with and evaluate their design, and to have a Cogent [55, 56, 58] is a purely functional language +good set of design guidelines [14] for them to write programs that was developed to reduce the cost of developing high- +that can be readily specified and verified. assurance systems components. Similar to the Rust lan- + In large-scale software verification projects, such as guage [39], Cogent is equipped with a uniqueness type sys- +seL4 [41], systems developers and verification experts are tem [8, 11, 25, 66] that ensures memory safety, easing the bur- +typically from two separate teams. We posit that PBT specifi- den of verification. Cogent’s type system allows imperative- +cations can be used to enhance the communication between style destructive updates, while retaining a purely functional +these two groups. While the properties are similar to formal semantics. The type system eliminates the need for a garbage +specifications, they represent tests and, as such, feel more collector, making the language more suitable for systems +familiar to software engineers than abstract proof require- code and also easier to verify. +ments. Since PBT gives almost immediate benefit to software The uniqueness types come at a cost: it is impossible in +engineers, there is an incentive for them to design their code Cogent to implement data structures and functions which, +such that these properties are meaningful and easy to ex- even temporarily, rely on sharing. Instead, they have to be +press, thereby structuring their code for formal specification, implemented in C, verified separately, and imported as ab- +making it amenable to verification. stract types and abstract functions through a foreign function + + + + 85 + Property-Based Testing: Climbing the Stairway to Verification SLE ’22, December 06–07, 2022, Auckland, New Zealand + + + manual legend 1 type H + Functional specification (Isabelle/HOL) 2 type Bag = { count : U32, sum : U32 } + generated + proof 3 newBag : H → + 4 freeBag : (H, Bag) → H + + + + + re nes + 5 + COGENT + source 6 addToBag : (U32, Bag) → Bag + generates Shallow embedding of 7 addToBag (x, b { count = c, sum = s }) + + + + + re nes + COGENT in Isabelle/HOL + 8 = b { count = c + 1, sum = s + x } + COGENT 9 + + + re nes + generates + compiler 10 averageBag : Bag! → + 11 averageBag b = if b.count == 0 then EmptyBag + generates 12 else Success (b.sum / b.count) + C C library + 13 + fi + 14 type List a + 15 reduce : ∀ (a, b). ((List a)!, (a!,b) → b, b) → b +Figure 1. An overview of Cogent’s verification framework 16 + 17 average : (H, (List U32)!) → (H, U32) + 18 average (h, ls) = newBag h + +interface (FFI) that requires the uniqueness constraints to 19 | Success (b, h') → + 20 let b' = reduce (ls, addToBag, b) +be satisfied at the interface level. Besides, Cogent does not 21 in averageBag b' !b' +natively support loops or recursion; they also need to be 22 | Success n → (freeBag (h', b'), n) +implemented in C. We refer to this collection of C code as 23 | EmptyBag → (freeBag (h', b'), 0) +the C library. 24 | Failure h' → (h',0) + + Cogent’s certifying compiler [58, 59], presented in Fig- +ure 1, generates C code, a shallow embedding of the Cogent Figure 2. A simple example of a Cogent program +code in the interactive theorem prover Isabelle/HOL [54], +and a proof connecting the two. The generated proof ensures +that the C code correctly refines the Isabelle/HOL shallow similar to Haskell’s IO monad. The newBag function returns a +embedding. As such any correctness properties proved about variant (or sum) type to indicate the possibility of allocation +the shallow embedding also hold for the C code. Automating failure. The addToBag function, which adds a new data point +the refinement proof from Cogent to C drastically reduced to the bag, is defined on lines 6–8. The averageBag function +the verification effort required compared to directly verifying (lines 10–12) returns, if possible, the average of the numbers +C code [4]. added to the Bag. The input type Bag! indicates that the input + While the Cogent compiler generates C refinement proofs is a read-only, non-unique view of a Bag, which is created +automatically, it cannot prove full functional correctness, on line 21 using the ! notation. Lastly, lines 17–24 define the +which is specified manually by the developer in a functional overall average function, which uses the Bag to compute the +correctness specification in Isabelle/HOL. This leaves two average of the elements of a List. +steps that require manual verification (the two solid arrows +in Figure 1): (1) verifying that the purely functional shallow 2.2 Property-Based Testing and QuickCheck +embedding of the Cogent code refines the overall functional PBT is a quick and effective method for detecting bugs and +correctness specification, and (2) verifying that each C ADT finding inconsistencies in specifications [38]. Similar to for- +refines its functional specification. The former, albeit manual, mal verification, PBT uses logical predicates to specify the +is eased by virtue of equational reasoning. The latter proof, desired behaviour of functions, by defining the allowed rela- +which is directly on the C level, is more involved. However, tions between inputs and outputs of the functions. It evalu- +the C library is to be shared across multiple systems and ates the properties on a large set of automatically generated +hence the effort is amortised over time. input values in search of counter-examples. + Figure 2 provides an example of a Cogent program. Given While PBT is effective, it is not universally applicable—in +an abstract List datatype with a reduce function (line 15) that practice, it is often hard to describe the full behaviour of +aggregates the List content using a provided aggregation a system solely in terms of logical properties [43]. In the +function and identity element, the function average (line 17) context of formal verification, however, using a functional +computes the average of a list of 32-bit unsigned integers. It specification to describe the behaviour of a systems is very +accomplishes this by storing the running total and count in a common. Thus proof engineers can first run extensive tests +heap-allocated data structure, called a Bag, defined on line 2, on the conjectures before attempting any proof development. +with external allocation and free functions on lines 3 and 4. This technique is not new and has witnessed great success +Because Cogent is a purely functional language, intrinsically in the verification community [10]. +impure functions, like the memory (de-)allocation functions, QuickCheck [20] is a combinator library in Haskell for +need to have the heap H threaded through them. This is PBT. While the QuickCheck functionality is now available + + + + 86 + SLE ’22, December 06–07, 2022, Auckland, New Zealand Z. Chen, C. Rizkallah, L. O’Connor, P. Susarla, G. Klein, G.Heiser, and G. Keller + + +in many programming languages [50] and theorem provers manual legend + Executable specification (Haskell) +[15, 29, 47], we interface Cogent to the Haskell QuickCheck generated +library, as it is mature, feature-rich and integrates well with testing + + + + + re nes +Cogent and C. (1) + COGENT + source + + + + + re nes + generates Shallow embedding of + (3) + + + + + re nes +2.3 Data Refinement COGENT in Haskell (2) + +Prior verification work in Cogent, e.g. of BilbyFs [3], con- COGENT + + + + + re nes +nects the functional specification to the Cogent implemen- compiler (4) +tation, and the Cogent implementation to the compiled C + generates +code [59] by proving refinement relations. The notation of C C library +refinement is also central to our testing framework, in which fi + + + +they are expressed as QuickCheck properties. We use a text- + Figure 3. An overview of the Cogent QuickCheck frame- +book definition of refinement [24]. Informally, a program 𝐶 + work +is a refinement of a program 𝐴 if every possible behaviour in +the model of 𝐶 is observable in that of 𝐴. + In an imperative setting, a simple model for both the ab- statement merely requires the single concrete result to cor- +stract specification and the concrete implementation would respond to one of the possible abstract results: +be relations on states, describing every possible behaviour of 𝑅𝑋 𝑖𝑎 𝑖𝑐 =⇒ ∃𝑜 𝑎 ∈ abs 𝑖𝑎 . 𝑅𝑌 𝑜 𝑎 (conc 𝑖𝑐 ) +the program as the manipulation of some global state. This +means that if we prove a property about every execution for Defining the notation +our abstract specification, we know that the property holds def + corres 𝑅 𝑎 𝑐 = ∃𝑜 ∈ 𝑎. 𝑅 𝑜 𝑐 +for all executions of our concrete implementation. + This state-based model for specifying the behaviours of the refinement statement can be formulated as: +systems is a very common paradigm in the world of model- 𝑅𝑋 𝑖𝑎 𝑖𝑐 =⇒ corres 𝑅𝑌 (abs 𝑖𝑎 ) (conc 𝑖𝑐 ) +based testing (MBT) [33, 43, 64]. However, as mentioned in Theorems that capture the functional correctness of Cogent +Section 1, Cogent’s purely functional semantics provides systems typically have this corres format. We therefore aim to +a simple formal model of a program’s behaviour; specifi- encode these as machine-testable properties in QuickCheck. +cally, it enables reasoning about programs using equational +principles. The equational semantics is fortunately widely 3 The Cogent QuickCheck Framework +available in PBT libraries, including QuickCheck. + The integration of PBT into the Cogent framework mirrors + Since Cogent is a purely functional, deterministic, total + the verification tasks, as shown in Figure 3. The developer +language, there is no global state, and all functions are mod- + manually writes a Haskell executable specification, which +elled as plain mathematical functions. In such a scenario, + plays a similar role to the Isabelle/HOL functional correct- +the only state involved consists of the inputs and outputs to + ness specification. The compiler now generates a Haskell +the function, simplifying the refinement statement. Given + shallow embedding of the Cogent code for PBT. Although +an abstract function abs :: 𝑋𝑎 → 𝑌𝑎 , and a concrete Cogent + not formally connected, the Haskell and Isabelle/HOL em- +function conc :: 𝑋𝑐 → 𝑌𝑐 , then, assuming the existence of re- + beddings are very similar. +finement relations 𝑅𝑋 and 𝑅𝑌 , we can express the statement + The framework supports testing the C implementation of +that conc refines abs as: + ADTs against the Haskell executable specification, shown as + arrow (2) in Figure 3; Section 5 provides an example. It fur- + 𝑅𝑋 𝑖𝑎 𝑖𝑐 =⇒ 𝑅𝑌 (abs 𝑖𝑎 ) (conc 𝑖𝑐 ) thermore supports testing the Cogent program along with + ADTs that the Cogent program uses, against the Haskell exe- +This, however, places unnecessary constraints on our ab- cutable specification. This is depicted as arrow (1) in Figure 3 +stract specification. While Cogent is deterministic and total, (the included ADTs are not shown in the figure); Section 6 +our abstract specification need not be. In fact, it is often de- provides a case-study. The included ADTs can either be real +sirable to allow non-determinism to reduce the complexity C implementations (via Haskell’s C FFI) or Haskell mocks, +of the abstract specification. In the context of testing, we are depending on whether the ADTs are also considered the +required to restrain the degree of non-determinism in the system under test. +specification, for the sake of efficient execution of the test The refinement relation between the C code and the +script. This, however, does not preclude us from having a Haskell embedding of the Cogent program (arrow (4)) can +non-deterministic specification. also be tested, although it does not concern us as much, since + We model non-determinism by allowing abstract func- it is certified by the automatic proof. One scenario where +tions to return a set of possible results. Then, our refinement this test can be beneficial is during the development of the + + + + 87 + Property-Based Testing: Climbing the Stairway to Verification SLE ’22, December 06–07, 2022, Auckland, New Zealand + + +Cogent compiler, before the automatic refinement proof when the Isabelle/HOL specification is developed prior to the +pipeline is fully restored. Haskell executable specification. This however is not always + The complete compiled executable, depicted in Figure 3 the case, and in fact in the workflow that we proposed, the +as the grey dotted box at the bottom, can be tested against Haskell specification is used to guide the formulation of the +the executable specification in theory, as indicated by arrow Isabelle/HOL one. +(3). However, we typically do not perform this test using +the QuickCheck framework in Cogent, as the gap between +their state spaces is usually too large to handle effectively. + 4 PBT and Systems Design Go +The final system can normally be deployed in the production Hand-in-Hand +environment and be tested against third-party test suites We argue that the employment of PBT and the design of the +for their specific application domain. In the context of the systems are interlinked with each other: appropriate systems +BilbyFs, for example, there exist tools such as fstest [9]. design assures the effectiveness of testing, and the use of + On the formal verification end, the Isabelle/HOL func- PBT encourages the programmers to design their systems in +tional correctness specification may be highly non- a fashion that is amenable to formal verification. +deterministic in order to succinctly characterise external fac- As a purely functional language, Cogent is well suited +tors such as the elapsed time of an operation, out-of-memory for PBT and verification: the result of a executing a function +errors or hardware errors. The Haskell specification must only depends on the input, with no hidden state. Instead, a +also be capable of modelling non-determinism, but in a more system state must be explicitly threaded through an impure +controlled manner, as the specification must be executable. function. If the function is not designed appropriately, it is +Simulating a non-deterministic model can be exponential possible that a PBT test suite hardly yields counter-examples. +in time and space. To allow modelling a minimal amount Systems code often involves large global states. However, a +of non-determinism in the Haskell specification, the tester function typically only accesses a small portion of the state. +has to ensure that the search domain is finite and reasonably If the entire state is passed in, any random variations to the +small by carefully examining the needed quantifiers in the parts of the state that are irrelevant to the function will have +specification. no effect on the execution of the function. In this case a large + For example, in the Isabelle/HOL abstract specification proportion of the randomly generated test cases in PBT will +of BilbyFs, the afs_get_current_time function is defined as be wasted, rendering the test suite ineffective. +follows: In practice, this means that to be suitable for PBT, the + definition functions must be designed to keep the inputs minimal and + afs_get_current_time :: afs_state ⇒ (afs_state × relevant, which is unlikely when naïvely translating exist- + TimeT) cogent_monad ing C code with global state into Cogent. While this may + where + afs_get_current_time afs ≡ do + seem like a high price to pay, a verification-friendly design + time ′ ← return (a_current_time afs); has the same requirement for modularity and compartmen- + time ← select {x. x ≥ time ′ }; talisation [3, 5]. Thus PBT imposes few restrictions beyond + return (afsL a_current_time := time M, time ′ ) existing requirements of verification, and instead helps guide + od the design. +It non-deterministically picks a time, which is no earlier than In the context of Cogent, developers typically do not have +the time stored in the file system state afs. This abstract a formal specification to begin with when implementing a +specification is not suitable for testing, due to the infinitely new system. Systems programmers, together with verifica- +large set of values. In contrast, on line 13 of Figure 5b, the tion experts, not only need to ensure that they are imple- +specification non-deterministically chooses an error code menting the systems right, but also to ensure that they are +from a small set of {eIO, eNoMem, eInval, eBadF, eNoEnt}. implementing the right systems. PBT helps them structure +This moderate state explosion can potentially be handled by the implementation, as well as the specification. Having +the testing framework, depending on the context in which good design decisions, such as keeping the states threaded +the afs_readpage function is applied. through small and relevant as we mentioned above, is dou- + The Haskell executable specification is thus often strictly bly rewarding: it keeps the refinement relation between the +less abstract than the Isabelle/HOL functional specification. concrete and the abstract states simple, both in PBT and in +Although it is not necessary to formally connect the two, verification. +as the gap only affects the quality of the tests, ideally we Expressing design requirements for verification is an on- +would want one specification to be generated from the going challenge, and we observed in the past that when veri- +other one. Automatic refinement mechanisms that allow fying real-world systems, it is difficult for proof engineers to +verified generation of Haskell from Isabelle/HOL have been communicate these requirements effectively to the software +explored [44, 45]. Generating the Haskell specification from engineers. The seL4 project [41] overcame this problem by +the Isabelle/HOL abstract specification is undoubtedly handy, using an executable Haskell specification of the system as + + + + 88 + SLE ’22, December 06–07, 2022, Auckland, New Zealand Z. Chen, C. Rizkallah, L. O’Connor, P. Susarla, G. Klein, G.Heiser, and G. Keller + + + prop_corres_wordarray_set_u8 :: Property the polymorphic wordarray_set function, whose refinement + prop_corres_wordarray_set_u8 = monadicIO $ statement is given in Figure 4. It can be read roughly as: + forAllM gen_wordarray_set_u8_arg $ \args → run $ do + for any type-correct concrete input ic and its abstraction + let ia = mk_hs_wordarray_set_u8_arg args + oa = uncurry4 hs_wordarray_set ia + ia, check that the result (i.e. oc) of applying the concrete + ic ← mk_c_wordarray_set_u8_arg args function cogent_wordarray_set_u8 and that of the abstract + oc ← cogent_wordarray_set_u8 ic function hs_wordarray_set (i.e. oa) are related via the refine- + corresM' rel_wordarray_u8 oa oc ment relation rel_wordarray_u8. The corresM' function is a + monadic variant of our corres notation for situations where +Figure 4. The refinement statement for wordarray_set (de- the specification is deterministic. +allocation is omitted for simplicity) Although the corres predicate contains an existential quan- + tifier for the result of the non-deterministic abstract specifi- + cation, our implementation does not require QuickCheck to +an interface between these two groups [40]. We posit that guess the quantified value from a set of all possible values. +QuickCheck properties is a highly suitable language for com- Instead, our test driver enumerates over all possible output +municating design requirements. They readily translate to values of the abstract function to find the existentially quan- +formal specifications, but are expressed in a programming tified value. In Section 6, we show how to restrict the size of +language, and thus familiar to software developers. As they the abstract function’s codomain for the enumeration to be +lead to effective test generation, software developers get im- tractable. +mediate benefit from using these specifications to structure For the WordArray type, we relate the abstract input data +their code to maximize their use, which consequently makes and the concrete input data in the following way: we ran- +the code easier to verify. domly generate test data on a middle-ground type, and + then use two thin wrappers mk_hs_wordarray_set_u8_arg +5 Example: The WordArray Library and mk_c_wordarray_set_u8_arg to convert the generated +We apply the Cogent QuickCheck framework to the data to the types expected by the abstract and the concrete +WordArray library, which implements common functions ma- functions. The test data generation is not very involved, be- +nipulating arrays of machine words and is shared by all cause the correspondence between the two types is straight- +of our systems implementations. Most of these WordArray forward, and the C type is not very convoluted in its under- +functions are implemented in C, and are invoked via the FFI lying representation, in particular it does not heavily use +mechanism available in Cogent. pointers. + We want to test whether each function observes the refine- Although in the refinement statement, the refinement re- +ment property from Section 2.3. For example, the behaviour lation between the input data is expressed as a predicate, this +of the ADT function wordarray_set (similar to memset in C)— is usually not the way to implement the test driver. Checking +which fills the first n elements starting at a certain index a predicate is often straightforward, but it requires two sets +frm into an array arr with a constant value a—is manually of random data generators and forces the two generators to +specified in Haskell as follows: be coupled. Otherwise the correspondence predicate is likely + -- Haskell spec. to reject the vast majority of the generated data, rendering + type WordArray a = [a] the test very inefficient (see Section 7.4). + hs_wordarray_set :: WordArray a → Word32 → Word32 Broadly speaking, it is more convenient to relate the input + → a → WordArray a data if we implement the refinement relation as an abstrac- + hs_wordarray_set arr frm n a = + let len = length arr in tion function, computing the abstract data according to its + if | frm > len = arr concrete counterpart. This is contrary to model-based testing + | frm + n > len approaches [64], in which the test cases are derived from the + = take frm arr ++ replicate (len - frm) a more abstract model. We use abstraction functions because + | otherwise + = take frm arr ++ replicate n a ++ + typically the concrete state contains more data than its ab- + drop (frm + n) arr stract counterpart. In order to derive a concrete input from + the randomly generated abstract input, more data need to be +In Cogent, the function is defined as an abstract function, + created and this calls for another set of random data genera- +whose definition is given in C. The Cogent function inter- + tors. On the other hand, when we generate a concrete input +face looks like: + and abstract it, it only requires a lossy abstraction function. + type WordArray a In the case of WordArray, we compute the abstract in- + wordarray_set : (WordArray a, U32, U32, a) → WordArray a + put data from the concrete one, relating them by construc- +While Cogent and Haskell both support polymorphism, C tion. However, not all values of a C type are valid inputs: +does not, and QuickCheck cannot perform genuine polymor- for instance, a null pointer does not correspond to a valid +phic testing [12]. In this example, we test the U8 instance of + + + + 89 + Property-Based Testing: Climbing the Stairway to Verification SLE ’22, December 06–07, 2022, Auckland, New Zealand + + +WordArray. To exclude invalid input data, we manually im- memcpy in C), the old implementation implicitly assumed that +plement a test data generator gen_wordarray_set_u8_args the index into the source array was always within bounds. +which generates values that are isomorphic to valid con- This precondition was satisfied by our file system implemen- +crete inputs only, and we convert them to Haskell inputs and tations, but it was unspecified. In fact, the wordarray_copy +C inputs using functions mk_hs_wordarray_set_u8_arg and function, as part of a generic library, should not carry this +mk_c_wordarray_set_u8_arg respectively. implicit precondition. Otherwise it may introduce bugs to + The refinement statement as shown in Figure 4 is largely other customers of this library function but do not perform +boilerplate code. To generate this code, we designed a small the check. +domain-specific language (DSL), whose prototype has been PBT also helped us uncover problems in the Isabelle/HOL +implemented [27]. In this DSL, programmers can specify the ADT specifications, which had overly specific assumptions +function names, the definition of the abstraction function for about inputs. While these assumptions are valid for the func- +the inputs and the refinement relation between the outputs, tions we verified, they do not hold in general. Thus, the +and other properties about the refinement statement, such specifications we had written did not represent a general +as the determinism of the abstract function and whether purpose specification of the function. +the concrete function needs to operate under the IO monad. The WordArray library in Cogent was initially axiomatised +The DSL is written in JSON format, which can be readily in the verification of the file systems [4], and then tested +parsed using third-party libraries such as aeson [57]. A piece using the PBT framework, before they were finally formally +of sample code is give below: verified [19]. This is an example of how the developers can + progressively increase their confidence in the correctness +1 { +2 "name" : "wordarray_set_u8", of the code by upgrading PBT to formal verification in a +3 "monad" : true, modular fashion. +4 "nondet": false, +5 "absf" : ... // the abstraction function +6 "rrel" : ... // ref. rel. between outputs + 6 Example: A Top-Level File System +7 } Operation +Haskell program texts can be embedded in the JSON struc- BilbyFs [3] is a flash file system that was designed from +ture as the values of the "absf" and "rrel" attributes (lines scratch, focusing on modularity and verifiability; it has 19 +5 and 6). This allows programmers to either call a Haskell top-level file system operations. Two functions have been +function defined elsewhere, or directly write the definition previously verified in Isabelle/HOL to demonstrate how Co- +in-place. The lens [42] style of code is particularly suitable gent facilitates equational reasoning. fsop_sync, a top-level +for accessing and relating parts of deeply nested algebraic function, consists of about 300 lines of Cogent code and +datatypes. took approximately 3.75 person months to verify with 5700 + In the refinement statement, the Cogent-compiled C code lines of proof. The other function, iget, directly called by the +can be called from Haskell using its C FFI facility. The Haskell top-level fsop_lookup function, consists of approximately +representation of C types, marshalling functions, and foreign 200 lines of code, and took about one person month to verify +function calls are generated by the Cogent compiler and with 1800 lines of proof. +are further compiled by FFI tools such as hsc2hs [32] and We conducted PBT on one of BilbyFs’s top-level func- +c2hs [16]. tion fsop_readpage [17], which had previously been formally + Running a small number of randomly generated tests specified in Isabelle/HOL but not yet verified. Figure 5 shows +(by default 100 but this can be customised) by passing the Isabelle/HOL specification as well as the manually writ- +prop_corres_wordarray_set_u8 to the quickCheck function, ten Haskell executable specification; they are very similar in +we get: this case. Therefore, testing gives us reasonably high assur- +*WordArray> quickCheck prop_corres_wordarray_set_u8 ance of the implementation with respect to the Isabelle/HOL ++++ OK, passed 100 tests. specification. As discussed in Section 3 , this is not always +We have specified most of the ADT functions for WordArrays the case, making it occasionally more difficult to connect +and tested them [17]. We found bugs in two C functions, the two specifications, and sometimes requiring additional +which had not been uncovered by our earlier test suites nor manual reasoning. +the file systems built with them. The bugs went undetected +as they involved invalid inputs and corner cases which were 6.1 The Haskell Executable Specification +handled by the callers, whereas the Haskell specification in In a nutshell, as shown in the Haskell specification in Fig- +our QuickCheck framework does not preclude these input ure 5a, the function hs_fsop_readpage fetches a designated +values. data block of a specific file to the buffer. The argument afs is + For example, for the wordarray_copy function that copies a a map from inode numbers to files; each file is represented as +number of bytes from one memory area to another (similar to a list of blocks of data. The hs_fsop_readpage function looks + + + + 90 + SLE ’22, December 06–07, 2022, Auckland, New Zealand Z. Chen, C. Rizkallah, L. O’Connor, P. Susarla, G. Klein, G.Heiser, and G. Keller + + + 1 hs_fsop_readpage :: AfsState + 2 → VfsInode + 3 → OSPageOffset + 4 → WordArray U8 + 5 → NonDet (Either ErrCode (WordArray U8)) + 6 hs_fsop_readpage afs vnode n buf = + 7 let size = vfs_inode_get_size vnode :: U64 + 8 limit = size `shiftR` bilbyFsBlockShift + 9 in if | n > limit → return $ Left eNoEnt +10 | n == limit && (size `mod` bilbyFsBlockSize == 0) → +11 return $ Right buf +12 | otherwise → return (Right $ fromJust (M.lookup (vfs_inode_get_ino inode) afs) !! n) <|> +13 (Left <$> [eIO, eNoMem, eInval, eBadF, eNoEnt]) + + (a) The Haskell executable specification + + 1 definition + 2 afs_readpage :: afs_state + 3 ⇒ vnode + 4 ⇒ U64 + 5 ⇒ U8 WordArray + 6 ⇒ (U8 WordArray × (unit, ErrCode) R) cogent_monad + 7 where + 8 afs_readpage afs vnode n buf ≡ + 9 if n > (v_size vnode >> unat bilbyFsBlockShift) then +10 return (WordArrayT.make (replicate (unat bilbyFsBlockSize) 0), Error eNoEnt) +11 else if (n = (v_size vnode >> unat bilbyFsBlockShift)) ∧ ((v_size vnode) mod (ucast bilbyFsBlockSize) = 0) +12 then return (buf, Success ()) +13 else do err ← {eIO, eNoMem, eInval, eBadF, eNoEnt}; +14 return (WordArray.make (pad_block ((i_data (the $ updated_afs afs (v_ino vnode))) ! unat n) + bilbyFsBlockSize), Success ()) ⊓ +15 return (buf, Error err) +16 od + + (b) The Isabelle/HOL functional specification + + Figure 5. Functional specifications of the fsop_readpage function + +up a file, whose inode number is given by vnode, in the map here is essentially a finite set containing all allowed be- +afs, and copies the n-th block of the file to buf. It returns haviours. This monad is commonly used in proving refine- +non-deterministically an updated buffer or an error code. ment (e.g. [3, 22]). The alternative operator (<|>) acts as a + As a first step, hs_fsop_readpage calculates the number of non-deterministic choice, admitting the behaviour of either +blocks that the wanted file occupies. If the block in question of its operands by taking the union of their behaviours. +is out of bounds (n > limit), the function returns a no-entry +error eNoEnt. If the file size is a multiple of the block size, +n points to the last block in the wanted file, and the last 6.2 Mock Implementations +block is empty (because the file data ends at the prior block + It is not always feasible to test systems code in its exact pro- +boundary), then the function returns the original buffer as + duction environment [53]. For instance, the fsop_readpage +there is no data to read. Otherwise, hs_fsop_readpage reads + example has many low-level functions which call into the +the block by looking up the inode number in the map (see + operating system’s kernel, and it is currently not feasible to +Figure 6 for a pictorial example). + run QuickCheck tests in kernel mode. Instead of testing the + This, however, is not the only possible correct behaviour. + monolithic object file obtained from compiling the C code, +As the implementation has to access buffers and read from + we mock up parts of the code in Haskell. A mock abstracts +the physical medium, this may fail, in which case it should + from low-level kernel calls and can be thought of as a black +throw an error. We specify this as a non-deterministic be- + box, which provides to its caller the same observable effects +haviour. The specification states that the function can read + as the actual implementation. +a block or it can give one of the following five errors: eIO, + Mocks can also be used as substitutes for unimplemented +eNoMem, eInval, eBadF, or eNoEnt. The NonDet monad used + functions, enabling systems developers to test functionality + before they have a full system implementation. The use of + + + + 91 + Property-Based Testing: Climbing the Stairway to Verification SLE ’22, December 06–07, 2022, Auckland, New Zealand + + + data the mock to the specific use case of fsop_readpage. The + mock ostore_read function can be modelled as a simple map + (A) lookup: given a map OstoreState and a key of type ObjId, it + returns the corresponding object or an error. The relevant + block 0 block 1 block 2 block 3 Haskell definitions are given as follows (the use of the Oracle + can be ignored for now; it will be explained shortly): + (B) + type OstoreState = Map ObjId Obj + data Res a e = Success a | Error e + data + ostore_read :: Oracle +Figure 6. An example of the read_page algorithm. In case → (OstoreState, ObjId) → Res Obj ErrCode +(A), limit = 3. When n = 0, 1, 2 we just read. When n = 3, ostore_read orc (ostore_st, oid) = + if orc == 0 then +because the size of the data is not perfectly aligned at the case M.lookup oid ostore_st of +end, we still read. When n ≥ 4, we return the no-entry error. Nothing → Error eNoEnt +In case (B), limit = 3. When n = 3, that’s the special case. Just obj → Success obj +We return the old buffer unmodified. else Error orc + + + 6.3 Oracles and Non-determinism +mocks restricts the scope of debugging to a small number of +functions, reducing the effort required to locate bugs. The Cogent implementation of ostore_read interacts with + The Cogent implementation of fsop_readpage calls a the physical media and kernel data structures, therefore its +read_block function to fetch one block of file data, which in behaviour is dependent on that of the underlying systems +turn retrieves the data with the function ostore_read. The and hardware. However, as we have introduced in Section 2.1, +read_block function, which retrieves the file data from the Cogent is a total, purely functional language, meaning that +physical medium, is conceptually simple. However it is com- all functions in Cogent have to be deterministic. This non- +plicated in its internal implementation, which involves a determinism, therefore, has to be modelled by threading a +red-black tree lookup to locate the address, several layers of global state SysState through the impure functions, similar +caching, and thorough error-handling. to the H type in Figure 2. + Because read_block relies on kernel mode access to caches In the Haskell mock implementation of ostore_read, the +and complex data structures, it is a good candidate for a non-determinism can be modelled in a different manner for +mock implementation. In addition to the ostore_read func- simplicity. When testing this function independently, we +tion, we also substitute some kernel ADT functions for emulate the non-determinism by adding an additional oracle +mock implementations. For WordArray functions invoked input orc.1 This oracle can be deemed to be the source of all +by fsop_readpage, we use the Haskell models described in non-determinism. A similar oracle is passed to our mocks of +Section 5 as mocks. many WordArray functions, such as wordarray_create, which + The implementation of a mock is simplified by the fact allocates memory and creates a fresh array. +that it does not need to provide the full functionality of the We have seen how oracles can be used in mock implemen- +operation, as long as the callers in the specific test cases tations to emulate non-determinism. The oracle technique +cannot observe the difference in its behaviours. can be similarly applied to the Haskell executable specifi- + For example, the original Cogent signature of the function cation. When we test that an oracle-carrying mock refines +ostore_read is: a non-deterministic specification, the specification can ab- + type RR x a e = (x, ) + stract over the values that the oracle can possibly possess + ostore_read : (SysState, MountState!, OstoreState, ObjId) with the NonDet monad. If the specification is to be made + → RR (SysState, OstoreState) Obj ErrCode more precise, we can also introduce an oracle to it to ascribe +The function takes a quadruple as input, containing a read- the source of the non-determinism. In this case, care needs +only (denoted by the ! operator) MountState, and returns the to be taken to ensure that the oracle in the specification and +parametric RR type, which is further defined as a pair of a that in the implementation are in synchronisation, so that +variant type and a result type x that they do not make conflicting choices. +is common to both cases. Using oracles in the specification can be problematic if + The purely functional nature of Cogent makes it easy the implementation is not a mock and is genuinely non- +for developers to identify the observable behaviours—they deterministic due to, say, the hardware or the operating sys- +are necessarily within the return type of a function. In the tem. There is in general no way to predict accurately which +case of the fsop_readpage function, the only behaviours 1 In our implementation, we pass the oracle around using GHC Haskell’s +of ostore_read that can be observed are the returned Obj implicit parameter extension [48], making it more transparent to users. In +value or the error code ErrCode. Therefore, we can tailor the presentation of this paper, however, we pass them explicitly for clarity. + + + + + 92 + SLE ’22, December 06–07, 2022, Auckland, New Zealand Z. Chen, C. Rizkallah, L. O’Connor, P. Susarla, G. Klein, G.Heiser, and G. Keller + + +execution path the concrete implementation will take (e.g. 6.5 Results +malloc failures). Hence, the specification and the implemen- The shape of the top-level refinement statement for the +tation can make inconsistent choices when they encounter Haskell shallow embedding of the Cogent fsop_readpage +non-determinism, which can lead to spurious test failures. In function (shown below) closely resembles that of the +this case, we have to step back and use a non-deterministic WordArray example. An oracle is also generated and passed to +specification with the NonDet monad instead. This, however, the Haskell embedding, which will be further passed to the +has a negative cosmetic effect on the entire Haskell specifica- mock implementation of ostore_read as discussed earlier. +tion, as the NonDet monad is infectious and it would render + prop_corres_fsop_readpage :: Property +all ancestor functions in the call graph monadic. + prop_corres_fsop_readpage = + To address this problem, we can establish an equivalence forAll gen_fsop_readpage_arg $ \ic → +relation between the non-deterministic specification using forAll gen_oracle $ \o → +NonDet and the oracle-carrying deterministic one by testing. let ia = abs_fsop_readpage_arg ic + oa = uncurry4 hs_fsop_readpage ia +Concretely, we test that the two specifications return the + oc = fsop_readpage o ic +same set of results, by enumerating every possible oracle in corres rel_fsop_readpage_ret oa oc +in the deterministic specification, collecting a finite set of +results, and then checking that set against the set of results From the counter-examples produced by QuickCheck, we +produced by the non-deterministic specification. found that the Haskell executable specification was flawed, + The NonDet monad and the oracle approach are two ex- which in turn exposed a problem with the Isabelle/HOL +tremes of the spectrum, and developers can choose a suitable abstract specification, from which the Haskell specification +degree of non-determinism by combining these two to meet was derived. These specifications did not take errors returned +the needs of a specific test case. from ostore_read into account. Testing the above property + helped us rectify this mis-specification. + + 7 Design Decisions and Key Takeaways + We have showcased two applications of the PBT framework +6.4 Test Data Generation in Cogent. Since the examples we examined are from a real +By using mocks, not only can we use simpler algorithms to file system, they have given us some good insights into how +simulate the functionality of the original components, but we much boilerplate code is required, which components of the +can also fine-tune test data generators to restrict the domain testing infrastructure can be automatically generated, and +of inputs given to the mock, allowing us to only implement how these pieces can be integrated. +a partial mock of the original code. + When testing a cluster of functions and the mock func- 7.1 Modular Testing and Whole-System Testing +tion’s input depends on the output of other functions, the Our QuickCheck machinery does not require the user to +aforementioned partial mock should be used with care. The test the entire system at once. Instead, the user may test +input to a function can be directly controlled by the tester refinement for each function or for a cluster of functions at +by defining appropriate test data generators, while the out- a time. Typically, the ADTs implemented in C form a com- +put of a function is not so easy to predict as it may have mon module, shared across many systems. Accordingly, our +been heavily processed and manipulated by the functions. framework allows developers to test the ADTs in isolation, +When such an input value reaches the partial mock imple- with no regard to how they are used within systems. This +mentation, it is harder to know a priori whether it falls into modularity is aided by Cogent’s functional semantics. +the unhandled sub-domain of the mock. It poses a greater For the fsop_readpage example, we chose to employ modu- +challenge in writing good test data generators to ensure the lar testing as opposed to whole-system testing, which would +pre-condition of the mock function is met even after the ran- have required extra effort in developing the infrastructure +domly generated data have flowed through other functions to run tests in kernel mode (see Section 7.3). Whole-system +in the system under test. More general remarks on this point testing allows for more abstract top-level properties to be +can be found in Section 7.4. specified: for instance, that read and write are inverse opera- + Domain-specific knowledge can be leveraged to write tions.2 Alternatively, these logical properties can be tested +good test data generators, which makes the checking pro- +cess more efficient and practicable. For example, when we 2 It might be surprising to some readers that we claim that this property + +generate the OstoreState, all entries we generate belong is suitable for whole-system testing, instead of PBT. After all, this kind +to the same inode. In reality, there are many data objects of round-trip properties are typical in the realm of PBT. The reason is + that, systems software, or file systems in this case, are not implemented +for other files, or other types of objects; but none of these cleanly in a purely functional manner. They always involve heavy I/O, +facts will be observed by its caller. This in turn simplifies the kernel interaction, locking, etc., which cannot be precisely and concisely +implementation of the mock and the abstraction functions. specified in the functional specification and thus fall under the global state. + + + + + 93 + Property-Based Testing: Climbing the Stairway to Verification SLE ’22, December 06–07, 2022, Auckland, New Zealand + + +on top of the executable specification rather than directly on such as KML [51], House [34] or HaLVM [35] to run PBT in +the concrete implementation. kernel mode. This would allow the testing environment to + As our specification becomes more abstract, the single more closely resemble the real run-time environment of the +step simulation style of refinement becomes less relevant, software. We leave it for future investigation. +because several low-level functions may be specified as a +single function on the abstract level. Modular testing, on 7.4 Test Generation Strategies +the other hand, is more comprehensive, as it also examines There are two main factors to consider when generating test +the interfaces among different components in a system. In data for PBT. The first is how to sample the data: we choose +this case, it uncovered issues in the WordArray implementa- user-guided random test generation à la QuickCheck in this +tion that whole-system testing would have, and indeed had, work. Exhaustive testing (for small values) is another popular +missed. strategy and has gained great popularity, e.g. SmallCheck for + Haskell [60]. However, the small scope hypothesis on which +7.2 Functional Specification Versus Logical SmallCheck is based does not hold in general in the context + Properties of systems software.3 For instance, integer overflow, which +Traditional PBT tests specifications against a set of logi- is a common bug in systems code, can hardly be triggered +cal properties (e.g. get and set are inverse operations on by small values. The second main concern is the effective +WordArrays). We instead test functions against a full exe- generation of test data which satisfies the premises of the +cutable specification that models the functions. This is con- properties. If a property has the form 𝑝 =⇒ 𝑞 and the premise +ceptually similar to model-based testing [43] (also see Sec- 𝑝 is very strong (i.e. difficult to satisfy), and the test data is +tion 8). The functional specification is most akin to the func- not sampled with great care, then a lot of them will falsify +tional notions of model paradigm as classified in the work the premise and thus be discarded in the test, rendering the +by Utting et al. [64, § 3.3]. test inefficient. All refinement statements in this work have + It is often easier to use a model rather than a set of prop- the form 𝑝 =⇒ 𝑞 with a strong precondition 𝑝. The Luck +erties to define the behaviour of functions [43]; our exper- framework [46] couples the predicates of the property and +iments concurred. For example, functions in the C library the test data generation, which could simplify writing custom +can be readily modeled in terms of Haskell library functions. test data generators. There is a rich body of research devoted +Moreover, low-level functions in systems programming, e.g. to test generation techniques [28]. In the future, we plan to +setting a flag, are often very simple in its functionality, but explore more options to automate our test data generators. +can hardly be characterised by traditional properties that are +abstract and intuitive enough for users to comprehend. 7.5 Shrinking + Using functional specifications encourages composition- Counter-example shrinking reduces the size of counter- +ality. The functional specification of one module can also examples before reporting them to testers, which helps +be used as a mock implementation when testing other developers better understand and fix bugs. The Haskell +modules that depend on this module. For instance, in our QuickCheck provides a customisable shrinking library with +fsop_readpage case study, we used the previously defined a default shrinking algorithm for many datatypes. A rich +Haskell functional specification of the WordArray functions body of research can be found on more advanced shrinking +as mocks. algorithms. For example, test data shrinking that preserve + Furthermore, functional specifications serve as a commu- invariants about the generated data has been explored in +nication interface between system programmers and proof [49, 62]. But due to the lack of recursively defined datatypes +engineers. They are key to designing verification-friendly in Cogent and thus in the Cogent-powered file systems, the +systems programs, whereas logical properties alone fall short effectiveness of shrinking is dubious, as the size of the input +in this aspect. data chiefly comes from the sheer complexity of the (non- + recursive) datatypes, rather than from recursion. Shrinking +7.3 Testing Kernel Modules + is nevertheless useful for testing ADTs, but basic shrinking +A file system is typically compiled as a kernel module and strategies work reasonably well in our context. +runs in kernel mode, while our test framework runs in user +mode. To handle this discrepancy, for our prototype, we have 8 Related Work +ported our file systems code to run in user mode, using mocks + QuickCheck has been used for testing a variety of high-level +to simulate the kernel APIs. Emulating the kernel is common + properties, such as information flow control [23, 37], mutual +practice in systems programming, with libraries such as +FUSE [31] facilitating user-space execution of kernel code. 3 The small scope hypothesis is stated in Runciman et al. [60]’s paper as: “(1) +However, these tools expect a complete kernel module, thus If a program fails to meet its specification in some cases, it almost always +precluding the use of mocks or other user-land code during fails in some simple case. Or in contrapositive form: (2) If a program does +testing. A possible alternative to explore is using a system not fail in any simple case, it hardly ever fails in any case.” + + + + + 94 + SLE ’22, December 06–07, 2022, Auckland, New Zealand Z. Chen, C. Rizkallah, L. O’Connor, P. Susarla, G. Klein, G.Heiser, and G. Keller + + +exclusion [21], and the functional correctness of AUTOSAR In the PBT framework we presented, as we test the re- +components [6, 53]. To the best of our knowledge, our frame- finement statement between the implementation and the +work is the first to use PBT for testing refinement-based Haskell executable specification, which can be considered +functional correctness statements. a conformance relation, it does appear that we are instead + The hs-to-coq tool [61] translates Haskell code into the conducting model-based testing [63, 64]. Our approach does +Coq proof assistant [13]. Breitner et al. [14] used it to verify indeed share a lot in common with MBT, but we identify +parts of Haskell’s container library in Coq. In addition to our approach as PBT for the following reasons. Firstly, in +proving the functional correctness of various functions in MBT, the starting point of testing is a model of the software +the library, they also verified that the QuickCheck proper- under test. In contrast, as we have demonstrated, testing in +ties that the library is tested against are correct. By contrast, our framework does not necessarily have an existing model +our QuickCheck properties are refinement properties that to start with. In developing formally verifiable operating +directly resemble the those used for full verification. Veri- systems components, which is the application domain that +fying these properties is already a substantial step towards concerns us, it is of paramount importance to find the right +proving functional correctness, and in some cases directly balance between verifiability and performance. PBT gives +implies functional correctness. developers insights in both aspects. Therefore, testing plays + QuickCheck is available as a built-in tool in Isabelle/HOL a role in the design of the system, and subsequently its spec- +and is used for quickly finding counter-examples to proposed ification. This is similar to the iterative development process +lemmas [10, 15]. We chose to build on Haskell’s QuickCheck reported in the seL4 formal verification work [36]. Secondly, +rather than Isabelle/HOL’s QuickCheck because it is easier test cases are systematically and algorithmically generated +for Cogent programmers to use a testing framework that from the model in MBT. Test inputs are typically concretised +lies in the ecosystem of a functional programming language from the abstract test suite and the test results are abstracted +rather than interact with a theorem prover. Haskell acts as to be validated against the model by an adapter. In contrast, +a good communication medium between programmers and as we have shown in the examples, our test cases are not gen- +proof engineers [14, 26]. Moreover, due to Isabelle/HOL’s erated from the specification; test data is directly produced +interactive nature, testers would have to wait for Isabelle to on the concrete level. Lastly, from the tooling perspective, +re-process the proof scripts affected by a change in a theory our approach uses a PBT library QuickCheck as the core of +file, before they can run tests again. Even if Isabelle’s quick- the testing infrastructure. +and-dirty mode is enabled, which skips proofs, testers would +still have to wait for Isabelle/HOL to process definitions. In +fact, a large portion of the time is spent on reading in the 9 Conclusion +deep embeddings of the Cogent program into Isabelle, due In this paper, we showed how we augmented the Cogent +to the large terms generated by the Cogent compiler. This verification framework with PBT. Testing and formal verifi- +would cause a significant and unnecessary reduction to their cation complement each other, which is well acknowledged +productivity, and destroy the user experience. among researchers and developers. In this work, we further + The SPARK language [2], a formally defined subset of Ada, demonstrated this common belief in the specific context of +also uses a combination of testing and verification to facil- PBT and interactive theorem proving. The central idea is to +itate the development of high-reliability software. SPARK mirror the refinement proof in testing, using a functional +developers can attach contracts, that is, specifications of pre- specification as the model instead of a set of logical proper- +and postconditions, to critical procedures. Tools of the frame- ties as commonly done in PBT. +work can use these contracts as input to automatically test Using this method, we tested an abstract data type from a +the procedures, or attempt to formally prove that the imple- library, as well as an operation of a real-world file system. +mentation observes these contracts. Ada language features The tests exposed several bugs in the ADT implementation +that are hard to verify, such as side-effects in expressions, and uncovered errors in the specification of the ADT and of +access types, allocators, exception handling and many others, the file system. +are not permitted in SPARK. SPARK focuses on selectively Besides the main purpose of testing—detecting bugs— +verifying safety critical components, rather than fully veri- we exhibited other benefits of employing PBT. It reduces +fied systems from high-level specification to machine code. the effort in formal verification, guides the development of + DoubleCheck [30] integrates PBT into Dracula [65], a ped- verification-ready specifications and programs, and acts as +agogical programming environment which enables students a precise and effective communication media among devel- +to develop programs and then prove theorems about them in opers. We believe PBT offers developers the opportunity +ACL2 [1], a theorem prover based on term rewriting. 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In Program- + ming Concepts and Methods. + + + + + 97 + \ No newline at end of file diff --git a/packages/opencode/specs/simulation-research/text/2023-quickercheck.txt b/packages/opencode/specs/simulation-research/text/2023-quickercheck.txt new file mode 100644 index 00000000000..c76656c4715 --- /dev/null +++ b/packages/opencode/specs/simulation-research/text/2023-quickercheck.txt @@ -0,0 +1,716 @@ + QuickerCheck + Implementing and Evaluating a Parallel Run-Time for QuickCheck + Robert Krook Nicholas Smallbone + krookr@chalmers.se nicsma@chalmers.se + Chalmers University of Technology Chalmers University of Technology + Gothenburg, Sweden Gothenburg, Sweden + + Bo Joel Svensson Koen Claessen + bo.joel.svensson@gmail.com koen@chalmers.se + Lind Art & Technology Chalmers University of Technology +arXiv:2404.16062v1 [cs.PL] 17 Apr 2024 + + + + + Stockholm, Sweden Gothenburg, Sweden + + ABSTRACT 1 INTRODUCTION + This paper introduces a new parallel run-time for QuickCheck, a QuickCheck [5] is a widely known Haskell tool for property-based + Haskell library and EDSL for specifying and randomly testing prop- random testing of programs. First, the programmer writes a prop- + erties of programs. The new run-time can run multiple tests for a erty of the program under test that they expect to always hold. + single property in parallel, using the available cores. Moreover, if a Then, to check the property, QuickCheck generates a number of + counterexample is found, the run-time can also shrink the test case random test cases to exercise the property. If the property always + in parallel, implementing a parallel search for a locally minimal held, the check is reported as successful. If a test case makes the + counterexample. property fail, a process called shrinking is invoked, which consists + Our experimental results show a 3–9× speed-up for testing of a greedy search for a (locally) minimal failing test case. + QuickCheck properties on a variety of heavy-weight benchmark For example, we may be testing an implementation of System F + problems. We also evaluate two different shrinking strategies; deter- [6], where we have the following types and functions: + ministic shrinking, which guarantees to produce the same minimal 1 type Expr −− expressions + test case as standard sequential shrinking, and greedy shrinking, 2 type Type −− types + which does not have this guarantee but still produces a locally 3 + minimal test case, and is faster in practice. 4 reduce :: Expr −> Maybe Expr + 5 typeOf :: Expr −> Type + CCS CONCEPTS The types Expr and Type stand for expressions and types of expres- + • Computing methodologies → Concurrent algorithms; Shared sions in System F. The function reduce takes one evaluation step, if + memory algorithms; • Theory of computation → Shared possible. The function typeOf computes the type of an expression. + memory algorithms; • Software and its engineering → Soft- Subject reduction is a property that says that evaluation of expres- + ware testing and debugging. sions does not cause their type to change. This can be expressed as + a QuickCheck property as follows: + KEYWORDS 1 prop_Preservation :: Expr −> Property + property-based testing, quickcheck, testing, parallel functional pro- 2 prop_Preservation e = + gramming, haskell 3 isJust r ==> typeOf e == typeOf (fromJust r ) + 4 where + ACM Reference Format: 5 r = reduce e + Robert Krook, Nicholas Smallbone, Bo Joel Svensson, and Koen Claessen. Here, the operator ==> specifies a precondition: only tests satisfying + 2023. QuickerCheck: Implementing and Evaluating a Parallel Run-Time for isJust r are of interest. + QuickCheck. In The 35th Symposium on Implementation and Application of To run QuickCheck, the user must also supply an Arbitrary + Functional Languages (IFL 2023), August 29–31, 2023, Braga, Portugal. ACM, + instance describing how to generate random well-typed Exprs1 (a + New York, NY, USA, 12 pages. https://doi.org/10.1145/3652561.3652570 + non-trivial task studied in e.g. [7]). QuickCheck will then generate + a configurable amount of random expressions, which by default is + 100, and evaluate the property for them. In fact, QuickCheck will + Permission to make digital or hard copies of part or all of this work for personal or typically evaluate the property even more times, because: + classroom use is granted without fee provided that copies are not made or distributed + for profit or commercial advantage and that copies bear this notice and the full citation + • QuickCheck discards any test case not satisfying the pre- + on the first page. Copyrights for third-party components of this work must be honored. condition isJust r, and continues until it has executed 100 + For all other uses, contact the owner/author(s). tests satisfying the precondition. + IFL 2023, August 29–31, 2023, Braga, Portugal + 1 There is no requirement by QuickCheck itself that the generator has to generate + © 2023 Copyright held by the owner/author(s). + ACM ISBN 979-8-4007-1631-7/23/08. well-formed terms. This is primarily required to meaningfully exercise the property in + https://doi.org/10.1145/3652561.3652570 question. + IFL 2023, August 29–31, 2023, Braga, Portugal Robert Krook, Nicholas Smallbone, Bo Joel Svensson, and Koen Claessen + + + • If a test case fails (for example if the function reduce contains total number of successful tests3 . So, the distribution of sizes during + a bug), shrinking searches for a smaller counterexample by testing only depends on the total number of successful tests so far, + executing the property on many smaller test cases. not on the total number of tests in general. This introduces a small + but significant data dependency preventing parallel evaluations of + All this happens sequentially at the moment in QuickCheck. If + tests; when a worker runs a test it must know the appropriate size +the evaluation of the property takes a long time, QuickChecking + of the test case to run, and the appropriate size depends on whether +it (and possibly shrinking the counterexample) will take an even + the previous tests were successful or not. This dependency needs +longer time. This is time often spent waiting by the programmer, + to be dealt with somehow in the parallelization. +perhaps wondering why their computer is roaring like a spaceship +while only one core is in use. The contribution of this paper is Shrinking. When a failing test case is found, QuickCheck +to propose and practically evaluate a way of performing both the searches for a smaller failing test case by applying a process called +testing phase as well as the shrinking phase of QuickCheck in shrinking [10]. The goal of shrinking is to produce a locally minimal +parallel2 . failing test case. Shrinking first produces a list of shrink candidates, + Note that our work aims to reduce waiting time for the program- variants of the test case that have been reduced in size in a vari- +mer while checking a single property. There exist frameworks (for ety of ways. This list is traversed from left to right until we find +example tasty [4]) that allow testing of multiple properties and unit a new failing test case. Shrinking is then applied recursively on +tests in parallel or even distributed on a cluster. These are typically the new failing test case until the current failing test case cannot +used in regression tests or continuous integration. Our work can be reduced anymore. Shrinking does not backtrack in search of a +not only speed up testing in these settings but also during active globally minimal counterexample, but only promises to yield a local +development, where programmers typically run QuickCheck on a minimum. +single property and wait for the result. To use shrinking, the user must define a shrink function. For a + type T, this is a function shrink :: T -> [T] which, given a test +2 WHAT ARE THE CHALLENGES? case, produces a list of shrink candidates, i.e. smaller or simpler + test cases to try. For example, suppose that we are testing System F +Even though running each test is supposed to be independent, + again, and the type of expressions is defined as follows: +and as such testing a property 100 times should be a so-called +embarrassingly parallel task, in practice parallelizing testing is not 1 data Expr +so easy. For one, individual tests may interact with each other, but 2 = Var String −− variable +luckily in Haskell, we often get the independence guarantees we 3 | App Expr Expr −− application +need from pure (or at least thread-safe) code. In this paper, we 4 | ... −− other constructors +assume that the property itself is thread-safe. Then we can define a shrink function as follows: + But the biggest problem is that QuickCheck’s algorithm is in- 1 shrink :: Expr −> [Expr] +herently sequential. This is not at all obvious at first glance. The 2 shrink (Var _) = [] +problem comes from two features in QuickCheck – adjustment of 3 shrink (App t u) = +test size, and shrinking. As we will see, these features introduce a 4 concat [ [ t , u ] +data dependency: the test case that we should try next depends on 5 , [ App t ' u | t ' <− shrink t ] +the result of the previous test. Addressing these dependencies was 6 , [ App t u' | u' <− shrink u ] +one of the main challenges in parallelizing QuickCheck. 7 ] + 8 shrink ( ... ) = ... −− other constructors + Test size. Many times it is enough to generate a small test input +to falsify a property. QuickCheck tries to generate smaller inputs A Var can not be shrunk further, so we return an empty list of can- +early on, and gradually increases the size as more and more tests didates. A function application App t u, however, can be shrunk +are passed. This is achieved by QuickCheck supplying the test-data further. We can remove the App constructor and one of the subex- +generator with a size. The generators are free to disregard the size pressions, leaving just t or u, which if successful may shrink the +completely but may use it if they wish to. As an example, the default expression considerably. We can also keep the App constructor but +generator for lists uses the size as an upper bound of the length shrink the subexpressions. +of the generated list. The size of the first test is always 0, while Note that QuickCheck always tries the shrink candidates in the +the default upper bound is 100. If the user specifies that 100 tests order they appear in the list, from left to right. Hence it is com- +should be executed, QuickCheck will make sure that the generator mon to return the greedy candidates first, those that remove large +has been provided with all sizes between 0 and 99. The authors parts of the value, as we do in this case. Ordering the shrink list +point out that so far everything discussed is easily parallelisable. appropriately can greatly improve the speed of shrinking. + However, properties in QuickCheck can not only succeed or fail, We propose to parallelize shrinking in two ways: +but also discard, which means that a pre-condition in the property (1) Greedy shrinking evaluates as many shrinking candidates +was not fulfilled. A discarded test case is not counted towards the in parallel as possible, and as soon as a candidate fails, it + recursively continues with that candidate. It may be that a + 3 The reason for this is that if the precondition of a property is more likely to succeed +2 The implementation can be found at https://github.com/Rewbert/quickcheck. The for small test data sizes, we still want to make sure that we exercise the property on +authors intend to eventually merge this work into mainline QuickCheck. larger sizes. + QuickerCheck IFL 2023, August 29–31, 2023, Braga, Portugal + + + candidate earlier in the shrink list (corresponding to a more 1 prop_metamorphic :: Program −> Property + aggressive shrink step) would also have failed if we had 2 prop_metamorphic program = ioProperty $ do + waited, and in that case, we may perform a smaller shrink 3 writeFile "p.c" (render program) + step than necessary. 4 writeFile "q.c" (render $ mutateInput program) + (2) Deterministic shrinking speculatively evaluates test cases in 5 output1 <− compileAndRun "p.c" + the search before we know we will need to, but always makes 6 output2 <− compileAndRun "q.c" + the same choices as in the sequential case. That is, when a 7 mapM removeFile ["p.c", "q.c" , "p.exe" , "q.exe"] + shrink candidate fails, it waits until it knows that no earlier 8 return (mutateOutput output1 == output2) + candidate fails The property executes both the original and modified programs + In our evaluation, greedy shrinking is usually faster than determin- after having first written them to the file system. The file system is + istic shrinking. cleaned up, after which the outputs are compared. The output of + the unmodified program is modified to reflect the change described + 3 QUICKERCHECK by the metamorphic relation. + We present QuickerCheck via two examples. We point out that the Unfortunately, running this property with quickCheckPar will + QuickCheck API for writing generators, shrinkers, and properties produce extremely strange test failures. The reason is that the prop- + remains unchanged, and only the internal evaluation of a property erty, while innocent-looking, is not thread-safe. There is an implic- + is modified. itly shared resource, the file system: if multiple instances of the + property execute in parallel, they will all write to the same files p.c + System F. In Section 1, we saw the property prop_Preservation + and q.c. This leads to obvious race conditions. There are different + :: Expr -> Property for testing subject reduction in System F. + ways to modify the property such that there are no race conditions, + To test this property with sequential QuickCheck we run: + one of which is to let the property create a temporary directory to + > quickCheck prop_Preservation which intermediary files are written. + +++ OK! Passed 100 tests. + 1 −− create a fresh temporary directory based on a baseline name + As the property is pure, it is safe to test in parallel using Quick- 2 −− withSystemTempDirectory :: String −> ( FilePath −> IO a) −> IO a + erCheck. To do so, we must compile the code with the -threaded 3 + and -rtsopts flags and pass in the -N option to the run-time sys- 4 prop_metamorphic :: Program −> Property + tem, to enable parallelism in GHC. Then all we have to do is invoke 5 prop_metamorphic program = ioProperty $ do + quickCheckPar instead of quickCheck. 6 withSystemTempDirectory "compiler_output" $ \ dir −> do + The output (assuming all tests passed) is 7 −− rest of property , now using dir as a + > quickCheckPar prop_Preservation 8 −− scratch space for temporary files + +++ OK! Passed 100 tests. + If we disregard other implicitly shared resources such as CPU + tester 0: 50 + caches, RAM, bandwidth, etc, this property can now be evaluated + tester 1: 50 + in parallel by using quickCheckPar. + The lines tester 0: 50 and tester 1: 50 show that two In general, using QuickerCheck requires three steps. (1) Make + threads were used (we happened to limit GHC to using two cores) sure that the property is thread-safe (only for properties doing + and that they each executed 50 test cases. What is not visible in the I/O). (2) Compile the program with threading options. (3) Run + output is that, since the tests were distributed among two cores, quickCheckPar instead of quickCheck. + QuickerCheck ran close to twice as fast. + Compiler testing. A function that is not necessarily embarrass- 4 QUICKERCHECK DESIGN AND + ingly parallel is one that is effectful. To test a compiler it is necessary IMPLEMENTATION + to perform IO actions, such as invoking the compiler under test or The extensions to QuickCheck described in this paper are designed + executing the compiled binary. Testing compilers is non-trivial, but such that as few observable behaviors as possible are changed. Some + a well-studied approach is metamorphic testing [3]. In this approach, design choices of QuickCheck do not lend themselves nicely to par- + assuming a function of type Program -> IO Output that compiles allelism, and QuickerCheck tries to make reasonable compromises + and runs the program, we define a function mutateProgram :: where possible. One notable case of this is the way QuickCheck + Program -> Program that mutates the program in some way, and computes sizes for a test case. The size is derived from the number + then specify how the output should change in response by a func- of tests that have passed so far, and the number of tests that have + tion mutateOutput :: Output -> Output. Mathematically, the been discarded since the last passing test. This means that we can + property that should hold is: not compute the size of a test until we have observed the outcome +1 −− compileAndRun :: Program −> IO Output of all tests that came before. This sounds sub-optimal for paral- +2 compileAndRun (mutateProgram p) = lelization; below, we explain what QuickerCheck does to address +3 fmap mutateOutput (compileAndRun p) this. + In practice, we also need to perform various housekeeping tasks Testing. The test loop in ordinary, sequential QuickCheck is a + such as writing the program source to a file and cleaning up output recursive function that maintains a state containing e.g. the count + files, so a more realistic property is: of how many tests were executed so far, how many were discarded + IFL 2023, August 29–31, 2023, Braga, Portugal Robert Krook, Nicholas Smallbone, Bo Joel Svensson, and Koen Claessen + + +due to a failed pre-condition, etc. It also holds the random seed +used to generate the test case. It generates and executes one test at +a time, adjusting the size of the test case whenever a test succeeds, +but not when a test is discarded. Once a test fails, the test loop +terminates and a shrinking routine is invoked. + The parallel test loop is implemented by running concurrent +instances of the sequential test loop. The main thread spawns con- +current testers that evaluate one test after another, and then goes to +sleep until the testers report that all tests have been executed, too +many tests were discarded, or a counterexample was found. The +test loop maintains a state that is updated after every test, recording Figure 1: An illustration of how size grows as more and more +how many tests have been passed so far, the next random seed, and tests are passed, and to which worker they are assigned. In +many other things. In order to facilitate multiple, concurrent testers, order to get a fair workload for the concurrent testers a stride +some of the state has been moved into MVars. As an example, the is applied when computing sizes. +integer representing the number of tests a particular thread has yet +to run resides in an MVar, enabling other threads to read it if they +wish to steal work from that thread. graceful. When a property is aborted as violently as this, by + Communication between threads occurs as little as possible in raising an asynchronous exception, there is a risk that there will be +order to not incur synchronization costs. When testing is initiated, artifacts left from a test. If a property e.g. creates a new file on the +the number of tests to run is divided equally between the testers, and file system that is normally deleted at the end, an interruption by +only when one thread has exhausted its budget of tests will it inspect an asynchronous exception may make the file erroneously persist. +the budgets of the concurrent testers. If work-stealing is enabled, a +thread may then decrement the counter of a sibling tester and run 1 prop :: Input −> Property +another test on its own. Each tester has its own random seed that 2 prop ip = ioProperty $ do +it splits before running a test, as sharing a seed between all testers 3 run $ writeFile "temp.txt " (show ip) +would incur synchronization overheads. Additionally, each tester 4 −− do some work +computes the sizes to use for test cases based on their individual 5 run $ deleteFile "temp.txt " −− we may never execute this +counters for how many tests they have passed, and how many To address this, we introduce a combinator graceful that takes +tests they have discarded since the last passing test. In an effort to an IO action and a handler. The handler will run if QuickCheck +explore the same set of sizes as in sequential QuickCheck, they each makes the choice to terminate evaluation of the property. +apply a stride: If we have 𝑘 threads, then thread number 𝑖 uses sizes +𝑖, 𝑖 + 𝑘, 𝑖 + 2𝑘, 𝑖 + 3𝑘, . . .. This is illustrated in figure 1. A compromise 1 −− graceful :: IO a −> IO ( ) −> PropertyM IO a +is made when a thread steals a test from a sibling tester, in which 2 + +case the local next size is used. This reduces synchronization costs, 3 prop :: Input −> Property +as the thread that ran the test doesn’t need to report the result 4 prop ip = ioProperty $ do +back to the other thread. With this approach, we explore the same 5 run $ writeFile "temp.txt " (show ip) +set of sizes as sequential QuickCheck, except when work stealing 6 graceful +happens. 7 (do −− do some work + As an alternative to strides, we have also implemented a strategy 8 deleteFile "temp.txt " ) +that divides the set of sizes into contiguous segments for each of 9 ( deleteFile "temp.txt " ) +the testers, by applying an offset to the size computation. There is The handler is implemented by intercepting the asynchronous +a risk, however, that test cases generated by e.g. smaller sizes will exception before the worker is restarted and running the handler +run faster than test cases generated with larger sizes. This would before rethrowing the exception. graceful can only capture a spe- +lead to the concurrent testers finishing their given workloads at cific exception thrown internally by QuickCheck. We choose to +different times. Computing sizes with an offset is implemented and implement this dedicated operator like this rather than relying on +can be chosen by configuring the arguments to quickCheckWith4 , existing bracket functionality, as both user code and QuickCheck +but the default behavior is to use a stride. might already have code in place to deal with exceptions. + When a thread finds a counterexample it wakes up the main graceful can be used not only for shrinking but also for testing. +thread by writing the used seed and size to an MVar. The main When one tester finds a counterexample the concurrent testers will +thread will then terminate the remaining testers before it shrinks be aborted. This combinator will make sure that cleanup occurs +the counterexample, by delivering asynchronous exceptions. This then as well. +is very abrupt, with the exceptions delivered at the next allocation +point. Shrinking. The existing shrink loop continually evaluates the + head of the candidate list until a new counterexample is found, at + which point the loop recurses, or until the list is empty, at which +4 The function quickCheckWith is a variant of quickCheck that accepts a configuration point shrinking is terminated. This is illustrated in figure 2a. The +parameter where default behavior can be overridden. design of the new loop is very similar. + QuickerCheck IFL 2023, August 29–31, 2023, Braga, Portugal + + + Rather than a single thread traversing the candidate list one ele- +ment at a time, the parallel shrink loop spawns concurrent worker +threads that cooperate and traverse the same list, now residing in +an MVar. If any of the concurrent workers finds a new counterex- +ample, they will update the shared list of candidates and signal to +their sibling workers that they should stop evaluating their current +candidate and instead pick a new one from the new list. + The behavior of this shrink loop might return a non-deterministic +result. Whereas the previous loop will always find the first coun- +terexample in the candidate list, the parallel loop might find a (a) Illustration of the existing QuickCheck +counterexample other than the first one. To emulate the determin- shrink-loop. It guarantees to always return +istic behavior, the new loop can choose to only signal a restart the same locally minimal counterexample. +to those concurrent workers that are evaluating candidates that +appeared after the current one in the candidate list, and tell them +to speculatively start shrinking the new counterexample. The other +workers will keep evaluating their current candidates, and if one of +them turns out to be a counterexample, the current progress will +be discarded, and shrinking will continue with the new counterex- +ample. In this case, we might do some unnecessary work, but we +will get the same deterministic result. Figure 2b illustrates this and +how this approach may make us evaluate candidates that we don’t +need. + Another alternative is that when any worker has found a coun- (b) The new deterministic shrink-loop +terexample, all concurrent workers are restarted and told to start promises to find the same local minimum +shrinking the new counterexample, regardless if this was the first every time, but it may speculatively eval- + uate other candidates in its search for the +counterexample or not. This might lead to a non-deterministic re- + final counterexample. +sult, as the path down the rose tree of shrink candidates is not the +leftmost one, as illustrated in figure 2c. Restarting a worker is done +by raising an asynchronous exception in the worker. The worker +will catch this exception and enter the shrink-loop anew, and begin +to search through the new list of candidates. + Repeatedly accessing a shared resource may incur overhead costs. +If two workers attempt to modify a shared resource at the same +time, one will have to wait for the other. As the list of candidate +counterexamples is shared between workers, if candidates are eval- +uated very fast, it is likely that using more threads will slow down +shrinking. (c) The greedy shrink-loop does not guar- + antee to find the same local minimum, po- +5 EVALUATION tentially returning a different final coun- +We evaluate QuickerCheck to answer the following four questions terexample. + + • Question 1: Is the sequential performance of the new im- + Figure 2: The three figures above illustrate how the search + plementation comparable with QuickCheck? + for a minimized counterexample happened. The dotted line + • Question 2: How does the parallel run-time scale as we add + represents the final path to the local minimum, green boxes + more cores? + are candidate counterexamples that turned out to not be + • Question 3: Can we find bugs faster by using more cores? + new counterexamples, and red boxes are counterexamples + • Question 4: Can we shrink counterexamples faster by using + that still falsified the property. Grey boxes are candidate + more cores? + counterexamples that were never evaluated. + • Question 5: Does the choice of shrinking algorithm affect + the quality of shrunk counterexamples? + To answer these questions we run properties and collect infor- intended to represent a diverse set of testing tasks. compiler testing +mation. We will refer to such properties as benchmarks, and the and compressid are effectful tasks making use of IO facilities, while +benchmarks we use are described in the following subsection. the other tasks are pure. + constant. The benchmark named constant is not one that anyone +5.1 Benchmarks + would write organically, but its inclusion as a benchmark in this +We perform all our evaluations using six distinct benchmarks. While set has a very specific purpose. The underlying property is +the first benchmark constant is artificial, the other benchmarks are + IFL 2023, August 29–31, 2023, Braga, Portugal Robert Krook, Nicholas Smallbone, Bo Joel Svensson, and Koen Claessen + + + like this will experience race conditions if multiple threads are used. + We test two alternative implementations that make the property + thread-safe in different ways. The first (tmpfs) generates fresh di- + rectories for each concurrent worker to write such files to, and the + second (nofs) uses pipes to pass values around, never using the file + system. + + verse. This property asserts the confluence of the rewrite system + for the Verse Core Calculus [2]. A rewrite system is confluent if, + regardless of which rewrite rules are applied in each step, the result + is always the same, single, normal form. + The property generates an arbitrary term and applies two arbi- + trary sequences of rewrite rules. If the two resulting normal forms + Figure 3: A high-level description of the internal testing loop. are different, the rewrite system is not confluent and the property + The loop begins by generating input and then invoking the is falsified. + property. After this, the loop inspects the outcome before it + system f. The system f benchmark is a pure property that gen- + either reports having found a counterexample, or loops back + erates arbitrary lambda terms and asserts the subject reduction + to repeat all steps. The bottom box and all arrows are part of + property, described in section 1, which states that the type of a + the internal testing loop, while the top two boxes are defined + term should not change after performing one reduction of said + by the user. + term. The code was taken from Etna, an evaluation platform for + Property-based testing frameworks[8]. + prop_constant :: ( ) −> Bool + twee. Twee [9] is a high-performance theorem prover for equa- +1 + + prop_constant ( ) = True + tional logic written in Haskell. A key component is the term index, +2 + + + The cost in execution time of running a test consists of three a data structure for finding equations matching a given term. The + parts – generating input, running the property, and the machinery twee benchmark is a pure property stating that, after any sequence + of the internal testing loop. This is illustrated in figure 3. As Quick- of update operations on a term index, the data structure’s invariant + erCheck only changes the workings of the testing loop, we want is preserved. + to measure the change in cost of just the testing loop. The above + property minimizes the execution time of both the generation of 5.2 Results and Discussion + test data and evaluation of the property. Generation and evaluation + Evaluation is done using an Intel I7-10700 8-core CPU with turbo- + are constant time as there are no random choices to make dur- + boost turned off. The evaluation system is equipped with 64GB of + ing generation and evaluation of the property is trivial. Measured + 2933MT/s RAM. + changes in the execution speed of QuickCheck vs QuickerCheck on + We use GHC to compile and execute Haskell code, using + this benchmark should primarily be a result of the different testing + the compile-time flags -threaded, -feager-blackholing, and + loops. + -rtsopts. We don’t try to mitigate garbage collection costs by in- + compiler testing. The underlying property of the compiler test- creasing the nursery size or try to improve the performance in any + ing benchmark asserts that a compiler for an imperative language other way, as we believe most people use QuickCheck without do- + generates correct output. The property is stated as a metamorphic ing this. All invocations of QuickCheck are made with the chatty + relation as described in section 3. flag set to False as printing would otherwise affect the results. In + In practice, the property does significantly more work than the appendix A it is illustrated how chatty affects experimentation. + other benchmarks. It generates a type-correct imperative program + Is the sequential performance of the new implementation compara- + and produces several executables that are invoked to assert the + ble with QuickCheck? We answer this by executing each benchmark + correctness. The generated programs may include non-terminating + several times both with QuickCheck and QuickerCheck, using only + loops, so the property might require some time to execute. Such + one core. We compute the median execution times and compare + loops are eventually broken by the property itself after consuming + them. The results are presented in figure 4. + too many resources. During evaluation, the property will spend a + Something that immediately stands out is the huge overhead ex- + significant amount of time in external processes. + perienced by the constant benchmark. This benchmark is intended + compressid. This benchmark composes the two Unix commands to act as a worst-case property and illustrate precisely what the + gzip and gunzip and verifies that the composition behaves as the overhead of the new testing loop is. The results indicate that, in + identity function. It generates an arbitrary string and invokes gzip, the worst case, QuickerCheck will incur a penalty of 70%. + passes the compressed result to gunzip, and asserts that the final The other benchmarks all perform some actual workload and + output is identical to the input. experience much more modest changes in performance. The system + This benchmark comes in three flavors – one is a naive imple- f property, just like the constant property, is very fast. By running + mentation (naive) that writes intermediary values directly to the many more tests it interacts much more with the new testing loop, + file system. Since the file system is a shared resource a property incurring more of the new costs. This shows up by QuickerCheck + QuickerCheck IFL 2023, August 29–31, 2023, Braga, Portugal + + + + +Figure 4: The performance of sequential QuickerCheck com- +pared to that of QuickCheck. A number of 1 means that + Figure 5: The acquired speedup relative to the sequential +there was no difference in performance, whereas a num- + execution time when running tests. +ber less than 1 indicates that QuickerCheck was faster than +QuickCheck (e.g. 0.5 shows that QuickerCheck finished in +half the time). A number greater than 1 indicates that Quick- +erCheck was slower than QuickCheck. + + + +requiring 11% more execution time to finish the same workload. +Some of the workloads experienced no change at all or even got +slightly faster. + Not accounting for the constant benchmark, it appears that there +is no major change in performance by using sequential Quick- +erCheck instead of QuickCheck. + + How does the parallel run-time scale as we add more cores? Each +of the benchmarks is executed several times for each core config- +uration, the median execution time is computed and the speedup +relative to the sequential running time is computed. The results are +presented in figure 5. + We first observe that many of the benchmarks scale very well +until the point where we exhaust the number of physical cores. The +highest speedup was achieved by the compiler testing benchmark + Figure 6: The acquired speedup relative to the sequential +which got more than eight times faster. The verse property is not + execution time when searching for a planted bug. +far behind. + The twee benchmark initially scales very well but starts to lose +momentum when we approach the limit of physical resources. + tests in the same time frame. The results seem to indicate that the +When hyper-threading is active performance slowly but surely de- + more time a property spends inside the body of the property, the +grades. The twee benchmark is very data-intensive and frequently + greater the potential speedup. +moves data around. While two hyper-threads appear to the operat- +ing system as two CPUs, they are actually two logical threads that Can we find bugs faster by using more cores? To evaluate this we +share hardware components required to execute machine instruc- plant a bug in 4 of the 6 benchmarks and let QuickerCheck run +tions, such as caches and the system bus. One potential explanation until it finds the bug. This is repeated 300 times after which the +for this degradation is that the different testers affect the cache in median execution time is computed. Figure 6 illustrates the speedup +unfavorable ways. acquired relative to the sequential execution time. + One noticeable difference between e.g. the compiler testing and We first note that the system f benchmark doesn’t reach as high +system f benchmark is that the compiler testing property is signifi- of a speedup as when we are running tests without a bug enabled. +cantly slower. The property may spend over a second evaluating While we can’t say with certainty what to attribute this to, we +a single test while the system f benchmark may run thousands of have a pretty good guess of what is happening. The shape of the + IFL 2023, August 29–31, 2023, Braga, Portugal Robert Krook, Nicholas Smallbone, Bo Joel Svensson, and Koen Claessen + + +curve is the same, except that it is pushed down towards lower +multiples. There are some new costs associated with starting up the +parallel test loop, and when we run tests without a bug enabled the +benchmark is allowed to run for a few seconds, running hundreds of +thousands of tests. The cost of starting up the test loop is amortized +over all these tests, while when a bug is enabled there are many +fewer tests. The bug was found after roughly 200 tests, running for +just a couple of milliseconds. + The overall shape of the twee benchmark is the same, but not +reaching quite as high of a speedup as when just running tests. The +compiler testing benchmark acquires a 10x increase in performance, +outperforming all other evaluated benchmarks. We believe this +speedup is higher than that achieved in figure 5 because many +concurrently running tests are aborted when a counterexample +is found. When evaluating speedup for question two, every test +that we began evaluating was expected to finish, whereas when we +evaluated question three, we terminated concurrent testers when +one of them found a counterexample. We will thus do slightly less Figure 7: The speedups acquired when using two cores to +work. We observe the inverse behavior in the system f property, shrink the compiler testing tests, using the deterministic +where the concurrent testers have time to run many additional tests algorithm. +before they are terminated by a tester who found a counterexample. + + Can we shrink counterexamples faster by using more cores? We +generate 200 random seeds that we know trigger bugs, such that +we can replay them to deterministically see the same counterexam- +ples. We replay the seeds and measure how long it takes to shrink +them, varying the number of cores and the choice of strategy (de- +terministic or greedy shrinking). We have done this for the three +benchmarks compiler testing, twee, and verse. Because it is imprac- +tical to show all the results, we have picked some subsets of data +that we find representative of the overall results. + The compiler testing results are presented in figure 7, 8, and +9. Figures 7 and 8 illustrate the relationship between sequential +and parallel execution time, using two cores. The red dots got +slower when two cores were used, whereas the blue dots achieved +a speedup. The further from the line a point lies, the more extreme +the achieved effect is. From the two figures, we can see that the +greedy algorithm appears to benefit more experiments and that +the achieved effects are greater. The blue dots in figure 7 appear to +tangent a line. This line traces the execution time that is twice as Figure 8: The speedups acquired when using two cores to +fast as the sequential one and illustrates the upper bound defined shrink the compiler testing tests, using the greedy algorithm. +by Amdahl’s law[1]. The results in figure 8 show some experiments +crossing this boundary, which is explained by the greedy algorithm +being able to return a completely different counterexample. + As more and more cores are added, the results indicate that more Figure 9 shows that there is a clear trend of counterexamples with +and more experiments got slower, while the remaining ones that a good efficiency not benefiting from parallel shrinking. If there +achieved a speedup achieved a much greater speedup. was not that much extra work to be done from the beginning, the + To try and answer which counterexamples may benefit from existence of more cores does not offer any substantial performance +parallel shrinking, we plot the efficiency of the shrunk counterex- improvements. +amples. The efficiency of a single counterexample is defined as The results observed from twee (figures 10, 11, and 12) tell a +the fraction of evaluated candidates that successfully shrunk the different story. The twee property finishes shrinking in a couple +counterexample, and as such is a number between 0 and 1. It is of milliseconds, and using more cores quickly makes all observed +clear that if the efficiency is one, there is nothing to be gained counterexamples shrink slower. The efficiency appears to make no +from parallelism as shrinking becomes a sequential search. As an difference and we believe that the overhead of the parallel search +example, the total number of evaluated candidates in figures 2a, overshadows any benefits of using more cores. The advantage of +2b, and 2c are 5, 7, and 8 respectively. In all 3 cases the number of having more cores at one’s disposal appears to mainly be beneficial +successful shrinks was 3, so the efficiencies are 0.6, 0.42, and 0.375. in cases where execution will require a non-trivial amount of time. + QuickerCheck IFL 2023, August 29–31, 2023, Braga, Portugal + + + + +Figure 9: This figure illustrates that the closer the efficiency is Figure 11: The greedy algorithm appears to perform roughly +to one, the higher the probability that the test will get slower the same as the deterministic one, with the exception of some +when shrinking. It also appears that the relative speedup is tests that did indeed shrink faster. +higher the lower the efficiency. + + + + + Figure 12: While the efficiency turned out to be an excellent +Figure 10: The results indicate that most tests finished shrink- indicator for whether a test got faster or not for the compiler +ing very fast when only two cores was used. testing benchmark, the same can not be said for twee. Using + 16 cores and the greedy algorithm, all tests got slower and + there was quite a spread of efficiencies. The overall efficiency + The verse benchmark, much like the compiler testing one, achieves + appears to be much lower, but there is still nothing to be +a noticeable speedup for the majority of candidates. This is illus- + gained by additional cores. +trated in figures 13 and 14. The efficiency of the shrinker is depicted +in figure 15, and shows that there is a slight trend towards can- +didates with a lower efficiency being more likely to benefit from + distribution of sizes of shrunk counterexamples is different for the +multiple cores. This benchmark shrinks quite rapidly, and as we + two algorithms. We evaluate this on two benchmarks, compiler +add more cores, more and more candidates become slower, with the + testing and verse. We collect 300 seeds from the compiler testing +final number at 16 cores showing that roughly half of the candidates + benchmark and 500 from the verse benchmark. These seeds imme- +experienced a slowdown. + diately falsify the property, allowing us to shrink them and record + Does the choice of shrinking algorithm affect the quality of shrunk the size using both algorithms. We define the size of a counterex- +counterexamples? The deterministic shrinking algorithm will al- ample as the number of constructors in it. We point out that both +ways yield the same locally minimal counterexample, while the algorithms produce identical results when only one core is used. +greedy algorithm may return another local minimum, of a poten- To compare the results from the two algorithms, we model the +tially different size. We are interested in finding out whether the measured sizes as negative binomial distributions. Whereas we + IFL 2023, August 29–31, 2023, Braga, Portugal Robert Krook, Nicholas Smallbone, Bo Joel Svensson, and Koen Claessen + + + + +Figure 13: The speedups acquired with two cores using the Figure 15: The efficiency of the verse shrinker shows that +deterministic algorithm, for the verse benchmark. there is a slight trend of lower efficiency indicating that there + is a speedup to have by using more cores. + + + + +Figure 14: The speedups acquired with two cores using the +greedy algorithm, for the verse benchmark. It can be observed Figure 16: The measured sizes are rendered as a histogram, +that the number of candidates that achieved a speedup in- together with a model that represents the distribution from +creased, compared to using the deterministic algorithm. which they were drawn. + + +only have one baseline model (the deterministic algorithm), we +have 16 models representing the greedy algorithm (one for each that the choice of algorithm does not impact the quality of shrunk +core configuration). The authors note that in the single-core case, counterexamples at all. +the two algorithms are identical. Figure 16 illustrates both the +measured sizes of the deterministic algorithm, as well as the model 6 RELATED WORK +representing them. QuickCheck, having proven itself an extremely useful framework + We compare the models representing the greedy algorithm to the for testing software, has been re-implemented in many program- +baseline model by computing the entropy between them. Figures ming languages. It appears that most other implementations don’t +17 and 18 illustrate the baseline model and the greedy model with support parallel execution of properties. The only other imple- +the highest relative entropy. In both measured benchmarks the mentation we could find that supports parallelism is fsCheck, a +difference is very small. While the verse benchmark shows little QuickCheck implementation for testing .NET code. The parallel +to no difference at all, the compiler testing benchmark has a small run-time is not described in any paper and the documentation is +but noticeable difference. This difference is not large enough to say sparse, but the implementation is discussed in a merge request +whether the distributions are different or not. The results indicate introducing the work. The discussion indicates that they initially + QuickerCheck IFL 2023, August 29–31, 2023, Braga, Portugal + + + The Haskell package tasty [4] lets the user define test suites with + individual tests in a suite being of different kinds. A test suite can + simultaneously include e.g. QuickCheck tests, SmallCheck tests, + and unit tests. This is possible by tasty using different test drivers + to execute the tests. tasty can execute individual tests in a test suite + in parallel, but it will not introduce parallelism in the underlying + test drivers. If a test suite contains many tests, with all but one test + terminating very quickly, the majority of execution time will be + sequential, waiting for the longest running test to terminate. + + + + + 7 CONCLUSIONS AND FUTURE WORK + Our results show that parallel testing is beneficial. If the property + being tested is slow to run the expected performance increase is + high, whereas a fast property stands to gain less (but not nothing). +Figure 17: The figure illustrates the distribution of the base- Thanks to the natural division of effectful and pure code in +line samples, as well as the greedy distribution with the high- Haskell, many properties are immediately able to benefit from +est relative entropy, from the compiler testing benchmark. the parallel run-time. We found that with slight modifications to + effectful properties, we could run them in a thread-safe manner. + Parallel shrinking is not as universally beneficial, but can still + yield good results. For all benchmarks evaluated, individual coun- + terexamples could go either way, either experiencing a slowdown + or a speedup. We can not conclude that parallel shrinking is always + beneficial. It depends on not only the property but also the specific + test case. As more cores are added, some counterexamples will get + significantly faster, while the likelihood of your counterexample + shrinking slower increases. There seems to be a good compromise + around using multiple cores, but a lower number. The greedy al- + gorithm appears to offer a greater speedup than the deterministic + one, without compromising on the quality of the counterexamples. + While the work presented in this paper represents a considerable + engineering effort, there are still many lines of future work to + pursue. While implementing the work described in this paper, it + became clear that the ad-hoc way of computing sizes in QuickCheck + does not lend itself nicely to parallelism. It imposes a sequential + ordering to test cases and is tricky to distribute over multiple cores. +Figure 18: The figure illustrates the distribution of the base- While we have implemented a best-effort attempt to maintain the +line samples, as well as the greedy distribution with the high- previous behavior, it is not a perfect imitation. The authors would +est relative entropy, from the verse benchmark. The distribu- like to implement and evaluate several different ways of computing +tions are practically the same. sizes and reach some conclusions about which strategies are most + efficient. + While the greedy algorithm is allowed to search for the fastest +used an offset to compute sizes for tests but switched to using a path to a counterexample, there may well be more efficient algo- +stride after observing an uneven workload between workers. rithms still. There is still a bias towards finding earlier paths. It + The largest framework for property-based testing by number would be interesting to see how a random walk would perform. +of users is the Python package Hypothesis. They have explicitly Currently, the user must explicitly request parallel QuickCheck +chosen not to provide support for parallel evaluation of properties by using quickCheckPar instead of quickCheck. This choice was +as it can not be determined beforehand whether the function being made because properties involving I/O can not always be safely ex- +tested is thread-safe or not. In a non-pure language like Python, ecuted in parallel. It would be possible to instead have QuickCheck +this might be a concern, but we believe that this concern is not as automatically execute tests in parallel when it is safe to do so. For +severe when it comes to Haskell code. Haskell code is usually split example, pure properties (not using 𝑖𝑜𝑃𝑟𝑜𝑝𝑒𝑟𝑡𝑦) can always be par- +up into its pure parts and effectful parts, with the pure parts being allelized. Properties doing I/O could be marked as thread-safe using +embarrassingly parallel from the get-go. Effectful code can in many a special combinator. +cases be refactored to be thread-safe, such that parallel testing may We are also working together with the QuickCheck maintainers +yield positive results. towards merging this line of work into mainline QuickCheck. + IFL 2023, August 29–31, 2023, Braga, Portugal Robert Krook, Nicholas Smallbone, Bo Joel Svensson, and Koen Claessen + + +REFERENCES of an effect this has on a sequential workload. The constant and + [1] Gene M. Amdahl. 1967. Validity of the single processor approach to achieving system f properties run extremely fast, and we observe that with + large scale computing capabilities. In American Federation of Information Process- the chatty flag set to True, QuickerCheck is significantly faster. + ing Societies: Proceedings of the AFIPS ’67 Spring Joint Computer Conference, April + 18-20, 1967, Atlantic City, New Jersey, USA (AFIPS Conference Proceedings, Vol. 30). The constant property finished evaluating in one-fifth of the time + AFIPS / ACM / Thomson Book Company, Washington D.C., New York, NY, USA, that QuickCheck required. + 483–485. https://doi.org/10.1145/1465482.1465560 + [2] Lennart Augustsson, Joachim Breitner, Koen Claessen, Ranjit Jhala, Simon + As we add cores, it appears that chatty might make the bench- + Peyton Jones, Olin Shivers, Guy L. Steele Jr., and Tim Sweeney. 2023. The marks scale slightly worse, but not a lot, as indicated in figure + Verse Calculus: A Core Calculus for Deterministic Functional Logic Program- 20. + ming. Proc. ACM Program. Lang. 7, ICFP, Article 203 (aug 2023), 31 pages. + https://doi.org/10.1145/3607845 + [3] Tsong Yueh Chen, S. C. Cheung, and Siu-Ming Yiu. 2020. Metamorphic Testing: + A New Approach for Generating Next Test Cases. CoRR abs/2002.12543 (2020). + arXiv:2002.12543 https://arxiv.org/abs/2002.12543 + [4] Roman Cheplyaka. 2013. tasty. https://hackage.haskell.org/package/tasty + [5] Koen Claessen and John Hughes. 2000. QuickCheck: a lightweight tool for + random testing of Haskell programs. In Proceedings of the Fifth ACM SIGPLAN + International Conference on Functional Programming (ICFP ’00), Montreal, Canada, + September 18-21, 2000, Martin Odersky and Philip Wadler (Eds.). ACM, New York, + NY, USA, 268–279. https://doi.org/10.1145/351240.351266 + [6] Jean-Yves Girard. 1972. Interprétation fonctionnelle et élimination des coupures de + l’arithmétique d’ordre supérieur. Ph. D. Dissertation. + [7] Michał H Pałka, Koen Claessen, Alejandro Russo, and John Hughes. 2011. Testing + an optimising compiler by generating random lambda terms. In Proceedings of + the 6th International Workshop on Automation of Software Test. 91–97. + [8] Jessica Shi, Alperen Keles, Harrison Goldstein, Benjamin C Pierce, and Leonidas + Lampropoulos. 2023. Etna: An Evaluation Platform for Property-Based Testing + (Experience Report). Proceedings of the ACM on Programming Languages 7, ICFP + (2023), 878–894. + [9] Nicholas Smallbone. 2021. Twee: An Equational Theorem Prover. In Automated + Deduction - CADE 28 - 28th International Conference on Automated Deduction, + Virtual Event, July 12-15, 2021, Proceedings (Lecture Notes in Computer Science, + Vol. 12699), André Platzer and Geoff Sutcliffe (Eds.). Springer, New York, NY, USA, + 602–613. https://doi.org/10.1007/978-3-030-79876-5_35 +[10] Andreas Zeller and Ralf Hildebrandt. 2002. Simplifying and Isolating Failure- + Inducing Input. IEEE Trans. Software Eng. 28, 2 (2002), 183–200. https://doi.org/ Figure 19: The sequential performance of QuickerCheck rel- + 10.1109/32.988498 ative to QuickCheck, evaluated with the chatty flag turned + on and off. The (c) suffix indicates that Chatty was set to True. +A THE EFFECT OF CHATTY +The chatty flag in QuickCheck controls whether QuickCheck +should continuously print what it is doing or not. While printing +is helpful in assessing the current progress, it can be a bottleneck +when it comes to performance. + QuickCheck prints the current progress before every test. If you +run just a few tests every second this is of no concern, but if your +property is a very fast one it has a huge effect on performance. +Running 10000 tests per second means that you will print 10000 +times per second, which is significantly more than a human eye +can observe. + QuickerCheck takes a different approach to printing. Since the +new run-time is multi-threaded anyway, QuickerCheck will spawn +a separate worker thread whose sole purpose is to periodically +print the progress to the terminal. The duration of the period can +be configured, and the default is 200 milliseconds. + While the property that now runs 10000 tests in one second +would previously have printed 10000 times, QuickerCheck would Figure 20: The speedup relative to sequential execution time, +only have printed 5 times. In figure 19 it can be observed how much when chatty is enabled. + \ No newline at end of file diff --git a/packages/opencode/specs/simulation-research/text/2024-llms-write-good-pbt.txt b/packages/opencode/specs/simulation-research/text/2024-llms-write-good-pbt.txt new file mode 100644 index 00000000000..00cb7ec5bf2 --- /dev/null +++ b/packages/opencode/specs/simulation-research/text/2024-llms-write-good-pbt.txt @@ -0,0 +1,1018 @@ + Can Large Language Models Write Good Property-Based Tests? + Vasudev Vikram Caroline Lemieux + Carnegie Mellon University University of British Columbia + Pittsburgh, PA, United States Vancouver, BC, Canada + vasumv@cmu.edu clemieux@cs.ubc.ca + + Joshua Sunshine Rohan Padhye + Carnegie Mellon University Carnegie Mellon University + Pittsburgh, PA, United States Pittsburgh, PA, United States + sunshine@cs.cmu.edu rohanpadhye@cmu.edu +arXiv:2307.04346v2 [cs.SE] 22 Jul 2024 + + + + + ABSTRACT 1 INTRODUCTION + Property-based testing (PBT), while an established technique in Property-based testing (PBT) is a powerful testing technique for + the software testing research community, is still relatively under- testing properties of a program through generation of inputs. Un- + used in real-world software. Pain points in writing property-based like traditional testing methods that rely on manually written test + tests include implementing diverse random input generators and cases and examples, PBT uses automatic generation of a wide range + thinking of meaningful properties to test. Developers, however, are of inputs to invoke a diverse set of program behaviors. PBT was + more amenable to writing documentation; plenty of library API first popularized by the Quickcheck [1] library in Haskell, and has + documentation is available and can be used as natural language been used to find a plethora of bugs in a variety of real-world soft- + specifications for PBTs. As large language models (LLMs) have re- ware [2–5]. Additional techniques built on top of PBT [6–8] have + cently shown promise in a variety of coding tasks, we investigate demonstrated potential in providing stronger testing for software. + using modern LLMs to automatically synthesize PBTs using two Despite its proven results and impact in the research community, + prompting techniques. A key challenge is to rigorously evaluate PBT is not as widely adopted by open source and industry soft- + the LLM-synthesized PBTs. We propose a methodology to do so ware developers. Using the Open Source Insights [9] dependency + considering several properties of the generated tests: (1) validity, dataset, we find that only 222 out of 180,000 PyPI packages list the + (2) soundness, and (3) property coverage, a novel metric that mea- Python PBT library Hypothesis as a dependency, despite it being a + sures the ability of the PBT to detect property violations through very popular project (6.7k+ stars on GitHub). Harrison et al. [10] + generation of property mutants. In our evaluation on 40 Python conducted a series of interviews and detail a set of challenges faced + library API methods across three models (GPT-4, Gemini-1.5-Pro, by professional developers when attempting to use PBT in their + Claude-3-Opus), we find that with the best model and prompting software. Developers reported difficulties in (1) writing random + approach, a valid and sound PBT can be synthesized in 2.4 samples data generators for inputs and (2) articulating and implementing + on average. We additionally find that our metric for determining properties that would meaningfully test their code. Furthermore, + soundness of a PBT is aligned with human judgment of property Harrison et al. describe the “critical mass problem” that PBT is still + assertions, achieving a precision of 100% and recall of 97%. Finally, relatively unknown and unpopular among the software industry. + we evaluate the property coverage of LLMs across all API meth- While developers have been reticent to adopt PBT, the practice + ods and find that the best model (GPT-4) is able to automatically of documenting code is widespread. Documentation for library API + synthesize correct PBTs for 21% of properties extractable from API methods is fairly common, especially for languages like Python, + documentation. and contains valuable information about input parameters and + properties of the output. An truncated version of the documentation + ACM Reference Format: for the numpy.cumsum API method can be seen in Figure 1. + Vasudev Vikram, Caroline Lemieux, Joshua Sunshine, and Rohan Padhye. Recently, the use of pre-trained large language models (LLMs) for + 2024. Can Large Language Models Write Good Property-Based Tests?. In code generation has become increasingly popular [11–13]. LLMs + Proceedings of ACM Conference (Conference’17). ACM, New York, NY, USA, have been effective at translating natural language specifications + 12 pages. https://doi.org/10.1145/nnnnnnn.nnnnnnn and instructions to concrete code [14, 15]. Additionally, LLMs have + shown potential to improve existing automated unit test generation + techniques [16], and even generate unit tests from scratch [17, 18]. + In this paper, we investigate the potential of using LLMs to generate + Permission to make digital or hard copies of all or part of this work for personal or + classroom use is granted without fee provided that copies are not made or distributed + property-based tests when provided API documentation. We believe + for profit or commercial advantage and that copies bear this notice and the full citation that the documentation of an API method can assist the LLM in + on the first page. Copyrights for components of this work owned by others than ACM producing logic to generate random inputs for that method and + must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, + to post on servers or to redistribute to lists, requires prior specific permission and/or a deriving meaningful properties of the result to check. + fee. Request permissions from permissions@acm.org. While LLMs have shown effectiveness in synthesizing unit + Conference’17, July 2017, Washington, DC, USA tests [19] and fuzz harnesses [20–22], synthesizing property-based + © 2024 Association for Computing Machinery. + ACM ISBN 978-x-xxxx-xxxx-x/YY/MM. . . $15.00 tests has unique challenges. In unit testing, the test oracles are usu- + https://doi.org/10.1145/nnnnnnn.nnnnnnn ally simple equality assertions between expected and actual outputs; + Conference’17, July 2017, Washington, DC, USA Vasudev Vikram, Caroline Lemieux, Joshua Sunshine, and Rohan Padhye + + + 1 from hypothesis import given, strategies as st + 2 import numpy as np + 3 + 4 # Summary: Generate random input parameters for + 5 # numpy.cumsum and test properties + 6 @given(st.data()) + 7 def test_numpy_cumsum(data): + 8 # Generating a list with varying length + 9 # and integer elements + 10 a = data.draw(st.lists( + 11 st.integers(min_value=-10, max_value=10), + 12 min_size=0, max_size=10)) + 13 + 14 # Generate random axis + 15 axis = data.draw(st.one_of(st.none(), + 16 st.integers(min_value=0, + 17 max_value=a.ndim-1))) + 18 + 19 # Call numpy.cumsum with generated input + 20 cumsum_result = np.cumsum(a, axis=axis) + 21 + 22 # Test property: output shape +Figure 1: Truncated Numpy documentation for the 23 # should be the same as input shape +numpy.cumsum API method. The documentation includes 24 # if axis is not None or input is 1-d array +descriptions of properties about the result shape/size and 25 if axis is not None or a.ndim == 1: + 26 assert cumsum_result.shape == a.shape +additional information about the last element of the result. 27 + 28 # Test property: output size should be the + 29 # same as input size + 30 assert cumsum_result.size == a.size +in PBT, a property assertion that holds generally for inputs must + 31 +be synthesized in the test. Similarly, fuzz harnesses usually only 32 # Test property: cumsum(a)[-1] should be +contain implicit oracles that capture unexpected behaviors such 33 # approximately equal to sum(a) for +as uncaught exceptions or crashes. Further, synthesizing property- 34 # non floating-point values +based tests requires generating custom logic for random input 35 if not np.issubdtype(a.dtype, np.floating): + 36 np.testing.assert_almost_equal( +generation over various types of inputs; unit tests do not require 37 cumsum_result.flatten()[-1], +this logic since there is only one input, and fuzz harnesses primarily np.sum(a)) +rely on inputs represented as raw byte streams. 38 # End program + An example of using LLMs for PBT can be seen in Figure 2, +which displays an LLM-synthesized property-based test for the Figure 2: A GPT-4 generated property based test for +numpy.cumsum method when provided the documentation in numpy.cumsum. The test first generates random integer ar- +Figure 1. First, the logic for generating random values for the in- rays between size 1 and 20 and a random axis. Then, the API +put parameters a and axis is in lines 10–17. Then, the cumsum method under test np.cumsum is invoked on the randomly +method is invoked on these arguments on line 20. Finally, lines 25– generated inputs. Finally, three properties are checked on +37 contain property assertions for the output cumsum_result. the output array, all derived from information in the API +We specifically note that these properties assertions match natural documentation. All comments are also generated by GPT-4. +language descriptions in the API documentation in Figure 1. The +documentation specifies that “result has the same size as a”, which +has a direct translation to the assertion in line 30. Similarly, the spec- do we know whether an LLM-synthesized property-based test is +ification that result has “the same shape as a if axis is not None or good enough? We characterize several desirable properties of these +a is a 1-d array” is checked conditionally as an assertion in lines 25– tests and propose a methodology to evaluate the LLM’s output: +26. Finally, the property assertion shown in lines 35–37 checks that property-based tests must be valid (free of compile-time or run-time +the last element of the result is equal to np.sum(a) if the array is errors), sound (only assert properties that must be true), and ideally +not of float type. This assertion translates information from the complete (i.e., actually check for properties that are mentioned in +notes section in the documentation into a useful property to check. the API documentation). To measure completeness of property +While not a perfect property-based test, this example demonstrates assertions, we introduce the notion of property coverage, which +the ability of LLMs to write logic for generating random inputs and uses mutation testing to measure the ability of a property-based test +derive meaningful property assertions from API documentation. to fail when the target API method behaves in a way that violates + In this paper, we study the use of state-of-the-art LLMs—Open its documented property. We evaluate our three models across two +AI’s GPT-4, Anthropic’s Claude-3-Opus, and Google’s Gemini-1.5.- prompting strategies on 40 API methods across 10 Python libraries. +Pro—to automatically synthesize property-based tests. We propose We find that with the best-performing approach (GPT-4 with two- +single stage and two stage approaches for using API documentation stage prompting), a valid and sound property-based test can be +to prompt the LLM to synthesize property-based tests. But how synthesized over 2.4 samples on average, and that a correct PBT + Can Large Language Models Write Good Property-Based Tests? Conference’17, July 2017, Washington, DC, USA + + +can be synthesized for over 20% of the documented properties. 1 from hypothesis import given, strategies as st +We thus find LLM-based PBT generation a suitable approach for 2 + 3 # Random list generator +automating some of the tedious process of writing property-based 4 @st.composite +tests. 5 def generate_lists(draw): + In summary, our contributions are the following: 6 return draw(st.lists(elements=st.integers(), + 7 min_size=1)) + (1) We propose an approach for using LLMs to synthesize 8 + property-based tests given API documentation. 9 # Property-based test for sorted with + 10 # separate generator + (2) We propose a methodology for evaluating LLM-synthesized 11 @given(lst=generate_lists()) + property-based tests considering validity, soundness, and 12 def test_sorted_separate(lst): + completeness. 13 sorted_lst = sorted(lst) + (3) We demonstrate alignment between our metric for sound- 14 assert all(sorted_lst[i] <= sorted_lst[i + 1] + 15 for i in range(len(sorted_lst) - 1)) + ness and human judgment through manual labeling. + 16 + (4) We propose a novel metric of property coverage for measuring 17 # Alternative property-based test + completeness with respect to documented properties. 18 # with inline generator + (5) We present an empirical evaluation of the validity, soundness, 19 @given(st.data()) + and property coverage of PBTs synthesized by three state-of- 20 def test_sorted_combined(data): + 21 lst = data.draw(st.lists(elements=st.integers(), + the-art commercial LLMs across two prompting strategies. 22 min_size=1)) + 23 sorted_lst = sorted(lst) + 24 assert all(sorted_lst[i] <= sorted_lst[i + 1] +2 BACKGROUND 25 for i in range(len(sorted_lst) - + 1)) +2.1 Property-based Testing +Property-based testing [1] aims to probabilistically test a program +by generating a large number of random inputs and checking Figure 3: Example property-based tests in Hypothe- +whether the corresponding outputs of the program adhere to a set sis for the Python sorted function to sort lists. The +of desired properties. A property-based test can be defined as the fol- test_sorted_separate function uses a separate gener- +lowing: given a function/method under test 𝑓 , an input space X, and ator, whereas the function test_sorted_combined com- +a property 𝑃, we want to validate that ∀𝑥 ∈ X : 𝑃 (𝑥, 𝑓 (𝑥)). Often, 𝑃 bines the generator and testing logic into one function. +is a conjunction of component properties, that is, 𝑃 = 𝑝 1 ∧𝑝 2 ∧. . . 𝑝𝑘 . +In practice, we are unable to enumerate all inputs in X. So, we write +a generator function gen that produces a random input in X, i.e. there is no assertion failure. Generally, if 𝑃 had multiple component +𝑥 = gen(). Then we write a parametrized test 𝑇 :: 𝑋 → {true, false} properties, there would be a list of assertion statements in 𝑇 . +that returns 𝑃 (𝑥, 𝑓 (𝑥)). The property is checked on many randomly Finally, to complete the property-based test, we must invoke our +generated 𝑥. A violation of the property causes the test to fail. Al- generator to sample random inputs and call the parametrized test +though PBT cannot prove the absence of property violations, it on the input. This is done using the Hypothesis @given decora- +improves over testing specific hard-coded inputs and outputs as is tor, as seen in line 11. The decorator specifies that the input lst +commonly done in unit testing. PBT is thus a form of fuzz testing. of our parametrized test test_sorted_separate should use + We next describe how our formal definition translates to code in generate_lists as the generator. +Hypothesis [7], a popular PBT library for Python. Another style of writing a Hypothesis test is to include the + Suppose our function under test is the Python sorted function, generator inside the parametrized test, as seen in the func- +which takes in a list as input and returns a sorted version. We tion test_sorted_combined in Figure 3. At line 19, the +want to test the property that the elements of the sorted list are @given(data()) decorator provides an object which can +monotonically increasing. be used to sample random input data of unspecified type. + First, we must write our generator gen that samples an input Lines 21–22 act as the generator, using the same logic as the +from the input space of lists. An example of such a generator is the generate_lists function to a generate random integer list +generate_lists function in lines 4–7 of Figure 3. Hypothesis of with minimum size 1. Lines 23–25 use the method invocation +has a built-in set of sampling strategies for various data structures. and assertion statements as is in test_sorted_separate. The +The lists and integers strategies in line 6 are used to ran- approach of including the generator in the parametrized test has +domly generate and return a Python integer list of size ≥ 1. particular advantages when the method under test has multiple + Next, we must write the parametrized test 𝑇 that takes in an input parameters that have dependencies with each other. In this +input 𝑥 and returns 𝑃 (𝑥, 𝑓 (𝑥)), where 𝑓 is the sorted function scenario, each argument can be sequentially generated one at a time +and 𝑃 is the property that the elements of the sorted list are mono- using generators that depend on previously generated arguments. +tonically increasing. An example of such a parametrized test is While the property-based tests shown in Figures 3 are valid and +test_sorted_separate in Figure 3. In line 12, the sorted will properly run, they are not necessarily the best property-based +function is invoked on the input lst. Then, lines 14–15 check the tests for the sorted function. Perhaps the user would like validate +property 𝑃 that elements of the sorted listed are increasing by us- the behavior of sorted on the empty list, which is not an input +ing an assertion statement. 𝑇 returns true if 𝑃 (𝑥, 𝑓 (𝑥)) is true, i.e. produced by our generator due to the min_size=1 constraint in + Conference’17, July 2017, Washington, DC, USA Vasudev Vikram, Caroline Lemieux, Joshua Sunshine, and Rohan Padhye + + +lines 7 and 22. Similarly, the assertions in lines 14–15 and lines 24–25 Single Stage Two Stage +do not capture all behavior of the sorted function. For instance, it + PBT Properties +does not check that lst and sortedlst share the same elements. Prompt Prompt +We discuss these types of challenges more in Section 3.2. + +2.2 Large Language Models LLM LLM +Pre-trained large language models (LLMs) [15, 23–28] are a class of Extracted properties +neural networks with a huge number of parameters, trained on large + Property- PBT Suite +corpora of text data. These models are trained in an autoregressive + Based Test Prompt +manner—i.e., trained to predict the next token in a sequence—which +allows them to be trained on a large volumes of unlabelled text. +This extensive pre-training allows them to function as one-shot or LLM +zero-shot learners [24]. That is, these models can perform a variety +of tasks when given only one example of the task, or a textual +instruction of the tasks. The natural-language instructions, along Property-Based +with any additional input data, that are passed to the LLM are called Test Suite +the prompt [29]. The practice of creating prompts that allow the +LLMs to effectively solve a target task is called prompt engineering. + Figure 4: Two methods of generating property-based test us- + Further, a number of LLMs have been trained extensively on + ing an LLM. The first is a single stage prompt of the LLM with +code [11, 30–33]. These models, as well as more general-purpose + zero-shot CoT instructions to (1) explain a generation strat- +LLMs, have been used for numerous software engineering tasks, + egy, (2) properties to test, and (3) generate a single property- +including program synthesis [12, 34], program repair [35–37], code + based test. The second method instructs the LLM to extract a +explanation [38], and test generation [16–18]. These techniques + list of properties from the API docs and continues the conver- +use the LLMs out-of-the-box, getting them to accomplish the tasks + sation, instructing the LLM to write a test for each property. +via prompt engineering alone. + Like prior work, we use pre-trained language models and adapt +them to our tasks only via prompt engineering. We discuss our +methods of constructing these prompts in Section 3. from the API (maximum five) and (2) instructing the LLM to create + individual property-based test functions for each property. The + first prompt contains user-level task instructions to extract five +3 THE PROPTEST-AI APPROACH properties that hold for all outputs of the API method. The second +3.1 Prompt Design prompt contains instructions to synthesize a PBT using Hypothesis +To synthesize a property-based test from the LLM, we first design for each of the properties generated by the LLM. Our full prompt +prompts that include the API documentation and instructions to templates are available in our data artifact. +write a property-based test for the input method. We explored two +prompting strategies: one to generate a single property-based test 3.2 Evaluation Methodology +and one to generate a property-based testing suite. Using our Proptest-AI methodology to prompt the LLM to syn- + Our high-level prompt templates contains: thesize property-based tests, how do we evaluate the quality of + (1) System-level instructions stating that the LLM is an expert these generated PBTs? While the effectiveness of unit tests has + Python programmer. been a well studied topic for decades [40–43], this is not the case + (2) The target API documentation, taken from the API website. for property-based tests. One difficulty in conducting these types of + (3) User-level task instructions to review the API documentation evaluations for PBT is the lack of readily available property-based + and perform a particular task. tests for software. Thankfully, LLMs can provide us a method of + (4) The desired output format. automatically generating property-based tests for which we can + design an evaluation methodology. + Based on this template, our first prompting strategy generates a We propose a PBT evaluation methodology and metrics focusing +single property-based test. The user-level task instructions begin on (1) the validity of the tests, (2) the soundness of the tests, and +with Chain of Thought [39] instructions to outline a generation (3) the property coverage (detailed in Section 3.2.3) of the tests. To +strategy and a list of properties to test before synthesizing the motivate each of these metrics, we include examples of inaccurate +property-based test. The prompt ends with instructions to generate LLM-synthesized PBTs and discuss the issues that impact each +a Hypothesis PBT and adds an output format including Hypothesis of these qualities. We then propose mitigation strategies for each +import statements, relevant API import statements, a boilerplate of the inaccuracies that improve the quality of the property-based +function signature, and an example Hypothesis PBT from the Hy- tests. All of our examples use the Hypothesis PBT library in Python. +pothesis documentation. We refer to this prompt to generate the +entire property-based test as the “PBT Prompt”, as seen in Figure 4. 3.2.1 Validity. One type of incorrect behavior in a property-based + The second prompting strategy we explore has a two stage test is a validity issue in which a run-time error is encountered when +prompting method of (1) instructing the LLM to extract properties the test is executed. The problem of hallucination is a well-known + Can Large Language Models Write Good Property-Based Tests? Conference’17, July 2017, Washington, DC, USA + + + 1 from hypothesis import strategies as st 1 @given(generate_array()) + 2 from datetime import timedelta 2 def test_cumsum(a): + 3 3 # Test that the shape of the output + 4 @given(days=st.integers(min_value=0), 4 # is the same as the input + 5 seconds=st.integers(min_value=0), 5 out_shape = np.cumsum(a).shape + 6 microseconds=st.integers(min_value=0), 6 assert out_shape == a.shape + 7 milliseconds=st.integers(min_value=0), + 8 minutes=st.integers(min_value=0), + 9 hours=st.integers(min_value=0), Figure 6: A Gemini-1.5-Pro generated property-based test con- +10 weeks=st.integers(min_value=0)) taining an unsound property for numpy.cumsum on line 6. +11 def test_timedelta_total_seconds(days, seconds, +12 microseconds, milliseconds, minutes, +13 hours, weeks): 1 import numpy as np +14 td = timedelta(days=days, seconds=seconds 2 +15 microseconds=microseconds, 3 # Violate Non-Decreasing Sequence +16 milliseconds=milliseconds, 4 def buggy_cumsum_1(a, +17 minutes=minutes, 5 axis=None, dtype=None, out=None): +18 hours=hours, 6 result = np.cumsum(a, axis=axis, dtype=dtype, +19 weeks=weeks) 7 out=out) +20 (...) 8 # Reverse the result to create decreasing elements + 9 return result[::-1] + +Figure 5: An example invalid datetime.timedelta PBT +produced by GPT-4. The datetime.timedelta construc- Figure 7: Example property mutant of numpy.cumsum pro- +tor on line 14 raises an OverflowError when the absolute duced by GPT-4. The mutant violates the property that the +magnitude of days exceeds 1,000,000. output of numpy.cumsum must be non-decreasing by revers- + ing the result. + +problem with using LLMs to generate code [44]. LLMs may gener- +ate plausible-looking but incorrect code that throws unexpected unsound property is higher than the likelihood of a bug. This is a +errors at runtime. This issue arises in property-based testing as well, weak assumption. We can capture the soundness of a property by +in which the LLM may synthesize test cases that are syntactically measuring the frequency at which the assertion fails across multiple +valid but result in a runtime error during execution. Since the test generated inputs. If an assertion fails on a significant percentage of +is executed on multiple random inputs, it is also possible that only the inputs, it is most likely an unsound property. +a percentage of randomly generated inputs result in runtime errors. A property-based test is determined as sound if 100% of test +An example is the generator in Figure 5 for timedelta objects function invocations do not result in assertion errors from the +in the Python datetime module. The generator function can pro- property checks. We specifically filter out any executions that result +duce values for the timedelta object constructor that may result in any other runtime errors, as these are related to the validity of +in an OverflowError raised by the datetime.timedelta the property-based test rather than the soundness. +constructor when the magnitude of days exceeds 1,000,000. Thus, + 3.2.3 Property Coverage. While validity and soundness indicate +we determine a property-based test as valid if 100% of test function + that a property-based test runs without errors, an additional mea- +invocations do not result in any run-time errors, excluding property + surement is needed to evaluate effectiveness at testing specific +assertion errors as these relate to soundness. + properties. A property-based test may execute correctly with 100% +3.2.2 Soundness. LLMs may also synthesize a property-based test validity and 100% soundness, yet inadequately test key properties +that is unsound, i.e., there exists an input/output pair that violates due to having weak assertions. Our goal is to establish a metric that +a property assertion but is valid given the specification. Figure 6 answers the question: how effective is the property-based test at +provides an example of an LLM-synthesized property-based test for detecting whether an API method violates a specific property? +the numpy.cumsum method that contains an unsound property One related idea is mutation testing, which measures the ability of +on line 6. The numpy.cumsum documentation specifies that for a test to detect bugs artificially bugs in the program under test [45]. +a given input array 𝑎, the output should have "the same shape as First, mutant versions of the program are created with an artificially +𝑎 if axis is not None or 𝑎 is a 1-d array". The synthesized prop- injected bug. If the test fails when executing the mutated programs, +erty is unsound because it unconditionally checks whether the then the mutant is killed; otherwise, the mutant survives. Mutation +output and input shapes match. A randomly generated input of testing provides a measurement related to the bug-finding capability +array([[0]] produces an assertion failure when this test is run of a particular test. +since the input shape is (1, 1) and the output shape is (1,); Mutation testing injects bugs by applying syntactic operators +this is not an actual bug and the behavior of the cumsum method on the source code; these types of syntactic operators may not +conforms with the API documentation. necessarily correspond to property violations of the API method. + If we encounter an assertion failure from a property check during We would like to construct a mutant that performs a property- +the test, how do we know whether it is due to an unsound property level mutation on the API method. More formally, given a method +or due to a bug in the API implementation? Given an assertion under test 𝑓 , we would like to generate a mutant 𝑓 ′ such that +failure, we assume that the likelihood of the LLM generating an ∀𝑥 ∈ X : ¬𝑃 (𝑥, 𝑓 ′ (𝑥)). + Conference’17, July 2017, Washington, DC, USA Vasudev Vikram, Caroline Lemieux, Joshua Sunshine, and Rohan Padhye + + + Thus, we define a property mutant as a buggy version of the Table 1: Modules selected for Proptest-AI evaluation. Selected +API method that returns an output violating a specific property. A modules consist of native Python libraries (e.g. datetime +property mutant 𝑓 ′ of a method under test 𝑓 is defined as follows: and statistics) and third-party libraries (e.g. networkx + and numpy). The number of API methods selected from each + library as well as average token length of the API method + 𝑓 ′ (𝑥) = mut(𝑓 (𝑥)) documentation, using the OpenAI tokenizer. + +where mut is a mutation operation on 𝑓 (𝑥). The property mutant # API Documentation +contains the same signature as the API method, invokes the original Library + Methods Length (tokens) +API method on the input, and finally performs a mutation operation + dateutil 2 643.5 ± 155.5 +on the output to violate the property. Generating this mutation + html 2 81.5 ± 5.5 +operation requires semantic reasoning about how an output would zlib 3 312.7 ± 116.8 +violate a property. cryptography.fernet 3 458.7 ± 100.9 + LLMs have been used to perform bug injection and create pro- datetime 4 212.8 ± 83.2 +gram mutants [46, 47]. We design a specific prompt for the LLM decimal 5 122.2 ± 68.8 +to generate property mutants of a method under test for a given networkx 5 592.8 ± 439.6 +property. An example of a property mutant for numpy.cumsum is numpy 5 766.2 ± 242.4 +shown in Figure 7. This mutant can return an output that violates pandas 5 1197.8 ± 569.7 +the property that the output must be non-decreasing by reversing statistics 6 318.6 ± 149.5 +the order of the output. In order to kill this mutant, the PBT must Total 40 - +contain an assertion checking this property and contain logic to +generate inputs of length greater than 1. + To check whether a property mutant is killed, we create a modi- 4.1 Experimental Setup +fied version of the property-based test. This modified version substi- Models. We chose three state-of-the-art language models for our +tutes the call to the original API method with the call to the mutant evaluation: OpenAI’s GPT-4 [48], Anthropic’s Claude-3-Opus [28], +API method. Assuming the original property-based test is valid and and Google’s Gemini-1.5-Pro [27]. 1 +sound, we check whether there is an assertion failure on the output +of the mutant API method in the modified property-based test. API Methods. We selected API methods from 10 different Python + We define the property mutation score of a property-based test as libraries to generate property-based tests across a variety of tasks +the percentage of killed property mutants of a given API method. and input data types. Table 1 displays the libraries and the number +The process of generating property mutants and measuring prop- of selected API methods for each library. The libraries include native +erty mutation score is described as follows: Python libraries as well as popular third-party libraries such has + pandas and numpy. All selected API methods are deterministic, + (1) Prompt the LLM to extract a list of properties from the API as this is necessary for property-based testing. The API method + documentation. documentation was extracted from the online documentation for + (2) Prompt the LLM to generate a set of property mutants for each API method. In total, we selected 40 API methods. The full list + each property. of API methods and documentation is provided in the data artifact. + (3) If the property-based test is sound, execute the property- + Approaches. We evaluate two methods of prompting the LLM to + based test with a substituted call to the property mutant API + generate a property-based test shown in Figure 4. (1) A single-stage + method instead of the original API method. + method to generate a single test function and (2) a two-stage method + (4) Check whether the property assertions fail in the modified + to extract properties and generate a property-based test suite of + property-based test. If so, then the mutant is killed. + test functions. With three models and two prompting methods, we +Finally, a property is considered covered if the PBT is able to kill have a total of 6 approaches. +any of the corresponding property mutants. The overall property Samples. For each approach, we sample the LLM five times with +coverage of a PBT is the percent of properties for which the PBT is a temperature of 0.7. In total, we synthesized 1,200 samples across +able to kill property mutants. all API methods and approaches. Out of these samples, only 16 + either contained no Python or were syntactically invalid Python +4 EVALUATION code. +Based on our proposed evaluation methodology, we structure our + 4.2 RQ1: Validity and Soundness +evaluation around three research questions: +RQ1: Are LLMs able to synthesize valid and sound property-based High validity and soundness for property-based tests are important +tests of API methods when provided documentation? for ensuring that the test can run without errors (e.g., calling a +RQ2: Is the execution-based soundness metric for property assertions nonexistent API or missing an import for a library). For RQ1, we +aligned with human judgment of soundness? report the validity and soundness of Proptest-AI synthesized PBTs +RQ3: Are LLMs able to synthesize property-based tests that cover 1We initially included Codellama-34B in our models, but preliminary experiments +documented properties of API methods? showed that the validity of generated PBTs was too low to warramt further evaluation. + Can Large Language Models Write Good Property-Based Tests? Conference’17, July 2017, Washington, DC, USA + + +Table 2: Proptest-AI synthesized valid and sound test functions across all API methods. 41.74% of the test functions synthesized +using the two-stage prompting approach with GPT-4 achieve 100% validity and 100% soundness. + + Model Approach Total Test Functions Valid Test Functions Valid and Sound Test Functions + Single Stage 215 53 (24.65%) 16 (7.44%) + Claude-3-Opus + Two Stage 931 423 (45.43%) 289 (31.04%) + Single Stage 220 39 (17.72%) 25 (11.36%) + Gemini-1.5-Pro + Two Stage 799 209 (26.16%) 124 (15.51%) + Single Stage 212 97 (45.75%) 54 (25.47%) + GPT-4 + Two Stage 733 400 (54.57%) 306 (41.74%) + Total - 3,110 1,221 (39.26%) 814 (26.17%) + + +across all API methods, models, and approaches. To measure valid- Valid and Sound Test Functions +ity, we call each property-based test function 1,000 times and check by Library (GPT-4) + Approach +for non-assertion errors; for soundness, we check for assertion 80% Single Stage + Two Stage +errors. 70% + + + + + Percentage Valid and Sound + Table 2 shows the percent of valid and sound test functions across 60% +all API methods for the single-stage and two-stage approaches. We + + + Test Functions +find that the two-stage prompting achieves significantly higher 50% +validity than the single-stage generation for all models. This is likely 40% +due to the test functions in the suite being smaller and only testing 30% +one specific property, thus having a smaller chance of hallucination. +Similarly, the soundness of test functions synthesized using the 20% +two-stage prompting is much higher. 10% + Overall, GPT-4 achieves the highest validity and soundness for 0% +both single-stage and two-stage prompting. The two-stage ap- + y + + e + + til + + al + + l + + x + + y + + as + + s + zlib + htm + + + + + tic + ph + + + + + ork + + mp + im + + + + cim + teu + + + + + nd + + tis + gra + + tet + + + + + tw + + nu + + pa + da +proach with GPT-4 is able to synthesized a valid and sound test + de + + + + + sta + da + + + + + ne + pto + cry + + + + +function within 2.4 samples on average. Figure 8 shows the dis- + Library +tribution of valid and sound test functions from GPT-4 across our +10 different libraries. We observe the performance varying across + Figure 8: Distribution of valid and sound property-based test +libraries, with validity and soundness much higher on libraries such + functions for GPT-4 across all libraries. Certain libraries such +as datetime and zlib. + as networkx and pandas have a smaller percentage of valid + We additionally report average soundness over each test func- + and sound test functions than zlib. +tion as the percentage of 1,000 invocations that do not result in +any assertion errors. Figure 10 shows the this distribution over all +synthesized test functions. Although only 814 out of 1,221 valid Table 3: Human labels of individual property assertions in +test functions achieve 100% soundness (Table 2), this distribution LLM samples. +shows that the soundness of many of these tests functions close +to 100%. This suggests that the property assertions are correct for + Model Sound Unsound +most inputs and outputs, but may fail to capture potential edge +cases. Claude-3-Opus 64 23 + Gemini-1.5-Pro 23 5 + GPT-4 86 18 + The best Proptest-AI approach with two-stage prompting and Total 173 46 + GPT-4 is able to synthesize valid and sound property-based test + functions in 2.4 samples on average. + + selected, evenly distributed for each library. Raters read the docu- +4.3 RQ2: Soundness Metric Alignment mentation for the corresponding API method and labeled the first +Our soundness metric reported in RQ1 provides an execution-based five assertions as sound or unsound. +measurement for property assertions. However, it is possible that Table 3 displays the results of the labeling. We note that the +certain property assertions in the test are not executed due to cer- difference in the number of labeled assertions per model is due to +tain program paths taken during execution. To further validate the difference in validity and the number of property assertions +the soundness of individual property assertions, we performed a in each test. We find that out of 219 labeled assertions, 173 (79%) +manual labeling of a sample of synthesized property-based test were sound. The soundness of assertions from each model were +assertions. Out of all valid property-based test samples, half were all similar, ranging from 74–83%. To ensure the reliability of this + Conference’17, July 2017, Washington, DC, USA Vasudev Vikram, Caroline Lemieux, Joshua Sunshine, and Rohan Padhye + + +Table 4: Property coverage of each model and prompting 1 import ... +approach across all valid and sound LLM samples. Five prop- 2 +erty mutants were generated for each API, and mutants with 3 # Test for networkx.find_cycle + 4 @given(st.data()) +runtime errors were filtered out. + 5 def test_find_cycle(data): + 6 (...) # Generator logic for graph G + Property Mutation Total 7 # verify the properties + Model Approach 8 try: + Score Mutants + 9 cycle = nx.find_cycle(G) + Single Stage 58.02% 293 10 except nx.exception.NetworkXNoCycle: + Claude-3-Opus 11 # The graph doesn't have enough edges + Two Stage 59.69% 258 + 12 # to form a cycle + Single Stage 43.57% 140 13 assert nx.number_of_edges(G) < num_nodes + Gemini-1.5-Pro + Two Stage 62.70% 244 14 + 15 # Test for date.isocalendar + Single Stage 79.78% 89 + GPT-4 16 @given(y=st.integers(min_value=1, max_value=9999), + Two Stage 51.88% 480 17 m=st.integers(min_value=1, max_value=12), + 18 d=st.integers(min_value=1, max_value=31)) + 19 def test_date_isocalendar(y, m, d): + 20 try: +manual labeling process, we computed the inter-rater agreement be- 21 d = date(y, m, d) +tween two raters using Cohen’s kappa coefficient (𝜅). The resulting 22 iso_year, iso_week, iso_weekday = d.isocalendar() +𝜅 value of 0.862 ± 0.133 indicates a high level of agreement between 23 +the raters, suggesting that the labeling process was consistent. 24 assert iso_week >= 1 and iso_week <= 53 + 25 assert iso_weekday >= 1 and iso_weekday <= 7 + We use our property assertion labels to determine soundness 26 assert iso_year == y or \ +for each sample—if any assertions were unsound, the sample was 27 (iso_week == 1 and iso_year == y + 1) +labeled as unsound. We compared these labels to the labels resulting 28 except ValueError: +from our soundness metric and found that our metric has a precision 29 pass +of 100% and recall of 97.14%. There was only one false negative +determined from the soundness metric due to the sample containing Figure 9: Example snippets from GPT-4 synthesized un- +an unsound assertion that was not executed with an edge-case input sound property-based tests for networkx.find_cycle and +in the 1,000 invocations. datetime.date.isocalendar. The second property as- + When labeling property-based tests, we noticed a variety of sertion in test_find_cycle checks a general property of +soundness issues, ranging from hallucination of properties outside graphs that was not included in the API documentation that +of the API documentation to assertions only failing due to very may be unsound when the graph is directed. The last asser- +specific edge cases. The first test in Figure 9 is an example in which tion in test_date_isocalendar performs a comparison +a property assertion checks that when there is no cycle, the number to the Gregorian year, but does not account for the case in +of edges in a graph is less than the number of nodes. This property which the first week of the Gregorian year does not contain +is true for undirected graphs, but not for directed graphs, which a Thursday. +can be generated as inputs in this PBT. + Another general pattern we noticed was that the property as- +sertions held for most of the generated inputs, but did not account containing very simple assertions. Property coverage, described in +for certain edge cases. This explains why many test functions have Section 3.2.3, measures the ability of the property-based test to kill +soundness of above 80% in the distribution shown in Figure 10. An property mutants over all properties. This provides a measurement +example of this is the second test in Figure 9. From the API docs, a of the completeness of synthesized property-based test. Following +property of the ISO calendar is that the “first week of an ISO year is the steps detailed in Section 3.2.3, we prompt GPT-4 to extract +the first (Gregorian) calendar week of a year containing a Thursday.” five properties from the documentation for each API method and +This PBT does not account for the case in which the first week of generate 5 property mutants for each property. In total, there are +the Gregorian year does not contain a Thursday, which occurs for 200 properties we use to calculate overall property coverage. +a small percentage of generated inputs. We first measure property mutation score over all valid and sound + LLM. The tests must be sound to ensure that property mutants + Through manual labeling on a set of LLM samples, we find are only killed due to assertions checking the property mutant, + that our soundness metric is aligned with human judgment, rather than errors in the original test. We additionally filter any + achieving 100% precision and 97% recall. We observed that mutants that are killed due to validity errors to specifically measure + unsound assertions arose from hallucination of properties and the completeness of the property assertions. For each approach, + failures to handle edge cases. we report the property mutation score as the average percent of + property mutants killed over all samples. Table 4 shows property + mutation score for each approach as well as the total number of +4.4 RQ3: Property Coverage mutants that were executed. +RQ3 focuses on evaluating whether LLM-synthesized PBTs can Overall, we observe that the valid and sound samples are able to +detect property violations. Tests can be valid and sound while kill 40–80% of property mutants. These results vary across libraries, + Can Large Language Models Write Good Property-Based Tests? Conference’17, July 2017, Washington, DC, USA + + + Average soundness of test functions Table 5: Property coverage of LLM samples over all 40 API + methods. In total, there were 200 properties across all API + 100% + methods. If any of the five samples kills a property mutant, + 80% + Average Soundness + (1,000 executions) + + + the property is covered. + + 60% + Property + Model Approach + Coverage + 40% + Single Stage 9% + Claude-3-Opus + 20% Two Stage 13% + Single Stage + Two Stage Single Stage 5.5% + 0% Gemini-1.5-Pro + Two Stage 12% + Claude-3-Opus Gemini-1.5-Pro GPT-4 + Model GPT-4 + Single Stage 7% + Two Stage 20.50% + Figure 10: Violin plot displaying soundness distribution + of valid test functions, aggregated across all API methods + Table 5 shows the property coverage for each of our approaches. + (higher is better). Results for both single-stage and two-stage + The best approach of two-stage prompting with GPT-4 is success- + approaches are shown for each model. Overall, GPT-4 with + fully able to synthesize property-based tests that are valid, sound, + two-stage prompting achieves the highest average soundness + and cover 20.5% of properties. We believe this is a promising re- + of 87% over all valid test functions. + sult, as Proptest-AI is able to automate a significant portion of + the property-based testing writing process and cover extracted + Property Mutation Score of Samples docuemntation properties. + + 80% The two-stage prompting approach with GPT-4 is successfully + able to automatically synthesize PBTs covering 20.5% of docu- +Percent of Killed Mutants + + + + + mented properties. + 60% + + 5 THREATS TO VALIDITY + 40% + 5.1 Construct Validity + 20% Our measurements of validity and soundness are dependent on + the executions of the property-based tests, which contain logic for + random input generation. Additionally, due to the nondetermin- + 0% istic nature of LLMs, it is possible to get a range of samples that + y + + e + + s + + til + + al + + l + + zlib + + + x + + as + htm + tic + ph + + + + + ork + im + + + + + cim + teu + + + + + achieve varying degrees of performance. We aim to mitigate this + nd + tis + gra + + tet + + + + + tw + + pa + da + + de + sta + da + + + + + ne + pto + + + + + nondeterminism by sampling from each LLM five times and exe- + cry + + + + + Library cuting the property-based tests 1,000 times, which is the standard + for Hypothesis property-based tests. + Figure 11: Distribution of property mutation score over li- + braries across all valid and sound tests (higher is better). Gen- 5.2 Internal Validity + erally, the tests achieve higher property mutation score from One threat to internal validity comes from our execution-based + native Python libraries such as statistics and datetime. definition of soundness. It is possible that an assertion error results + Property mutants from networkx require stronger asser- from an actual bug rather than an unsound assertion. Our manual + tions to detect. labeling process independently evaluated the soundness of property + assertions, thus providing a stronger judgment. + Another threat to internal validity is the existence of equivalent + as shown in Figure 11. Samples achieve higher property cover- mutants, which is a well studied problem in mutation testing [49]. + age in native Python libraries such as datetime and decimal. Many equivalent mutants arise due to the mutation at the source + networkx requires stronger assertions that are more difficult to code level not propagating to the output of the program [50]. Our + synthesize due to the complexity of graph properties. formulation of property mutants applies the mutation directly to + We finally calculate the property coverage of all approaches on the output of the API method rather than the source code, which + the entire set of 40 Python APIs. With five samples of an LLM for mitigates this issue. However, in specific cases the output may + a synthesized PBT, how many properties can be covered? For a remain equivalent after the mutation operator. + property to be covered, the sample must be valid, sound, and kill at Finally, since we do not have access to the training set for any + least one property mutant. This measures the overall ability of the of the selected LLMs, we cannot confirm whether existing PBTs for + LLM to synthesize a PBT achieving all of our desired properties. our API methods are part of this set. However, we checked each + Conference’17, July 2017, Washington, DC, USA Vasudev Vikram, Caroline Lemieux, Joshua Sunshine, and Rohan Padhye + + +of our selected Python library repositories and did not find any assertions. However, the approaches have the potential to detect +Hypothesis PBTs for any of the selected API methods. bugs in the implementation being analyzed, unlike regression ora- + cles. As these tools use traditional NLP, the concerns of validity are +5.3 External Validity less severe than for hallucination-prone LLM-based techniques. + Specialized deep learning techniques have also been proposed +We selected Python as a target language since LLMs have tradition- + to generate oracles. ATLAS [63] trains a Neural Machine Trans- +ally performed well with Python and Hypothesis is an extensive + lation model on a dataset of (test case, oracle) pairs, and uses the +Python property-based testing library. We do not know of our + trained model to generate oracles on new test cases. The NMT +conclusions will generalize to other programming languages or + model predicts token sequences, avoiding some basic syntactic +property-based testing libraries since this will impact the ability of + validity problems. TOGA [64] avoids the problem of validity by +the LLM to generate valid code. Another threat to external validity + defining a grammar of possible assertions, and having the deep +is the selection of our evaluation targets of Python API methods. + learning model choose a production in this grammar. However, the +We synthesized and evaluated property-based tests for a variety of + problems of soundness and strength remain. +native and popular Python libraries for which API documentation + Unlike regular unit tests, which encode properties of a sin- +is readily available. Since these are established Python libraries, it + gle input, the PBTs we generate encode properties over arbitrary +is likely that the API documentation and source code exist in the + generator-generated inputs. The problem of effectively searching +training data of the LLMs. While we do not know of our conclusions + the input space, so that the PBT shows a bug, is orthogonal to our +will generalize to new libraries and APIs, prior work [51, 52] has + current work. LLM-synthesized generators could be paired with cov- +shown the effectiveness of providing documentation to LLMs to + erage guidance [6, 8], validity-biased guidance [65], reinforcement- +perform code generation for unknown APIs and languages. + learning guidance [66], or behavioral diversity guidance [67], to + produce more “interesting” test inputs. Fuzz4All [68] applies LLMs +6 RELATED WORK to guide and mutate input generation in fuzzing. +To the best of our knowledge, no work has yet attempted to use The problem of fuzz harness or fuzz driver generation bears sim- +LLMs to automate the creation of property-based tests. ilarity to our property generation problem [69, 70]. In fuzz driver + LLMs have been used to aid in various testing tasks, including: generation, the goal is to take unstructured byte data provided +generating tests cases for search-based unit test generation [16], by the fuzz tester, and use it to exercise the program under test +co-generating code and unit-tests in an interactive manner [17], and in a meaningful manner. The generated fuzz drivers resemble the +generating unit tests [18, 53–55]. TestPilot [18] uses fully automated “combined” PBT shown in Figure 3, which consumes random data +prompt refinement when generating unit tests. In particular, when and uses it directly to construct inputs to exercise the API. As fuzz +a test fails with an error, they enrich the prompt with various forms testing typically relies only on the crashing oracle (or on crashing +of information—including documentation snippets, the function oracles provided by instrumentation techniques such as ASAN), +signature, or the error encountered. these works do not engage with the question of soundness or prop- + In contrast, in TiCoder [17], the goal is to synthesize the im- erty coverage in the same manner we do. Nevertheless, the need for +plementation of a function from natural language. The system reasonable assertions emerges from a desire to reduce false positive +concretizes this natural language spec by generating possible unit bugs. The authors of UTopia [71], which extracts fuzz drivers from +tests for the function being synthesized, and asking the user to unit tests, note that some unit tests assertions (e.g., checking null +approve the correctness of suggested input/output pairs. pointers) must be preserved to maintain property validity. LLMs + Regardless of whether they use machine learning, automated also have been applied for the task of fuzz driver generation [20]. +unit test generation techniques face some of the challenges we OSS-Fuzz [22] has a workflow to prompt LLMs for automated fuzz +have outlined. Randoop [56] generates only regression assertions. driver generation. +Regression assertions simply capture the (possibly buggy) behavior Finally, retrieval augmented code generation is a technique in +of the program under test at test generation time, and so, their natural that aims to improve the performance of code generation +soundness with respect to the system specification is in question. models by incorporating external knowledge from a large corpus +The 𝜇Test [57] approach uses mutation testing to reduce the num- of source code and related documentation. DocPrompting [51] uses +ber of assertions, and has been adopted in test suite generation retrieval to fetch relevant documentation pieces for a given natural- +systems such as Evosuite [58] and Pynguin [59]. This addresses language-to-code task. ARKS [52] proposes active retrieval for code +the completeness of assertions, by keeping around only those asser- generation, which evolves a “knowledge soup” integration many +tions which can kill mutants. However, the problem of assertion different forms of knowledge to prompt the LLM. We believe these +soundness remains. strategies may provide methods of retrieving additional information + The field of oracle generation typically considers the problem that could be relevant to synthesizing property-based tests. +of generating an oracle (i.e., a set of property assertions) for a +given test case that lacks assertions. One idea is to extract these +from structured natural language information, such as JavaDoc 7 DATA AVAILABILITY +comments. From JavaDoc comments, TORADOCU [60] extracts We have included evaluation data in the anonymized repository +exception oracles; MeMO [61] extracts metamorphic relation ora- at: https://zenodo.org/doi/10.5281/zenodo.10967487. This data con- +cles; and CallMeMaybe [62] extracts temporal property oracles. Of tains all of the evaluation data for Proptest-AI, including synthe- +course, imprecision in the JavaDoc comments may lead to unsound sized property-based tests, property mutants, and measurements + Can Large Language Models Write Good Property-Based Tests? Conference’17, July 2017, Washington, DC, USA + + +for validity, soundness, and property coverage. The API method test-driven user-intent formalization,” arXiv, August 2022. [Online]. Avail- +documentation and prompt templates are also included. able: https://www.microsoft.com/en-us/research/publication/interactive-code- + generation-via-test-driven-user-intent-formalization/ + [18] M. Schäfer, S. Nadi, A. Eghbali, and F. Tip, “Adaptive test generation using a large + language model,” 2023. +8 CONCLUSION [19] M. Schäfer, S. Nadi, A. Eghbali, and F. Tip, “An empirical evaluation of using +In this paper, we explored and identified the unique challenges in large language models for automated unit test generation,” IEEE Transactions on + Software Engineering, 2023. +using LLMs to synthesizing property-based tests. We characterized [20] C. Zhang, M. Bai, Y. Zheng, Y. Li, X. Xie, Y. Li, W. Ma, L. Sun, and Y. Liu, “Un- +important properties of good property-based tests to propose an derstanding large language model based fuzz driver generation,” arXiv preprint + arXiv:2307.12469, 2023. +evaluation methodology that allows us to rigorously evaluate the [21] L. Huang, P. Zhao, H. Chen, and L. Ma, “Large language models based fuzzing +LLM outputs. These properties include validity, soundness, and techniques: A survey,” arXiv preprint arXiv:2402.00350, 2024. +coverage of properties in the documentation. [22] D. Liu, J. Metzman, and O. Chang, “Open Source Insights,” https://security. + googleblog.com/2023/08/ai-powered-fuzzing-breaking-bug-hunting.html, 2023, + In our evaluation on 40 Python API methods and three state retrieved February 27, 2024. +of the art language models, we find that our two-stage prompting [23] M. Shoeybi, M. Patwary, R. Puri, P. LeGresley, J. Casper, and B. Catanzaro, +approach with GPT-4 is able to produce valid and sound PBTs in 2.4 “Megatron-lm: Training multi-billion parameter language models using model + parallelism,” arXiv preprint arXiv:1909.08053, 2019. +samples on average. This approach can automatically synthesize [24] T. Brown, B. Mann, N. Ryder, M. Subbiah, J. D. Kaplan, P. Dhariwal, A. Neelakan- +PBTs that cover 21% of the documented properties. tan, P. Shyam, G. Sastry, A. Askell et al., “Language models are few-shot learners,” + Advances in neural information processing systems, vol. 33, pp. 1877–1901, 2020. + [25] A. Chowdhery, S. Narang, J. Devlin, M. Bosma, G. Mishra, A. 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Lahiri, “Toga: a neural method for + test oracle generation,” in Proceedings of the 44th International Conference on + \ No newline at end of file diff --git a/packages/opencode/specs/simulation-research/text/2024-pbt-in-practice.txt b/packages/opencode/specs/simulation-research/text/2024-pbt-in-practice.txt new file mode 100644 index 00000000000..9439baed07a --- /dev/null +++ b/packages/opencode/specs/simulation-research/text/2024-pbt-in-practice.txt @@ -0,0 +1,797 @@ + Property-Based Testing in Practice + Harrison Goldstein Joseph W. Cutler Daniel Dickstein + University of Pennsylvania University of Pennsylvania Jane Street + Philadelphia, PA, USA Philadelphia, PA, USA New York, NY, USA + hgo@seas.upenn.edu jwc@seas.upenn.edu ddickstein@janestreet.com + + Benjamin C. Pierce Andrew Head + University of Pennsylvania University of Pennsylvania + Philadelphia, PA, USA Philadelphia, PA, USA + bcpierce@seas.upenn.edu head@seas.upenn.edu + +ABSTRACT Python’s Hypothesis framework [37] had an estimated 500K users +Property-based testing (PBT) is a testing methodology where users in 2021 according to a JetBrains survey [32]. Still, there is plenty of +write executable formal specifications of software components and room for growth. Half a million Hypothesis users represent only 4% +an automated harness checks these specifications against many of the total Python user base, whereas the Hypothesis maintainers +automatically generated inputs. From its roots in the QuickCheck estimate [15] that the “addressable market” is at least 25%. (For +library in Haskell, PBT has made significant inroads in mainstream comparison, the most popular testing framework, pytest, has 50% +languages and industrial practice at companies such as Amazon, market share.) +Volvo, and Stripe. As PBT extends its reach, it is important to un- To help move PBT toward wider adoption, the research commu- +derstand how developers are using it in practice, where they see nity (ourselves included) needs to better understand the practical +its strengths and weaknesses, and what innovations are needed to strengths and weaknesses of PBT and the places where further +make it more effective. technical advances are required. Existing work in the software engi- + We address these questions using data from 30 in-depth inter- neering literature has studied how other bug-finding tools are used +views with experienced users of PBT at Jane Street, a financial tech- in practice (see §6), but PBT offers a unique set of tools and warrants +nology company making heavy and sophisticated use of PBT. These its own investigation. Accordingly, we interviewed PBT users at +interviews provide empirical evidence that PBT’s main strengths Jane Street, a financial technology firm that makes significant use +lie in testing complex code and in increasing confidence beyond of PBT, to learn how they use PBT, where they see its value, and in +what is available through conventional testing methodologies, and, what ways they think it might be improved. Concretely, we aimed +moreover, that most uses fall into a relatively small number of high- to answer two main questions: +leverage idioms. Its main weaknesses, on the other hand, lie in the RQ1: What are the characteristics of a successful and mature PBT +relative complexity of writing properties and random data genera- culture at a software company? +tors and in the difficulty of evaluating their effectiveness. From these RQ2: Are there opportunities for future work in the PBT space +observations, we identify a number of potentially high-impact areas that are motivated by the needs of real developers? +for future exploration, including performance improvements, dif- +ferential testing, additional high-leverage testing scenarios, better The first question aims both to offer guidance for engineers and +techniques for generating random input data, test-case reduction, managers considering whether PBT might fit well in their organi- +and methods for evaluating the effectiveness of tests. zations and to provide a basis for evaluating and comparing PBT + technologies. The second question aims to help shape further re- +1 INTRODUCTION search to maximize the impact of PBT. + Our findings contribute a wide range of observations about de- +Property-based testing (PBT) is a powerful tool for evaluating soft- + velopers’ experiences with PBT, adding nuance to the research +ware correctness. The process of PBT starts with a developer decid- + community’s understanding of PBT’s real-world usage. Through +ing on a formal specification that they want their code to satisfy + our interviews, we gleaned several new insights about the situa- +and encoding that specification as an executable property. An au- + tions in which property-based tests are deployed in practice. We +tomated test harness checks the property against their code using + found that developers use PBT mainly for testing components of +hundreds or thousands of random inputs, produced by a generator. + complex systems, expecting the tests to provide greater confidence +If this process discovers a counterexample to the property—an input + than conventional example-based unit tests yet still run quickly as +value that causes it to fail—the developer is notified. + part of their normal test suite. Interestingly, we also found that de- + The research literature is full of accounts of PBT successes, e.g., + velopers leverage PBT for the secondary benefit of communicating +in telecommunications software [2], replicated file [31] and key- + specifications: properties serve as a form of persistent documen- +value [8] stores, automotive software [3], and other complex sys- + tation, demonstrating the semantics of the software to readers—a +tems [30]. PBT libraries are available in most major programming + benefit less commonly discussed in the literature. Finally, we found +languages, and some now have significant user communities—e.g., + that at Jane Street, PBT is primarily used in “high-leverage” sce- +ICSE 2024, April 2024, Lisbon, Portugal narios, where properties are especially easy to identify and test. +2024. Beyond deepening our understanding of when and why developers + ICSE 2024, April 2024, Lisbon, Portugal Harrison Goldstein, Joseph W. Cutler, Daniel Dickstein, Benjamin C. Pierce, and Andrew Head + + +reach for PBT, we also found that PBT technology can be improved trees will be discarded, wasting precious generation time. A better +in several ways to better support developers. In particular, study strategy is to hand-craft a generator that only produces valid BSTs, +participants reported struggling to generate distributions of test but such generators can be nontrivial to write. +examples that they were convinced effectively exercised the prop- If the property ever fails during testing, the failing value is pre- +erty, and sometimes viewed the process of designing random data sented to the user. This value might be overly complex, with parts +generators as a distraction. They also lamented the lack of visible that are irrelevant to the failure of the property, so most PBT frame- +feedback on the effectiveness of their testing. works provide tools for test-case reduction [36], usually called + From these findings, we extract a list of opportunities for future shrinking [29] in the PBT literature. +research, including understanding the nuances of PBT performance The BST example above uses OCaml’s QuickCheck library, but +requirements, exploring better support for differential testing, and the general approach—a module under test, a concise property, a +expanding the high-leverage scenarios in which PBT is most effec- data generator, and a shrinker—is shared by all PBT tools, from +tive. We also highlight opportunities around improving languages the original Haskell QuickCheck [11] to Python’s Hypothesis li- +for random data generators, designing interfaces for test-case reduc- brary [37] and beyond. The power of PBT comes from the ability +tion (“shrinking”), evaluating testing success, and using developer to test a huge number of system inputs with a single specification +feedback to improve the testing process. and generator, often uncovering edge and corner cases that the + We begin with background on PBT (§2), then present our study developer might not have considered. It thus hits a useful midpoint +methodology and discuss of potential threats to validity (§3). We between example-based unit tests and heavier-weight formal meth- +present the study’s main results (§4) and detail lessons learned in ods, retaining the precision of traditional formal specifications and +the form of observations (§5.1) and research opportunities (§5.2) their ability to characterize a system’s behavior on all possible in- +before discussing related work (§6) and concluding (§7). puts, but offering quick, best-effort validation instead of requiring + developers to write formal proofs. +2 BACKGROUND Of course, PBT is only one among many testing methodologies. +Properties are executable specifications of programs. For example, Two primary alternatives are especially relevant to our study. +suppose a developer is working on a new implementation of binary Example-based unit testing [13] (as supported by pytest, JUnit, +search trees (BSTs)—tree structures where each internal node is and other frameworks) evaluates a program by testing it on indi- +labeled with a data value that is greater than any labels in its left vidual example inputs. For each input, the developer writes down a +subtree and less than any in its right subtree. They know that all the short snippet of code that checks that the program’s output is cor- +operations on BSTs (insert, delete, etc.) must preserve this validity rect for this input. (We call this style “example-based unit testing” +condition: given a valid BST, they should always produce a valid BST. throughout the paper, rather than just “unit testing,” because PBT +To enforce this condition, they might write the following test for is also typically used to test individual units within larger systems.) +the insert function using OCaml’s Core QuickCheck library [19]: Fuzz testing, invented by Miller [4, 39] and popularized by tools + let test_insert_maintains_bst () = like AFL [56], also aims to find bugs by randomly generating pro- + QuickCheck . test gram inputs. The technical foundations of fuzz testing and PBT + ( both int_gen ( filter valid_bst tree_gen )) overlap to a large (and increasing [34, 53]!) degree, but existing tools + ( fun (x , t ) -> valid_bst ( insert t x )) from the two communities tend to be tuned for different situations: + fuzz testing is typically used in integration testing of complete sys- +The second argument to QuickCheck.test (on the last line) is the tems, to detect catastrophic bugs like crash failures and memory +property: It says, given an integer x and a BST t, that insert t x unsafety, while PBT is used to flush out logical errors in smaller +should return a BST. The first argument to QuickCheck.test is a software modules. +random data generator, which here generates a pair of both an int +and an arbitrary BST (obtained by generating an arbitrary binary + 3 METHODOLOGY +tree using tree_gen and using filter to discard trees that are not +valid BSTs). QuickCheck.test randomly generates hundreds or To address the research questions described in §1, we conducted an +thousands of pairs (x, t) and invoke the property to check each interview study of developers who use PBT in their work. This study +pair. If this check ever fails, we have discovered a bug in insert. was conducted in accordance with the ACM SIGSOFT Empirical + Generators like tree_gen are usually written using an embedded Standards for qualitative surveys. +domain specific language (eDSL) provided by the PBT framework, +which includes base generators like int_gen and combinators like 3.1 Population +both that can be used to create generators for complex data types As the setting for our study, we chose Jane Street, a financial tech- +from generators for their parts. The generator language is embedded nology firm that uses PBT extensively. We recruited 31 participants +in OCaml (in this case), giving generator writers access to the full and carried out 30 interviews (one was a joint interview). Partici- +power of the host language. Generators can require some careful pants were recruited by a Jane Street developer who volunteered +tuning to find bugs effectively. This is often because properties have to coordinate the study: they found instances of PBT in the source +preconditions that define what it means for an input to be valid. For tree and contacted the authors of those libraries; announced the +example, “filter valid_bst tree_gen” is a correct generator of study on an internal blog; and carried out snowball sampling by +BSTs: it simply discards trees until tree_gen happens to generate asking participants for others we should talk to. All participants +a valid BST. However, this means that the majority of the generated had some experience with PBT, and most self-reported as having + Property-Based Testing in Practice ICSE 2024, April 2024, Lisbon, Portugal + + +Table 1: Participant backgrounds. Columns 3–5 reflect op- Jane Street’s overall financial operations are supported by a di- +tional questions; participants that didn’t respond to these verse set of software engineering efforts. We spoke to developers +are listed at the bottom. ★Measured in years. ★★Stated com- working on core data structures, distributed systems, compilers, +fort with PBT on a Likert scale: 7 most comfortable, 1 least. graphical interfaces, statistical computation, and even custom hard- +† Participant indicated skepticism of PBT. ‡ Pair interview; + ware. Study participants spanned fifteen teams in four main areas: +coded as one participant. (At Jane Street’s request, we do not Trading (2/30, across 2 teams), working directly with traders to +associate individuals with their teams or company divisions.) develop technology specific to individual trading desks; Trading + Infrastructure (13/30, across 5 teams), building platforms to sup- + ID Role SE Exp.★ PBT Exp.★ Comfort★★ port Jane Street’s trading; Quantitative Research (5/30, across 2 + 1 Tester 12 3 (6) teams), writing software to enable research on trading algorithms; + 3 Maint. 22 17 (7) and Developer Infrastructure (11/30, across 6 teams), designing + 4 Maint. 15 16 (6) tools and languages upon which Jane Street’s applications are built. + 5 Tester 5 7 (6) Jane Street developers primarily work in OCaml, a programming + 6 Tester 16 16 (7) language with strong typing, good mechanisms for modularity, + 9 Tester 4 4 (5) and a focus on performance. OCaml is thought of as a functional + 11 Maint. 10 7 (6) language, but it has strong support for imperative programming as + 14 Tester 8 7 (5) well. + 15 Tester 2 2 (6) + 16 Tester 8 8 (3) 3.2 Protocol + 18 Tester 1 1 (5) We conducted a semi-structured one-hour interview with each + 20† Tester 5 2 (5) participant; Goldstein and Cutler led the interviews. For testers, the + 23 Tester 6 6 (5) prompts were: + 25‡ Testers 26 20 (5) (1) Tell us about a noteworthy time that you applied PBT. + 26 Tester 2 2 (6) (a) What kinds of properties did you test? + 28 Tester 7 1 (5) (b) How did you generate test inputs? + 29 Tester 4 5 (6) (c) How did you evaluate the effectiveness of your testing? + Other Testers: 2, 7, 8, 10, 12, 13, 17, 19† , 21, 22, 24, 27, 30 (d) What did you do to shrink your failing inputs? + (2) Which parts of the PBT process are the most difficult? + (3) What role does PBT play in your development workflow? +positive experiences. We also explicitly asked for participants who (4) To whom would you recommend PBT? +reported neutral or negative feelings about PBT, but they were (5) In what contexts is PBT most useful? +difficult to find: most felt they did not have enough experience to (6) Is there anything that would make PBT more useful to you? +speak to those feelings. Two self-described PBT-critical developers +participated in the study. More details about the study participants The script was designed to attain depth by encouraging reflection +can be found in Table 1. on real, memorable experiences with PBT. It evolved somewhat + Most of those we interviewed were testers (26/30), who use PBT over the course of the study, allowing us to validate interesting or +tools in their day-to-day work, but we also spoke to several main- unexpected observations from earlier interviews. +tainers (4/30) who play a role in building and maintaining Jane A separate script was used with maintainers: +Street’s PBT infrastructure. These two groups were given different (1) Have you seen the type of adoption that you want from your +prompts (see below), reflecting our expectation that the maintain- PBT tools? +ers would be able to offer a more “global” perspective, but their (2) How can QuickCheck be improved? +responses were coded uniformly since they address the same re- (3) What do you think it would take to get everyone at Jane +search questions. Street using PBT? Would that be a good thing? + Participants who answered an optional background question- (4) What do you hope we’ll learn from this study? +naire had between 1 and 26 years of professional Software Engineer- Time permitting, we also asked maintainers about their use of PBT. +ing experience (median 7) and between 1 and 20 years using PBT We did not explicitly interview until saturation; we simply tried +(median 6). This wide range of experience (for PBT, almost as wide to recruit a reasonably sized group that was representative of PBT +as possible, since the first paper on PBT is only 23 years old! [11]) users at the company. However, as we neared the end of the study +also means we heard from developers at many different points in we felt we were no longer learning about new aspects or perspec- +their careers and with differing levels of software development tives on PBT, and we saw convergence on many of our findings (as +experience. When asked to rate their comfort with PBT on a Likert evidenced by the numbers we report in §4). Thus, we do not expect +scale, these participants were overall quite comfortable with PBT there are significant holes in our results. +(median 6 out of 7): all but one were at least “somewhat comfortable” Once the interviews were complete, they were transcribed using +(5 out of 7). Working with developers who are already relatively an automated transcription service [42] and analyzed to extract im- +fluent users of PBT allowed us to benefit from their well-informed portant themes following a thematic analysis process [7]. Goldstein +ideas about how to make PBT better, as well as their frustrations and Cutler carried out an open coding pass (reading through the +and challenges. transcripts and assigning thematic codes as they went). The codes + ICSE 2024, April 2024, Lisbon, Portugal Harrison Goldstein, Joseph W. Cutler, Daniel Dickstein, Benjamin C. Pierce, and Andrew Head + + +we chose focused on participant goals, benefits of PBT, challenges 50,000 places across the code base” to establish reliable behavioral +encountered, and opportunities for improvement. Once the set of contracts for library consumers (P13). Another participant used +codes stabilized, they were validated by a third co-author, then clar- PBT to check software that interacted with information they were +ified by the whole team to obtain a final set of clean codes. Finally, “sending to the [stock] exchange” (P25), which, should it contain +one co-author performed an axial coding pass (reading through errors, could incur serious financial costs. An advantage of PBT +the transcripts and codes again to make connections and ensure in these cases was its ability to explore edge cases (mentioned by +consistency) with the updated codebook. Our codebook is available 10/30) since, in the words of one participant, “the bugs are always +online1 . going to happen in cases you didn’t think of” (P21). + For many participants, PBT served to increase confidence that +3.3 Threats to Validity their software was robust. They described code tested with PBT as +While our study covered a wide variety of software teams and tasks, “solid” (P6, P28), and some (9/30) explicitly mentioned that PBT in- +it should be noted that participants mostly described using a single creased their “confidence” that the code was correct. One described +PBT toolset, in a single language and software development ecosys- using PBT when they “wanted peace of mind” (P11). Confidence +tem. Our findings may under-represent the usage patterns and was accompanied by material evidence of success: a third of partic- +challenges experienced by those working with other PBT toolsets ipants (10/30) said their property-based tests found bugs that they +in other languages. To help us develop findings that generalize had not found via other methods. +beyond the Jane Street toolset, we designed our interview protocol A less obvious benefit of PBT was its ability to help participants +to focus considerable attention on the conceptual and methodolog- better understand their work. One participant described properties +ical aspects of PBT, rather than on details of OCaml’s QuickCheck as tools that “force [the developer] to think clearly” (P30) about +implementation or specifics of how it is used at Jane Street. (In the their code, and another pointed out that sometimes properties fail +cases where we make observations that are toolset-specific, e.g., because the specification (rather than the code) is wrong (P10). +where we know tools outside of OCaml address some of the prob- In such cases, failing tests can highlight gaps in the developer’s +lems we observed, we state this explicitly.) In addition, participants understanding of the problem space that could lead to issues later. +were mostly experienced developers who were comfortable with Outside of the testing loop, properties were useful for docu- +PBT. This means that our study under-reports the experiences of mentation and communication (12/30). One participant noted that +novice developers. Finally, as discussed above, we did not measure properties “are part of the interface and part of the documentation” +saturation as interviews progressed, so there is a chance that more (P3) and emphasized that, unlike other documentation, properties +interviews may still have uncovered new insights. never fall out of date: whereas a textual description in a comment + Another threat comes from the inherent limitations of inter- might drift from the code’s actual behavior, a property is repeatedly +view studies. For one thing, participants may not always accurately re-checked as the code changes. Many also talked about the value +recall the particulars of their experiences with tools. We did our of PBT in the code review process (18/30) as a compact way to +best to mitigate this threat by asking developers to tell us about express what a particular program does. One remarked: “I feel like +specific experiences—a standard technique for studies like ours. [PBT] is very nice for review. . . I really dread seeing 10,000 lines of +Additionally, our own biases as interviewers may naturally have tests where you just need to spend hours to read code and under- +skewed the results; Goldstein and Cutler, who carried out the inter- stand what’s going on. . . And I think, if there is a QuickCheck test +views, and Pierce and Head, who also participated with additional and you look at the property that’s been tested, which is usually +questions, are all property-based testing researchers who have a much shorter. . . it gives you much more confidence that the code is +vested interest in the outcome of the study. Outcomes that show correct.” (P19) +PBT in a positive light may have unintentionally been highlighted, The benefits of PBT were such that even those who were critical +and criticisms that we have addressed in our prior work may have of it found it to be beneficial in some situations. During the recruit- +received extra attention. ing process we tried to explicitly recruit participants who said they + did not like PBT; we found two (P19 and P20), but the criticism +4 RESULTS in their interviews turned out to be constructive suggestions that +We now present our findings. We start by describing the benefits were echoed by PBT’s proponents as well, and both primarily spoke +that PBT delivered to developers and how it fit with the other testing about situations where PBT was valuable. +approaches they used. Then we describe in detail their experiences Moreover, some participants who liked PBT really liked it: one +writing specifications, designing generators, debugging, and evalu- said that they “use QuickCheck for everything” (P13) and another +ating testing success, focusing both on challenges they experienced asserted that “everyone should be aware of it” (P27). Yet another +and on opportunities for improving PBT tools and workflows. participant argued that “[PBT] is so useful that it’s worth trying + to reorganize your code into the form that it is applicable. PBT is +4.1 Benefits of PBT so helpful that if you can reinvent things that way, you should.” + (P10) Several participants (8/30) also talked about evangelizing PBT, +As might be expected, the primary reason participants used PBT was + encouraging others to use it and increasing its adoption across the +to assess whether their code was correct. Participants often used + organization. +PBT to validate widely used or mission-critical code. For example, + We found that this sort of evangelism benefited all parties: PBT +one participant described using PBT for code that was “used in + becomes more useful as more people on a team or in an organization +1 https://doi.org/10.5281/zenodo.10407686 use it. A culture of supporting PBT can save work: P24 and P27 + Property-Based Testing in Practice ICSE 2024, April 2024, Lisbon, Portugal + + +both noted that PBT would be easier to use if more developers in Expect tests and PBT were both used to test individual software +the organization provided generators for the types exported by units during development. PBT was almost always described as +their modules, making it much easier to test code in other modules running in Jane Street’s build system, and many developers actu- +that uses those types. In addition, treating property-based tests as ally test their properties “locally after each edit” (P2) Participants +documentation, as many (12/30) did, requires that others in the described strict time budgets for PBT—no more than “30 seconds” +organization can read and understand such documentation. (P27) and as low as “50 milliseconds” (P11)—to ensure it would not + slow down the build. These time budgets serve to keep PBT from + triggering the 1-minute-per-library timeout that many Jane Street + developers set for their unit test suite (P7). +4.2 Comparisons to Other Testing Approaches Alongside these fast-turnaround unit testing tools, developers +The most common approach to testing at Jane Street is not PBT, also used fuzzing tools like AFL [56] and AFL++ [20] for integration +but rather an example-based unit testing framework called “expect testing. A third of participants (10/30) mentioned fuzzing, and a few +tests” [40]. Expect tests are basically conventional example-based (3/30) described using AFL alongside PBT as part of their testing +unit tests with editor integration that helps developers create unit process. In contrast to the strict timeouts set for expect and property- +tests from the outputs that the system produces. With expect tests, based tests, one participant described a fuzzer that was forgotten +developers add code to the system under test that that logs in- and left running for a year and a half on a spare server (P9). Others +teresting data to the standard output channel; the expect testing did not run fuzzing this long, but still considered it to be running +framework then checks that the output matches the output string “out of band” (P28), outside of the normal continuous integration +that was captured from the previous run of the system—it is up and at time scales on the order of hours or days. The upshot is that +to the developer to decide which output is intended. Expect tests fuzzing tools are given much longer to run than PBT tools. +are integrated into Jane Street’s editor workflow, and they are used +pervasively in much the same way as frameworks like pytest and +JUnit are used in other languages. Thus, we can use comparisons 4.3 Writing Specifications +with expect tests as a proxy for comparisons with example-based The previous sections have dealt with PBT at a high level; we now +tests in general where the specifics of expect tests are not relevant. begin a deeper dive into the specifics of the PBT process and how + From a legibility perspective, PBT was sometimes seen as better, developers described actually using PBT tools. The first step in this +sometimes worse than expect tests. Expect tests were described as process is defining one or more properties to test. While participants +more transparent and “often easier to understand” (P5). P18 said did describe struggling with this stage, many ultimately developed +“expect tests. . . explain what they’re doing to a better degree. And powerful strategies for finding properties. +it’s easier for someone to come in and review my test,” and P27 Many participants (16/30) said the process of writing specifica- +made a similar point. But expect tests can sometimes go past from tions slowed their progress. P4 summed it up like this: “I think the +“transparent” to just verbose. P17 complained that reading a whole most common failure mode is actually not knowing what properties +output string was onerous, and another participant complained to test.” Challenges ranged from systems that seemed not to have +“[with expect tests] it’s easy to get into a mode where you just like properties at all—P1 talked about “a server that serves queries. . . and +write a test, and you just print out a bunch of crap. And then it’s has some. . . nuanced behavior” that is not compatible with “logical +really annoying to like code review that test because there’s just properties”—to systems whose properties were hard to articulate +too much stuff” (P7). Properties are more concise. in the form of QuickCheck tests: “With [example-based unit tests], + PBT and expect tests also present different strengths and weak- I kind of look at it, I can just make a snap judgment as to whether +nesses when it comes to test writing. One participant said that this is okay or not. Trying to formalize that judgment sometimes +writing an individual expect test is “way easier than writing invari- can be very difficult.” (P2) +ants,” but they highlighted that at the scale of a whole test suite Challenges in articulating properties can come from the way code +they “love not writing specific unit tests cases” (P13). is written. P7 explained that mutable state (e.g., a hidden variable + Ultimately there was no universal preference for properties or that may change between calls to the same function) gets in the way +expect tests—both should be available in a developer’s toolkit. We of writing properties: “there’s. . . this hidden state component. . . that +might infer from participant responses that when code is simple kind of makes it harder for me to think about what are the right +enough and examples communicate its behavior well enough, ex- laws.” P22 also pointed out that “integrating the outside world +pect tests are an attractively lightweight option. In cases where and. . . dealing with the interaction of very large and complicated +the code is particularly difficult to get right or where writing out systems” makes it less clear how to “meaningfully test with PBT.” +enough examples becomes tedious, it seems PBT may be a better (These findings are not surprising. It is well known that code that +choice. interacts with its environment is also a challenge for testing in + One area where properties seem to be at a clear advantage over general, not just PBT: stateful code uses mutable data structures +expect tests is in the confidence they provide developers. P25 re- such as hash tables, which might introduce differences between +marked of Jane Street developers that “[they] go to randomized runs of the same test if the state is not reset properly; and effectful +testing when [they’re] not so confident of what [they’ve] done.” code might rely on external files, databases, or networks, which +As discussed above, around a third of participants talked directly may not be safe to access over and over during testing.) +about PBT building confidence, and the same proportion reported Despite these difficulties, the developers we spoke to were gener- +PBT finding bugs that had not been found with other methods. ally enthusiastic about PBT. One might therefore wonder: Did they + ICSE 2024, April 2024, Lisbon, Portugal Harrison Goldstein, Joseph W. Cutler, Daniel Dickstein, Benjamin C. Pierce, and Andrew Head + + +simply forge ahead regardless, or did they have specific techniques 4.4 Generating Test Data +for circumventing the difficulties of writing specifications? Participants had several goals for generating inputs. First and fore- + What we found was that developers often succeeded in apply- most, many participants (17/30) talked about needing to generate +ing PBT by being opportunistic in their choice of when to apply values that satisfy some precondition. This can be extremely impor- +it. Rather than try to apply PBT to every program at all times, tant for effective testing: if too few of the generated values satisfy +participants looked for situations where it offered high leverage: the property’s precondition, then testing will fail to exercise the +more confidence for less work. Some participants described this in code in interesting ways; in the worst case, it may even report false +general terms as “go[ing] for the low hanging fruit” (P2) or finding positives. A few of the preconditions mentioned by participants +places where “the properties are sort of obvious” (P28), but many are easy to satisfy randomly—for example non-empty strings or +enumerated specific situations where they would reach for PBT. lists—but most are quite hard to satisfy: valid postal addresses, well- + Classical Properties (11/30). Certain forms of properties are fa- structured XML documents, red-black trees, and syntactically valid +miliar from the PBT literature and from library documentation for S-expressions are extremely unlikely to be generated by a naïve ran- +PBT frameworks. These include mathematical properties (e.g., the dom generator. Participants also described test data requirements +commutativity of addition), properties drawn from CS theory (e.g., going beyond precondition validity. Some (5/30) said they wanted +repeated sorting has no effect), and properties that naturally fall their test data to be “realistic”—i.e., similar to the distributions of +out of a data structure’s invariants (e.g., the ordering condition of a data the application was likely to see in the real world. Others de- +BST). These properties may be more accessible because they are scribed heuristics for the distribution of the input data, for example +naturally top-of-mind. generating lists or trees of a “reasonable size” (P9). + Round-Trip Properties (11/30) are also common in the literature; Participants described a few different ways that they generated +we heard about them so much more often than the other classical inputs. Most talked about either handwritten random generators +cases that they seem worth calling out on their own. These proper- (19/30), which are the default approach in libraries like QuickCheck, +ties check that a pair of functions are inverses of one another—for or derived generators (19/30), which are inferred based on the types +example, parsing and pretty-printing or encoding and decoding of the data to be generated (e.g., the type int list implies a generic +functions. This situation is easy to notice and easy to test since the generator for lists of integers). +properties are incredibly succinct (you call one function, then its The need for handwritten generators seemed to be a source of +inverse, and then check that the final result matches the original friction for many participants. P6 said that writing generators for +input), so round-trip properties are a popular choice. data that satisfies property preconditions is “the biggest annoyance + Catastrophic Failure Properties (7/30). Rather than write logical with trying to use QuickCheck” and many participants thought +specifications, some participants used PBT to try to provoke cata- of writing generators as “tedious” (6/30) or “high-effort” (7/30). P2 +strophic failures such as assertion failures and uncaught exceptions. described the task of writing generators as intruding into their de- +In general, these kinds of properties provide less confidence in code velopment process and contributing to a general perception of PBT +quality (there can still be logical errors, even if the code does not as “high cost and low value.” Since PBT was usually described as an +crash), but they help to rule out worst-case scenarios and they are integral part of the development process, rather than as a separate +easy to write. (These kinds of specifications are identical to the ones quality-assurance task, it makes sense that requiring detours into a +often used for fuzzing; the line between the techniques is blurry, lengthy generator design process might make PBT less desirable. +but since the participants were using PBT tools—including complex Besides requiring significant effort to use, available tools for writ- +generators—and testing small units of software, we still consider ing generators by hand do not easily enable developers to produce +this relevant for our purposes.) precondition-satisfying values that are also well distributed in the + Differential Properties (17/30). A “differential property” (in sense way they would like. Writing a precondition-satisfying generator +of differential testing [25]) compares the system under test to a on its own can be a large task—whole papers have been written +reference implementation of the same functionality that serves as about generators for a single complex data type [43]—and account- +a specification; these are often also called model-based properties ing for distributional considerations adds even more friction. P13 +(c.f. model-based testing [54]), especially when the reference imple- said, “there’s a tension in. . . all these handwritten generators be- +mentation is designed to be an abstract model of the original code. tween ‘I want kind of coverage of everything’ and ‘I want coverage +Differential properties were by far the most widely implemented that is realistic for most inputs.’” As a solution, P13 suggested that +kind of property. Differential properties were described as a “natural one might be able to carefully combine two different handwritten +place to use property based testing” (P3)—indeed, one participant generators to achieve these competing goals, but thought “that way +remarked that PBT was challenging in a particular situation in part lies madness”. Other participants had an idea of the kinds of values +because a good reference implementation was not available (P1). they wanted to generate more or less frequently, but they were + The common theme of the high-leverage scenarios described not sure how to get there: “What should [the probabilities in my +above is the availability of a succinct abstraction that can be used generator] look like?. . . I’m sure if I studied probability and statis- +in writing a property. These PBT scenarios were summed up by tics and fully understood how the QuickCheck generating system +P9 with the following mantra: “[PBT is] most useful when. . . you worked, I could give better guesses. But all my guesses. . . they’re +have a really good abstraction with a complicated implementation.” not educated guesses. They’re just random. . . And that’s a little bit +We discuss how these high-leverage scenarios should be taken into of a mental strain.” (P20) +account to accelerate research in PBT in §5. + Property-Based Testing in Practice ICSE 2024, April 2024, Lisbon, Portugal + + + In Jane Street’s ecosystem, derived generators are enabled via intermediate values that were found during shrinking. P1 said “the +the ppx_quickcheck library, which provides a preprocessor that shrinker gets it right. . . but [it’s] still useful to see the evolution.” +runs before the compiler and synthesizes generator code from type +information. Ideally, this approach is totally automatic, providing a +generator without any additional user input, and it was described 4.6 Understanding Success +fondly by participants. Many included it in their workflows (19/30), Property-based testing not only requires a developer to understand +and one called it “f***ing amazing” (P5). P13 went so far as to suggest test failures; it also requires developers to understand whether +that “you shouldn’t really be handwriting generators, you should passing a test actually means the software is correct. If the inputs +be changing the structure of your type [to improve generation].” provided by the test harness fail to adequately exercise buggy code, +(For example, if a function being tested takes an int flag but the a property-based test may pass misleadingly. One participant de- +only valid values are 0, 1, and 2, then replacing int with an appro- scribed this situation, recalling a bug in published code that their +priate enumerated type causes ppx_quickcheck to derive a better property-based tests failed to catch because the generator was “not +generator.) Others (7/30) leveraged a combination of derived and generating the case that [they] had in mind” (P19). P14 worried +handwritten generators, using derived generators as a foundation they could not trust their generators because they had “no idea +on which to build more complex generator programs. what it’s generating.” (P14) + For both handwritten and derived generators, Jane Street devel- But, while participants understood that, in principle, tests could +opers recognized opportunities for tool improvements. P4 described pass erroneously, 11 of them—more than a third—said they did not +the process of hand-writing a generator for a mutable data structure think as hard as they should about testing effectiveness, or whether +as “overwhelming,” and P6 suggested that libraries could do a better they had adequately tested their software with their generators. +job supporting that use case. As for improving PPX-derived genera- Some (3 of the 11) reported seeing their property catch a couple +tors, P26 wanted better support for generating values of generalized of bugs and deciding that they did not have to improve their prop- +algebraic data types (GADTs), special types in OCaml and some erties any further; the rest trusted that the generators provided +other languages that can express fine-grained properties of data. by OCaml’s QuickCheck library or the ones they derived or wrote + themselves would be good enough. While this group is a minority + of our sample, even a signal of this size is striking: PBT tools such +4.5 Understanding Failure as derived generators should make it easy for developers to get +Debugging is often tricky, but participants described ways that started; they should not (but evidently sometimes do) discourage +tracking down bugs detected by PBT can be especially so. One developers from being critical of their test suite. +participant described their debugging process: after finding a large, On the other hand, several participants described techniques for +unwieldy counter-example with PBT, “you have to pull that failure validating their PBT tests: +into a separate sort of regression test. . . which runs the same infras- Mutation Testing (7/30). Some participants intentionally added +tructure but does it with much more detail. . . Having done that, it bugs to their code and checked that their tests successfully found +is still sometimes unclear—like what about this example actually those bugs. This technique is standard in the testing literature [44, +causes us to fail?” (P1) This is an instance of a broader problem: 47] and used in testing benchmarks such as Magma [27] and Etna [50]. +random test generators often produce failing examples that are Example Inspection (8/30). An even simpler way to assess a gen- +too large to make sense of during debugging. To help developers erator’s distribution is to look at a handful of examples that the +understand failing examples, PBT frameworks offer shrinkers that generator produces; one participant (P26) even designed a small +transform large inputs into smaller inputs that (presumably) intro- utility to graphically render one example at a time, to make them +duce the same bug. One participant in our study deemed shrinking easier to understand at a glance. +“necessary” (P15), and two who implemented their own ad-hoc PBT Code Coverage (2/30). Participants evaluated the code coverage +frameworks (P8 and P21) insisted that shrinking was one of the achieved by their tests and used code coverage measurements as +most important features they implemented. an indication that their properties were thoroughly exploring the + That said, participants found it difficult to use the shrinking space of program behaviors. +functionality in QuickCheck, which resembles shrinking in many Property Coverage (1/30). Another participant measured coverage +PBT frameworks. In such frameworks, shrinking is achieved by not of the system under test, but of the property itself. This is a +having users manually write functions that incrementally reduce a weaker measurement, since it does not say anything about the +large value (e.g., a string, list, or other more complex data structure) system under test, but it is much easier to make because it can be +to a smaller one that triggers the same failure. Participants saw measured without complex tooling. +writing shrinkers as an undesirable activity: one plainly stated, “I A couple of participants (2/30) compensated for gaps in their +hate writing shrinkers” (P4). One challenge of writing shrinkers property-based tests by supplementing them with example-based +was writing them in a way that preserved important non-trivial unit tests. In these cases, example-based tests were written to test +invariants: “It’s easy to write a shrinker that accidentally does not complementary functionality that could not be easily tested with +preserve some invariant, and that makes your test fail.” (P13) This properties. As one participant put it, “it’s kind of not a good idea to +led one participant to ask for a “generic solution [for shrinking], use QuickCheck in isolation” (P6), as doing so limits the breadth of +rather than having the user write shrinkers” (P10). software behaviors that can be tested. + A few participants also described wanting more information How might PBT frameworks provide better support these (and +from the shrinking process—for example, the progressively smaller other) techniques that give insight into how thoroughly properties + ICSE 2024, April 2024, Lisbon, Portugal Harrison Goldstein, Joseph W. Cutler, Daniel Dickstein, Benjamin C. Pierce, and Andrew Head + + +have been tested? P15 described their ideal interaction with PBT part of their testing toolbox, using it to gain confidence when they +tools, where the tools give “insight into what [PBT] is doing. . . I were unsure of code’s correctness, especially where correctness +think a combination of knowing what it’s doing and having more was of critical importance. PBT gave them confidence that their +control of the space that it’s exploring would be interesting.” Partici- software was operating correctly, finding bugs in code that had not +pants desired greater awareness of what their tools were doing: P16 been found via other methods. +called this “visibility”, and P30 called it “inspectability.” Many par- OB2: Properties are used as devices for communicating specifications. +ticipants wanted greater visibility to better understand the breadth Tests are generally a valuable form of documentation, and proper- +of inputs generated. P18, for instance, desired “visualization of the ties are no exception. Jane Street developers use them as executable +test [inputs] being generated”. Others wished to see details such evidence that code satisfies a specification, which has significant ad- +as “the answer [of the function under test] on a smaller set of ex- vantages over traditional documentation that might go stale as the +amples” (P9), “statistics on. . . edge cases” (P18), statistics describing code changes. As shown in §4.1 and §4.2, properties were deemed +generated inputs such as “the average length of [a generated] list” especially useful for communication during code review: when +(P25), and code coverage (P9). properties were available, they were considered a strong signal that + the code was correct, and when unavailable reviewers sometimes +4.7 Tradeoffs asked the submitter to write some. These auxiliary uses for proper- +As the earlier sections indicate, using PBT is not without costs. ties are worth keeping in mind for PBT framework designers; for +From coming up with properties to evaluating testing success, par- example, some property languages try to make properties easier to +ticipants found friction in many steps of PBT. Participants described +seeing themselves as employing PBT more often if its “overhead” +could be lowered (P26), or if there was less “effort necessary to +integrate [it] into [their] workflow” (P10). Observations + Amidst these costs, PBT was often seen as worth the effort. For OB1 Property-based testing is being used successfully +some participants, development of properties was unremarkable. to build confidence in complex systems. +For others with more involved implementation, it was still worth + OB2 Properties are used as devices for communicating +the costs: in the words of P6,“[It was] a huge slog, but I was like + specifications. +‘this needs to be right,’ and. . . I’m glad I did it.” P17 describes the +tradeoffs of using PBT as follows: “doing PBT is both putting in OB3 Property-based tests need to be fast; they are +more effort and saving oneself effort as well.” expected to perform as well as other unit tests. + OB4 Property-based testing is used opportunistically +5 LESSONS LEARNED in high-leverage scenarios where properties are +In this section we answer our research questions, setting a course readily available; developers rarely go out of +for upcoming PBT research and tool development that is grounded their way to write subtle specifications. +in findings from the study. Our recommendations cut across the OB5 Developers see writing generators as a distrac- +PBT process, and establish new goals and priorities for different tion, preferring to use derived generators. +areas of PBT research. We first answer RQ1 with observations of OB6 Developers may not interrogate properties that +PBT’s practice that offer a reality check to PBT researchers and tool- do not find bugs, even in cases where they ac- +builders (§5.1), then we answer RQ2 with a technical and empirical knowledge they should. +research agenda motivated by our study (§5.2). + Research Opportunities +5.1 The State of Practice + RO1 Understand time constraints for property-based +Recall that RQ1 asks, “What are the characteristics of a successful tests. +and mature PBT culture at a software company?” Based on the + RO2 Improve support for differential and model-based +results of our study, we answer: A mature PBT culture considers + testing. +PBT a tool to be opportunistically applied in situations of high +leverage to gain confidence in software and document its behavior; RO3 Make more testing scenarios high leverage. +developers try to keep PBT “out of their way,” expecting it to work RO4 Streamline the process of writing well- +quickly and easily. In this section, we synthesize the results from distributed, precondition-satisfying generators. +the previous section into observations that expand on these ideas. RO5 Improve interfaces for shrinking. +Some observations point forward to §5.2, where we present ideas RO6 Improve tools for evaluating testing effective- +for future research based on our findings. ness. +OB1: Property-based testing is being used successfully to build confi- RO7 Connect evaluation of testing effectiveness and +dence in complex systems. The broader research community some- generator improvement. +times situates PBT as a lower-effort, lower-reward alternative to +formal proofs of correctness, but that perspective underestimates +PBT as a practical tool for improving software quality. In §4.1, we +show that the developers at Jane Street found PBT to be a valuable Figure 1: Summary of major outcomes. + Property-Based Testing in Practice ICSE 2024, April 2024, Lisbon, Portugal + + +write by providing terse syntax and expressive defaults, but those Instead, as seen in §4.4, many participants opted to test with gener- +features may cause problems if they hurt readability. ators derived from the types of the data that their programs operate + on. +OB3: Property-based tests need to be fast; they are expected to perform This has two implications. First, it means that ongoing work to- +as well as other unit tests. The PBT literature is not always clear wards improving generator automation is critical. After all, as easy +about exactly when in the software engineering process they expect as current derived generators are to use, they are not always suffi- +properties to be written, but in §4.2 we observe that PBT’s niche is cient. The well-liked ppx_quickcheck library, for example, cannot +testing module-level code during development. This is in contrast derive generators for properties with complex preconditions. Broad- +with fuzz testing, which, when used by Jane Street developers, is ening applicability of derived generators lowers barriers to using +treated as a separate step and run outside of the standard testing PBT. Second, it means that developers of manually written genera- +workflow. This discrepancy makes sense in view of the differing tor languages must carefully consider any added friction. Languages +goals that we observed for PBT and fuzzing: PBT is used for module- that make generators more difficult to write, perhaps because do- +level tests with often-complex logical specifications, while fuzzing ing so enables desirable new features, should be cautious—these +is used for integration-style tests of whole applications, to check features may be unlikely to see adoption. +for relatively basic (e.g., assertion failure or uncaught exception) Separately, languages and tools for writing generators should +errors. (Look ahead to RO1 in §5.2.) provide a wealth of sensible defaults, and they should optimize the + Properties live alongside other unit tests, so they are expected user experience around common patterns. Participants indicated +to run as quickly as other unit tests. Knowing this may change that there was room for improvement in all of these areas, at least +priorities for some PBT researchers. If users are only testing their in OCaml’s QuickCheck. (Look ahead to RO4 in §5.2.) +properties for 50 milliseconds, research advances that increase input +generation or property execution speed might make the difference OB6: Developers may not interrogate properties that do not find bugs, +between bugs being found or not. Conversely, approaches that make even in cases where they acknowledge they should. A passing prop- +generators more thorough but significantly slower may not be used erty sometimes means that a program is free of bugs, but it may also +unless developers are given reason to accept longer execution times. mean that the input values are not the right ones to trigger a latent + bug. Developers acknowledged this fact, and they had expectations +OB4: Property-based testing is used opportunistically in high-leverage around the kinds of input values that they wanted when testing +scenarios where properties are readily available; developers rarely go their properties. (Besides satisfying property preconditions, they +out of their way to write subtle specifications. Conventional wisdom wanted them to be realistic, well-distributed in the space, inter- +in the PBT community sometimes assumes that developers decide esting enough to cover corner and edge cases, and more.) But, as +to use PBT and then try to think of a specification, but the study shown in §4.6, when it came time to decide if their generators met +participants generally did the opposite: they saw an obvious testable expectations, developers did not analyze them closely. Developers +property and then decided to use PBT. We call situations with these of PBT frameworks, and especially PBT automation, should keep +readily available properties “high-leverage” testing scenarios. this in mind: automated tools for generating test inputs risk giving + The high-leverage scenarios varied—we are not confident that developers a false sense of security. They must ensure that their +we have documented all of the ones available in practice—but a few tools test thoroughly, because testers may not. (Look ahead to RO6 +are described in §4.3. The most popular was differential or model- in §5.2.) +based testing, which compares the code under test to some other +available implementation. (We are not surprised our participants 5.2 Research Opportunities +found these techniques useful, after all both differential and model- Now we tackle RQ2: “What opportunities exist for future work in +based testing have rich literatures on their own, but we did not the PBT space, motivated by the needs of real developers?” Based on +expect to see them so seamlessly incorporated into PBT workflows.) our results, we conclude: Exciting avenues for PBT research include +Other high-leverage properties include round-trip properties that further studies into performance and usability of PBT generators, +check an inverse relationship between functions and catastrophic broader and deeper support of high-leverage PBT scenarios, better +failure properties that make sure a program does not fail completely. tools for shrinking, and better visibility into the testing process. + What does this opportunistic use of PBT mean for researchers This section discusses research opportunities in software engineer- +and tool builders? Frameworks can optimize for and automate these ing, programming languages, and human-computer interaction +scenarios—tools like Hypothesis Ghostwriter [16] have already research that will unlock the yet-unrealized potential of PBT. Some +begun incorporating common PBT scenarios into an automation research opportunities point backward to §5.1, where we synthesize +framework—improving the common case and accelerating PBT use observations that inform these ideas. +even further. High-leverage scenarios should also be incorporated +into PBT benchmarks like Etna [50] to make sure that the perfor- RO1: Understand time constraints for property-based tests. Future +mance of PBT algorithms is evaluated in a way that reflects their studies should more thoroughly explore how long developers across +use in real-world scenarios. (Look ahead to RO2 and RO3 in §5.2.) the software industry actually budget for running PBT. In this + study, we heard about numbers between 50 milliseconds and 30 +OB5: Developers see writing generators as a distraction, preferring seconds; that difference is massive, and tools that support PBT +to use derived generators. Since PBT is often done in the midst of cannot make optimal decisions around optimization without clearer +development, developers are reluctant to slow down and write a data. Furthermore, future research should develop a sense of how +generator; the task was seen as both difficult and time-consuming. long is “enough” for common kinds of properties and software so + ICSE 2024, April 2024, Lisbon, Portugal Harrison Goldstein, Joseph W. Cutler, Daniel Dickstein, Benjamin C. Pierce, and Andrew Head + + +tools have the data to argue for larger time budgets where required. continue to look for ways to use current active-tuning strategies +Moreover, developers of tools that combine ideas from PBT and for pre-tuning (e.g., by saving inputs to be run later) and ways to +fuzzing need to carefully examine their performance and recognize make pre-tuned generators easier to use (e.g., with interfaces that +that many PBT users set strict timeouts that may preclude the help developers write complex generators). +overhead of measuring code coverage while running tests. This is When it comes to precondition-satisfying generators, many seek +encouraging for tools like Crowbar [17] and HypoFuzz [26] that to unify languages for writing generators with ones for writing +allow developers to transition between short-running PBT and preconditions. One approach, used in the QuickChick PBT frame- +longer-running fuzzing with the same properties. (See OB3 in §5.1.) work [46], uses inductive relations as a language for both properties +RO2: Improve support for differential and model-based testing. As and generators [35, 45]. This approach works well in the Coq proof +the most popular high-leverage scenario for PBT, differential test- assistant, but complex inductive relations are not expressible in +ing seems particularly interesting as a topic of further research. mainstream languages or accessible to non-specialists. Researchers +Differential testing has a rich literature, as discussed in §6, but should consider ways to generalize these results. Alternatively, ded- +in the context of PBT there are still advances within reach. For icated languages such as ISLa [53] use a common language that +example, in languages like OCaml with rich module structures, is closer to the logical connectives one might use in a standard +researchers should aim to increase automation around differential programming language; more research should be done to evaluate +testing and produce a test harness for comparing modules without if this approach can be applied in common PBT scenarios. Whatever +requiring any manual setup; Hypothesis Ghostwriter has begun to dual-purpose language is chosen, this is a compelling path forward. +incorporate similar ideas with Python’s classes. (See OB4 in §5.1.) (See OB5 in §5.1.) + +RO3: Make more testing scenarios high leverage. Some testing situa- RO5: Improve interfaces for shrinking. It is clear from the study +tions are just barely outside the realm of “high-leverage” scenarios, results that shrinkers would be far more useful if they were both +and improved tooling could make the difference. For example, P5 more automated and more informative. As we mention above, we +described a technique that they used to test a poorly abstracted recommend that existing frameworks improve automation by in- +module with an overly complicated interface: instead of writing corporating internal test-case reduction [36, 52], which uses gener- +normal properties, they instrumented the module with log state- ators to aid in shrinking, where possible. Internal shrinking has the +ments, wrote properties about what those logs should look like, added benefit of always producing valid values, which is difficult +and then tested the module via an external interface that hides to achieve otherwise. +many of its internal details. Generalizing and operationalizing this Participants also asked to see more intermediate examples from +technique—e.g., perhaps with temporal logic in the style of Quick- the shrinking process. Indeed, there are cases where the smallest +strom [41]—would allow for better testing leverage in cases where failing example is not the most helpful one: e.g., if the shrinker +poor abstraction prevents traditional PBT. outputs the tuple (0, 0), one might conclude that any tuple of + Other testing situations might be supported better as well. Po- integers triggers the bug, but it may be that the bug is only found +tential opportunities include improving PBT support for code with if the first component is actually 0. This example motivated Hy- +mutable state (e.g., by saving memory snapshots for repeatable pothesis to begin developing a tool that will give users a variety of +tests) and code that interacts with the environment (e.g., via robust tools for exploring failing tests. Debugging cases using shrinking +integration with tools for mocking [38]). Increasing the scenarios in might mean showing many shrunk examples to the user, following +which PBT works out of the box will naturally make it higher-value related work in the model-finding literature [14, 18], or even provid- +for developers. (See OB4 in §5.1.) ing control over the shrinking process (e.g., with novel interactions + allowing the user to click on components of a value to shrink only +RO4: Streamline the process of writing well-distributed, precondition- + those components). +satisfying generators. This has been a research goal for the PBT +community since the beginning. Our study clarifies some promising RO6: Improve tools for evaluating testing effectiveness. Participants +paths forward, including improving tools for automated tuning, reported ad-hoc, piecemeal approaches to understanding their test- +generalizing unified languages for defining generators alongside ing effectiveness, and they asked for better ways to visualize test- +properties, and supporting alternatives to randomness as first-class. ing feedback. As a simple first step, tools should always announce + There are two main options for tuning generator distributions. counts of discarded test cases (i.e., ones that failed the property’s +Actively tuned generators modify their distribution live, in re- precondition) so the developer can catch problems early. Many PBT +sponse to feedback, whereas pre-tuned generators compute dis- tools provide some way to aggregate statistics while a property is +tributions ahead of time. Actively tuned generators are the norm running (see Haskell QuickCheck’s label and collect functions) +in the fuzzing literature [20] and have been ported to PBT in many but OCaml’s QuickCheck hides output when tests succeed, which +forms [17, 23, 34, 48], but they spend precious testing time on tuning obscures that information, and more should be done around the +analysis, making them less useful in time-constrained PBT scenar- usability and legibility of these kinds of aggregations. Going further, +ios. Pre-tuned generators can be much faster, but they currently participants desired (1) better interfaces for scanning through ex- +require too much programmer effort. For example, reflective genera- amples of generated values, (2) better ways of visualizing generated +tors [22] (which build on example-based tuning à la the Inputs from distributions, and (3) better integration of code and branch cov- +Hell approach [51]) automate the process of generating realistic erage information. These could significantly improve developers’ +test inputs, but this automation is only possible if a reflective gen- understanding of how thoroughly their code has been tested. (See +erator is already available. Moving forward, the community should OB6 in §5.1.) + Property-Based Testing in Practice ICSE 2024, April 2024, Lisbon, Portugal + + +RO7: Connect evaluation of testing effectiveness and generator im- Beller et al. coined the term “Test Guided Development” to describe +provement. How might a developer clearly express their test data the strategy that programmers actually use. Our study agrees with +goals and ensure that the generator achieves them? Future tools the idea that developers use testing to guide their thinking during +could tighten the feedback loop wherein a developer evaluates and development (§4.1). We also corroborate challenges that another +then expresses how to improve their generator at the same time. study found around integration testing: Greiler et al. [24] found +For instance, a future user interface might display a generator’s that while unit testing is common, integration testing is difficult +distribution in some graphical form like a bar chart and allow the and often left to the the software’s users; in our study, developers +developer to directly manipulate the distribution by dragging bars struggled to use PBT for integration testing because it is difficult to +up and down. Alternatively, the developer might be able to click write specifications of entire systems’ behaviors. (§4.3). +on those annotations to request that the distribution try harder to Our study also suggests that PBT addresses testing difficulties +cover a particular line or balance a particular branch, in the style raised in the literature. Aniche et al. [1] observed that developers +of AFLGo [10]. In an ideal world, an insufficient generator could be try to write relatively “random” test cases, with the hope of acciden- +caught and fixed in a few clicks, without allowing bugs slip by. tally stumbling on bugs; this is related to developers’ goals for PBT + generators, discussed in §4.4, although PBT has the advantage of au- + tomating this process in many cases. Another study [25], focusing +6 RELATED WORK on differential testing, found PBT to be a valuable tool in a devel- +We focus, in this section, on related work exploring the usability of oper’s toolbox, providing a coherence check for important code; +testing and formal methods tools. Prior work on PBT, testing, and however, they also found some problems with differential testing +formal methods usability has made important observations about systems, such as naïve sampling algorithms that failed to trigger +the challenges of specification and bug finding, but it has lacked the bugs and large counter-examples that were difficult to reason about. +depth and domain focus to paint a clear picture of PBT, its usage, Our study suggests new tools may address these problems. +and opportunities for improvement. Formal methods. PBT is sometimes described as a “lightweight + Property-based testing. As a precursor to this study, our group did formal method.” Indeed, a recent position paper [49] argued that +a smaller-scale pilot study with developers using Hypothesis [21]. testing techniques like PBT and fuzzing were important steps on +The full-scale study is far more in-depth, and presents more detailed the way towards more formal verification. Formal methods as a +and nuanced findings, although talking to Python developers did field have seen similar calls for usability improvements. A report +raise a few concerns that were less prevalent at Jane Street, espe- out of the Naval Research Lab [28] says, “to be useful to software +cially when it comes to difficulty coming up with specifications. practitioners, most of whom lack advanced mathematical training + A study analyzing open-source libraries using Hypothesis [12] and theorem proving skills, current formal methods need a number +evaluated the kinds of properties that developers test in practice, of additional attributes, including more user-friendly notations, +and found significant overlap with our “high-leverage” testing sce- completely automatic (i.e., pushbutton) analysis, and useful, easy +narios. In particular, they found that both round-trip and differential to understand feedback.” This report was published in 1998, but, as +or model-based testing are overrepresented in real-world tests. our study shows, some of their usability criteria are still not ade- + An experience report from Amazon [9] described differential test- quately met by modern PBT tools. A more contemporary account +ing as a major use-case of PBT and reported that developers used agrees that “the user experience of formal methods tools has largely +shrinking tools for debugging and mutation testing to ensure test- been understudied” [33] and calls for better education and tools for +ing effectiveness. Our study confirms these patterns and explores writing and understanding specifications. +further PBT use-cases (§4.3), insights around shrinking (§4.5), and +concerns about testing effectiveness (§4.6). 7 CONCLUSION + Other studies highlight a more narrow set of specific challenges + Our study reveals that, even after two decades of active exploration— +faced by developers using PBT. One experience report describing + and, increasingly, exploitation—of PBT, there is still much to learn +PBT use at DropBox [31] cited usability problems when testing + about how it is being used and what challenges it faces in practice. +timing-dependent code. The report found that sequences of timed + We contribute a wealth of observations about PBT’s use in an +operations resist shrinking, often remaining unwieldy, and that + industrial setting, along with well-founded ideas for future research +timing dependence caused tests to be flaky. An education-focused + in PBT that that we, with the help of the broader community, hope +study using PBT [55] observed that the PBT community lacks good + to pursue in the coming years. +motivating examples. While the former concern only appeared in +passing in our study (when discussing PBT’s handling of stateful +software), the latter—a dearth of good motivating examples—might ACKNOWLEDGMENTS +be ameliorated by our characterization of high-leverage testing We would like to thank John Hughes, Hila Peleg, Zac Hatfield- +scenarios in §5. Dodds, and Shriram Krishnamurthi for their input and feedback + Testing more generally. Beyond PBT, there is considerable work on drafts of this paper. Also, thank you to Ron Minsky and others +studying usability software of testing in general. Our study sheds at Jane Street for being open to this kind of collaboration. We ap- +light into how these common testing issues manifest in PBT specif- preciate the support of the University of Pennsylvania’s PLClub +ically. Two studies of developers who use IDEs [5, 6] conclude that and Penn HCI. This work was financially supported by NSF awards +testing, especially Test Driven Development, is not as prevalent #1421243, Random Testing for Language Design and #1521523, Expe- +as conventional wisdom would suggest. Based on these studies, ditions in Computing: The Science of Deep Specification. + ICSE 2024, April 2024, Lisbon, Portugal Harrison Goldstein, Joseph W. Cutler, Daniel Dickstein, Benjamin C. Pierce, and Andrew Head + + +REFERENCES [20] Andrea Fioraldi, Dominik Maier, Heiko Eißfeldt, and Marc Heuse. 2020. {AFL++} + [1] Maurício Aniche, Christoph Treude, and Andy Zaidman. 2022. How Developers : Combining Incremental Steps of Fuzzing Research. https://www.usenix.org/ + Engineer Test Cases: An Observational Study. 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Towards making formal methods normal: meeting developers + \ No newline at end of file diff --git a/packages/opencode/specs/simulation-research/text/2026-agentic-pbt.txt b/packages/opencode/specs/simulation-research/text/2026-agentic-pbt.txt new file mode 100644 index 00000000000..36b19d2a723 --- /dev/null +++ b/packages/opencode/specs/simulation-research/text/2026-agentic-pbt.txt @@ -0,0 +1,1411 @@ + Agentic Property-Based Testing: + Finding Bugs Across the Python Ecosystem + + + Muhammad Maaz Liam DeVoe Zac Hatfield-Dodds Nicholas Carlini + MATS, Anthropic Northeastern University Anthropic Anthropic +arXiv:2510.09907v1 [cs.SE] 10 Oct 2025 + + + + + Abstract + Property-based testing (PBT) is a lightweight formal method, typically imple- + mented as a randomized testing framework. Users specify the input domain for + their test using combinators supplied by the PBT framework, and the expected + properties or invariants as a unit-test function. The framework then searches for + a counterexample, e.g. by generating inputs and calling the test function. In this + work, we demonstrate an LLM-based agent which analyzes Python modules, in- + fers function-specific and cross-function properties from code and documentation, + synthesizes and executes PBTs, reflects on outputs of these tests to confirm true + bugs, and finally outputs actionable bug reports for the developer. We perform + an extensive evaluation of our agent across 100 popular Python packages. Of the + bug reports generated by the agent, we found after manual review that 56% were + valid bugs and 32% were valid bugs that we would report to maintainers. We + then developed a ranking rubric to surface high-priority valid bugs to developers, + and found that of the 21 top-scoring bugs, 86% were valid and 81% we would + report. The bugs span diverse failure modes from serialization failures to numerical + precision errors to flawed cache implementations. We reported 5 bugs, 4 with + patches, including to NumPy and cloud computing SDKs, with 3 patches merged + successfully. Our results suggest that LLMs with PBT provides a rigorous and + scalable method for autonomously testing software. Our code and artifacts are + available at: https://github.com/mmaaz-git/agentic-pbt. + + + 1 Introduction + Property-based testing (PBT) is a software testing paradigm that aims to verify whether a general + property holds over a predefined input domain. In contrast to traditional example-based testing, it + does not require specific examples of expected outputs. Instead, PBT allows the developer to define + invariants that should hold for all inputs, which are then checked on a diverse set of automatically- + generated inputs. A property might require that the output of a function is always non-negative, that + some f and g commute for all x (f (g(x)) = g(f (x))), or that an interpreted program has equivalent + semantics to its compiled form. Popularized by QuickCheck in Haskell (Claessen and Hughes, 2000), + there now exist PBT libraries for many of the common programming languages, including Python’s + Hypothesis (MacIver et al., 2019), the focus in this work. PBT can be more robust than example-based + testing which inherently relies on the developer to anticipate edge cases (MacIver, 2019). + Despite its theoretical appeal, property-based testing is less popular than example-based testing due + to the challenge of identifying meaningful properties to test (Goldstein et al., 2024). Specifying + meaningful properties, especially as codebases get more complex, often requires significant domain + expertise and time investment. Recent advances in large language models (LLMs) have demonstrated + remarkable code understanding, which makes it possible to automatically mine for properties. + However, existing work on using LLMs for PBTs focuses on a single function at a time, and has only + a single generation step. + + 39th Conference on Neural Information Processing Systems (NeurIPS 2025) Workshop: The 4th Deep Learning + for Code Workshop. + In our work, we introduce agentic property-based testing, an approach leveraging the multi-step rea- +soning capabilities of coding agents and the rigor of PBT. We develop an agent that can autonomously +crawl through and understand entire codebases, look for high-value properties (including across +functions and classes), write PBTs and run them, and then analyze failing tests for validity. After the +agent runs for several rounds, it either surfaces a bug, or states it is unable to identify one. +We demonstrate the effectiveness of agentic PBT through a large-scale evaluation across the Python +ecosystem, testing 100 popular Python packages with billions of downloads. Manual evaluation +of the bug reports generated by our agent showed that it successfully identified genuine bugs in +several widely-used libraries: for example, our agent autonomously finds a bug in NumPy, the +pre-eminent numerical library in Python with more than 500 million monthly downloads, which was +acknowledged by the maintainers, showing the real-world applicability of our approach. This work +represents the largest systematic evaluation of AI-driven property-based testing to date, establishing a +new paradigm for scalable software auditing. + + + + +2 Agent + + +Our agent is built on top of Anthropic’s Claude Code, a terminal-based coding agent (Anthropic, +2025b), that allows Claude to execute bash commands and read/write files. Our agent is implemented +as a natural language prompt, stored in a Markdown file, that is passed to Claude Code. As it +is a prompt, our agent is easily portable to other agent implementations, like OpenAI’s Codex +OpenAI (2025), or general frameworks like ReAct (Yao et al., 2022). Our main contribution is our +comprehensive evaluation which demonstrates that LLM-based PBT works at scale, finding diverse +bugs with few false alarms. +Our agent is built to work with Python codebases, and generates Hypothesis PBTs to test that +code. It takes a single argument, which points the agent towards a particular target, either a sin- +gle Python file (e.g., normalizers.py), module (e.g., numpy, scipy.signal), or function (e.g., +requests.get(), json.loads()). +We developed the prompt by using industry best-practices (Anthropic, 2025a), collating high-value +information from the Hypothesis documentation (Hypothesis Contributors, 2025), and iterative +refinement from manual inspection of agent runs. The full prompt is in Appendix A. +Prompt Overview The agent is given the following six instructions, paraphrased below: + 1. Analyze the target: Figure out if the target is a module, function, or a file. + 2. Understand the target: Find and read documentation, function signatures, source code, etc. + 3. Propose properties: Look for properties grounded in the information from the past step. + Some examples of high-value properties, e.g., invariants, round-trip, metamorphic, are given. + Thoroughly understand the input domain, e.g., by looking at functions that call the function + under test. + 4. Write tests: Translate these properties into Hypothesis property-based tests. + 5. Execute and triage tests: Run tests with pytest. For failing tests, reflect using a rubric. If + the failing test is a false alarm, go to Step 4 and refine the testing strategy. For passing tests, + verify that the test is meaningful. + 6. Report bugs: If convinced a bug is genuine, create a bug report in a Markdown file, following + a standard format including a summary of the bug, the PBT that exposed the bug, a short + reproducing script, why it is a bug, and possibly a proposed patch. +Finally, we provide the agent with a short reference to Hypothesis, which shows essential patterns, +some key testing principles, and links to online documentation which can be fetched if needed. +Key Design Choices Our agent maintains a to-do list to track its progress through the 6-step cycle, +as well as to keep track of, e.g., which properties it would like to test. We attempt to reduce false +alarms throughout by emphasizing that proposed properties should be strongly supported by evidence, +asking the agent to reflect on failing tests carefully, and to focus on a few high-value properties. +Lastly, we let the agent have broad autonomy: it decides which functions to target, and decides when +a failing property is truly a bug (with some direction from a rubric). + + + 2 + 3 Experiment + +We evaluate our agents ability to find bugs by curating a diverse corpus of 100 Python packages. We +combine three complementary sampling approaches to ensure comprehensive coverage: + + • Hand-selected from the standard library (n = 15): json, pathlib, collections, + itertools, functools, datetime, re, os, urllib, statistics, decimal, base64, + uuid, html, csv. + • Hand-selected from third-party PyPI packages (n = 15): numpy, pandas, requests, + flask, sqlalchemy, matplotlib, scipy, beautifulsoup4, pydantic, fastapi, + django, tornado, keras, httpie, black. + • Random sample from the top 5,000 PyPI packages, by downloads (n = 70): Variety of + domains including data, cloud computing, and machine learning. The full list is provided + with our code. + +For each package, we test the agent on the main module (e.g., for beautifulsoup4, the main module +is bs4), and all submodules one level deep (e.g., numpy.linalg). In total, we ran on 933 modules. +We used Claude Opus 4.1 Anthropic (2025c) as the LLM for all agent runs. Each agent was run in +an isolated virtual environment containing the package under test and its dependencies, along with +Hypothesis. Agents were run in parallel, with up to N = 20 concurrently. Agents had read/write +permission within their working directory, could execute python and pytest bash commands, had +read access to the virtual environment for source code, and internet access. The experiment was run +on a RunPod Ubuntu 20.04 container with 8 vCPUs, 16 GB RAM, and 50 GB disk. +Evaluation Definitive validation of reported bugs across such diverse libraries is difficult as it +requires domain expertise in each specific codebase. First, we developed an initial scoring rubric with +the goal of eliminating clear false alarms and got Claude Opus 4.1 to grade all reports. We randomly +sampled n = 50 bug reports from the top 80% by score. Two of the authors independently scored +each bug report, using two criteria: “Is this a valid bug? If yes, would we reasonably report this +to the maintainers?". Disagreements were discussed to arrive at a final consensus. Using insights +from the initial rubric, we developed a final rubric (see our code) which scores bug reports out of +15, got Claude Opus 4.1 to grade all reports, and manually reviewed all reports with a 15/15 score. +To validate our agents with maintainers with actual domain expertise, we (manually) reported some +particularly interesting bugs to their respective repositories. + +4 Results + +Summary statistics We evaluated our agent across 100 Python packages covering 933 modules. +The agent generated 984 bug reports, discovering issues in 786 modules (84.2%) and averaging just +over one bug per module. Total agent runtime was 136.6 hours (82 min/package, 8.8 min/module) +and total API cost was $5,474.20 ($54.74/package, $5.87/module, $5.56/bug report). Individual +module costs ranged from $0.65 to $15.42, with a median of $5.81. Each agent run involved roughly +110 turns. In aggregate, the agents used 2.21 billion (input & output) tokens (2.37 million/module). +Manual review Inter-rater agreement on the initial review was κ = 0.31. After reaching consensus, +56.0% (95% CI: 42.2%, 69.8%) of reports were determined to be valid bugs, and 32.0% (95% CI: +19.1%, 44.9%) were valid and worth reporting. With the final rubric, 18 of the 21 top-scoring reports +were valid, and 17 of those were both valid and worth reporting. +Reported bugs While examining reports, we selected the following particularly interesting bugs +to report to the original developer. The corresponding bug reports generated by the agent are in +Appendix B. They demonstrate the range of issues discoverable through our approach: + [numpy] (numpy.random) + Property: Wald distribution should only return non-negative samples. + Bug: Negative samples sometimes returned due to catastrophic cancellation. + Status: Bug acknowledged. Patch merged. [PR #29609] + [aws-lambda-powertools] (aws_lambda_powertools.shared.functions) + Property: slice_dictionary() splits a dictionary into chunks which should be able to + be recombined into the original dictionary. + + + 3 + Bug: It returns the same (first) chunk repeatedly, due to not incrementing the iterator. + Status: Bug acknowledged. Patch merged. [PR #7246] + [cloudformation-cli-java-plugin] (rpdk.core.jsonutils.utils) + Property: item_hash() function should produce different outputs for different inputs. + Bug: All list inputs hash to hash(None), due to use of the in-place .sort() method, which + returns None. + Status: Patch submitted. [PR #1106] + [tokenizers] (tokenizers.tools) + Property: EncodingVisualizer.calculate_label_colors() should return a valid + HSL color format. + Bug: The returned string is missing a closing parenthesis. + Status: Bug acknowledged. Patch merged. [PR #1853] + [python-dateutil] (dateutil) + Property: easter() should be on a Sunday. + Bug: Returns a non-Sunday date for the Julian calendar in various years. + Status: Issue reported. Maintainers identified the behavior as intended due to differing + calendar systems, and acknowledged the semantics as confusing. [Issue #1437] + +5 Discussion and Conclusion + +Our evaluation demonstrates that LLM-guided property-based testing can systematically uncover +bugs missed by traditional testing. With a cost of $5.56/bug report, and extrapolating from our manual +grading that 56% of these are valid bugs, our agent can find bugs for $9.93/valid bug. This is an upper +bound on the real-world cost, where developers with domain expertise can be more judicious with +where to target the agent. The diversity of issues, spanning numerical issues to business logic issues, +show the power of PBT, and the ability of agents to autonomously mine for such properties. +Limitations The primary limitation is that we did not manually review all 984 bug reports. However, +our review of a subset of reports shows that the false discovery rate has a 95% CI of [30.2%, 57.8%]. +The secondary limitation is intent ambiguity: the agent cannot distinguish intentional design violations +from bugs. An example of this is a bug report about LookupDict from the requests library: based +on its name and the fact it subclasses from the built-in dict, our agent tested whether it exhibits +dict-like behavior, which it in fact does not. The same issue was raised on GitHub in 20221 , but +the maintainer replied that it was not meant to work like dict. In practice, both limitations can be +mitigated by developers’ domain expertise rather than blind exhaustive testing as we did. +Comparison to Related Work Vikram et al. (2023) study converting library documentation into +Hypothesis PBTs for 40 functions across 10 popular Python libraries (e.g., numpy). With their best +model and prompting strategy, only 41% of generated PBTs ran without error and passed on the +implemented code, and at most 21% of documented properties were captured. In contrast, we do +better by using an agentic approach, which is better able to capture more complex properties due +to multiple steps. More recent work He et al. (2025) propose a different take on this problem: a +“generator" LLM produces candidate code while a “tester" LLM synthesizes PBTs from the problem +description. PBT failures are fed back to guide code refinement, yielding improvements over example- +based test-driven development. There is also extensive work on LLMs for software testing in general: +see Wang et al. (2024) for a review. +Conclusion We presented an automated approach for bug discovery using LLM-guided property- +based testing, which discovered real bugs across several popular Python libraries. The properties +and failing test cases discovered show the utility of combining LLMs with PBT. While such a tool +is useful for developers, a possible malicious use is autonomous discovery of vulnerabilities. As +LLMs improve and get cheaper, agentic PBT could become an increasingly valuable complement to +traditional testing, helping developers systematically explore code behavior and find bugs. + + + + + 1 + https://github.com/psf/requests/issues/6238 + + + 4 + References + +Anthropic. Claude Code: Best practices for agentic coding. https://www.anthropic.com/ + engineering/claude-code-best-practices, Apr. 2025a. Accessed: 2025-08-20. +Anthropic. Claude Code. https://www.anthropic.com/claude-code, 2025b. Accessed: 2025- + 08-20. +Anthropic. System Card Addendum: Claude Opus 4.1. Technical report, Anthropic, + Aug 2025c. URL https://assets.anthropic.com/m/4c024b86c698d3d4/original/ + Claude-4-1-System-Card.pdf. +K. Claessen and J. Hughes. QuickCheck: a lightweight tool for random testing of haskell programs. + In Proceedings of the fifth ACM SIGPLAN international conference on Functional programming, + pages 268–279, 2000. +H. Goldstein, J. W. Cutler, D. Dickstein, B. C. Pierce, and A. Head. Property-based testing in practice. + In Proceedings of the IEEE/ACM 46th International Conference on Software Engineering, pages + 1–13, 2024. +L. He, Z. Chen, Z. Zhang, J. Shao, X. Gao, and L. Sheng. Use property-based testing to bridge llm + code generation and validation. arXiv preprint arXiv:2506.18315, 2025. +Hypothesis Contributors. Hypothesis documentation. https://hypothesis.readthedocs.io/ + en/latest/, 2025. Accessed: 2025-08-20. +D. MacIver. In praise of property-based testing. URL: https://increment. com/testing/in-praise-of- + property-based-testing, 2019. +D. R. MacIver, Z. Hatfield-Dodds, et al. Hypothesis: A new approach to property-based testing. + Journal of Open Source Software, 4(43):1891, 2019. +OpenAI. OpenAI Codex. https://openai.com/codex/, 2025. Accessed: 2025-08-20. +V. Vikram, C. Lemieux, J. Sunshine, and R. Padhye. Can large language models write good property- + based tests? arXiv preprint arXiv:2307.04346, 2023. +J. Wang, Y. Huang, C. Chen, Z. Liu, S. Wang, and Q. Wang. Software testing with large language + models: Survey, landscape, and vision. IEEE Transactions on Software Engineering, 50(4): + 911–936, 2024. +S. Yao, J. Zhao, D. Yu, N. Du, I. Shafran, K. Narasimhan, and Y. Cao. ReAct: Synergizing + reasoning and acting in language models. arXiv preprint arXiv:2210.03629, 2022. URL https: + //arxiv.org/abs/2210.03629. Accessed: 2025-08-20. + + + + + 5 + A Agent prompt + + Note: some characters may not render properly in the PDF; we provide the full prompt file in our + code release. + + 1 --- + 2 description: Property-based testing agent + 3 --- + 4 + 5 # Property-Based Testing Bug Hunter + 6 + 7 You are a **bug-hunting agent** focused on finding genuine bugs through property-based testing with Hypothesis. Your mission: + discover real bugs by testing fundamental properties that should always hold. + 8 + 9 ## Your Todo List +10 +11 Create and follow this todo list for every target you analyze: +12 +13 1. [ ] **Analyze target**: Understand what you’re testing (module, file, or function) +14 2. [ ] **Understand the target**: Use introspection and file reading to understand implementation +15 3. [ ] **Propose properties**: Find evidence-based properties the code claims to have +16 4. [ ] **Write tests**: Create focused Hypothesis tests for the most promising properties +17 5. [ ] **Test execution and bug triage**: Run tests with ‘pytest‘ and apply bug triage rubric to any failures +18 6. [ ] **Report or conclude**: Either create a bug report or report successful testing +19 +20 Mark each item complete as you finish it. This ensures you don’t skip critical steps. +21 You can use the ‘Todo‘ tool to create and manage your todo list. +22 Use the ‘Todo‘ tool to keep track of properties you propose as you test them. +23 +24 ## Core Process +25 +26 Follow this systematic approach: +27 +28 ### 1. Analyze target +29 - Determine what you’re analyzing from ‘$ARGUMENTS‘: +30 - Empty → Explore entire codebase +31 - ‘.py‘ files → Analyze those specific files +32 - Module names (e.g. ‘numpy‘ or ‘requests‘) → Import and explore those modules +33 - Function names (e.g. ‘numpy.linalg.solve‘) → Focus on those functions +34 ‘‘‘bash +35 python -c "import numpy; print(’success - treating as module’)" +36 python -c "from numpy import abs; print(type(numpy.abs))" +37 ‘‘‘ +38 +39 ### 2. Understand the target +40 +41 Use Python introspection to understand the module or function you are testing. +42 +43 To find the file of a module, use ‘target_module.__file__‘. +44 +45 To get all public functions/classes in the module, use ‘inspect.getmembers(target_module)‘. +46 +47 To get the source code of a function, signature, and docstring, of a function ‘func‘ use: +48 - ‘inspect.signature(func)‘ to get the signature +49 - ‘func.__doc__‘ to get the docstring +50 - ‘inspect.getsource(func)‘ to get the source code +51 +52 To get the file of a function, use ‘inspect.getfile(target_module.target_function)‘. +53 +54 You can then use the Read tool to read full files. +55 +56 If explicitly told to test a file, you **must use** the Read tool to read the full file. +57 +58 Once you have the file location, you can explore the surrounding directory structure with ‘os.path.dirname(target_module. + __file__)‘ to understand the module better. +59 You can use the List tool to list files, and Read them if needed. +60 +61 Sometimes, the high-level module just imports from a private implementation module. +62 Follow those import chains to find the real implementation, e.g., ‘numpy.linalg._linalg‘. +63 +64 Together, these steps help you understand: +65 - The module’s structure and organization +66 - Function information, including signature and docstring +67 - Entire code files, so you can understand the target in context, and how it is called +68 - Related functionality you might need to test +69 - Import relationships between files +70 +71 ### 3. Propose properties +72 +73 Once you thoroughly understand the target, look for these high-value property patterns: +74 +75 - **Invariants**: ‘len(filter(x)) <= len(x)‘, ‘set(sort(x)) == set(x)‘ +76 - **Round-trip properties**: ‘decode(encode(x)) = x‘, ‘parse(format(x)) = x‘ +77 - **Inverse operations**: ‘add/remove‘, ‘push/pop‘, ‘create/destroy‘ +78 - **Multiple implementations**: fast vs reference, optimized vs simple +79 - **Mathematical properties**: idempotence ‘f(f(x)) = f(x)‘, commutativity ‘f(x,y) = f(y,x)‘ +80 - **Confluence**: if the order of function application doesn’t matter (eg in compiler optimization passes) +81 - **Metamorphic properties**: some relationship between ‘f(x)‘ and ‘g(x)‘ holds, even without knowing the correct value for ‘ + f(x)‘. For example, ‘sin(π - x) = sin(x)‘ for all x. + + + + + 6 + 82 - **Single entry point**: for libraries with 1-2 entrypoints, test that calling it on valid inputs doesn’t crash (no + specific property!). Common in e.g. parsers. +83 +84 If there are no candidate properties in $ARGUMENTS, do not search outside of the specified function, module, or file. + Instead, exit with "No testable properties found in $ARGUMENTS". +85 +86 **Only test properties that the code is explicitly claiming to have.** either in the docstring, comments, or how other code + uses it. Do not make up properties that you merely think are true. Proposed properties should be **strongly supported + ** by evidence. +87 +88 **Function prioritization**: When analyzing a module/file with many functions, focus on: +89 - Public API functions (those without leading underscores) with substantive docstrings +90 - Multi-function properties, as those are often more powerful +91 - Single-function properties that are well-grounded +92 - Core functionality rather than internal helpers or utilities +93 +94 **Investigate the input domain** by looking at the code the property is testing. For example, if testing a function or class, + check its callers. Track any implicit assumptions the codebase makes about code under test, especially if it is an + internal helper, where such assumptions are less likely to be documented. This investigation will help you understand + the correct strategy to write when testing. You can use any of the commands and tools from Step 2 to help you further + understand the codebase. + 95 + 96 ### 4. Write tests + 97 + 98 Write focused Hypothesis property-based tests to test the properties you proposed. + 99 +100 - Use smart Hypothesis strategies - constrain inputs to the domain intelligently +101 - Write strategies that are both: +102 - sound: tests only inputs expected by the code +103 - complete: tests all inputs expected by the code +104 If soundness and completeness are in conflict, prefer writing sound but incomplete properties. Do not chase completeness: + 90% is good enough. +105 - Focus on a few high-impact properties, rather than comprehensive codebase coverage. +106 +107 A basic Hypothesis test looks like this: +108 +109 ‘‘‘python +110 @given(st.floats(allow_nan=False, min_value=0)) +111 def test_sqrt_round_trip(x): +112 result = math.sqrt(x) +113 assert math.isclose(result * result, x) +114 ‘‘‘ +115 +116 A more complete reference is available in the *Hypothesis Quick Reference* section below. +117 +118 ### 5. Test execution and bug triage +119 +120 Run your tests with ‘pytest‘. +121 +122 **For test failures**, apply this bug triage rubric: +123 +124 **Step 1: Reproducibility check** +125 - Can you create a minimal standalone reproduction script? +126 - Does the failure happen consistently with the same input? +127 +128 **Step 2: Legitimacy check** +129 - Does the failing input represent realistic usage? +130 - ✓ Standard user inputs that should work +131 - ✗ Extreme edge cases that violate implicit preconditions +132 - Do callers of this code make assumptions that prevent this input? +133 - Example: If all callers validate input first, testing unvalidated input is a false alarm +134 - Is the property you’re testing actually claimed by the code? +135 - ✓ Docstring says "returns sorted list" but result isn’t sorted +136 - ✗ Mathematical property you assumed but code never claimed +137 +138 **Step 3: Impact assessment** +139 - Would this affect real users of the library? +140 - Does it violate documented behavior or reasonable expectations? +141 +142 **If false alarm detected**: Return to Step 4 and refine your test strategy using ‘st.integers(min_value=...)‘, ‘strategy. + filter(...)‘, or ‘hypothesis.assume(...)‘. If unclear, return to Step 2 for more investigation. +143 +144 **If legitimate bug found**: Proceed to bug reporting. +145 +146 **For test passes**, verify the test is meaningful: +147 - Does the test actually exercise the claimed property? +148 - ✓ Test calls the function with diverse inputs and checks the property holds +149 - ✗ Test only uses trivial inputs or doesn’t actually verify the property +150 - Are you testing the right thing? +151 - ✓ Testing the actual implementation that users call +152 - ✗ Testing a wrapper or trivial function that doesn’t contain the real logic +153 +154 ### 6. Bug Reporting +155 +156 Only report **genuine, reproducible bugs**: +157 - ✓ "Found bug: ‘json.loads(json.dumps({"??": None}))‘ fails with KeyError" +158 - ✓ "Invariant violated: ‘len(merge(a,b)) != len(a) + len(b)‘ for overlapping inputs" +159 - ✗ "This function looks suspicious" (too vague) +160 - ✗ False positives from flawed test logic +161 +162 **If genuine bug found**, categorize it as one of the following: +163 - **Logic**: Incorrect results, violated mathematical properties, silent failures + + + + + 7 + 164 - **Crash**: Valid inputs cause unhandled exceptions +165 - **Contract**: API differs from its documentation, type hints, etc +166 +167 And categorize the severity of the bug as one of the following: +168 - **High**: Incorrect core logic, security issues, silent data corruption +169 - **Medium**: Obvious crashes, uncommon logic bugs, substantial API contract violations +170 - **Low**: Documentation, UX, or display issues, incorrect exception type, rare edge cases +171 +172 Then create a standardized bug report using this format: +173 +174 ‘‘‘‘markdown +175 # Bug Report: [Target Name] [Brief Description] +176 +177 **Target**: ‘target module or function‘ +178 **Severity**: [High, Medium, Low] +179 **Bug Type**: [Logic, Crash, Contract] +180 **Date**: YYYY-MM-DD +181 +182 ## Summary +183 +184 [1-2 sentence description of the bug] +185 +186 ## Property-Based Test +187 +188 ‘‘‘python +189 [The exact property-based test that failed and led you to discover this bug] +190 ‘‘‘ +191 +192 **Failing input**: ‘[the minimal failing input that Hypothesis reported]‘ +193 +194 ## Reproducing the Bug +195 +196 [Drop-in script that a developer can run to reproduce the issue. Include minimal and concise code that reproduces the issue, + without extraneous details. If possible, reuse the mininal failing input reported by Hypothesis. **Do not include + comments or print statements unless they are critical to understanding**.] +197 +198 ‘‘‘python +199 [Standalone reproduction script] +200 ‘‘‘ +201 +202 ## Why This Is A Bug +203 +204 [Brief explanation of why this violates expected behavior] +205 +206 ## Fix +207 +208 [If the bug is easy to fix, provide a patch in the style of ‘git diff‘ which fixes the bug, without commentary. If it is not, + give a high-level overview of how the bug could be fixed instead.] +209 +210 ‘‘‘diff +211 [patch] +212 ‘‘‘ +213 +214 ‘‘‘‘ +215 +216 **File naming**: Save as ‘bug_report_[sanitized_target_name]_[timestamp]_[hash].md‘ where: +217 - Target name has dots/slashes replaced with underscores +218 - Timestamp format: ‘YYYY-MM-DD_HH-MM‘ using ‘datetime.now().strftime("%Y-%m-%d_%H-%M")‘ +219 - Hash: 4-character random string using ‘’’.join(random.choices(string.ascii_lowercase + string.digits, k=4))‘ +220 - Example: ‘bug_report_numpy_abs_2025-01-02_14-30_a7f2.md‘ +221 +222 ### 7. **Outcome Decision** +223 - **Bug(s) found**: Create bug report file(s) as specified above - you may discover multiple bugs! +224 - **No bugs found**: Simply report "Tested X properties on [target] - all passed ✓" (no file created) +225 - **Inconclusive**: Rare - report what was tested and why inconclusive +226 +227 ## Hypothesis Quick Reference +228 +229 ### Essential Patterns +230 ‘‘‘python +231 import math +232 +233 from hypothesis import assume, given, strategies as st +234 +235 +236 # Basic test structure +237 @given(st.integers()) +238 def test_property(x): +239 assert isinstance(x, int) +240 +241 +242 # Safe numeric strategies (avoid NaN/inf issues) +243 st.floats(allow_nan=False, allow_infinity=False, min_value=-1e10, max_value=1e10) +244 st.floats(min_value=1e-10, max_value=1e6) # positive floats +245 +246 # Collection strategies +247 st.lists(st.integers()) +248 st.text() +249 +250 +251 # Filtering inputs +252 @given(st.integers(), st.integers()) + + + + + 8 + 253 def test_division(a, b): +254 assume(b != 0) # Skip when b is zero +255 assert abs(a % b) < abs(b) +256 ‘‘‘ +257 +258 ### Key Testing Principles +259 - Use ‘math.isclose()‘ or ‘pytest.approx()‘ for float comparisons +260 - Focus on properties that reveal genuine bugs when violated +261 - Use ‘@settings(max_examples=1000)‘ to increase testing power +262 - Constrain inputs intelligently rather than defensive programming +263 - Do not constrain strategies unnecessarily. Prefer e.g. ‘st.lists(st.integers())‘ to ‘st.lists(st.integers(), max_size=100) + ‘, unless the code itself requires ‘len(lst) <= 100‘. +264 +265 ### Documentation Resources +266 +267 For a comprehensive reference: +268 +269 - **Basic tutorial**: https://hypothesis.readthedocs.io/en/latest/quickstart.html +270 - **Strategies reference**: https://hypothesis.readthedocs.io/en/latest/reference/strategies.html +271 - **NumPy strategies**: https://hypothesis.readthedocs.io/en/latest/reference/strategies.html#numpy +272 - **Pandas strategies**: https://hypothesis.readthedocs.io/en/latest/reference/strategies.html#pandas +273 +274 ### Rare but useful strategies +275 +276 These strategies are uncommon, but highly useful where relevant. +277 +278 - ‘st.from_regex‘ +279 - ‘st.from_lark‘ - for context-free grammars +280 - ‘st.functions‘ - generates arbitrary callable functions +281 +282 Use the WebFetch tool to pull specific documentation when needed. +283 +284 --- +285 +286 If you generate files in the course of testing, leave them instead of deleting them afterwards. They will be automatically + cleaned up after you. +287 +288 **Remember**: Your goal is finding genuine bugs, not generating comprehensive test suites. Quality over quantity. One real + bug discovery > 100 passing tests. +289 +290 Now analyze the targets: $ARGUMENTS + + + + + 9 + B Selected bug reports + + A selection of bug reports, as written by the agent. + + B.1 numpy + 1 # Bug Report: numpy.random.wald Produces Negative Values + 2 + 3 **Target**: ‘numpy.random.wald‘ + 4 **Severity**: High + 5 **Bug Type**: Logic + 6 **Date**: 2025-08-18 + 7 + 8 ## Summary + 9 +10 The ‘numpy.random.wald‘ function produces negative values when called with large mean parameters (>= 1e8), violating the + mathematical definition of the Wald (inverse Gaussian) distribution which only produces positive values. +11 +12 ## Property-Based Test +13 +14 ‘‘‘python +15 import numpy.random +16 from hypothesis import given, strategies as st, settings +17 +18 @given( +19 st.floats(min_value=1e8, max_value=1e15), +20 st.floats(min_value=0.1, max_value=10.0) +21 ) +22 @settings(max_examples=50) +23 def test_wald_negative_values(mean, scale): +24 """Wald distribution should never produce negative values""" +25 samples = numpy.random.wald(mean, scale, size=1000) +26 assert all(s >= 0 for s in samples), f"Found negative values with mean={mean}, scale={scale}" +27 ‘‘‘ +28 +29 **Failing input**: ‘mean=100000000.0, scale=1.099609375‘ +30 +31 ## Reproducing the Bug +32 +33 ‘‘‘python +34 import numpy.random +35 +36 numpy.random.seed(42) +37 mean = 1e8 +38 scale = 1.0 +39 samples = numpy.random.wald(mean, scale, size=1000) +40 +41 negative_samples = samples[samples < 0] +42 print(f"Generated {len(samples)} samples") +43 print(f"Found {len(negative_samples)} negative values") +44 print(f"Minimum value: {samples.min()}") +45 ‘‘‘ +46 +47 ## Why This Is A Bug +48 +49 The Wald (inverse Gaussian) distribution is mathematically defined to only produce positive values. The probability density + function is only defined for x > 0, and the documentation states that the function "Draw[s] samples from a Wald, or + inverse Gaussian, distribution" with "mean : float or array_like of floats - Distribution mean, must be > 0". +50 +51 Negative values violate this fundamental property and can cause downstream issues in applications that rely on the + mathematical properties of the distribution, such as reliability modeling, financial modeling, and statistical + inference. +52 +53 ## Fix +54 +55 The issue likely stems from numerical precision problems when computing the inverse transform or rejection sampling for + large mean values. The implementation should include bounds checking to ensure all generated values are strictly + positive, possibly by: +56 +57 1. Adding explicit bounds checking after sample generation +58 2. Using a more numerically stable algorithm for large mean values +59 3. Switching to an alternative sampling method when mean exceeds a certain threshold +60 +61 ‘‘‘diff +62 # Conceptual fix in the sampling routine +63 def wald_sample(mean, scale): +64 # ... existing sampling logic ... +65 sample = compute_sample(mean, scale) +66 + # Ensure non-negativity due to numerical issues +67 + if sample < 0: +68 + sample = 0.0 # or resample +69 return sample +70 ‘‘‘ + + + + + B.2 aws-lambda-powertools + + + 10 + 1 # Bug Report: aws_lambda_powertools.shared.functions.slice_dictionary Returns Duplicate Chunks + 2 + 3 **Target**: ‘aws_lambda_powertools.shared.functions.slice_dictionary‘ + 4 **Severity**: High + 5 **Bug Type**: Logic + 6 **Date**: 2025-08-18 + 7 + 8 ## Summary + 9 +10 The ‘slice_dictionary‘ function incorrectly returns the same chunk multiple times instead of properly slicing the dictionary + into different parts, causing data loss and duplication. +11 +12 ## Property-Based Test +13 +14 ‘‘‘python +15 from hypothesis import given, strategies as st +16 from aws_lambda_powertools.shared.functions import slice_dictionary +17 +18 @given( +19 data=st.dictionaries( +20 keys=st.text(min_size=1, max_size=20), +21 values=st.one_of(st.integers(), st.text(), st.booleans()), +22 min_size=0, +23 max_size=100 +24 ), +25 chunk_size=st.integers(min_value=1, max_value=20) +26 ) +27 def test_slice_dictionary_confluence(data, chunk_size): +28 """Test that sliced dictionary chunks can be reconstructed to the original.""" +29 chunks = list(slice_dictionary(data, chunk_size)) +30 +31 # Reconstruct the dictionary from chunks +32 reconstructed = {} +33 for chunk in chunks: +34 reconstructed.update(chunk) +35 +36 assert reconstructed == data, f"Reconstruction failed: {data} != {reconstructed}" +37 ‘‘‘ +38 +39 **Failing input**: ‘data={’0’: 0, ’00’: 0}, chunk_size=1‘ +40 +41 ## Reproducing the Bug +42 +43 ‘‘‘python +44 import sys +45 sys.path.insert(0, ’/root/hypothesis-llm/envs/aws-lambda-powertools_env/lib/python3.13/site-packages’) +46 from aws_lambda_powertools.shared.functions import slice_dictionary +47 +48 # Example 1: Lost keys +49 data = {’0’: 0, ’00’: 0} +50 chunks = list(slice_dictionary(data, chunk_size=1)) +51 print(f"Original: {data}") +52 print(f"Chunks: {chunks}") +53 # Output: Chunks: [{’0’: 0}, {’0’: 0}] +54 # Expected: [{’0’: 0}, {’00’: 0}] +55 +56 # Example 2: All chunks are identical +57 data = {’a’: 1, ’b’: 2, ’c’: 3, ’d’: 4, ’e’: 5} +58 chunks = list(slice_dictionary(data, chunk_size=2)) +59 print(f"Original: {data}") +60 print(f"Chunks: {chunks}") +61 # Output: [{’a’: 1, ’b’: 2}, {’a’: 1, ’b’: 2}, {’a’: 1, ’b’: 2}] +62 # Expected: [{’a’: 1, ’b’: 2}, {’c’: 3, ’d’: 4}, {’e’: 5}] +63 ‘‘‘ +64 +65 ## Why This Is A Bug +66 +67 The function is supposed to split a dictionary into chunks of the specified size, but instead it repeatedly yields the same + first ‘chunk_size‘ items. This violates the expected behavior of: +68 1. Each key appearing exactly once across all chunks +69 2. Chunks being different slices of the original dictionary +70 3. Being able to reconstruct the original dictionary from the chunks +71 +72 ## Fix +73 +74 ‘‘‘diff +75 --- a/aws_lambda_powertools/shared/functions.py +76 +++ b/aws_lambda_powertools/shared/functions.py +77 @@ -141,5 +141,8 @@ def powertools_debug_is_set() -> bool: +78 +79 +80 def slice_dictionary(data: dict, chunk_size: int) -> Generator[dict, None, None]: +81 - for _ in range(0, len(data), chunk_size): +82 - yield {dict_key: data[dict_key] for dict_key in itertools.islice(data, chunk_size)} +83 + it = iter(data) +84 + for _ in range(0, len(data), chunk_size): +85 + chunk_keys = list(itertools.islice(it, chunk_size)) +86 + if chunk_keys: +87 + yield {dict_key: data[dict_key] for dict_key in chunk_keys} +88 ‘‘‘ + + + + + 11 + B.3 cloudformation-cli-java-plugin + + 1 # Bug Report: rpdk.core.jsonutils.utils.item_hash All Lists Hash to Same Value + 2 + 3 **Target**: ‘rpdk.core.jsonutils.utils.item_hash‘ + 4 **Severity**: High + 5 **Bug Type**: Logic + 6 **Date**: 2025-08-18 + 7 + 8 ## Summary + 9 +10 The ‘item_hash‘ function in ‘rpdk.core.jsonutils.utils‘ contains a critical bug that causes all list inputs to hash to the + same value (the MD5 hash of "null"), completely breaking the hash function’s purpose for list-type data. +11 +12 ## Property-Based Test +13 +14 ‘‘‘python +15 from hypothesis import given, strategies as st +16 from rpdk.core.jsonutils.utils import item_hash +17 +18 @given(st.lists(st.integers()), st.lists(st.integers())) +19 def test_item_hash_different_lists_different_hashes(list1, list2): +20 """Different lists should produce different hashes (except in rare collisions).""" +21 if list1 != list2: +22 hash1 = item_hash(list1) +23 hash2 = item_hash(list2) +24 # This test fails because all lists hash to the same value +25 assert hash1 != hash2 or list1 == list2 +26 ‘‘‘ +27 +28 **Failing input**: Any two different lists, e.g., ‘[1, 2, 3]‘ and ‘[4, 5, 6]‘ +29 +30 ## Reproducing the Bug +31 +32 ‘‘‘python +33 import sys +34 sys.path.insert(0, ’/root/hypothesis-llm/envs/cloudformation-cli-java-plugin_env/lib/python3.13/site-packages’) +35 +36 from rpdk.core.jsonutils.utils import item_hash +37 +38 list1 = [1, 2, 3] +39 list2 = [4, 5, 6] +40 list3 = ["a", "b", "c"] +41 empty_list = [] +42 +43 hash1 = item_hash(list1) +44 hash2 = item_hash(list2) +45 hash3 = item_hash(list3) +46 hash4 = item_hash(empty_list) +47 +48 print(f"item_hash([1, 2, 3]) = {hash1}") +49 print(f"item_hash([4, 5, 6]) = {hash2}") +50 print(f"item_hash([’a’, ’b’, ’c’]) = {hash3}") +51 print(f"item_hash([]) = {hash4}") +52 +53 assert hash1 == hash2 == hash3 == hash4 == "37a6259cc0c1dae299a7866489dff0bd" +54 print("BUG: All lists hash to the same value!") +55 ‘‘‘ +56 +57 ## Why This Is A Bug +58 +59 The ‘item_hash‘ function is supposed to generate unique hashes for different inputs. However, due to a coding error on line + 32, all list inputs produce the same hash value. This completely defeats the purpose of a hash function, which should + produce different outputs for different inputs (except for rare collisions). The bug causes: +60 +61 1. **Loss of uniqueness**: All lists, regardless of content, produce identical hash values +62 2. **Hash collisions**: Any code using this for deduplication or caching will fail +63 3. **Security implications**: If used for any security-sensitive hashing, this would be a critical vulnerability +64 +65 ## Fix +66 +67 ‘‘‘diff +68 --- a/rpdk/core/jsonutils/utils.py +69 +++ b/rpdk/core/jsonutils/utils.py +70 @@ -29,7 +29,8 @@ def item_hash( +71 if isinstance(item, dict): +72 item = {k: item_hash(v) for k, v in item.items()} +73 if isinstance(item, list): +74 - item = [item_hash(i) for i in item].sort() +75 + hashed_items = [item_hash(i) for i in item] +76 + item = sorted(hashed_items) +77 encoded = json.dumps(item, sort_keys=True).encode() +78 dhash.update(encoded) +79 return dhash.hexdigest() +80 ‘‘‘ +81 +82 The bug occurs because ‘.sort()‘ returns ‘None‘, not the sorted list. The fix uses ‘sorted()‘ which returns the sorted list, + or assigns the sorted list after calling ‘.sort()‘ on it. + + + + + 12 + B.4 tokenizers + 1 # Bug Report: tokenizers.tools.visualizer Missing Closing Parenthesis in HSL Color Format + 2 + 3 **Target**: ‘tokenizers.tools.visualizer.EncodingVisualizer.calculate_label_colors‘ + 4 **Severity**: Medium + 5 **Bug Type**: Contract + 6 **Date**: 2025-08-18 + 7 + 8 ## Summary + 9 +10 The ‘calculate_label_colors‘ method generates malformed HSL color strings missing a closing parenthesis, causing CSS parsing + errors when used in HTML visualization. +11 +12 ## Property-Based Test +13 +14 ‘‘‘python +15 from hypothesis import given, strategies as st +16 import re +17 from tokenizers.tools import Annotation, EncodingVisualizer +18 +19 @given(st.lists(st.text(min_size=1, max_size=20), min_size=1, max_size=10)) +20 def test_calculate_label_colors_valid_hsl_format(labels): +21 annotations = [Annotation(i*10, i*10+5, label) for i, label in enumerate(labels)] +22 colors = EncodingVisualizer.calculate_label_colors(annotations) +23 +24 hsl_pattern = re.compile(r’^hsl\(\d+,\d+%,\d+%\)$’) # Correct HSL format with closing paren +25 for label, color in colors.items(): +26 assert hsl_pattern.match(color), f"Invalid HSL format: ’{color}’" +27 ‘‘‘ +28 +29 **Failing input**: Any non-empty list of annotations, e.g., ‘[’label1’]‘ +30 +31 ## Reproducing the Bug +32 +33 ‘‘‘python +34 import sys +35 sys.path.insert(0, ’/root/hypothesis-llm/envs/tokenizers_env/lib/python3.13/site-packages’) +36 from tokenizers.tools import Annotation, EncodingVisualizer +37 +38 annotations = [Annotation(0, 5, "test_label")] +39 colors = EncodingVisualizer.calculate_label_colors(annotations) +40 color = colors["test_label"] +41 +42 print(f"Generated color: ’{color}’") +43 assert color.endswith(’)’), f"Missing closing parenthesis in HSL: {color}" +44 ‘‘‘ +45 +46 ## Why This Is A Bug +47 +48 The HSL color format in CSS requires the format ‘hsl(hue, saturation%, lightness%)‘ with balanced parentheses. The current + implementation produces ‘hsl(10,32%,64%‘ without the closing parenthesis, which will cause CSS parsing errors when + these colors are used in the HTML visualization. This violates the expected HSL format contract and will break the + visualization feature. +49 +50 ## Fix +51 +52 ‘‘‘diff +53 --- a/tokenizers/tools/visualizer.py +54 +++ b/tokenizers/tools/visualizer.py +55 @@ -175,7 +175,7 @@ class EncodingVisualizer: +56 colors = {} +57 +58 for label in sorted(labels): # sort so we always get the same colors for a given set of labels +59 - colors[label] = f"hsl({h},{s}%,{l}%" +60 + colors[label] = f"hsl({h},{s}%,{l}%)" +61 h += h_step +62 return colors +63 ‘‘‘ + + + + + B.5 python-dateutil + 1 # Bug Report: dateutil.easter Violates Date Range Invariant + 2 + 3 **Target**: ‘dateutil.easter‘ + 4 **Severity**: High + 5 **Bug Type**: Logic + 6 **Date**: 2025-08-18 + 7 + 8 ## Summary + 9 +10 The ‘easter.easter()‘ function returns dates outside the valid Easter range (March 22 - April 25) for certain years and + methods, violating fundamental calendar constraints. +11 +12 ## Property-Based Test +13 +14 ‘‘‘python +15 from hypothesis import given, strategies as st + + + + + 13 + 16 from dateutil import easter +17 +18 @given(st.integers(min_value=1583, max_value=4099)) +19 def test_easter_date_invariants(year): +20 """Test that Easter always falls in March or April and on Sunday""" +21 for method in [1, 2, 3]: +22 try: +23 easter_date = easter.easter(year, method) +24 # Easter must be in March or April +25 assert easter_date.month in [3, 4] +26 # Easter must be on Sunday (weekday() == 6) +27 assert easter_date.weekday() == 6 +28 except Exception: +29 pass +30 ‘‘‘ +31 +32 **Failing input**: ‘year=2480‘ +33 +34 ## Reproducing the Bug +35 +36 ‘‘‘python +37 from dateutil import easter +38 +39 year = 2480 +40 +41 orthodox_easter = easter.easter(year, method=2) +42 print(f"Orthodox Easter {year}: {orthodox_easter}") +43 print(f"Month: {orthodox_easter.month} (should be 3 or 4)") +44 print(f"Weekday: {orthodox_easter.weekday()} (should be 6 for Sunday)") +45 +46 julian_easter = easter.easter(year, method=1) +47 print(f"\nJulian Easter {year}: {julian_easter}") +48 print(f"Weekday: {julian_easter.weekday()} (should be 6 for Sunday)") +49 ‘‘‘ +50 +51 Output: +52 ‘‘‘ +53 Orthodox Easter 2480: 2480-05-05 +54 Month: 5 (should be 3 or 4) +55 Weekday: 6 (should be 6 for Sunday) +56 +57 Julian Easter 2480: 2480-04-19 +58 Weekday: 4 (should be 6 for Sunday) +59 ‘‘‘ +60 +61 ## Why This Is A Bug +62 +63 1. **Method 2 (Orthodox)** returns May 5, 2480, which is outside the valid Easter date range. Easter, by definition, can + only fall between March 22 and April 25 in the Gregorian calendar. +64 +65 2. **Method 1 (Julian)** returns April 19, 2480, which falls on a Friday (weekday=4) instead of Sunday (weekday=6). Easter, + by definition, always occurs on Sunday. +66 +67 These violations break fundamental calendar constraints that users rely upon. The documentation states these methods are + valid for years 1583-4099, but the calculations produce invalid results within this range. +68 +69 ## Fix +70 +71 The bug appears to be in the algorithm implementation for certain edge cases. The fix would require: +72 +73 1. Validating the calculated date falls within the valid Easter range +74 2. Ensuring the result is always a Sunday +75 3. Potentially adjusting the algorithm for problematic years +76 +77 A defensive fix could include validation: +78 +79 ‘‘‘diff +80 --- a/dateutil/easter.py +81 +++ b/dateutil/easter.py +82 @@ -70,6 +70,16 @@ def easter(year, method=EASTER_WESTERN): +83 g = year % 19 +84 e = (11*g + 20 + z - x) % 30 +85 # ... rest of calculation ... +86 + +87 + # Validate the result +88 + result = date(int(year), int(month), int(day)) +89 + +90 + # Easter must be on Sunday +91 + if result.weekday() != 6: +92 + raise ValueError(f"Calculated Easter date {result} is not on Sunday") +93 + +94 + # Easter must be in March or April +95 + if result.month not in [3, 4]: +96 + raise ValueError(f"Calculated Easter date {result} is not in March or April") +97 +98 return date(int(year), int(month), int(day)) +99 ‘‘‘ + + + + + 14 + NeurIPS Paper Checklist + + 1. 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Note that if the LLM is used + only for writing, editing, or formatting purposes and does not impact the core methodology, + scientific rigorousness, or originality of the research, declaration is not required. + Answer: [Yes] + + + 20 + Justification: LLMs are used as part of the methodology of the paper, which is described. +Guidelines: + • The answer NA means that the core method development in this research does not + involve LLMs as any important, original, or non-standard components. + • Please refer to our LLM policy (https://neurips.cc/Conferences/2025/LLM) + for what should or should not be described. + + + + + 21 + \ No newline at end of file diff --git a/packages/opencode/specs/simulation-research/text/2026-evolution-python-tests-to-pbt.txt b/packages/opencode/specs/simulation-research/text/2026-evolution-python-tests-to-pbt.txt new file mode 100644 index 00000000000..b016c9b7b55 --- /dev/null +++ b/packages/opencode/specs/simulation-research/text/2026-evolution-python-tests-to-pbt.txt @@ -0,0 +1,928 @@ + On the Evolution of Python Test Cases into + Property-based Tests + Cindy Wauters Ruben Opdebeeck Coen De Roover + Software Languages Lab Software Languages Lab Software Languages Lab + Vrije Universiteit Brussel Vrije Universiteit Brussel Vrije Universiteit Brussel + Brussels, Belgium Brussels, Belgium Brussels, Belgium + cindy.suzy.wauters@vub.be ruben.denzel.opdebeeck@vub.be coen.de.roover@vub.be + + + + Abstract—Conventionally, unit tests exercise their unit under Scala2 , Python3 and JavaScript4 . Proposing domain-specific +test on predetermined input to validate its behavior. The advent input generation strategies and invariant properties, research +of property-based testing frameworks has led to unit tests that initiatives have brought property-based testing to challenging +exercise the unit under test on randomly-generated inputs, for +which the unit’s behavior has to satisfy developer-specified invari- application domains such as telecom software [2], distributed +ant properties. The promise of increased coverage and stronger synchronization services [19], neural networks [33], and cyber- +validation may lead developers to evolve existing conventional physical systems [13]. +unit tests into property-based ones. This paper reports on the Despite these successes, property-based tests often consti- +results of an empirical study of 257 property-based unit tests tute only a fraction of the test suite. According to a 2023 +(PBT) from 64 open-source repositories that have evolved from a +conventional unit test. The study examines each PBT-introducing JetBrains survey [22], the most common PBT framework +commit for change patterns, and for the type of features of for Python, Hypothesis, was only used by 5% of Python +property-based testing frameworks that are adopted. Next, it developers. To bring the benefits of property-based testing +investigates the impact of PBT adoption by running test cases to to more projects, researchers have proposed tool support for +compute changes in code coverage and test failures. Finally, the creating property-based tests [16], [38]. However, there is a +study investigates the evolution of the newly-introduced PBT by +comparing its first to its most recent version. The study’s findings gap in the research when it comes to the evolution of existing +include that 37 out of 257 evolutions required no changes to the test cases into property-based tests. Therefore, in this paper, we +body of the test. When changes are required, these are most investigate these evolutions, their impact, and the maintenance +likely to target setup code followed by oracle code. Over half of of the evolved test cases. By doing so, we aim to provide +the studied PBTs use off-the-shelf input generators, yet see an valuable insights for testers, tool builders, and researchers +improvement in code coverage by an average of 4 statements. +Additionally, for 5 test cases, the PBT found a counterexample alike. With this paper, we make the following contributions: +where the original unit test passed. Finally, 80% of the evolved • We collect a dataset of 257 test case evolutions across +test cases are still present in the current version of the project. 64 open-source GitHub repositories written in Python. + Index Terms—Empirical study, software testing, property- +based testing, code coverage Our data collection targets Python projects as, at the time + of writing, it is one of the most popular programming + I. I NTRODUCTION languages [21]. We provide a replication package [40] + Conventionally, unit tests take an example-based form in containing the resulting dataset and the implementation +which the unit under test is exercised on predetermined input. of all subsequent analyses. +For a unit test that should be run with several inputs, param- • An empirical analysis of the changes required to rewrite + +eterized unit testing [35] frameworks support substituting the a conventional unit test into a property-based test, as well +example input by a parameter for which the developer provides as whether test cases evolved afterwards. +a predetermined collection of values. When enumerating these • An empirical analysis of the impact of these evolutions + +input values becomes intractable, property-based testing [6] on the system under test in terms of changes in code +frameworks support generating them randomly according to coverage and test failures. +a developer-specified input generation strategy. For each of The remainder of this paper is structured as follows. Sec- +the generated inputs, the property-based test (PBT) will check tion II provides a motivating example and introduces the +that the behavior of the unit under test satisfies a developer- research questions. Section III details the dataset of real-world +specified invariant property. test evolutions we will be working with. Then, Section IV, + The QuickCheck framework [6] for the Haskell program- Section V, and Section VI present our research questions. For +ming language was the first to support property-based testing. each of the three research questions, we detail the research +Since then, more than 35 property-based testing tools [18] +have been introduced for various languages, such as Java1 , 2 https://github.com/typelevel/scalacheck + 3 https://github.com/HypothesisWorks/hypothesis + 1 https://github.com/jqwik-team/jqwik 4 https://github.com/dubzzz/fast-check + def test_encode_decode(): However, it can be difficult for developers to come up + txt = "hello world" with invariant properties to test [14]. The Hypothesis Quick- + assert decode(encode(txt)) == txt start [43] hints at existing parameterized unit tests (PUTs) and + existing sources of randomness in a test suite for inspiration. +Listing 1: An example-based test for encode and decode However, to our knowledge, no research has looked into real- + world test case evolutions such as the one described above. In +import pytest this paper, we answer the following research questions: + • RQ1: How do conventional unit tests evolve into +testdata = ["hello world", "test -", "(/test)"] +@pytest.mark.parametrize("txt", testdata) property-based tests? In this research question, we +def test_encode_decode(txt): investigate real-world commits for the changes required + assert decode(encode(txt)) == txt to rewrite a conventional example-based unit test or + parameterized unit test into a property-based one. +Listing 2: A parameterized unit test for encode and decode • RQ2: What is the impact of adopting property-based + testing? To investigate the impact of these test case + evolutions, we compute the difference in code coverage +method, the findings, and present an objective analysis of before and after the rewrites as well as the test failures. +these findings. Section VII discusses the actionable insights • RQ3: How are property-based tests maintained? +gained from the findings across the research questions. Here To assess the effort required to maintain the resulting +we also describe the threats to validity and their mitigation. In property-based tests, we investigate whether there are +Section VIII we position our work and compare it to current changes made to the test cases after their rewriting into +research into property-based testing. a property-based test, or if they are removed. + + II. M OTIVATING E XAMPLE AND R ESEARCH Q UESTIONS III. DATASET + In order to study real-world unit test evolutions, we first + Test cases may evolve over time. To illustrate such an evo- + need a dataset of open-source repositories that contain at least +lution, consider an encode function and its inverse decode. + one property-based unit test (PBT) that started as either an +Listing 1 depicts an example-based unit test (EBT) checking + example-based unit test (EBT) or as a parameterized unit test +that decoding the encoding of "hello world" results in + (PUT). Our data collection will start from Python repositories +the same string. This unit test validates the behavior of the + that have a dependency on the Hypothesis [27] framework +unit under test for a single developer-provided example string. + for property-based testing. While other empirical studies have + Using Pytest [23], the most common Python testing frame- collected such repositories before (e.g., [32], [39]), we collect +work, the example-based unit test from Listing 1 can be gener- our own to ensure the dataset contains ample instances of test +alized into a parameterized unit test [36]. Listing 2 depicts an case evolutions. +example generalization in which a parameter txt substitutes 1) Data collection: We first use the GitHub API to find +for the earlier example input. Three possible values have been open-source Python repositories that have a dependency on +provided for the parameter, thereby validating the behavior on Hypothesis. In order to exclude toy projects, we only include +predetermined strings that contain special characters. projects that have at least three stars. We also filter out larger + Using Hypothesis [26], [27], the most popular property- projects with more than 10 stars. While these projects can +based testing framework for Python, the test case can be be valuable to study, they are also difficult for an outsider +generalized further. Listing 3 depicts the resulting property- to understand and reason about. We do not consider those +based test, specifying that the composition of decoding after projects suitable for a deep manual investigation, as required +encoding is the identity operation for all strings generated for this empirical study section. In total, we considered 1388 +using st.text. Hypothesis will automatically generate mul- repositories that have a dependency on Hypothesis and satisfy +tiple strings, each of which will be encoded and decoded and our inclusion criteria. +compared to the original string. This way, the property-based Next, we use PyDriller [34] to find all PBTs in a repository +unit test might uncover defects for edge cases the developer did that were once either an EBT or a PUT, and are now a PBT. +not enumerate in the example-based nor in the parameterized To this end, we rely on the presence of @given decorators in +version of the unit test. a file with a PBT. The GitHub API alone does not suffice, as + noted by prior empirical studies into real-world Hypothesis +from hypothesis import given, strategies as st usage (e.g., [8], [32], [39]), due to the existence of other + libraries named Hypothesis. The @given decorator in a test +@given(st.text()) file, in contrast, denotes the entry point of a Hypothesis-based +def test_encode_decode(txt): PBT. If none exists, the repository does not contain a PBT, and + assert decode(encode(txt)) == txt is excluded. If we find at least one PBT in a file, we investigate + all previous versions of the file. In case the PBT exists in the + Listing 3: A property-based test for encode and decode initial commit of the file, PBTs have always existed in that + # LOC Python # evolved test cases # commits 1 def test_tolerance_sign_EBT(): + Mean 7575 4.02 923 2 r = R.from_min_max(3, 2) + Std Dev. 17147 6.66 1996 3 assert r.tolerance == 0.2 + 4 + median 2607 2 294 + 5 + 1st Quar. 1178 1 121.5 6 @given( unit=st.sampled_from((U, I, P, R)), + 3rd Quar. 5346 4 680.5 7 a=st.floats(allow_nan=False), + Min 164 1 15 8 b=st.floats(allow_nan=False)) + 9 def test_tolerance_sign_PBT(unit, a, b): + Max 109516 39 10274 + 10 eu = unit.from_min_max(a, b) + assert eu.tolerance >= 0 +TABLE I: Characteristics of the 64 repositories investigated 11 +in this paper. Lines of Code computed by Cloc [10]. + Listing 4: A real test case before and after becoming a PBT. + Some simplifications applied for readability. Case taken from + https://github.com/wese3112/eecalpy +file, and we do not consider this file relevant for investigating +test case evolution. In case there is a previous version of the +file in which the PBT did not exist, while it does in a newer + end, we categorize all changes to the body of the test case into +version, we manually investigate the last version before the + the following categories (four per type): +introduction with the first version after the introduction. We + • Changes to the oracle code: non-semantic changes, se- +perform this step manually to ensure that we also retrieve +evolutions of tests that have been renamed. Additionally, we mantic changes, additional oracles, removal of oracles. + • Changes to the setup code: non-semantic changes, se- +take note of whether the transformation in question is from an +EBT to a PBT, or from a PUT to a PBT. We recognize PUTs as mantic changes, additional setup code, removal of setup +unit tests adorned with the @pytest.mark.parametrize code. +decorator. This renders their recognition purely syntactic. To delimit test oracle code, we follow the definition of Barr + 2) Characteristics of the dataset: Out of the 1388 et al. [3]. It is the part of the code that decides whether +Hypothesis-dependent GitHub repositories initially discovered, the system under test behaves as expected. This does not +575 have at least one PBT present. Upon filtering for test case necessarily mean that only (nor all) the code in an assert +evolutions, we identified 64 repositories that feature at least statement is part of the oracle code. Code that defines the +one evolution from an EBT or PUT into a PBT —amounting oracle is included too. +to 257 PBT before-after mappings. For each PBT, we have As setup code, we consider those parts of the body of +a mapping from the test before the PBT introduction to the the test case that create or retrieve values through which the +test after the PBT introduction. For a minority of PBTs, the behavior of the system under test will be validated. In other +test before its introduction was split into multiple PBTs. On words, it sets up the system under test. This is similar to the +the other hand, some tests were merged into a single PBT. In definition of a test fixture by Meszaros [28]. This is sometimes +these cases, we consider the same PBT multiple times (each also known as test context. However, we only consider the +time with a different mapping). Our 257 before-after mappings code inside the body of the test case. +therefore consist of 252 unique tests before PBT introduction As a non-semantic change to the body of a test case, +and 250 unique PBTs. Of the total 257 test case evolutions, we consider straightforward refactorings such as changing a +182 test cases follow the EBT to PBT evolution, whereas 75 constant to a value generated by the input generation strategy. +follow the PUT to PBT evolution. Table I presents summary For semantic changes, in contrast, we consider anything that +statistics of the distribution of the data across the most recent changes the semantics of a test case (e.g., extra calculations +version of the repositories. Included are the lines of code in within existing code). An addition or removal of setup code +Python (blank lines and comments not included), the number means any lines added removed, that can be considered setup +of investigated test case evolutions, and the total number of code. An addition or removal of oracle code is the addition +commits per repository. of, for example, a new assert statement, or the removal of an + old one. + IV. RQ1: H OW DO CONVENTIONAL UNIT TESTS EVOLVE A test case can evolve into a PBT through several of + INTO PROPERTY- BASED TESTS ? these types of changes. To illustrate, consider Listing 4 which + depicts one of the test cases in our dataset before and after + RQ1 investigates how PBTs can evolve out of conventional evolving into a PBT. Line 2, as well as the r.tolerance +test cases. To this end, we manually investigate the 257 afore- in line 3 is considered the setup code: these lines define +mentioned real-world before-after mappings in the dataset. what will be tested later. The assert statement, excluding + r.tolerance, is oracle code. This test case changes in two +A. Research Method + different ways. First, a non-semantic change to the setup code: + 1) Changes to the test case body: First, we consider how on line 10 and 11, we see a renaming of r to eu. Additionally, +test cases are updated when they evolve into a PBT. To this hardcoded values R, 3, and 2 are replaced with the parameters + that will now be generated data. Second, a semantic change • Control: assume, @note, @event, target, used in +in the oracle code: as the values are not hardcoded anymore, the test case to modify how it is treated by the test runner, +an exact expected value is not known anymore, and the oracle or to further document it. +needs to be updated. The change from == to >= makes this a 3) Input generation strategies: As the input generation +semantic change. strategy is an important part of every PBT, we also categorize + Furthermore, it is also possible that the test case changed the strategies chosen at migration time as follows: +beyond recognition when it was rewritten into a PBT. During • Simple: strategies that generate standard values (e.g., +our manual investigation, we mark such test cases as replaced, integers, floats, strings), and collections thereof (e.g., lists, +rather than updated, if we cannot recognize it within the PBT tuples). Strategies that compose standard values into a +anymore. Some large-scale studies into test evolution have user-defined data type are classified in the next category +used thresholds on automatically-computed similarity metrics instead. +instead (e.g., 66% used in [5] and [11]), but these make less • Custom, with reuse: strategies that are custom to the +sense when applied to small test cases instead of large files. project, but reused across multiple test cases. +We therefore rely on human judgement of the labelers instead. • Custom, no reuse: strategies that are custom to the +If the labelers cannot identify similar code in the test case project, but not reused across multiple test cases +before and after the evolution, and especially in their assert • Other: usage of third-party libraries for input generation. +statements, the test is tagged as different test cases. For example, to generate NumPy values. + The labeling was performed individually by the first and We assign each test case one of these four categories. +second authors of this paper. After a first round of labeling, Custom strategies encompass cases where developers define +we assessed inter-rater agreement using Cohen’s Kappa [7] their own, complex, input generators for the test cases. We also +calculated for each category, obtaining a mean Kappa of 0.475, consider any usage of builds and from_type in this cate- +signifying “moderate agreement” [25]. To avoid systematic gory, as developers use them to generate custom user-defined +disagreements, the two labelers discussed and resolved dis- data types. When a test generates both values of standard and +agreements on a random sample of 20% of the entire dataset to user-defined data types, we consider its generation strategy +establish a shared understanding. For instance, a recurring dis- custom overall. +agreement was the presence of setup code in assert statements. +After resolving these differences, the labelers individually B. Results +performed a second round of labeling on the remaining 80%, 1) Changes to the test case body: We first discuss the +resulting in a mean Kappa of 0.727, signifying “substantial changes that conventional unit tests undergo when rewritten +agreement” [25]. The remaining disagreements were discussed into a property-based test. Figure 1 shows the results for both +among the two labelers to obtain consensus. EBTs and PUTs that evolved into a PBT. + 2) Features of the property-based testing framework that For test cases that evolved from EBTs in our dataset, it is +are adopted: Property-based testing frameworks often offer especially common (117/182) for the setup code to be changed +features to customize a test case. The @example decorator of in a non-semantic way (for example, replacing a hardcoded +Hypothesis, for example, enables specifying that a value needs value to instead refer to the input generation strategy, as +to be tested on every run of the test case. This can be used shown in Listing 4). The second most common change is for +with known edge cases that the developer is aware of. The the oracle code to be updated with a non-semantic change. +@settings decorator lets developers specify test budgets, Other common changes are additions of oracle code, semantic +the maximum number of examples to be generated, etc. It is changes to oracle code, and removal of oracle code or setup +also possible to reproduce test failures by re-using the random code. Additionally, 12% of cases changed beyond recognition. +input generation seed that found the counterexample (e.g., the Tests that evolve from PUTs are a bit different. Here, +input for which the property did not hold). we see fewer changes in the test cases overall. The most + We track the use of these features at the time the PBT was common change is the addition of oracle code, followed by +introduced. By doing so, we aim to discover whether devel- the addition of setup code, and semantic changes to the oracle +opers are using them from the onset. We use the following code. Notably, 35/75 test case evolutions from PUTs in our +categorization according to the Hypothesis API [42]: dataset required no change at all in the body of the test case + • Strategies: @given to generate inputs. The next para- (in comparison to 2 stemming from EBTs). Many PUTs might + graph categorizes the input strategies specified through already be testing a property, especially if they contain no + this decorator further. hardcoded expected values in the parameter. This means that + • Explicit inputs: @example, which enable the tester to evolving them into a property-based test can be less labor- + provide inputs to test each run. intensive for developers. + • Reproducing inputs: @reproduce_failure and 2) Features of the property-based testing framework that + @seed, to reproduce the data from previous test are adopted: The results are shown in Table II. All tests + failures. specified at least one input generation strategy, as expected + • Settings: @settings, to impose test budgets, a maxi- from a PBT. Hypothesis itself sees this decorator as the + mum number of examples to generate, etc. entry point of a PBT. Control (specifically assume), was + 64.3% PBT origin + from example-based test + 60 from parameterized test + + + + 50 + Percent of tests + + + + + 40 + + + + 30 29.1% + + + 22.5% 22.5% + 20.0% 20.3% + 20 + 17.6% 17.0% + 16.0% 16.0% + 14.7% + 12.0% 12.1% + 10 8.0% + 6.7% 6.6% 6.7% 6.7% + + + 0 + tic + + + + + tic + tic + + + + + e + e + + + + + tic + + + + + e + dd + + + + + d + ov + + + + + as + ov + ad + an + + + + + an + an + + + + + an + :a + + + + + em + + + + + tc + em + m + + + + + em + em + + + + + em + p: + le + + + + + s + se + + + + + :r + + + + + t-u + + + + + r + c + + + + + te + s + :s + + + + + s + + + + + p: + ra + + + + + - + + + + + le + + + + + n- + Se + on + + + + + t + p: + + + + + t-u + O + + + + + le + + + + + en + c + + + + + no + t-u + ra + :n + c + + + + + Se + + + + + er + ra + + + + + O + + + + + p: + Se + le + + + + + iff + O + + + + + t-u + c + + + + + D + ra + + + + + Se + O + + + + +Fig. 1: The changes example-based (blue) and parameterized (orange) unit tests undergo when evolving into a property-based +test. Each test case can undergo multiple changes from different categories. + + + From EBT From PUT novice users of the framework, or because the test cases did + Feature # of test cases % # of test cases % not yet have the time to evolve and be tailored to the project. + Strategies 182 100 75 100 Therefore, we also investigate how the evolved test cases are + Explicit inputs 4 2.20 2 2.67 maintained in Section VI-B2. + Reproducing inputs 0 0 0 0 3) Input generation strategies: Table III depicts the results + Settings 11 6.04 8 10.67 for our analysis of the input generation strategies used. The + Control 2 1.10 14 18.67 majority of PBTs that evolve from an EBT have a simple input + generation strategy for standard data types. However, for 76 of +TABLE II: Features initially adopted from PBT framework. the 120 simple cases (a majority), more refined configurations + are used of these simple input generators (such as min/max + bounds for integers). 60 of the EBTs that evolved into PBTs +the second most common feature, followed by @settings now have a custom input generation, of which 24 are reused +(mostly imposing deadlines on the test cases) and explicit multiple times across different test cases. +inputs (@example). The fact that we see no PBT using When considering PBTs that have evolved from a PUT, just +failure-reproducing features is not surprising, as it is the first over half of the PBTs have a simple input generation strategy. +PBT-version of the test cases. They might not yet have run Of those 43 PBTs, 35 refined configurations. All custom input +enough to want to reproduce a specific failure-inducing input. generation strategies are reused across multiple test cases. It is + Compared to test cases that evolved from EBTs, test cases common for evolved PUTs from the same project to already +that evolved from PUTs are more likely to adopt these features share the same input parameter before their evolution into a +of the PBT framework. One reason for this could be that PBT. In our dataset, the use of libraries for input generation is +the developers are already more familiar with more advanced not common (only two instances). The only used library was +testing frameworks. the Hypothesis NumPy extension5 . + Corgozinho et al. [8] also performed a preliminary study Several test cases already contained some form of random- +into commonly used features across 86 PBTs. Their dataset ization before being rewritten into a PBT. Afterwards, this +does not consider the initial PBT introduction, and contains randomization is still reflected in the input generation strategy. +more well-established, big projects that make use of property- For example, if a test case previously contained a statement a +based testing. In their dataset, they observe a higher feature +adoption rate compared to ours. This could be because devel- 5 https://hypothesis.readthedocs.io/en/latest/reference/strategies.html# +opers evolving a PBT from an existing test might be more hypothesis-numpy + From EBT From PUT that define behavior in their test files, these should indeed + # % # % be considered. For others, including test files can lead to a + Custom, with reuse 36 19.78 32 42.67 wrong conclusion when the test cases themselves have shrunk + Custom, no reuse 24 13.19 0 0 or increased in size. We therefore report both on the absolute + Simple 120 65.94 43 57.33 and relative coverage twice, once with the test files included + Other 2 1.10 0 0 and once with the test files excluded. + We were able to run 219 of the test cases before PBT- +TABLE III: Input generation strategies used within PBTs introduction, and 219 test cases after PBT-introduction. How- +evolved from an EBT or a PUT. ever, not all were able to obtain code coverage. In the end, + we were able to run and obtain code coverage for 211 test + case evolutions before and after the introduction of the PBT += np.random.randint(1, 10), a strategy of the test (meaning a total of 422 test cases). To ensure the test cases ran, +case would become @given(st.int(1, 10)). some minimal changes to the code were needed. For example, + one test case contained a broken import. Upon correcting this + RQ1 Non-semantic changes to the setup code are es- import, the test case did run. However, we made sure to not + pecially common in evolutions stemming from EBTs change the semantics of the system under test. In some cases, + (117/182). For evolutions from PUTs, it is more common tests failed but still resulted in some code coverage. Their + to require no changes in the body of the test case at all results are also included. + (35/75). The addition of settings is the most common + 3) Test failures: Code coverage is not the only way to deter- + feature (19/257) early on in the adoption of the PBT + mine whether tests are effective. During the data collection of + framework. Most test cases use simple input generation + Section V-A2, not all test cases passed, and some test oracles + strategies (163/257). + threw an assertion error. For some test cases, this happened + before their evolution into PBT, whereas for others, the PBT + V. RQ2: W HAT IS THE IMPACT OF ADOPTING + did not pass. We investigate how often this occurs, and the + PROPERTY- BASED TESTING ? + failed assertions in each. + With research question two, we aim to find the impact +of introducing PBTs. We consider commit messages, code B. Results +coverage, and test failures of the 257 test evolutions. 1) PBT-introducing commits: First, we report on our anal- + ysis of the commit messages of the PBT-introducing commits. +A. Research Method Only eight commit messages mention anything positive or + 1) PBT-introducing commits: We investigate and report on negative about Hypothesis or property-based testing (beyond +73 commit messages across 64 repositories that evolve at least simply stating that they have started using it). One commit +one conventional test case into a PBT. We aim to uncover message mentions improving code coverage to find more +reasons as to why the developer decided to evolve their test errors across the code. Two commit messages mention the new +case, and their potential opinions on this change. PBTs failing (a bug was found, but not yet fixed). Finally, five + 2) Code coverage: We first explore whether code coverage commit messages use the words better, trickier, or improved. +improves once a conventional test case has evolved into a Four commit messages also mentioned bug fixes of some +PBT. Improving coverage can be a goal for some PBT- sort, meaning the PBT was introduced at the same time as a +introducing developers, even though it does not necessarily bug fix. This can indicate that the PBT at introduction might +improve test suite effectiveness [20]. Moreover, research has have found a bug that the initial conventional test case did +proposed variants of PBT with that explicit aim (i.e., coverage- not, after which the developer fixed the bug. Alternatively, the +guided PBT [24], [29], [30]). developer may also be introducing bug fixes and PBTs at the + We run each test case with statement coverage before same time to ensure their most recent bug fix is tested more +and after the introduction of Hypothesis while measuring in the future. We did not find any evidence in the commit +coverage using Coverage.py [4], a well-established Python message supporting either hypothesis, but Section V-B3 looks +library for test coverage. We only compute the coverage for into test case failures before and after the commit. +each individual test case, instead of for the entire test suite as a 2) Code coverage: To verify whether there is a difference +whole. For relative coverage (i.e., in percentage), we normalize in coverage before and after the evolution into PBT, we use a +the executed statements by those in the files executed by the Wilcoxon signed-rank test [41] as our data is non-parametric +test case rather than by those in the entire project. We opted and paired (code coverage of a test case before and after the +for this design as coverage across all statements of the entire PBT-introducing commit). We consider a p-value of <0.05 +project would be very low for individual test cases. We also statistically significant. The test results are listed in Table IV. +report on coverage in absolute numbers. This can be useful For all 4 cases, we observe a statistically significant difference. +for test cases that lead to the execution of several files. Note First, we look at the change in number of statements +that, by default, coverage.py considers all executed Python covered. Figure 2 shows box plots for the distribution of the +files including the files that define the test case. For projects absolute statement coverage before and after the test case + Stmt (all) % (all) Stmt (no test) % (no test) coverage ∆ # Stmt (all) % (all) # Stmt (no test) % (no test) + p-value 0.006 2.497 × 10−20 1.477 × 10−13 0.045 Mean +13.09 +2.31 +4.01 -0.82 + Std Dev. 27.79 6.06 16.81 5.5 +TABLE IV: p-values of change in coverage, in terms of + median +11 +0.57 +0 +0 +absolute and relative statement coverage. + 1st Quar. +2 -0.06 +0 -1.26 + total # ran tests # passing # failing with coverage 3rd Quar. +17 +2.46 +3 +0.28 + Before PBT 219 199 20 211 Min -78 -10.09 -75 -21.90 + After PBT 219 207 12 211 Max +223 +32.61 +77 +32.52 + +TABLE V: Number of passing and failing test cases. We could TABLE VI: Changes in code coverage, both in terms of +not obtain coverage for all tests (as shown by the last column). number of statements covered and change in the coverage + percentage, for both all files and all files without test files + included. + + 2500 + evolution, taking into account all executed files (denoted “all” + in the plot) and all executed files without test files (denoted + 2000 “no test”). While we see a slight improvement in median + and quartiles when all executed files are taken into account, + 1500 + the change becomes much more subtle when excluding the + executed test files. One reason could be that property-based + test cases execute more lines of test code. Even if the tests + 1000 + themselves are not necessarily longer, the inclusion of input + generators can add more test code to cover —especially for + 500 projects that have defined custom ones in test files. + Figure 3 on the other hand shows the relative statement + coverage in percentage. As mentioned before, by default, + 0 + coverage.py only takes into consideration files that have at + Before (all) After (all) Before (no test) After (no test) + least one executed line of code, meaning files that are never + covered by the test case are not considered. Here we also see + an improvement when taking into account test files, but once +Fig. 2: Statements covered by test cases before and after PBT- + they are removed from the data, we notice a slight decrease +introduction. The first two plots show coverage across all files, + in code coverage on average. +the second two without test files included. + Table VI shows the deltas for each of the four measure- + ments. While the mean absolute number of covered statements + without test files included does improve slightly (4.01), the + relative coverage percentage goes down slightly. This could + 100 be due to extra files being discovered, or more code being + introduced during the PBT-introducing commit. Most notice- + 80 ably, one project’s covered statements decreases by 75. Upon + further investigation, the test case in question contained many + assert statements. While the conventional test case before + 60 + PBT-introduction passed, Hypothesis found a counterexample + on the first assert, thereby stopping the test case and not + 40 executing the subsequent assert statements (leading to a drastic + decrease in coverage). Additionally, 26 test cases from the + same repository all had one additional change when evolved + 20 + into PBT: the removal of a call to the logging function (which + was three statements), leading to a decrease of coverage of + 0 indeed 3 statements for these 26 test cases. + Before % (all) After % (all) Before % (no test) After % (no test) 3) Test failures: Table V shows the number of tests failed + before and after PBT-introduction. Two test cases did not pass + as a conventional unit test, nor after having been rewritten into +Fig. 3: Coverage percentage by test cases before and after a PBT. For 18 test cases, the initial conventional test did not +PBT-introduction. The first two plots show coverage across pass, but the updated PBT did pass. In another ten cases, the +all files, the second two without test files included. initial test passed but the resulting PBT did not. + In terms of the before, one project with one evolution • Updates to the test case encompassing both semantic and +had a test case that resulted in an assertion error. The PBT- non-semantic changes. +introducing commit also contained a bug fix. Another project We make one exception for 39 test cases originating from +had three failing test cases that returned a type error. After the one repository. In the most recent version of that repository, +introduction of the PBT, all three passed. However, the PBT- most Python code has been removed, and is scheduled to be +introducing commit does not introduce a bug fix (meaning added at a later stage. Because of this drastic rewrite affecting +the bug was in the test code itself). Another project had two the latest version in the repository, we instead consider its most +failing test cases, with an attribute error and a type error. For recent version with the test cases still present. +both, the PBT versions did pass. In one of the bigger projects Additionally, we report on the survival rate of the test cases +in our dataset, with 16 evolved test cases, ten tests did not by looking at the number of commits since introduction, or +pass before the evolution. In three cases this was because of the number of commits between introduction and removal. +an assertion error (with the other seven not passing due to a 2) Are more parts of the PBT framework adopted?: As de- +value not being defined). All ten of these test cases passed after velopers become more acquainted with property-based testing +being updated to a PBT. These results suggest that people are in their projects, they might discover features unbeknownst +introducing PBTs when fixing known errors, perhaps to ensure to them before. Therefore, similar to Section IV-A2, we +more thorough testing of those parts of the system. investigate whether the most recent version of their PBT + When looking at the failing tests cases after the introduction uses more features of the PBT framework. We use the same +of PBTs, we found five test cases for which Hypothesis categories of features from the Hypothesis API [42] to classify +reported a counterexample for which the original test case the additions. As all PBTs already had an input generation +passed. Further, as mentioned in Section V-B1, some commits strategy when they were introduced, we investigate whether +did contain additional bug fixes. This indicates that PBTs can this strategy has been updated in the meantime. +uncover bugs not found by conventional test cases validating +the same behavior, thus improving bug detection. For the B. Results +other 5 non-passing PBTs, we found other errors (such as 1) Do Property-based Test Cases Change?: To answer this +ValueErrors), even though the original test case passed before. question, we compare the most recent commit in the GitHub + repository to the PBT-introducing commit. Table VII shows + RQ2 8 PBT-introducing commit messages convey an the number of commits the test cases have survived (for those + intent to improve test cases to improve coverage or find that are still present in the current version of their project, + bugs. We observed a statistically significant change in i.e., the number of commits between introduction and the + statement coverage, with on average an increase of 4 most current commit), or how many repository commits they + statements. We also found evidence of PBTs being intro- survived before their deletion. Most test cases in our dataset + duced along with a fix for a bug in the code, and of PBTs (110) are unchanged. Their corresponding repositories have + finding counterexamples where the original corresponding also enjoyed the fewest commits since the PBT-introducing + conventional test passed. one (with 99 on average, with a standard deviation of 205). + Interestingly, one test case survived 1728 repository commits + VI. RQ3: H OW ARE PROPERTY- BASED TESTS without undergoing any changes itself. A total of 90 test cases + MAINTAINED ? + did undergo changes since their introduction, both semantics- + We consider the most recent version of the 250 unique PBTs preserving and semantics-affecting ones. We observe that these +from the in total 257 test case evolutions, and investigate the test cases also survived more commits, with on average 642 +changes (or removals) they have been subject to since. commits and a higher standard deviation. This is expected as + PBTs need to co-evolve with their system under test. +A. Research Method + Finally, 50 PBTs were removed from the projects since + For each test case, we compare the version resulting from their initial introduction. These test cases also survived fewer +the PBT-introducing commit to the version in the most recent commits; 352 on average. However, one test case survived +commit in its repository. We consider the following: 3573 commits to the repository before being removed. Reasons + 1) Do Property-based Test Cases Change?: We investigate cited for the deletion of these test cases were removal of the +whether the 250 PBTs in our dataset change over time, for functions they tested (5), unexpected behavior (3), and the tests +instance in response to changes in the system under test. For being slow (1). +each PBT, we manually compare against the same test case in 2) Are more parts of the PBT framework adopted?: Finally, +the most recent version of the GitHub repository. For each of we consider the changes made to PBTs in terms of the parts of +our test cases, we consider the following: the PBT framework that are adopted. Table VIII describes the + • No changes to the test case. The rest of the project and results. In 65 test cases, the input generation strategies were + other test cases might have changed, but the investigated updated after their introduction. One repository in particular + PBT has not. mentions doing so to improve the running time of the test + • Removal of the test case. In this case, we also investigate cases. Only one repository added an explicit input to test for on + possible reasons why. each run. Additionally, one test case added a seed decorator + No changes Changes Removal easier to evolve unit tests that exercise the unit under test on + Mean 99 642 352 inputs of standard data types (e.g., integers) into a PBT with + Std Dev. 205.31 1450.79 967.80 such a strategy. Our findings should motivate practitioners to + median 51 146 34 prioritize their generalization efforts on those unit tests first. + 1st Quar. 48 64 17 Finally, a study by Goldstein et al. [14] reports that PBT + 3rd Quar. 63 146 71 adopters have difficulty identifying the properties to test for. + Min 1 17 7 Using existing test cases, rather than creating new ones, might + Max 1728 5886 3573 + help. This is especially true for parameterized unit tests (PUT), + and especially those that do not list expected outputs for every +TABLE VII: Number of commits since the introduction of the given input, as those might already be testing a property (but +PBT. Data split for the test cases that did not change at all, for not yet randomly generating input). Indeed, for 35/75 PBTs +those with changes, and for those removed in the meantime. that evolved from a PUT (Section IV-B), no changes to the + body of the test case were required at all. This suggests that + Feature # of test cases PUTs can be considered a stepping stone towards, or even an + Change in strategies 65 intermediate step in a planned introduction of PBTs. + Addition of explicit inputs 1 For tool developers: Recent years have seen the introduc- + Addition of reproducing inputs 1 tion of tool support for creating PBTs. From Hypothesis’ + Addition of settings 19 own ghostwriter6 , over using LLMs to write PBTs [13], [38], + Addition of control 0 to tools that aim to aggregate similar test cases into one + Addition of exceptions 0 PBT [31]. Tools that take EBTs and transform them into PUTs + also exist [37]. However, there remains a need for tools that +TABLE VIII: Changes in used PBT features in the most recent support developers in evolving existing, dissimilar, test cases +versus the initial PBT-introducing commit of the test case. into PBTs. Our findings for RQ1 (Section IV-B), and our + supporting dataset, can inspire tool builders with examples of +to reproduce inputs. 19 of the test cases eventually got some real-world transformations that can be partially automated. +form of settings added, which doubles their total number. As shown in Section IV-B2, not all features of the property- + based testing framework are immediately adopted in newly- + RQ3 Most PBTs (200/250) in our dataset have survived evolved PBTs. In Section VI-B2 we found that features such + since their introduction, with 90 having gone through as PBT settings are often included only later in the life of + changes. Removed test cases survived on average 352 a PBT. We also saw that inside some PBTs, developers were + commits to the repository. 65 test cases saw a change using if-statements, where an assume might have been more + in their input generation strategy since their introduction. appropriate. Therefore, future tools could not only help with + Finally, 19 test cases received additional settings. the evolution of test cases into PBTs, but also aid with the + introduction of features to optimize existing PBTs. + VII. D ISCUSSION For researchers: There are still few empirical work that + We now distil the actionable insights from our findings, for compares conventional unit tests to PBTs. Ours is, to our +software testers, tool builders, and researchers alike. We also knowledge, the first to do so in a one-to-one comparison of test +discuss the threats to the validity of our findings. cases before and after their evolution into property-based ones. + Our comparison on test failures and code coverage has been +A. Actionable insights insightful, and could inspire other one-to-one comparisons on + For software testers: As evidenced by our findings for other metrics. For instance, mutation score (recently used in +RQ2 (Section V-B), evolving well-chosen unit tests into prior work [32], see Section VIII) has not yet been explored +property-based ones can increase their code coverage. We in a one-to-one comparative setting. +moreover found evidence of such real-world evolutions finding + B. Threats to validity +counterexamples where the original test passed without any +failures, leading to a deeper validation of the system under Following standard practice in empirical software engineer- +test. We even found instances of these evolutions being con- ing, we discuss potential threats to the validity of our results. +ducted alongside bug fixes, most likely to test for regressions For each threat, we describe the applied mitigation strategies. +more thoroughly. Our findings should motivate practitioners Construct validity: We considered test case evolutions that +to consider unit tests that have missed edge cases in the past are found in open-source GitHub repositories, which can +as candidates to be evolved into property-based ones. raise quality concerns. We mitigated this threat by applying + Prior studies have found that implementing input generation strict inclusion criteria, resulting in 575 high-quality candidate +strategies for a PBT can be tedious and effort-intensive [14]. repositories with at least one PBT. As most of those PBTs did +Nonetheless, our findings for RQ1 (Section IV-B) indicate not result from an evolution, we were left with fewer test case +that many evolved PBTs in our dataset use but a simple, 6 https://hypothesis.readthedocs.io/en/latest/reference/integrations.html# +built-in input generation strategy. Practitioners may find it ghostwriter + evolutions to study, but the study subjects still stem from 64 Goldstein et al. [14] interviewed 30 developers from a +different repositories, ensuring diversity. fintech company, to find insights about how people experience + Further, while false negatives cannot be excluded, all test PBT in practice. Another paper by Goldstein et al. [15] reports +case evolutions were manually inspected by both the first that developers experience difficulties in finding properties to +and the second author, ensuring the dataset is free of false test for. Our research looks at open-source projects rather than +positives. The same goes for the before-after mappings for the industry, and investigates existing test cases. +each test case evolution, which were created by the first author A study by Wauters and De Roover [39] looked into the use +and inspected and confirmed by the second author. of PBTs by 28 open-source machine learning projects. The + Manual labeling of test case evolutions was also used to study investigated common positive and negative sentiments +answer RQ1. We mitigated the threat of subjective bias by expressed in GitHub commits and code comments, which +having multiple labelers and multiple labeling rounds until parts of a project were tested, as well as the complexity of +a substantial inter-rater agreement was reached. To answer data generation strategies. Our study also investigates data +RQ2, we used tools to execute test cases and compute their generation strategies but does not focus on ML-intensive +code coverage. To mitigate the threat of measurement bias projects that often require more complex data. +introduced by the tooling, we only used mature open-source Ravi and Coblenz [32] recently performed a large-scale +tools that are well-established within the community. empirical study on PBTs in 426 Python programs. Their study + Internal validity: For RQ2, we measure changes in code uses a data flow analysis to automatically categorize real-world +coverage induced by the evolution into a PBT. However, the PBTs into 12 categories. Additionally, they used mutation +introduction of a PBT is not always the only change in a testing to investigate how many mutations a project’s existing +commit. If additional changes are present, the total number PBTs can find compared to the project’s existing conventional +of statements may change, which can confound the observed tests. Our research looks at the impact of evolving test cases, +coverage differences and lead to incorrect conclusions. To and compares a test case before its evolution into a PBT to +mitigate this threat, we manually inspected commits exhibiting the resulting PBT. This means we compare two test cases that +large coverage changes. In addition, we report both absolute are equivalent in terms of the behavior they are supposed to +and relative coverage, computed with and without the test files validate, and we do so one-to-one. +included, as test files are more likely to change due to the Unlike our study, the aforementioned papers do not inves- +introduction of PBTs. tigate the evolution of PBTs, but rather consider snapshots of + External validity: Finally, our study focuses on Python PBTs at one point in time. +test cases that use the Hypothesis framework. Hypothesis IX. C ONCLUSION AND F UTURE W ORK +is the most widely recognized PBT framework for Python, This paper studied the evolution of property-based unit tests +and Python is ranked among the most popular programming from conventional ones, the impact of such PBT-introducing +languages. Nevertheless, our findings may not generalize to evolutions, and how the resulting PBTs are maintained after- +other programming languages nor to other PBT frameworks. wards. We found that the evolution of parameterized unit tests + into a PBT commonly requires no updates to their test body + VIII. R ELATED W ORK + at all. For example-driven unit tests, in contrast, the evolution + Several studies have investigated the introduction and main- commonly required non-semantic changes to the test body. +tenance of various types of test cases, from tests in general [1], These account for the introduction and usage of a randomly +[9], [44] over GUI tests [5] to performance tests [11]. A generated input value. The input generation strategy of PBTs +few studies have also looked into changes in code coverage that evolved from existing unit tests is often simple. Impact- +induced by software patches, e.g., [12] and [17]. However, wise, we found that code coverage can improve when unit tests +our work is the first to study how PBTs can evolve from are replaced by PBTs. More importantly, we found evidence +conventional unit tests, and to study the impact on code of bugs found through or alongside the introduction of these +coverage —rather than changes in code coverage over time PBTs. Most of the PBTs in our dataset are still present in the +or induced by changes to the system under test. most recent version, with almost half having gone through + Zooming in on other studies targeting property-based test- some maintenance during their life time. The adoption of +ing, Corgozinho et al. [8] sampled 86 PBTs from GitHub, and additional PBT features is not uncommon either. +categorized each of them manually according to the testing One avenue for future work is investigating the long-term +patterns they adhere to, which stem from an influential blog impact of PBT-introducing test case evolutions. Another is +post7 . They also study the use of Hypothesis features in developer support in the form of a tool that identifies candidate +those PBTs, similar to us. However, while they investigate unit tests for such an evolution, and for partially automating +bigger, established projects, we investigate the adoption of the necessary test changes. +these features in test cases that were previously not a PBT. + ACKNOWLEDGEMENTS +We also study whether those features are adopted later on, +while the PBT matures. This research was partially funded by the Research Foun- + dation Flanders (FWO) Grant No. 1SHFI24N and by the + 7 https://fsharpforfunandprofit.com/posts/property-based-testing-2/ Cybersecurity Research Program Flanders (CRPF). + R EFERENCES [18] John Hughes. Experiences with QuickCheck: Testing the Hard Stuff and + Staying Sane, pages 169–186. Springer International Publishing, Cham, + [1] Maurı́cio Aniche, Christoph Treude, and Andy Zaidman. 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Api reference - hypothesis 6.148.3 documen- + \ No newline at end of file diff --git a/packages/opencode/specs/simulation-research/text/2026-nl-to-executable-properties-mobile.txt b/packages/opencode/specs/simulation-research/text/2026-nl-to-executable-properties-mobile.txt new file mode 100644 index 00000000000..ddf20d106f5 --- /dev/null +++ b/packages/opencode/specs/simulation-research/text/2026-nl-to-executable-properties-mobile.txt @@ -0,0 +1,1266 @@ + From Natural Language to Executable Properties for + Property-based Testing of Mobile Apps + YIHENG XIONG, East China Normal University, China + TING SU, East China Normal University, China + JINGLING SUN, University of Electronic Science and Technology of China, China + JUE WANG, Nanjing University, China + QIN LI, East China Normal University, China +arXiv:2603.21263v1 [cs.SE] 22 Mar 2026 + + + + + GEGUANG PU, East China Normal University, China + ZHENDONG SU, ETH Zurich, Switzerland + Property-based testing (PBT) is a popular software testing methodology and is effective in validating the + functionality of mobile applications (apps for short). However, its adoption in practice remains limited, largely + due to the manual effort and technical expertise required to specify executable properties. In this paper, we + propose a novel structured property synthesis approach that automatically translates property descriptions in + natural language into executable properties, and implement it in a tool named iPBT. Our approach decomposes + the problem into UI semantic grounding and executable property synthesis. It first builds an enriched widget + context via multimodal LLMs to align visual elements with their functional semantics, and then uses an LLM + with in-context learning to generate framework-specific executable properties. We evaluate iPBT with a + closed-source LLM (GPT-4o) and an open-source LLM (DeepSeek-V3) on 124 diverse property descriptions + derived from an existing benchmark dataset. iPBT achieves 95.2% (118/124) accuracy on both LLMs. Notably, an + ablation study reveals that the enriched widget context contributes to an absolute improvement of up to 20.2% + (from 75.0% to 95.2%). A user study with 10 participants demonstrates that iPBT reduces the time required to + write executable properties by 56%, suggesting substantially lower manual effort. Furthermore, evaluations on + 1,180 linguistically diverse variations demonstrate iPBT’s robustness (87.6% accuracy), indicating its capability + to handle varied expressions. + + 1 Introduction + Property-based testing (PBT) has emerged as a powerful testing methodology that validates software + program correctness by checking properties. Unlike example-based testing [11] which relies on + specific input-output pairs to determine test outcomes, PBT systematically generates a large number + of inputs to verify whether the system under test satisfies the defined properties. The pioneering PBT + framework QuickCheck [10] has inspired many other PBT frameworks that successfully uncover + bugs difficult to detect with traditional testing techniques across various software domains. [5, 24, + 25, 27, 43, 55, 75]. + Recently, several research efforts have applied PBT in testing mobile apps [29, 61, 62, 75] to address + the oracle problem, determining whether an app’s behavior aligns with expected outcomes. In + these work, users specify expected behaviors as executable properties, and then the PBT framework + automatically generates GUI event sequences to validate them. For example, consider Amaze [1], + a popular file management app. A typical property is that when a user clicks on a directory (e.g., + "Download"), the app should open that directory and display its contents, rather than triggering a + file-opening dialog (which is only expected for files). Fig. 1(a) illustrates the expected app behavior. + Fig. 1(b) shows the corresponding executable property written in Kea [75], a recent effective PBT + framework for finding functional bugs in mobile apps. The property consists of a precondition + Authors’ Contact Information: Yiheng Xiong, East China Normal University, , China, xyh@stu.ecnu.edu.cn; Ting Su, East + China Normal University, , China, tsu@sei.ecnu.edu.cn; Jingling Sun, University of Electronic Science and Technology + of China, , China, jingling.sun910@gmail.com; Jue Wang, Nanjing University, , China, juewang591@gmail.com; Qin + Li, East China Normal University, , China, qli@sei.ecnu.edu.cn; Geguang Pu, East China Normal University , , China, + ggpu@sei.ecnu.edu.cn; Zhendong Su, ETH Zurich, , Switzerland, zhendong.su@inf.ethz.ch. + + + , Vol. 1, No. 1, Article . Publication date: March 2026. + 2 SMU Classification: + Yiheng Xiong, Ting Su, Jingling Sun, Jue Wang, Qin Li, Geguang Pu, and Zhendong Su + Restricted + + + + Expected behavior 1 @precondition( + Amaze 2 findWidget(id="line").exists() and + /storage/Download 3 findWidget(id="Search").exists() + Files 4 ) + picture.png 5 @property + xx.xx + Precondition video.mp4 + 6 def test_open_directory(): + xx.xx 7 item_count = findWidget(id="line").count + Amaze 8 for index in range(item_count): + /storage + 9 directory_name = findWidget(id="line")[index].get("text") + Files 10 if "." not in file_name: + Download + xx.xx 11 findWidget(id="line")[index].click() + Data 12 break + xx.xx Property violation 13 assert directory_name in findWidget(id="path").get("text") + todo.txt + xx.xx + Amaze (b) An example of executable properties in Kea + /storage + + Files Precondition: The list item and search button exist + Open As Function body: + Download + Text + xx.xx + Image + 1. Get the names of all items + Data + Video 2. Select an item name that does not contain "." + xx.xx + Other + todo.txt 3. Click it + xx.xx 4. Assert the path contains the item name + (a) The app’s expected behavior (c) The property description in natural language + + Fig. 1. An example of the property in app Amaze. + + + +(lines 1-4) to check the presence of the file and search button; an interaction scenario (lines 7-12) +simulates a click action to open the directory; and a postcondition (line 13) checks whether the +path contains the directory name. Then, the PBT framework can generate a large number of GUI +events to verify this property and report bugs when the property is violated. + However, these PBT frameworks see limited adoption because testers must translate high-level +intents into framework-constrained, executable properties, which demands substantial manual +effort and expertise. Testers must learn framework-specific DSLs, including specialized syntax, +APIs, and conventions. This imposes a steep learning curve, particularly for those without a strong +programming background. Moreover, specifying executable properties requires the tedious manual +inspection of the app’s view hierarchy to locate low-level UI widget identifiers (e.g., id="Search"). +It also requires correctly implementing complete executable properties under the constraints of +the testing framework, both of which are non-trivial and error-prone in practice. Together, these +barriers create a significant gap that restricts the widespread application of PBT. + To bridge this gap, we enable testers to specify properties in natural language, which is more +intuitive and lightweight. To reduce ambiguity while preserving accessibility, we structure property +descriptions in a widely-used Hoare logic format, like Given-When-Then used in Gherkin [20] for +Behavior-Driven Development [59]. Fig. 1(c) illustrates such a structured description. While translat- +ing natural language into executable code has been studied, classic rule-based approaches [12, 48, 63] +are insufficient for mobile PBT due to two main limitations. First, rule-based approaches lack flex- +ibility. Enumerating rules to cover diverse paraphrases of user intent (e.g., “open the folder” vs. +“navigate into the directory”) does not scale and itself incurs substantial manual effort. Second, +these approaches lack semantic grounding. They struggle to accurately map high-level widget +descriptions (e.g., “search bar”) to the low-level widget identifiers. + More fundamentally, these limitations expose a deeper challenge: grounding the informal test +intent into concrete executable properties. To address this challenge, we propose a structured +property synthesis approach that automatically translates natural-language property descriptions +into executable properties. We decompose this problem into two distinct phases: UI semantic +grounding and executable property synthesis. We first tackle UI semantic grounding by extracting + +, Vol. 1, No. 1, Article . Publication date: March 2026. + From Natural Language to Executable Properties for Property-based Testing of Mobile Apps 3 + + +comprehensive GUI information (e.g., view hierarchies and screenshots) from the app and con- +structing enriched widget contexts for each UI widget. We employ Multimodal Large Language +Models (MLLMs) to generate semantic annotations for each widget by jointly reasoning over visual +appearance and structural information. These annotations serve as grounding signals, enabling ac- +curate mapping between user-described widgets (e.g., "item name") and concrete widget identifiers +(e.g., "line"), even when the identifiers themselves are not descriptive. Building on this grounded +widget context, we then perform executable property synthesis. We leverage LLMs as inference +engines to synthesize executable properties that integrate (i) the property description, (ii) enriched +widget context, (iii) framework APIs, and (iv) few-shot demonstrations [51]. This design eliminates +the need for handcrafted rules while enabling the model to adapt to the specific constraints of +property generation. + We implemented our approach as a tool named iPBT. To evaluate its effectiveness, we conduct +experiments with a closed-source LLM (GPT-4o [45]) and an open-source LLM (DeepSeek-V3 [13]) +on 124 diverse properties from the Kea benchmark [75]. iPBT correctly synthesizes executable +properties for 118 out of 124 cases (95.2%) with both models. Notably, our ablation study reveals +that the enriched widget context contributed to a 20.2% absolute increase in accuracy, highlighting +its critical role in grounding UI semantics. Beyond accuracy, a user study demonstrated the practi- +cal utility of iPBT, reducing property authoring time by 56% compared to manual composition. +We further evaluate robustness by using another LLM, Llama-3.1 [39], to generate 1,180 diverse +paraphrased variants of the original property descriptions. Under these variations, iPBT achieves +87.6% accuracy (1,034/1,180) with GPT-4o and 87.5% (1,032/1,180) with DeepSeek-V3. These results +indicate that iPBT is robust to the variability of natural language property descriptions. + In summary, this paper has made the following contributions: + +• At the conceptual level, we introduce a novel approach that reduces the manual effort and lowers + the technical barrier for property-based testing of mobile apps. +• At the technical level, we have implemented our idea as a tool named iPBT that (i) constructs + enriched widget contexts via UI semantic grounding to align user-described widgets with concrete + UI elements, and (ii) leverages LLMs with in-context learning to synthesize framework-specific + executable properties. +• At the empirical level, we construct a new evaluation dataset with 124 human-written natural + language property descriptions derived from real-world bugs. We further generate 1,180 linguistically + diverse LLM-based variants for robustness evaluation. Based on this dataset, we conduct compre- + hensive evaluations and summarize practical lessons learned on applying LLMs to property-based + testing. + +2 Background +2.1 Large Language Models +Large language models (LLMs) have been shown to perform well on a wide range of tasks in natural +language processing [41] and software engineering [22, 83]. LLMs, such as GPT-4o, DeepSeek-V3, +are deep neural networks trained on massive amounts of text data, enabling them to generate human- +like text, understand complex queries, and perform different tasks. These models are typically +based on the Transformer architecture [66], which relies on self-attention mechanisms to process +and generate text efficiently at scale. Recently, Multimodal Large Language Models (MLLMs) have +emerged, which extend the capabilities of traditional LLMs by incorporating additional modalities +such as images, audio, or structured data alongside text [78]. This multimodal integration allows +MLLMs not only to process natural language but also to understand and reason about visual or + + , Vol. 1, No. 1, Article . Publication date: March 2026. + 4 Yiheng Xiong, Ting Su, Jingling Sun, Jue Wang, Qin Li, Geguang Pu, and Zhendong Su + + + Preparation Phase I: UI Semantic Grounding Phase II: Executable Property Synthesis + + Page Information Widget Information Key Components + + 12:00 Property Description + Preview Test + + Test Enriched Widget Context + User + + Data Collection SHOW ANSWER + Raw Widget Attributes Framework APIs + "text": "Test", + "resource_id": "qa", + "content_description": "", Few-shot Demonstrations + "App name": "AnkiDroid", "class": "android.view.View" + "Activity name": "Previewer" + + + + + Synthesizer + Generated Semantic Information + + View hierarchies "semantic label": "Question text display", Executable Property + LLM + and screenshots Annotator MLLM "functionality": "Displays the question..." + + + + Fig. 2. Overview of iPBT. + + + +other non-textual inputs. In the context of GUI testing, MLLMs are particularly useful as they can +jointly leverage textual descriptions and GUI screenshots to better interpret UI semantics. + +2.2 In-Context Learning +LLMs are typically pre-trained on large corpora of text and code data. To adapt LLMs on customized +tasks, fine-tuning [15], which requires training on a pre-trained model with additional massive data, +and prompt engineering [51] (e.g., chain-of-thought [69], in-context learning [51], and multi-step +reasoning [85] ) are two common approaches. In-context learning refers to the ability of LLMs to +perform customized tasks with a few examples provided in the input prompt, without requiring +model training. In our approach, we adopt in-context learning, which enables LLMs to perform +custom tasks using just a few examples included directly in the input prompt. + +3 Approach +At a high level, iPBT operates as a structured synthesis approach designed to translate natural +language property descriptions into executable properties. Fig. 2 presents the overall workflow +of iPBT, which consists of two main phases: (i) the UI Semantic Grounding phase (§3.1), which +extracts the GUI information of the app under test, leverages MLLMs to generate functionality +annotations for widgets, and constructs the enriched widget context for each UI element; and (ii) +the Executable Property Synthesis phase (§3.2) that generates executable properties by encoding user +APIs, UI widget identifiers, property description and examples into a carefully designed prompt. +Collectively, these two phases enable iPBT to effectively bridge the gap between informal user +intent and concrete implementation details for property-based testing. We next describe each phase +in detail. + +3.1 Phase I: UI Semantic Grounding +In Android app testing, UI widget identifiers (e.g., resource_id, text, and content_description) are +commonly used to locate and interact with target widgets displayed on the screen. Consequently, + +, Vol. 1, No. 1, Article . Publication date: March 2026. + From Natural Language to Executable Properties for Property-based Testing of Mobile Apps 5 + + +a critical prerequisite for synthesizing executable properties is grounding high-level natural lan- +guage descriptions onto these concrete identifiers. For instance, an instruction like “click the +Settings button” must be accurately mapped to a specific widget, such as text="Settings" or +id="action_settings". However, relying solely on raw identifiers is often insufficient. In practice, +these identifiers are frequently opaque, poorly maintained, or generic (e.g., id="button1"), failing +to reflect the widget’s true functionality. To bridge this semantic gap, we extract comprehensive +GUI information and leverage Multimodal LLMs (MLLMs) to generate semantic functionality anno- +tations for each widget. The resulting enriched widget context consists of raw attributes (e.g., text, +resource_id) with MLLM-inferred semantics. This context serves as a robust bridge, enabling the +subsequent executable property synthesis phase to accurately match user-described widgets to the +correct identifiers. +3.1.1 Widget Context Extraction. In Android apps, the layout defines the structure of each page, +while widgets (e.g., Button) handle user-triggered events (e.g., onClick) [3]. To extract the contextual +information of these widgets, the first step is to collect the necessary GUI data (view hierarchies +and screenshots). Notably, our approach supports GUI data acquisition via various methods, in- +cluding: (1) manual interaction by testers; (2) automated exploration using testing tools; and (3) +direct provision from app vendors. From the collected GUI data, we extract two complementary +components that facilitate MLLM understanding and the generation of functionality annotations +for widgets: +• Page information provides high-level context about the app page under test, including the app + name, activity name, and page screenshot. Specifically, the app name typically reflects the domain + or type of the app (e.g., SimpleNote implies a note-taking app), offering prior knowledge about its + overall functionality. The app name is obtained by statically analyzing the AndroidManifest.xml + file. The activity name, parsed from the runtime layout file, specifies the functionality of the + current page within the app (e.g., LoginActivity for user authentication, SettingsActivity for + configuration). The page screenshot, captured via the Android Debug Bridge (ADB), preserves the + visual layout and arrangement of the UI widgets. It serves as a direct reference that complements + textual and structural information. The target widget is highlighted with a red bounding box in + the screenshot to help the MLLM accurately locate it. +• Widget information provides fine-grained details about the interactive widgets on each page. + It consists of two parts: the cropped widget image and the widget attributes. The widget im- + age is obtained by cropping the page screenshot according to the widget bounds. The widget + attributes are extracted from the view hierarchy file. We focus on four commonly used fields: + "text", "resource_id", "content_description", and"class", as they provide valuable signals about + the intended behavior of the widget. Specifically, the "text" field corresponds to the string dis- + played on the widget (e.g., "Login"), often directly indicating its functionality. The "resource_id" + is a developer-assigned identifier that may encode semantic hints about the widget’s role or + logical grouping (e.g., id=btn_submit). The "content_description" field, typically designed for + accessibility [2]. Finally, the "class" specifies the Android class type of the widget (e.g., Button, + EditText, ImageView), which reflects the type of interaction it supports. + These two components together provide complementary structural and visual information, +enabling the MLLM to better reason about widget semantics. Crucially, the extraction of these +artifacts is fully automated. The extracted widget context serves as the foundation for the subsequent +phase, where MLLMs are leveraged to generate accurate functionality annotations for each widget. +3.1.2 Widget Functionality Annotations Generation. Leveraging the extracted widget context, we +employ an MLLM to synthesize functionality annotations. We construct a structured prompt to + + , Vol. 1, No. 1, Article . Publication date: March 2026. + 6 Yiheng Xiong, Ting Su, Jingling Sun, Jue Wang, Qin Li, Geguang Pu, and Zhendong Su + + + Table 1. The prompt design for generating functionality annotation of the widget. + + ID Prompt Component Instantiation + ① Role Assignment You are a professional mobile app UI semantic annotation assistant. + Please annotate the provided UI widget with the semantic label and functionality + description based on the given context. + ② Task - The full page screenshot, where the target widget is highlighted with a red box. + - The cropped widget image and its attributes. + - The provided app name and foreground activity name. + ③ Few-shot Demonstrations [example input] + [example output] + ④ Input [page information]+[widget information] + ⑤ Constraints [Strict rules] + + + + +guide the model, as illustrated in Table 1. The prompt is organized into five components: Component +① defines the role of the model to establish a professional persona. Component ② specifies the +Task, directing the MLLM to infer semantics based on the provided visual and structural context. +Component ③ provides two demonstrations that serve as the concrete reference selected from the +SimpleNote app [58]. They illustrate the expected mapping from the raw widget context to the +target semantic label and functionality description. Empirically, we found that two representative +demonstrations are sufficient for the MLLM to grasp the task requirements and generate high- +quality annotations. Component ④ gives the input of context, including page information and +widget information extracted in the previous step. Component ⑤ outlines the constraints to ensure +output consistency. + Given these instructions, the MLLM generates two key fields for each widget: semantic label +and functionality. The semantic label is a concise identification of the widget, e.g., login button, or +settings option. The functionality offers a description of its behavior, e.g., allows the user to log +into their account, or navigates to settings screen. + For example, consider the target widget shown in the green box in Fig. 2. Sole reliance on these +raw attributes is insufficient to deduce its functionality. To resolve this ambiguity, we construct an +enriched widget context by aggregating page information, such as the app name AnkiDroid and +activity Previewer, with the widget information. This combined information enables the MLLM to +effectively anchor the widget’s semantics. Consequently, iPBT produces functionality annotations, +augmenting the original attributes with a semantic label ("Question text display") and a precise +functionality description ("Displays the question text to the user for review"). These enriched +widget contexts serve as the foundation for generating executable properties in the next phase. + +3.2 Phase II: Executable Property Synthesis +3.2.1 Writing Property Descriptions. To ensure that property descriptions are both intuitive for +testers and structured for synthesis, we adopt a Hoare logic-style representation. This style aligns +with industry-standard practices, such as Gherkin [20] widely employed in Behavior-Driven Devel- +opment (BDD) [59]. In the context of PBT in mobile apps, an executable property is formalized as a +triple ⟨𝑃, 𝐼, 𝑄⟩, where (1) 𝑃 is the precondition, which defines the when could check the property, +(2) 𝐼 is the interaction scenario, which defines the sequence of user actions to execute the target +functionality, and (3) 𝑄 is the postcondition, which specifies the expected UI state after the interac- +tion. To facilitate this formalization, we structure the natural language property description into +two segments: + +, Vol. 1, No. 1, Article . Publication date: March 2026. + From Natural Language to Executable Properties for Property-based Testing of Mobile Apps 7 + + + Table 2. The prompt design for generating executable properties. + + ID Prompt Component Instantiation + You are an expert in Python programming and Android app testing, and your role is + ① Role Assignment + to write test snippets for Android apps. + The following APIs are available for writing property: + ② Framework APIs widget: findWidget(identifier); click: widget.click() long click: widget.long_click(); get + text: widget.get("text"); exists: widget.exists(); back: press("back"); ... + The app’s UI widget identifiers are detailed below for reference, ensuring + accurate element selection in tests: + ③ Enriched Widget Context { "text": "Download", "resource_id":"line", "description": "null", "class": "an- + droid.widget.TextView", "semantic label": "File name text", "functionality": "Display + the name of the file" }, ... + Here are the two example test snippets that you might write, based on the given + ④ Few-shot Demonstrations + property descriptions: [Example property description and executable properties] + Your task: Using the available APIs, UI widget identifiers and following the + example format, please write a test snippet for the following property: + Precondition: The list item and search button exist + Function body: + ⑤ Property Description + 1. Get the names of all items + 2. Select an item name that does not contain "." + 3. Click it + 4. Assert the path contains the item name + Respond only with the Python code, strictly adhering to the given property description. + ⑥ Constraints + Do not include any explanations, comments, or text outside the code block. + + +• Precondition: This segment maps directly to 𝑃. It describes the initial visible state required to + trigger the property (e.g., the file name exists”). +• Function Body: This segment encapsulates both 𝐼 and 𝑄. It contains the execution steps of the + target functionality (e.g., select a file name that does not contain ‘.’ and click it”) and explicitly + states the expected effects (e.g., “verify the path contains the file name”). + +3.2.2 Constructing Prompt and Generating Executable Properties. Table 2 illustrates the structured +prompt employed by iPBT to synthesize executable properties. The prompt comprises six distinct +components, labeled ① through ⑥, designed to guide the LLM’s synthesis process: +• Role Assignment (①): This component defines a specialized persona for the LLM, priming it to + focus on the domain of mobile app testing and code generation. +• Framework APIs (②): To ensure the synthesized code is syntactically valid, we provide the + complete list of user-facing APIs supported by the target framework (Kea in our implementation). + We curated the set of APIs like click() and exists() by analyzing the framework’s official docu- + mentation and source code. Crucially, these APIs are **app-agnostic**, allowing this component + to be reused across different apps. Note that this component is modular and can be substituted + with APIs from other PBT frameworks if desired. +• Enriched Widget Context (③): This component supplies the Enriched Widget Context con- + structed in Phase I. By integrating raw identifiers with MLLM-generated semantic annotations, + this section enables the LLM to ground the natural language descriptions to the correct UI widget + identifiers. +• Few-shot Demonstrations (④): To facilitate in-context learning, we crafted two concrete + examples derived from the SimpleNote app [58]. Our selection follows two principles to ensure + robustness: (1) To avoid bias, the examples originate from an app distinct from the subject apps + + , Vol. 1, No. 1, Article . Publication date: March 2026. + 8 Yiheng Xiong, Ting Su, Jingling Sun, Jue Wang, Qin Li, Geguang Pu, and Zhendong Su + + + used in our evaluation. (2) The examples representatively demonstrate the usage of key APIs (e.g., + findWidget, exists) and the mapping to the target Hoare logic structure (⟨𝑃, 𝐼, 𝑄⟩). Empirically, + we found that two diverse examples are sufficient for the model to generalize the generation + pattern while maintaining token efficiency. +• Property Description (⑤): The component describes the task with the property description and + highlights that the output should follow the format of the example executable properties. +• Constraints (⑥): To ensure the output is machine-readable, we enforce strict constraints. We + explicitly instruct the LLM to generate only the code snippet without verbose explanations or + markdown formatting, which facilitates the automated extraction of the generated properties. + Upon construction, the complete prompt is fed into the LLM, which then synthesizes the final +executable properties. + +4 Evaluation +We aim to answer the following research questions: +• RQ1: What is the correctness of executable properties generated by iPBT based on property + descriptions? How important are the widget functionality annotations in affecting the correctness? +• RQ2: To what extent can iPBT reduce manual effort? What are the differences in the complexity + of the natural language property descriptions and executable properties generated by iPBT? +• RQ3: How robust is iPBT in generating executable properties based on diverse property descrip- + tions? +Large Language Models. We evaluate our approach using two representative large language +models for executable property generation: one closed-source model (GPT-4o) and one open-source +model (DeepSeek-V3). This selection allows us to assess the effectiveness of our approach across +different model ecosystems. In addition, we employ a multimodal large language model (GPT-4o +mini) to generate functionality annotations for UI widgets, as it supports both textual and visual +inputs. +Writing property descriptions. To evaluate our approach, we construct property descriptions +based on the dataset from the prior work Kea [75], which provides 124 diverse executable properties +across eight popular open-source Android apps covering diverse app categories, e.g., tools, editor, +education, and audio player. Importantly, each property is derived from a distinct real-world +historical bug, ensuring that the dataset reflects practical issues encountered in diverse app contexts. +Since these bugs span different functional modules of the apps (e.g., navigation, data management, +and configuration), the resulting properties capture a broad spectrum of app behaviors. Moreover, +as a benchmark originally curated for evaluating property-based testing of Android apps, this +dataset offers both diversity and practical relevance, making it well-suited for our evaluation. The +dataset also includes the corresponding bug reports to facilitate understanding and reproduction of +each bug. + To construct the natural language property descriptions, we followed a three-step process: +(1) Property collection. We collected 124 properties from Kea’s dataset, including the executable +properties, associated bug reports, and APK files. (2) Property understanding. Each line of an +executable property typically represents a UI event, making it difficult to infer the corresponding +widget based solely on its identifier. To gain a comprehensive understanding, we manually installed +the associated APK files on mobile devices and interacted with the apps to reach the states satisfying +the precondition. Then, we executed the executable properties on the app to observe each step. +This process can help us understand each component of the executable properties, including the +precondition, interaction scenario, and postcondition. (3) Property description construction. One +author wrote each property description in natural language based on the executable properties + +, Vol. 1, No. 1, Article . Publication date: March 2026. + From Natural Language to Executable Properties for Property-based Testing of Mobile Apps 9 + + +and observed app behavior. To ensure clarity and correctness, the remaining co-authors discussed +together to resolve any inconsistencies or ambiguities through iterative revision. +Constructing enriched widget context. The first step of iPBT aims to construct the enriched +context for the widgets in each app. While our approach supports diverse data collection methods +(as detailed in Section 3.1.1), we employed an automated strategy in our evaluation to minimize +manual intervention. We utilized DroidBot [71], a popular open-source automated GUI testing +framework, extended with a random exploration strategy, to perform a three-hour exploration on +each app [60]. We acknowledge that achieving full coverage via automated exploration remains a +long-standing challenge in both research and practice. However, advancing exploration algorithms +is orthogonal to our primary contribution of property generation. To decouple the effectiveness of +our generation approach from the limitations of the exploration tool, we additionally executed the +"main path" provided in the dataset, comprising events from the app entry to the state satisfying the +property’s precondition. This ensures that all relevant UI widgets involved in the target properties +are captured, providing a fair basis for evaluating iPBT’s generation capabilities. Finally, iPBT +extracts the page and widget information and leverages GPT-4o mini to construct the enriched +context. +Correctness of the generated executable properties. The 124 executable properties in the Kea +dataset are derived from 124 historical bugs. Thus, verifying whether the generated executable +properties by iPBT can reproduce the associated bug serves as a primary indicator of its correctness. +Specifically, for each executable property, we follow these steps: (1) Start from the app’s entry +point and navigate along the bug-triggering path. (2) Interact with the app until reaching the state +that satisfies the preconditions described in the executable property. (3) Execute the generated +executable properties to determine whether it successfully triggers the historical bug. The whole +process can be automatically performed by running the scripts (from app entry to the state satisfying +the precondition) and executable properties in Kea. + For a few cases, even the generated executable properties are able to trigger the historical +bug, they may not faithfully capture the intended logic of the original property. For example, the +generated executable property may omit some conditions in the precondition. To address this, we +additionally evaluate whether the generated properties preserve original intent from the following +two dimensions: +• Precondition and postcondition. We verify whether the clauses and logical operators in + the generated executable properties match those in the ground-truth. Missing or incorrect + preconditions or postconditions can lead to inconsistencies in specific scenarios. +• Interaction scenario. First, we check whether the event sequence in the interaction scenario + matches the ground-truth, where each event contains the event action and the target UI widget. + Second, for executable properties containing conditional branches, we check whether these + branches are consistent with the intended logic. Extra or missing branches may still allow bug + reproduction but fail to reflect the precise execution flow of the original executable property. + To ensure reliability, two co-authors of this paper independently evaluated each executable prop- +erty. We measured inter-rater agreement using Cohen’s Kappa, achieving a substantial agreement +(𝜅 = 0.96). Any disagreements were resolved through discussion. + In Android app testing, UI widgets are located using identifiers (e.g., resource_id, text). Therefore, +the same UI widget can be matched through different identifiers. For example, text="Settings" +and resourceId="app.settings" both refer to the same button, which navigates to the system +configuration interface when clicked. When evaluating the widget matching in the generated +executable properties, we treat such cases as correct matches as long as the different attributes +refer to the same underlying widget. + + , Vol. 1, No. 1, Article . Publication date: March 2026. + 10 Yiheng Xiong, Ting Su, Jingling Sun, Jue Wang, Qin Li, Geguang Pu, and Zhendong Su + + + + +(a) Page of Antennapod (b) Page of Antennapod (c) Page of Markor (d) Page of Markor (e) Page of AnkiDroid (f) Page of AnkiDroid + (Correct) (Incorrect) (Correct) (Incorrect) (Correct) (Incorrect) + + +Fig. 3. Examples of failure cases. The green boxes annotate the correct widgets and red boxes annotate the +incorrect widgets. + + + + +4.1 RQ1: Correctness +Evaluation setup. To evaluate the correctness of iPBT in generating executable properties, we +constructed 124 prompts with 124 property descriptions based on the designed prompt template +(Table 2). To ensure deterministic and stable results, we set the temperature parameter of the LLM +to 0, a setting commonly used in prior work [18, 46, 77]. For each prompt, we sequentially invoked +the LLM and recorded the generated executable properties as the output. Moreover, we conduct +an ablation study to evaluate the contribution of the widget functionality annotation module. +Specifically, we removed the functionality annotation of each widget and then repeated the same +experimental procedure to assess its impact. We also conduct the ablation study in RQ2 and RQ3 in +the same process. +Evaluation results. Based on our experimental statistics, for all 124 property descriptions, both +GPT-4o and DeepSeek-V3 successfully generated 118 correct executable properties, achieving an +accuracy rate of 95.2%. These results demonstrate the effectiveness of iPBT and highlight its ability +to reliably translate natural language descriptions into executable properties. + For the six failure cases, all errors manifested as incorrect widget identifiers generated by iPBT. +Upon further analysis, we found that in five cases, the failures were caused by the presence of other +widgets within the same app that shared similar functionality with the target widget, which misled +iPBT during the matching process. In the remaining case, the error originated from an ambiguous +functionality annotation generated by iPBT, which subsequently caused the executable property to +be matched to the wrong widget. Fig. 3 presents three examples from different apps, where the +correct widgets are highlighted with green boxes and incorrect ones with red boxes. The first two +cases (Fig. 3(a)–(d)) failed because different widgets in the same app shared similar functionality. +The third case (Fig. 3(e)–(f)) failed due to ambiguity in the functionality annotation generated by +iPBT. Specifically, iPBT produced the semantic label "Current card number" and the functionality +description "Indicates the number of the current card being viewed". In reality, the widget represents +the number of the currently selected card, which differs subtly from the generated annotation and +led to an incorrect mapping. + Ablation study. The result shows that after removing the functionality annotation of widgets, +iPBT successfully generated 93 and 96 correct executable properties on GPT-4o and DeekSeek-V3, +corresponding to accuracy rates of 75.0% and 77.4%, respectively. Compared with the full setting +(118 correct executable properties, 95.2% accuracy), this represents a performance drop of 20.2 +and 17.8 percentage points, respectively. This substantial decrease highlights the importance of + +, Vol. 1, No. 1, Article . Publication date: March 2026. + From Natural Language to Executable Properties for Property-based Testing of Mobile Apps 11 + + + Table 3. Groups in user study + + + Group (Participant ID) Writing property descriptions Writing executable properties + Group A (P1-P5) Property 1, 3, 5 Property 2, 4, 6 + Group B (P6-P10) Property 2, 4, 6 Property 1, 3, 5 + + + +functionality annotations in helping the LLM accurately understand widgets and generate correct +executable properties. + +4.2 RQ2: User study +Evaluation setup. In RQ2, we conduct a controlled human-subject experiment to assess how +iPBT actually supports users in practice. Specifically, participants were asked to write executable +properties manually, as well as to provide property descriptions for iPBT to generate executable +properties. We then analyzed their time cost and correctness across various tasks to evaluate how +iPBT can save manual effort. Our experimental design follows prior work [32, 61, 76]. + Dataset of the user study. We selected 124 executable properties from RQ1 and categorized them +into three groups (low, medium, and high complexity) using the metric defined in Kea. This metric +accounts for the number of logical clauses and operators in the pre- and postconditions, as well as +the number of events in the interaction scenario. From each complexity group, we randomly selected +2 executable properties from different apps, resulting in a final dataset of 6 executable properties: +Property 1 and Property 2 (low complexity), Property 3 and Property 4 (medium complexity), and +Property 5 and Property 6 (high complexity). By selecting executable properties from different +complexity levels, we ensure that the evaluation captures diverse levels of difficulty while keeping +the number of tasks manageable for participants. For each property, we installed the corresponding +app on an Android emulator and recorded a video walkthrough. Each video demonstrated how to: +(1) reach the state that satisfies the precondition, (2) perform the functionality in the interaction +scenario, and (3) verify the expected behavior in the postcondition. + Participants. We recruited 10 participants for our user study, a sample size similar to previous +related work [9, 61, 84] (which recruited 10, 8, and 12 participants, respectively). All participants +are graduate students majoring in software engineering, with at least four years of programming +experience and familiarity with Python programming. This ensured that they had the necessary +technical background to understand and write the executable properties without using iPBT. A +prior study has shown that graduate students can serve as professionals in software engineering +tasks [54]. In addition, none of the participants was from the authors of this paper. + Procedure. We designed the study as a conventional within-subject controlled experiment, in +which each participant was required to write both property descriptions and executable properties. +To avoid learning bias caused by increased familiarity, no participant wrote both the description and +executable version of the same property. To achieve this, the 10 participants were evenly divided +into two groups (Group A and Group B) with comparable programming expertise, and each group +was assigned different tasks for the same property (as shown in Table 3). In total, this resulted in 60 +property-writing tasks. + At the beginning, participants attended a dedicated tutorial introducing the study’s background, +the concept of properties in Android apps, and the procedures for writing them. Following the +tutorial, each participant was given an example property video and asked to write both the property +description and the corresponding executable properties. This warm-up exercise, which lasted ap- +proximately 45 minutes, familiarized participants with the task and provided step-by-step guidance. + + , Vol. 1, No. 1, Article . Publication date: March 2026. + 12 Yiheng Xiong, Ting Su, Jingling Sun, Jue Wang, Qin Li, Geguang Pu, and Zhendong Su + + + 1750 Writing property descriptions + 1500 Writing executable properties + 1250 + 1000 + 750 + 500 + 250 + 0 + L1 L2 M1 M2 H1 H2 +Fig. 4. Time consumption of participants in writing property descriptions and executable properties. The +x-axis represents different properties, and the y-axis represents the time spent (in seconds). + + + After the tutorial, participants independently completed six distinct tasks. For each task, they +were provided with recorded videos containing the necessary information. The study was conducted +in a preconfigured desktop environment, where participants used Visual Studio Code to write their +property descriptions and executable properties. To ensure fairness, code auto-completion features +were disabled. + We recorded the time each participant spent on the tasks (including the time spent on writing +property descriptions or executable properties, reading the documentation when needed, and self- +checking the written properties). We also collected all written property descriptions and executable +properties. For each collected property description, we leverage iPBT to generate the corresponding +executable properties. The correctness of the generated code was then assessed using the evaluation +metrics described in our experimental setup. + Complexity of property description and code. We measured the complexity of the 124 property +descriptions and their corresponding executable properties using character count. For instance, the +natural language step "click the undo button" has a complexity of 21 characters. This measurement +allows us to quantitatively compare the writing effort required for natural language descriptions +versus executable properties. +Evaluation results. We conducted a detailed analysis of the time efficiency and correctness of +executable property generation under two settings: (1) writing property descriptions in natural +language and generating executable via iPBT, and (2) manually writing executable properties. +• Time efficiency: Fig. 4 shows the time spent per task in both approaches. We can see that + writing natural language property descriptions significantly reduces the time required to produce + executable properties. On average, our approach achieved a 56% reduction in time, compared to + manual writing property descriptions (272.7s vs 625.7s). For low-complexity executable properties + (e.g., L2), time savings reached up to 72%, highlighting the efficiency gains of leveraging LLMs + for code generation. +• Correctness: Table 4 presents the number of correctly generated executable properties in different + approaches. Writing property descriptions with iPBT produced 29 correct executable properties, + outperforming the manual approach, which yielded 26 correct executable properties. One incorrect + executable property generated by iPBT approach stemmed from a user typo (a long-click was + mistakenly written as a click). In contrast, most errors in the manually written executable + properties were caused by participants’ unfamiliarity with the Kea framework, such as incorrect + API usage in postconditions. + To better understand these differences, we identified two main contributing factors. First, when +manually writing executable properties, participants needed additional time to inspect UI attributes + +, Vol. 1, No. 1, Article . Publication date: March 2026. + From Natural Language to Executable Properties for Property-based Testing of Mobile Apps 13 + + + Table 4. The correctness of the executable properties generated by different ways. + + Task LLM Setting L1 L2 M1 M2 H1 H2 Total + with annotations 5 5 5 4 5 5 29 + GPT-4o + without annotations 4 5 5 1 4 5 24 + Writing property descriptions + with annotations 5 5 5 4 5 5 29 + DeepSeek-V3 + without annotations 4 5 0 1 4 2 16 + Writing executable properties 5 5 4 5 3 4 26 + + + Property Descriptions + 1200 Executable Properties + 1000 + 800 + 600 + 400 + 200 + 0 + OmniNotes Markor SimpleTask Amaze ActivitydiaryAntennapod AnkiDroid Transistor + +Fig. 5. Comparison of the complexity (measured in character count) between natural language property +descriptions and their corresponding executable properties across eight Android apps. + + +for widget identification, while iPBT automated this process based on matching widgets from +property descriptions. Second, even though all participants received training on Kea, we observed +frequent consultation of the documentation during manual writing, especially for framework- +specific APIs. By contrast, iPBT allows users to focus on specifying intended behaviors in natural +language, while delegating low-level implementation details to the LLM. This not only improves +efficiency but also reduces errors caused by limited familiarity with the framework. + Ablation study. In Table 4, we can see that without functionality annotations, iPBT only generated +24 and 16 correct executable properties, respectively. This result indicates the necessity of the +designed functionality annotations in our approach. + Complexity comparison. Fig. 5 presents the complexity comparison between the 124 natural +language property descriptions and their corresponding executable properties, across eight popu- +lar Android apps. The x-axis denotes the app names, while the y-axis represents the complexity, +quantified by the number of characters. On average, the property descriptions contain 211.3 char- +acters, whereas the corresponding executable properties contain 555.0 characters. This significant +difference in complexity highlights the efficiency of the natural language-based approach. Property +descriptions are inherently easier to write than their corresponding executable properties, further +emphasizing the practicality of iPBT in executable properties generation. + +4.3 RQ3: Robustness +Evaluation setup. Building on the user study in RQ2, which evaluates how iPBT supports users +in practice, RQ3 serves as a complementary experiment that examines robustness. While RQ2 +considers the property descriptions actually written by participants, RQ3 evaluates whether iPBT + + , Vol. 1, No. 1, Article . Publication date: March 2026. + 14 Yiheng Xiong, Ting Su, Jingling Sun, Jue Wang, Qin Li, Geguang Pu, and Zhendong Su + + +can generate correct executable properties when faced with semantically equivalent but differently +worded property descriptions, simulating the natural variation in how different users might express +the same intent. + Prior work has shown that LLMs can generate high-quality paraphrases with greater lexical and +syntactic diversity than those produced by crowd workers [7, 8]. Following this line of work, we +use an LLM to automatically generate paraphrased versions of each original property description. + To avoid bias from using the same model for both paraphrasing and code generation, we employ +a different LLM, Llama-3.1-405B, for paraphrase generation. For each property description, we +invoke Llama-3.1 multiple times to generate a pool of candidate paraphrases. Specifically, for each +property description, we invoke the Llama-3.1 10 times using the designed prompt (the prompt is +provided in the artifact due to space limitations), generating 10 paraphrased descriptions per call, +resulting in a total of 100 paraphrased variations per property description. + However, the LLM-generated variations may not be mutually diverse between them. To select a +diverse subset of 10 paraphrases per property description, we employed the BLEU score [50] to +quantify lexical similarity and guide the selection process. The BLEU score was originally developed +for assessing machine translation quality by measuring the similarity between machine-generated +translations and human-written reference translations. In the context of paraphrasing, a lower BLEU +score indicates higher diversity compared to the original text. Specifically, we adopted a greedy +selection strategy to identify a set of paraphrases that are mutually diverse. First, we identified the +two most mutually diverse paraphrases (i.e., the pair with the lowest BLEU score between them) +to initialize the selection set 𝑆. Then, in each subsequent iteration, we computed the Self-BLEU +score [86] between each remaining candidate and the current set 𝑆, which quantifies similarity +to the existing set. The candidate with the lowest Self-BLEU score was added to 𝑆. This process +continued until 𝑆 contained 10 paraphrased descriptions. Formally, the objective of our selection +process is to identify a subset 𝑆 ⊆ 𝐶 of size 𝑘, where 𝐶 is the set of all candidate paraphrases and 𝑘 += 10) that minimizes the Self-Bleu score: + + 1 ∑︁ + arg min BLEU(𝑥, 𝑦) + 𝑆 ⊆𝐶, |𝑆 |=𝑘 |𝑆 |(|𝑆 | − 1) 𝑥,𝑦 ∈𝑆 + 𝑥≠𝑦 + + +This selection strategy ensures that the chosen paraphrases are not only diverse relative to the +original text but also mutually diverse within the set, resulting in a robust dataset for evaluating +our approach under varied natural language expressions. + In RQ3, we focus on 118 property descriptions from RQ1 that were successfully translated into +correct executable properties. Using the paraphrasing procedure described above, we generate +10 paraphrases for each property description, resulting in a total of 1,180 paraphrased property +descriptions. We then evaluate whether iPBT can still generate executable properties from these +paraphrases. +Evaluation results. As shown in Fig. 6, GPT-4o and DeepSeek-V3 generated 1,034 and 1,032 +correct executable properties, respectively, achieving accuracy rates of 87.6% and 87.5%. Specifically, +both models successfully generated correct executable properties for 81.0% (956/1,180) of the +descriptions, demonstrating that iPBT is robust to variations in natural language expressions. +Among the remaining cases, 6.6% (78/1,180) of the descriptions were handled correctly by GPT-4o +but not by DeepSeek-V3, while 6.4% (76/1,180) were correctly processed by DeepSeek-V3 but not by +GPT-4o. In 5.9% (70/1,180) of the cases, both models failed to generate correct executable properties. + To further understand the effectiveness of iPBT in executable property generation, we analyzed +the symptoms of the failure cases. Finally, we identified four main categories of failure symptoms. + +, Vol. 1, No. 1, Article . Publication date: March 2026. + From Natural Language to Executable Properties for Property-based Testing of Mobile Apps 15 + + + 70 69 + Widget Mismatch 70 84 + (5.9%) + 39 (5.9%) + Logic Incompleteness 30 + 78 956 76 78 956 76 + 11 + (6.6%) (81.0%) (6.4%) Logic Redundancy + (6.6%) 9 (81.0%) (6.4%) + GPT-4o + G D G + Semantic Deviation 27 + 25 D DeepSeek-V3 + 0 20 40 60 80 + +Fig. 6. Venn diagrams of executable prop- Fig. 7. Failure symptom distribution. +erty generation. G: GPT-4o; D: DeepSeek- +V3. + + + + Fig. 7 presents the distribution of failure symptoms in the incorrect executable properties gener- +ated by iPBT with two LLMs. The results reveal that UI widget mismatch is the most frequent error +type, accounting for 47.3%(69/146) and 56.8%(84/148) of the total failures in executable properties +generated by GPT-4o and DeepSeek-V3, respectively. This indicates that while LLMs demonstrate +a general understanding of UI semantics, they still struggle to precisely align UI descriptions +with their corresponding identifiers in some cases. Incomplete code is the second most common +symptom, responsible for 26.7%(39/146) and 20.3%(30/148) of the errors. This is followed by other +logic errors (18.5%(27/146) and 16.9%(25/148)), which typically involve incorrect API usage or faulty +postcondition assertions. Redundant code ranks fourth, contributing 7.6%(11/146) and 6.1%(9/148) +of the failures. The similar distribution of errors across GPT-4o and DeepSeek-V3 demonstrates that +iPBT performs robustly across different LLMs, while also revealing typical challenges in executable +property generation. +• Widget Mismatch. Widget mismatch occurs when the generated executable properties fail + to match the intended UI widget. As shown in Fig. 8(a), an example of incorrect executable + properties generated by GPT-4o for the app AntennaPod [4]. The expected UI event is to click + the option button, but the UI widget identifier highlighted in red fails to match the target widget. + In contrast, Fig. 8(b) shows the expected correct executable properties, where the UI widget + identifier accurately matches the target UI widget. +• Logic Incompleteness. Logic incompleteness refers to generated executable properties that + omit statements needed. This manifests primarily as (1) incomplete preconditions/postconditions, + (2) missing conditional branches in interaction logic. Such incompleteness may lead to two + consequences during execution: (1) execution failures during the property checking, (2) false + positives in test results. Fig. 8(c) shows an incomplete code example, which was generated by + DeepSeek-V3 for the app OmniNotes [44]. The precondition fails to verify the existence of the + "note title" UI widget, causing the testing framework to raise an exception while executing the + interaction scenario when the widget is absent. Fig. 8(d) shows correct implementation, which + includes the necessary existence check for the UI widget ( highlighted in green). +• Logic Redundancy. Logic Redundancy refers to the generated code containing unnecessary + statements, primarily manifested as redundant UI events (e.g., click) in interaction logic. Such + errors typically lead to execution failures during property checking. Fig. 8(e) shows an example, + which was generated by GPT-4o for the app AntennaPod. The last line (highlighted in red) + introduces an unnecessary event to open the notification page. Then, since the GUI state changes + to the notification page, the assertion statement will fail during the property checking. Fig. 8(f) + shows the expected executable properties. + + , Vol. 1, No. 1, Article . Publication date: March 2026. + 16 SMU Classification: + Yiheng Xiong, Ting Su, Jingling Sun, Jue Wang, Qin Li, Geguang Pu, and Zhendong Su + Restricted + + + + + Failure Symptom: UI widget mismatch Failure Symptom: Redundant code + # Tap the settings icon # Ensure a notification appears, indicating the queue has no + findWidget(id="butShowSettings").click() episodes. + open_notification() + (a) Incorrect property code + assert findWidget(id="emptyViewTitle").click() + # Click the option button + findWidget(description="More options").click() (e) Incorrect property code + # Assert there is a text exists that indicates there is no episode + (b) Expected property code in the queue + assert findWidget(id="emptyViewTitle").click() + Failure Symptom: Incomplete code (f) Expected property code + # A search query is available and a note title is known, with + no "SETTINGS" text found Failure Symptom: Other logic error + @precondition( + # Identify the file with the ".zip" suffix + findWidget(id="search_query").exists() and + zip_file = self.device(textContains=".zip") + not findWidget(text="SETTINGS").exists() + zip_file_name = zip_file.get_text() + ) + # Select the identified file + (c) Incorrect property code zip_file.long_click() + # Search query exists and note title exists and text (g) Incorrect property code + "SETTINGS" not exists + @precondition( # Get the zip file whose name contains ".zip" + findWidget(id="search_query").exists() and zip_file = self.device(textContains=".zip") + findWidget(id="note_title").exists() and not zip_file_name = zip_file.get_text() + findWidget(text="SETTINGS").exists() # Click it + ) zip_file.click() + + (d) Expected property code (h) Expected property code + + +Fig. 8. Illustrative examples of failure symptoms. Incorrect and correct implementations are marked in red +and green, respectively, with property descriptions in gray (code snippets are simplified for clarity). + + +• Semantic Deviation. This refers to other semantic errors, such as incorrect API usage or + assertions in postconditions. These types of errors often result in property execution failures or + inaccurate test results, including false positives and false negatives. Fig. 8(g) shows an example, + which was generated by DeepSeek-V3 for the app Amaze [1]. The implementation (highlighted + in red) tries to long-click a file. However, the property description indicates that it should click + the file. Fig. 8(h) shows the expected executable properties. + Ablation study. We remove the widget functionality annotations from the prompt. The results +show that iPBT generated 833 and 822 correct executable properties on GPT-4o and DeekSeek-V3, +corresponding to accuracy rates of 70.6% and 69.7%, respectively. In comparison, the full setting +achieved 87.6% and 87.5% accuracy. This represents a performance drop of 17.0 and 17.8 percentage +points, respectively, highlighting the critical role of functionality annotations in guiding the LLM +to generate correct executable properties. + +5 Discussion and Lessons + Generality of our work. First, the evaluation results demonstrate that our approach is effective in +translating natural language property descriptions into executable properties for 124 properties. +These 124 properties are collected from the existing dataset [75] that contains 124 real functional +bugs across 8 popular apps. It is interesting to further understand the generality of the approach +on a larger set of apps. Second, our work’s core methodology is translating informal specifications +into formal properties in mobile apps, and it can be extended naturally to other similar applications, +e.g., web applications (which also have UI widgets and user interactions) and formal specification +generation in program verification. For example, many verification tools (e.g., Dafny [53]) require +formal pre/post-conditions or invariants, which share structural similarities with PBT properties. + +, Vol. 1, No. 1, Article . Publication date: March 2026. + From Natural Language to Executable Properties for Property-based Testing of Mobile Apps 17 + + + Applying LLMs to PBT of mobile apps. Although existing PBT frameworks are effective, specifying +properties requires significant manual effort and deep familiarity with UI structures and framework- +specific APIs. Allowing testers to write properties in structured natural language shifts this burden. +In practice, this change enables testers to focus on what the app should do, rather than how to +encode it, substantially lowering the barrier to using PBT. + Importance of UI semantic grounding. A central lesson is that UI semantic grounding is essential. +Without widget functionality annotations, LLMs frequently select incorrect UI widgets, even +when the generated code logic is otherwise correct. Our ablation results confirm that raw widget +identifiers alone are insufficient in real-world apps, where identifiers are often ambiguous or poorly +named. + Designing natural language as an effective specification interface. We found that natural language +property descriptions should not be treated as completely free-form input. In practice, adopting a +lightweight structure (precondition–interaction–postcondition) significantly reduces ambiguity +and improves generation quality. This indicates that natural language specifications function as an +interface between humans and LLMs, and even minimal structural constraints can greatly enhance +reliability without harming usability. + What the failures reveal. Most failures arise from UI widget mismatch, not from incorrect control +flow or API usage. This indicates that current LLMs can generally synthesize reasonable test logic, +but still struggle with fine-grained UI disambiguation when multiple widgets have similar semantics. +In addition, paraphrased descriptions sometimes omit implicit constraints, leading to incomplete +preconditions or redundant actions. This suggests that LLM-based property synthesis is robust to +linguistic variation, but sensitive to semantic underspecification. + Complementing rather than replacing existing PBT frameworks. Rather than replacing existing +property-based testing frameworks, iPBT complements them by addressing one of their most +labor-intensive stages: executable property authoring. Since iPBT does not modify the execution or +input generation mechanisms of PBT, it can be integrated into existing workflows with minimal +disruption. This design choice proved important for maintaining practicality. + Threats to Validity. Our work may suffer from some threats to validity. First, the properties in our +experiment may not fully represent those in real-world apps. To mitigate this threat, we selected +properties from the Kea dataset [75], where each property is derived from a real historical bug and +covers important app functionalities. In the future, we will include a broader range of properties +from industrial apps. Also, as we utilize dynamic exploration to collect the UI widget identifier +list, it may not capture all the UI widgets in the app. This insufficient exploration is also identified +as a common challenge of input generation in testing apps [6, 60]. Second, the natural language +property descriptions may differ from how practitioners describe properties in practice. To mitigate +this, the initial descriptions were authored by an experienced property-based testing expert and +carefully reviewed by all co-authors. In addition, RQ2 evaluates descriptions written by 10 real users, +and RQ3 further assesses robustness under diverse paraphrased descriptions. Third, our evaluation +considers only two LLMs (GPT-4o and DeepSeek-V3), which may limit generalizability. We selected +them as representative closed-source and open-source state-of-the-art models, and future advances +in LLMs are expected to further improve performance. Finally, there is a potential concern that +the models may have seen the evaluated properties during training. This threat is unlikely, as +both models were trained before the release of the Kea dataset, and all property descriptions were +manually created and have not been publicly available. To further avoid bias, we used a different +LLM (Llama-3.1) for paraphrasing in the robustness evaluation. + + , Vol. 1, No. 1, Article . Publication date: March 2026. + 18 Yiheng Xiong, Ting Su, Jingling Sun, Jue Wang, Qin Li, Geguang Pu, and Zhendong Su + + +6 Related Work +LLM for SE tasks. The rapid advancement of LLMs has spurred significant research into their +application across various software engineering domains. In code completion [16, 42, 81], LLMs have +demonstrated strong capabilities in providing context-aware suggestions and recommendations. +The domain of program repair [73, 82] has also benefited from LLMs’ ability to understand and +fix bugs in code. Moreover, comprehensive studies [22, 83] have systematically evaluated LLMs’ +capabilities across multiple software engineering tasks, understanding the applications, effects, and +limitations. Our work specifically addresses the area of executable property generation for PBT. +Automated test generation. The research on automated test generation can be categorized +into two types: traditional and deep learning-based approaches. Traditional approaches include +techniques such as fuzzing [40], symbolic execution [21, 56, 64], search-based [19, 47]. These +approaches primarily aim to achieve high test coverage. However, these approaches often struggle +to generate assertions [49, 57]. + Deep learning-based approaches leverage the capabilities of pre-trained language models to +generate tests from code snippets [28, 65, 77, 79]. For example, AthenaTest [65] leverages a +transformer model, BART [30], to generate unit test cases based on the given method input. In +recent years, LLM-based approaches have shown promising results in test generation [14, 26, 28, 79]. +TiCoder [28] leverages LLMs to formalize user intent into tests, and ChatTester [79] can generate +unit tests through interactive conversations with LLMs. While these approaches focus on generating +unit test cases, some recent work has moved closer to property-based testing. Endres et al. [17] +conduct a study to evaluate the LLM’s capability of generating postconditions for individual +functions based on the function comments. Vikram et al. [67] propose an approach to leverage +LLM for generating property-based tests from specifications for Python libraries. Liu et al. [34] +target properties for smart contracts. In contrast, our approach focuses on mobile apps, generating +executable properties (including preconditions, interaction scenarios, and postconditions) from +natural language descriptions to capture real app behavior while reducing manual effort. + In mobile app testing, recent work like Kea [75], PBFDroid [61], and PDTDroid [62] has demon- +strated the effectiveness of PBT in detecting functional and privacy bugs. However, these frame- +works primarily focus on the execution and input generation phases, assuming the existence of +high-quality executable properties. Consequently, they still require significant manual effort and +domain expertise to write executable properties. Our work complements these approaches by +automating the executable property generation. + Some work leverages LLM to analyze GUI pages during the dynamic exploration to find data +inconsistency bugs [23], functional bugs [36], or inconsistencies between app design and implemen- +tation [33]. Our work differs from these approaches in its focus: rather than detecting bugs directly, +we generate executable properties that can be used by existing PBT frameworks. Recently, different +agents have been proposed to automatically perform tasks on mobile apps [52, 68, 70, 71, 80]. These +works focus on executing user-specified tasks, whereas our work centers on generating executable +properties to guide property-based testing. +UI widget understanding. Various approaches try to understand the widget from different +perspective [31, 35, 37, 38, 72, 74]. For example, IconIntent [74] leverages program analysis and +computer vision techniques to identify sensitive UI widgets in Android apps. DroidGem [38] +leverages deep neural networks to predict the permissions behind the UI widgets. HintDroid [35] +aims to generate hint-text of the UI widget to improve the accessibilty for low-vision users. In +contrast, our work focuses on constructing UI widget context for matching the property description +with widget identifiers in PBT. + + + +, Vol. 1, No. 1, Article . Publication date: March 2026. + From Natural Language to Executable Properties for Property-based Testing of Mobile Apps 19 + + +7 Conclusion +In this work, we presented a novel approach to automatically generate executable properties +from natural language property descriptions. Our approach lowers the manual effort and technical +expertise required for property-based testing of mobile apps. In detail, we first construct the enriched +widget context by extracting GUI information and leveraging MLLMs to generate functionality +annotations of widgets. Then, we employ in-context learning to guide LLMs in generating executable +properties with the carefully designed prompt. 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Publication date: March 2026. + \ No newline at end of file diff --git a/packages/opencode/specs/simulation-research/text/2026-propgen-mobile-app-testing.txt b/packages/opencode/specs/simulation-research/text/2026-propgen-mobile-app-testing.txt new file mode 100644 index 00000000000..274eeebaba6 --- /dev/null +++ b/packages/opencode/specs/simulation-research/text/2026-propgen-mobile-app-testing.txt @@ -0,0 +1,859 @@ + From Exploration to Specification: LLM-Based Property + Generation for Mobile App Testing + Yiheng Xiong Shiwen Song Bo Ma + Singapore Management University Singapore Management University East China Normal University + Singapore Singapore China + yihengx98@gmail.com swsong@smu.edu.sg boma@stu.ecnu.edu.cn + + Ting Su Xiaofei Xie + East China Normal University Singapore Management University + China Singapore +arXiv:2604.13463v1 [cs.SE] 15 Apr 2026 + + + + + tsu@sei.ecnu.edu.cn xfxie@smu.edu.sg + + Abstract the functional correctness of mobile apps [24, 26]. However, it is + Mobile apps often suffer from functional bugs that do not cause brittle, costly to maintain, and typically covers only pre-defined + crashes but instead manifest as incorrect behaviors under specific happy paths, often missing non-trivial functional bugs [66]. + user interactions. Such bugs are difficult to detect by conventional Property-based testing (PBT) offers a promising direction for + automatic testing techniques because they often lack explicit test addressing this challenge [5]. Recent work has demonstrated that + oracles. Property-based testing can effectively expose them by spec- carefully designed properties can reveal non-trivial functional bugs + ifying intended behavior as properties and checking them under that are missed by other techniques [52, 66]. In mobile app testing, + diverse interactions. However, its practical use is limited by the need developers specify expected behaviors as properties, and a PBT + for manually written properties, which are difficult and expensive framework then automatically generates a large number of GUI + to construct. events to explore diverse GUI states and check whether these prop- + To address this limitation, this paper explores the use of large erties hold. Compared with validating only a fixed set of manually + language models (LLMs) to automate property construction for crafted GUI test cases, this paradigm provides a more efficient way + property-based testing of mobile apps. This process is challenging to assess functional correctness across diverse GUI states. + in two ways. First, it is difficult to systematically uncover and exe- However, the effectiveness of PBT fundamentally depends on + cute diverse app functionalities. Second, it is difficult to derive valid the availability of high-quality properties, whose manual construc- + properties from functionality execution results, because a single ex- tion remains a major barrier to practical adoption [15, 16]. This + ecution provides only limited evidence about what behavior should challenge is especially pronounced for mobile apps, where explicit + generally hold. To address these challenges, we introduce Prop- behavioral specifications are often unavailable. As a result, testers + Gen, which performs functionality-guided exploration to collect must manually understand app functionalities, abstract their ex- + behavioral evidence from execution results, synthesizes properties pected behaviors into executable properties, and refine the proper- + from the collected evidence, and refines imprecise properties based ties when reported violations are false positives. This manual and + on testing feedback. We implemented PropGen and evaluated it iterative process substantially limits the broader adoption of PBT. + on 12 real-world Android apps. The results show that PropGen To address this limitation, a promising direction is to leverage + can effectively identify and execute app functionalities, generate the reasoning and code-generation capabilities of Large Language + valid properties, and refine most imprecise ones. Across all apps, Models (LLMs) to automate property construction. However, di- + PropGen identified 1,210 valid functionalities and correctly exe- rectly asking an LLM to generate properties is often unreliable, due + cuted 977 of them, compared with 491 and 187 for the baseline. It to both the lack of explicit behavioral specifications in mobile apps + generated 985 properties, 912 of which were valid, and successfully and the tendency of LLMs to hallucinate. Instead, an effective solu- + refined 118 of 127 imprecise ones exposed during testing. Using the tion should be able to identify app functionalities, infer properties + resulting properties, we found 25 previously unknown functional from execution-derived behavioral evidence, and refine imprecise + bugs in these apps, many of which were missed by existing testing properties based on testing feedback. + techniques. Challenges. However, achieving this goal is far from straight- + forward and presents two key challenges: broad functionality ex- + 1 Introduction ploration and property abstraction from execution traces. First, the + Mobile apps are highly interactive and stateful systems whose func- approach must explore as many meaningful app functionalities as + tionalities are largely driven by user interface interactions. Despite possible, but this is difficult in mobile apps. Many functionalities are + extensive testing efforts, functional bugs (e.g., incorrect interaction not directly visible on the current screen. They may only become + logic) remain prevalent in real-world apps [67]. These bugs often available after several navigation steps, under specific UI states, or + do not manifest as crashes, making them difficult to detect using through transient interface elements such as menus and dialogs. As + conventional GUI testing techniques that mainly emphasize code a result, systematically exposing a large and diverse set of function- + coverage or crash discovery [8, 17, 29, 31, 33, 38, 47, 58, 61]. Manual alities through app exploration is non-trivial. Without sufficient + testing (e.g., writing GUI tests) is widely used in practice to validate functionality exposure, the generated properties can cover only + Conference’17, July 2017, Washington, DC, USA Yiheng Xiong, Shiwen Song, Bo Ma, Ting Su, and Xiaofei Xie + + +a limited portion of app behavior. Second, even after a function- In summary, this paper makes the following contributions: +ality is executed, it is still difficult to infer a valid property from + • We propose a novel approach that automatically explores app +the execution traces. This is because a property must capture the + functionalities and generates properties from runtime behavioral +essential behavior of the functionality, rather than merely describe + evidence, without relying on manual specifications. +one observed execution. In practice, however, the execution trace + • We design a hypothesis-driven behavioral evidence construction +(e.g., events and screenshots) is often noisy and low-level, and only + technique that infers functionalities from GUI states and sum- +provides a single concrete behavioral instance. Moreover, the in- + marizes execution traces into structured representations suitable +ferred property can become inaccurate: it may encode details that + for property synthesis. +happen to hold in the current trace, but do not necessarily hold in + • We develop a property synthesis and refinement approach that +other valid contexts. Such imprecision can lead to false positives + derives properties from behavior evidence and refines imprecise +during testing and reduce the usefulness of the generated proper- + properties through execution feedback. +ties. Importantly, this difficulty is also faced by human developers + • We implement our approach as PropGen and conduct an exten- +when manually writing properties. + sive evaluation on 12 real-world Android apps. The results show +Our approach. To address the first challenge, we design a function- + that PropGen can cover a large number of app functionalities +ality hypothesis-guided exploration strategy that systematically + while achieving high functionality and property validity, and can +uncovers executable app functionalities and collects behavioral evi- + effectively refine most imprecise properties. +dence from their executions. Given a GUI state, our approach infers +candidate functionalities and grounds each of them in concrete 2 Background +actionable widgets, making the inferred functionality hypothesis + Property-based testing. Property-based testing is a powerful test- +both reliable and directly executable. Based on these hypotheses, + ing methodology that validates whether a program satisfies general +our approach performs targeted functionality execution. During + properties rather than specific input-output examples [5]. Instead +this process, it incrementally expands the functionality pool when + of writing example-based test cases, testers specify high-level prop- +new functionality appears, reuses previously inferred function- + erties that describe the expected behavior of the system. Then, a +alities across recurrent GUI states, and falls back to lightweight + PBT framework automatically generates a large number of test +random exploration only when no functionality is available. This + inputs and executes them to verify whether the properties hold. +hybrid strategy improves functionality coverage and enables richer + For example, for a sorting function sort, rather than enumerating +behavioral evidence collection under a limited exploration budget. + concrete examples (e.g., sort([3,1,2])== [1,2,3]), one can de- + To address the second challenge, PropGen adopts property gen- + fine a general property such as idempotence: sort(sort(x)) = +eration from behavior evidence followed by feedback-driven re- + sort(x). The PBT framework then generates a large number of +finement. Instead of generating properties directly from execution + inputs to verify this property and reports any violating input as a +results, PropGen first abstracts each functionality execution trace + counterexample. +into a compact condition–action–outcome representation, derives + GUI state, event, and functionality. Android applications are +a structured property description, and then translates it into the + GUI-driven and event-based. When an app A runs, its runtime +executable property. Because properties inferred from limited evi- + state is represented by its current GUI layout, which we denote as a +dence may still over-generalize, PropGen further refines those that + GUI state 𝑠. A GUI state corresponds to a hierarchical tree ℓ, whose +trigger false positives during testing. Each refinement is anchored + nodes are GUI widgets 𝑤 (e.g., Button, TextView, EditText) with +to the behavioral evidence, allowing PropGen to localize whether + attributes (e.g., text, resourceId) and interaction capabilities. +the issue lies in the precondition, interaction, or postcondition + User interactions are modeled as events. An event is defined as +and apply a targeted refinement. Through this process, PropGen + 𝑒 = ⟨𝑡, 𝑤, 𝑑⟩, where 𝑡 is the event type (e.g., click), 𝑤 is the target +improves property precision and robustness while preserving the + widget, and 𝑑 is optional data (e.g., text input). An app execution is +original intent. + modeled as a sequence of events. Given 𝐸 = [𝑒 1, . . . , 𝑒𝑛 ], executing +Evaluation and results. We implemented our approach as a tool 𝑒1 𝑒𝑛 + A produces a trace 𝜏 = 𝑠 0 −→ 𝑠 1 → − · · · −−→ 𝑠𝑛 , or 𝑠 0 ⇝ 𝑠𝑛 , where + 𝐸 +named PropGen and evaluated it on 12 real-world popular and +diverse Android apps. Across all apps, PropGen inferred 1,282 func- 𝑠 0 is the initial state. Then, we define a functionality as a tuple 𝑓 = +tionalities, of which 1,210 (94.4%) were valid and 977 (76.2%) were ⟨𝑑, 𝜏⟩, where 𝑑 is a semantic intent of a functionality (e.g., "create a +correctly executed. In comparison, the baseline approach inferred note"), and 𝜏 is an execution trace that realizes this functionality. +575 functionalities, with 491 valid and 187 correctly executed. It fur- Concretely, 𝜏 has the form 𝑠 ⇝ 𝑠 ′ , where 𝐸 is a sequence of one or + 𝐸 + +ther generated 985 property descriptions, 912 (92.6%) of which were more events executable from GUI state 𝑠. Executing 𝜏 completes +valid. During property-based testing, 127 properties were found the corresponding functionality and produces a concrete effect on +to be imprecise, and 118 (93.7%) of them were successfully refined the app state. +by our refinement technique. Using the generated properties, we Property-based testing for mobile apps. In property-based test- +found 25 previously unknown functional bugs in the latest versions ing for mobile apps, a property specifies an expected behavior of +of the subject apps, whereas existing functional testing techniques the app. A property can be defined as a tuple 𝜙 = ⟨𝑃, 𝐼, 𝑄⟩, where 𝑃 +could find only 3 of them in practice. These results demonstrate specifies the GUI states where the property applies, 𝐼 is the interac- +the effectiveness of our approach in automating property construc- tion scenario, and 𝑄 specifies the expected outcome after executing +tion for mobile apps, as well as the bug-finding capability of the 𝐼 . During testing, when a GUI state 𝑠 satisfies 𝑃, the interaction +resulting properties. scenario 𝐼 is executed from 𝑠 to reach a new state 𝑠 ′ . The property + From Exploration to Specification: LLM-Based Property Generation for Mobile App Testing Conference’17, July 2017, Washington, DC, USA + + +is satisfied when (𝑠 |= 𝑃 ∧𝑠 ⇝ 𝑠 ′ ) ⇒ 𝑠 ′ |= 𝑄; Otherwise, a property + 𝐼 + Algorithm 1 Behavioral Evidence Construction +violation is reported. Require: Target app A, time budget 𝐵 + Ensure: Behavioral evidence set T̂ + 1: Launch A; obtain initial state 𝑠 +3 Approach + 2: G𝐹 ← ∅, U ← ∅, T̂ ← ∅ +Overview. Given an app, PropGen automatically generates prop- 3: while elapsed time < 𝐵 do +erties from runtime executions and further refines imprecise ones 4: 𝑢 (𝑠) ← Extract(𝑠) ⊲ Extract the widgets +based on testing feedback. Figure 1 presents the overall workflow, 5: if UnseenWidgets(𝑢 (𝑠), U) then +which consists of three stages. First (§3.1), PropGen performs 6: 𝐹 (𝑠) ← Inferhypothesis(𝑠) ⊲ infer the hypothesis +hypothesis-driven dynamic exploration to construct behavioral 7: G𝐹 ← G𝐹 ∪ 𝐹 (𝑠) ⊲ add the hypothesis into global pool +evidence. For each encountered GUI state 𝑠, it infers functionality 8: U ← U ∪ 𝑢 (𝑠) +hypothesis grounded in the visible UI widgets, executes selected 9: end if +functionalities, and summarizes the resulting execution traces into 10: if HasUnexplored(G𝐹 (𝑢 (𝑠))) then +behavioral evidence for downstream property generation. Second 11: 𝑓 ← Select(G𝐹 (𝑢 (𝑠))) +(§3.2), PropGen synthesizes properties directly from the behavioral 12: (𝜏 𝑓 , 𝑠 ′, G𝐹 , U) ← Execute(𝑓 , 𝑠, G𝐹 , U) +evidence constructed in the first stage. Specifically, it first generates 13: T̂ ← T̂ ∪ {Summarize(𝜏 𝑓 )} ⊲ evidence summary +natural-language property descriptions that capture the intended 14: MarkExplored(𝑓 , G𝐹 ) +condition–event–outcome relation, and then translates them into 15: 𝑠 ← 𝑠′ +executable properties. Third (§3.3), PropGen validates the gener- 16: else +ated properties by the PBT framework and refines properties that 17: 𝑠 ← RandomExplore(𝑠) +are found to be improperly specified. 18: end if +Illustrative example. Figure 2 illustrates the workflow of Prop- 19: end while +Gen on a note-taking app. Starting from the first page in Figure 2 20: return T̂ +(a), PropGen performs behavioral evidence construction by infer- +ring multiple candidate functionality hypotheses from the current +GUI state. It then selects one hypothesis, attaching a photo to the +note, and executes the corresponding interaction sequence, i.e., Given a target app A and a time budget 𝐵, PropGen first launches +opening the attachment menu, choosing Camera, taking a photo, the app and initializes the global functionality pool G𝐹 , the set of +and returning to the note page. The execution trace is summarized observed UI contexts U, and the behavioral evidence set T̂ (Lines 1– +into structured behavioral evidence (as shown in Figure 2(c)), from 2). It then iteratively explores the app until the budget is exhausted +which PropGen synthesizes an executable property describing the (Lines 3–19). In each iteration, PropGen extracts the current GUI +expected behavior of this functionality (Figure 2(d)). context from the current GUI state (Line 4). If the context contains + The initial synthesized property may be imprecise and thus previously unseen widget evidence, PropGen invokes a Multimodal +produce false positives during execution. In this example, its post- Large Language Model (MLLM) to infer functionality hypotheses +condition checks whether the app returns to a page containing the for the current state, adds them to G𝐹 , and updates U (Lines 5–8). +text “Notes” and whether the newly added attachment is displayed PropGen then checks whether the current context contains any +as an attachment thumbnail. This postcondition is too specific. Af- unexplored functionality hypothesis (Line 10). If so, it selects one +ter taking a photo, the app may legitimately return to either the hypothesis together with its triggering widget, executes it to obtain +Notes page or the Archive page, depending on where the note was a functionality trace, and summarizes the trace into a behavioral +opened. Moreover, under reduced view, the attached photo may not evidence item added to T̂ (Lines 11–15). Otherwise, PropGen per- +appear as a thumbnail, but instead as a compact attachment icon forms lightweight random exploration to leave the current local +(Figure 2(b)). Therefore, the synthesized property may incorrectly GUI region and expose new interaction opportunities (Lines 16– +flag a failure even though the photo has been successfully attached. 17). The process repeats until the time budget is exhausted, after +PropGen then refines the property by relaxing these assertions which PropGen returns the collected behavioral evidence set T̂ +to allow multiple valid return pages (use the menu button that (Lines 19–20). +both pages contain) and attachment representations (thumbnail or +icon). After validating this property using the PBT tool Kea, we 3.1.1 Functionality Hypothesis Generation. Given a GUI state 𝑠 +uncovered a new functional bug: opening audio recording before encountered during exploration, this step aims to infer which app +taking a photo prevents the photo attachment from appearing. functionalities may be executable under the current interface con- + text. To support subsequent execution, each inferred functionality + is associated with a concrete triggering widget in the current state. +3.1 Behavioral Evidence Construction Semantic context construction. To support functionality infer- +The goal of this stage is to construct execution-grounded behavioral ence, PropGen first constructs a semantic context for the current +evidence for downstream property synthesis. Instead of relying on GUI state 𝑠. This context includes three parts: the screen-level con- +external specifications, PropGen systematically explores executable text of the current state, app-level semantic cues, and cross-state +app functionalities and records their runtime interaction traces as functionality memory. The screen-level context is derived from +behavioral evidence. Algorithm 1 summarizes the workflow. the current GUI screenshot, where each interactive widget 𝑤 in 𝑠 + Conference’17, July 2017, Washington, DC, USA Yiheng Xiong, Shiwen Song, Bo Ma, Ting Su, and Xiaofei Xie + + + + Behavioral Evidence Construction Property Synthesis from Behaviroal Evidence + + Property Description Generation Executable Property Translation + Semantic Context + Functionality selection + Construction + + Feedback-Driven Property Refinement Output + Event Planing and + Hypothesis Inference + Execution Executable Property Validation by PBT tool Property + Description + Failed Infomation + Behavioral Imprecise Property + Property + Functionality Evidence + App Under Test Refinement + Hypothesis Summarization Executable + Failure Evidence Property + + + + Figure 1: Overview of PropGen. + + + + + (a) An execution trace of the functionality. (b) Suspicious violation. + ① Behavior Evidence Construction + + + + ② Property + Synthesis + ③ Feedback-Driven Property Refinement + + (c) Behavior evidence. (d) Generated property. + + +Figure 2: An Illustrative Example of Behavioral Evidence Construction, Property Synthesis, and Feedback-Driven Property +Refinement for a Note-Taking App. + + +is annotated with a unique numeric label. These labels turn visu- ⟨𝑓𝑘 , 𝑤𝑘 ⟩], where each functionality hypothesis 𝑓𝑖 is a concise natural- +ally distributed UI elements into explicit references, allowing the language description of a candidate app functionality, and 𝑤𝑖 de- +inferred functionalities to be grounded in concrete widgets. The notes its corresponding triggering widget. This widget grounding +app-level semantic cues include the app name and the list of activity serves two purposes. First, it constrains the MLLM to infer func- +names extracted from the AndroidManifest.xml file, helping the tionalities that are supported by the current GUI state, reducing +MLLM interpret the current screen under the broader semantic unsupported or non-actionable predictions. Second, it makes the in- +context of A. Finally, the cross-state functionality memory stores ferred functionalities directly executable in subsequent exploration. +previously inferred functionalities, helping avoid repeatedly redis- The inferred functionality hypothesis, together with their associ- +covering semantically similar functionalities in later GUI states. ated triggering widgets, are then stored in the global functionality +Together, these components provide the contextual information pool G𝐹 to support later execution and cross-state reuse. +needed for inferring plausible user-facing functionalities from 𝑠. Inference triggering and hypothesis reuse. To avoid redun- +Functionality hypothesis inference. Using the constructed se- dant MLLM invocations on similar GUI states, PropGen triggers +mantic context, PropGen invokes a MLLM to infer candidate func- functionality inference only when a newly visited state introduces +tionality hypothesis for the current GUI state 𝑠. Formally, the in- unseen widget evidence. It maintains a global set of explored UI +ferred hypothesis are represented as 𝐹 (𝑠) = [⟨𝑓1, 𝑤 1 ⟩, ⟨𝑓2, 𝑤 2 ⟩, . . . , contexts U = {𝑢 1, 𝑢 2, . . .}, where each context is defined as 𝑢 (𝑠) = + From Exploration to Specification: LLM-Based Property Generation for Mobile App Testing Conference’17, July 2017, Washington, DC, USA + + +⟨𝑎(𝑠),𝑊 (𝑠)⟩, with 𝑎(𝑠) denoting the activity and 𝑊 (𝑠) the set of widget 𝑤𝑖 is specified by its numeric label, and 𝑑𝑖 ) specifies the +signatures of leaf-level interactive widgets. attached data (e.g., input text). Before executing 𝑒𝑖 , PropGen ver- + For each state 𝑠, PropGen compares 𝑊 (𝑠) with existing con- ifies that the referenced widget 𝑤𝑖 is present in the current state +texts under the same activity. If no new widget signatures are 𝑠𝑖 . If the predicted widget identifier is invalid, the event is skipped +observed, it reuses previously inferred functionality hypotheses; and directly labeled as a failed step. This guarded execution mecha- +otherwise, it invokes the MLLM to infer new functionalities and nism prevents invalid model-predicted interactions and improves +updates the global pool G𝐹 . To enable stable comparison across execution robustness. + 𝑒𝑖 +screens, each widget 𝑤 is represented by a signature of attributes After execution produces a state transition 𝑠𝑖 −→ 𝑠𝑖+1 , PropGen +⟨𝑐𝑙𝑎𝑠𝑠, 𝑟𝑒𝑠𝑜𝑢𝑟𝑐𝑒𝐼𝑑, 𝑡𝑒𝑥𝑡, 𝑑𝑒𝑠𝑐𝑟𝑖𝑝𝑡𝑖𝑜𝑛⟩, which are commonly used to evaluates whether the step has advanced the selected functionality. +identify unique widgets in practice [47, 49, 64]. To reduce noise This evaluation jointly considers the pre- and post-event GUI states, +from dynamic content, PropGen retains only app-defined text in the functionality hypothesis 𝑓 , and the accumulated execution his- +signatures by filtering widget text against a whitelist extracted via tory 𝐻𝑖 . Based on this evidence, the MLLM assigns an outcome +static analysis. This avoids treating semantically identical screens label 𝑜𝑖 ∈ {success, fail, complete} to the current step. Here, success +with transient text differences as distinct contexts. indicates meaningful progress toward the functionality goal, fail + indicates that the event was unproductive for the intended func- +3.1.2 Hypothesis-Guided Functionality Execution. Given the global tionality, and complete indicates that the functionality goal has been +functionality pool G𝐹 generated in § 3.1.1, the goal of this step is achieved. The resulting step and outcome are then incorporated +to expand behavioral coverage under a limited exploration budget into the execution history for subsequent planning, while complete +by executing app functionalities in a targeted manner. Instead of terminates execution of the current functionality. +interacting with A through arbitrary GUI events, PropGen treats Behavioral evidence summarization. To support downstream +each functionality hypothesis in G𝐹 , together with its associated property synthesis, PropGen summarizes each executed interac- +triggering widget, as an explicit execution target, and prioritizes tion trace into compact behavioral evidence. This step is necessary +the execution of previously unexplored functionality hypothesis. because raw execution traces are low-level, noisy, and specific to a + Executing a selected functionality hypothesis ⟨𝑓 , 𝑤⟩ may require single execution, whereas property synthesis requires a higher-level +one or more concrete GUI events, thereby inducing state transitions representation of the condition–event–outcome relation exhibited + 𝐸 +of the form 𝑠 → − 𝑠 ′ . Such functionality-guided execution serves two by the app behavior. To bridge this gap, PropGen incrementally +purposes simultaneously: it exercises already identified app behav- 𝑒𝑖 + converts each interaction step 𝑠𝑖 −→ 𝑠𝑖+1 into a structured transition +iors to collect behavioral evidence, and it drives the app into new with five elements: the state summary before the event, an event +GUI states 𝑠 ′ from which additional functionality hypothesis 𝐹 (𝑠 ′ ) summary describing the interaction performed, the state summary +can be inferred and inserted into G𝐹 . In this way, execution and after the event, a state-diff summary capturing the visible difference +hypothesis generation form a closed exploration loop that progres- between the two GUI states, and an outcome label 𝑜𝑖 indicating +sively broadens the functionality space explored by PropGen. how the event affected progress toward the selected functionality. +Functionality selection. At each GUI state 𝑠, PropGen retrieves The state summaries are functionality-oriented: they describe the +from G𝐹 the candidate functionality hypothesis associated with screen context, visible actionable elements, current content state, +the current UI context 𝑢 (𝑠), denoted as G𝐹 (𝑢 (𝑠)). Since the explo- and observable feedback cues. In contrast, the state-diff summary +ration budget is limited, PropGen does not execute these candi- focuses on the concrete GUI changes induced by the interaction. +dates arbitrarily, but prioritizes those with higher expected explo- Together, these summaries preserve the behavioral evidence needed +ration utility. This prioritization is implemented using lightweight to capture the executed functionality’s condition–event–outcome +heuristics guided by three considerations: whether the functional- relation while filtering out incidental GUI details. The resulting +ity corresponds to a main app behavior, whether it is semantically summarized trace, denoted as 𝜏ˆ𝑓 , serves as the behavioral evidence +different from previously executed functionalities, and whether it used in the subsequent property synthesis stage. +is likely to be successfully executed in the current context. Based Exploration beyond local hypothesis exhaustion. As explo- +on these heuristics, the top-ranked unexplored functionality hy- ration proceeds, PropGen may reach GUI states where all available +pothesis ⟨𝑓 , 𝑤⟩ is selected as the next execution target. The selected functionality hypothesis have already been executed and no new +hypothesis is then passed to a goal-directed interaction loop that hypothesis can be triggered. In such cases, continued MLLM-guided +incrementally plans, executes, and evaluates UI actions until the exploration becomes less effective, because the MLLM is most use- +functionality is completed or a step limit is reached. ful when acting toward an explicit functionality goal. When no +Event planning and execution. Once a functionality hypothesis such goal is available, the task is no longer to reason about how to +⟨𝑓 , 𝑤⟩ is selected, PropGen executes it through a goal-directed in- execute a functionality, but simply to move the app into a new GUI +teraction loop consisting of event planning, guarded execution, and region where new functionality hypothesis may emerge. For this +post-event evaluation. At each step 𝑖, PropGen first predicts the purpose, lightweight random exploration is both more efficient and +next GUI event based on three sources of information: the function- less costly. Therefore, once local functionality-guided exploration is +ality goal 𝑓 , the execution history 𝐻𝑖 of prior events and their out- exhausted, PropGen switches to random exploration. It continues +comes, and the current GUI state 𝑠𝑖 , represented as a screenshot with traversing the app through random GUI events until it reaches a +labeled widgets. The predicted event is denoted as 𝑒𝑖 = ⟨𝑡𝑖 , 𝑤𝑖 , 𝑑𝑖 ⟩, state that either contains unexecuted functionality hypothesis or +where the event type 𝑡𝑖 is chosen from a predefined event space exposes unseen widget evidence for new hypothesis generation. +including click, long-click, edit, swipe, and back, the target + Conference’17, July 2017, Washington, DC, USA Yiheng Xiong, Shiwen Song, Bo Ma, Ting Su, and Xiaofei Xie + + +In the former case, PropGen resumes functionality-guided execu- already been made explicit in the preceding natural-language for- +tion directly; in the latter, it first performs functionality hypothesis mulation step, this translation primarily serves to operationalize the +generation and then continues execution. This design combines structured specification rather than to perform further behavioral +the strength of goal-directed MLLM-guided execution with the effi- inference. +ciency of random exploration for escaping locally exhausted GUI This step is implemented by prompting the LLM with the gen- +regions. erated natural-language specification together with framework- + specific APIs and widget attributes, with reference to the prompt +3.2 Property Synthesis from Behavior Evidence design in prior work on translating natural-language properties +The goal of this stage is to derive executable properties from the into executable ones [65]. The resulting code is then passed to the +behavioral evidence collected during functionality exploration. As subsequent validation and refinement stage. +input, PropGen takes the summarized trace 𝜏ˆ𝑓 produced in Sec- +tion 3.1, which compactly captures how a functionality is exercised +and what observable GUI outcome it induces. Each synthesized + 3.3 Feedback-Driven Property Refinement +property takes the form 𝜙 = ⟨𝑃, 𝐼, 𝑄⟩, where 𝑃 is a precondition, 𝐼 Properties automatically generated from functionality traces may +is an interaction scenario, and 𝑄 is a postcondition assertion. still be imprecise and therefore trigger false positives during test- + Rather than generating 𝜙 directly from 𝜏ˆ𝑓 , PropGen decomposes ing. However, a reported failure should not be refined by simply +property synthesis into two steps, separating semantic property adapting the property to that single execution, because such a fix +formulation from executable code generation. It first constructs a may overfit the observed case and drift away from the original +natural-language property specification that explicitly captures the functionality intent. +intended ⟨𝑃, 𝐼, 𝑄⟩ relation, and then translates this intermediate Our key idea is that refining a false-positive-inducing property +specification into executable property code. requires first recovering the property’s original testing intent, and +Natural-language property description generation. Based on then revising it so that it remains valid for both the original intended +the summarized trace 𝜏ˆ𝑓 , PropGen first prompts the MLLM to con- execution and the newly observed legitimate execution. To this end, +struct a natural-language property specification 𝜙 𝑁 𝐿 = ⟨𝑃, 𝐼, 𝑄⟩ for we ground refinement in the source summarized trace from which +the functionality captured by the behavioral evidence. The sum- the property was originally inferred, rather than treating refinement +marized trace provides structured evidence about the execution as unconstrained rewriting. +context, performed interactions, observable state changes, and step Specifically, PropGen reasons about the refinement using both +outcomes. Rather than merely restating these observations, the the source summarized trace and the failure-triggering execution. +MLLM is guided to abstract from 𝜏ˆ𝑓 a generalized behavioral rule Specifically, it first recovers the original testing intent of the prop- +that should hold across executions of the same functionality. erty by locating the relevant segment in 𝜏ˆ𝑓 that matches the prop- + The inferred specification 𝜙 𝑁 𝐿 consists of three parts: a pre- erty’s triggering context, interaction scenario, and expected out- +condition 𝑃 describing the observable GUI context in which the come. It then compares this trace-grounded intended behavior with +property should be checked, an interaction scenario 𝐼 capturing the the failing execution to explain why the violation occurs and iden- +user events needed to exercise the functionality, and a postcondition tify which component of 𝜙 has become imprecise, i.e., the precon- +𝑄 specifying the immediate visible effect that should hold after- dition 𝑃, the interaction scenario 𝐼 , or the postcondition 𝑄. +ward. To improve precision and executability, PropGen constrains Based on this diagnosis, PropGen refines only the faulty compo- +this inference process in three ways. First, 𝑃 must be grounded in nent through a minimal modification. More specifically, it strength- +observable UI evidence and sufficiently specific to avoid triggering ens 𝑃 when additional UI guards are needed, revises 𝐼 when the +the property on unrelated screens with superficially similar wid- event sequence does not faithfully reflect the intended behavior, and +gets. Second, 𝑄 must focus on effects that are directly and reliably relaxes or simplifies 𝑄 when the assertion is overly specific. In this +verifiable from the GUI, such as the appearance, disappearance, or way, the refined property remains consistent with both the source- +modification of visible widgets or content. Third, the inferred speci- trace execution and the newly observed legitimate execution, while +fication should avoid trace-specific brittle details, such as incidental preserving the original testing intent as much as possible. +text instances or unstable widget states, and instead capture func- +tionality semantics in a form that remains robust across executions. + In this way, PropGen lifts concrete execution evidence into a 4 Implementation +generalized, testable property abstraction. The resulting natural- We implemented PropGen as an end-to-end prototype for auto- +language specification makes the intended property semantics ex- mated property generation on Android apps. The system is pri- +plicit before code generation, thereby separating behavioral under- marily written in Python and JavaScript, and integrates three key +standing from executable realization. capabilities: GUI state acquisition and interaction, multimodal LLM- +Executable property translation. Given the inferred natural- based reasoning, and executable property generation for Kea [66]. +language property specification 𝜙 𝑁 𝐿 = ⟨𝑃, 𝐼, 𝑄⟩, PropGen trans- At runtime, PropGen uses uiautomator2 [56] to retrieve GUI layouts +lates it into executable property code for the target PBT frame- and Android Debug Bridge (ADB) [53] to capture screenshots and +work. Specifically, this step realizes the precondition 𝑃, interaction issue GUI actions, including click, long-click, edit, swipe, and +scenario 𝐼 , and postcondition 𝑄 using the framework’s property back. The generated properties are translated into the executable +structure and API conventions, thereby producing a runnable prop- format expected by Kea and can be directly executed within its +erty implementation. Since the intended property semantics have property-based testing workflow. + From Exploration to Specification: LLM-Based Property Generation for Mobile App Testing Conference’17, July 2017, Washington, DC, USA + + +Table 1: App subjects used in our experiment (K=1,000, hours for behavioral evidence construction and property synthesis. +M=1,000,000) After that, we used Kea to perform property-based testing with + the generated properties for 6 hours per app, following the testing + App Name App Feature #Downloads #Stars LOC budget adopted in Kea’s paper [66]. + OmniNotes Note Manager 100∼500K 2.8K 57,529 Baselines. We use five baselines for different research questions, + Markor Text Editor - 5.3K 79,749 + RetroMusic Audio Player 1∼5M 5K 110,065 according to their evaluation goals. For RQ1, we compare Prop- + Amaze File Manager 1∼5M 6.1K 159,040 Gen with DroidAgent [69], a representative LLM-based mobile + MyExpenses Financial Assistant 1∼5M 1.1K 317,899 app functionality exploration approach, which can automatically + AntennaPod Podcast Manager 1∼5M 7.7K 130,925 + AnkiDroid Flashcards Manager 10∼50M 10.9K 403,785 + identify and execute functionalities in mobile apps. For RQ4, which + OuterTune Youtube Music Player - 4.8K 89,673 evaluates bug-finding capability, we compare PropGen with four + NewPipe Video Player - 37.5K 187,187 representative prior techniques for Android functional bug detec- + Storage Browser 1∼5M 8K 95,705 + MaterialFiles + tion: Genie [48], Odin [60], PBFDroid [49], and VisionDroid [30]. + Orgzly To-do Lists Manager 100∼500K 2.8K 72,042 + uhabits Habit Tracker 5∼10M 9.7K 69,652 Among them, Genie and Odin rely on designed automated oracles, + PBFDroid is a property-based testing technique for data manipu- + lation functionalities (DMFs), and VisionDroid is an LLM-based +5 Evaluation multi-agent approach for functional bug detection. +We evaluate PropGen from four perspectives: functionality explo- Evaluation method of RQ1. RQ1 aims to evaluate whether Prop- +ration and property generation, property refinement, bug detection, Gen can correctly infer and execute app functionalities and synthe- +and comparison with prior related techniques. Accordingly, we size valid properties from the collected behavioral evidence. This +investigate whether PropGen can accurately explore app func- evaluation cannot be performed fully automatically, because mo- +tionalities and generate semantically correct executable properties, bile apps typically lack precise functional specifications. Therefore, +to what extent the generated properties suffer from imprecision we manually assess the validity of both the inferred functionali- +that leads to false positives and whether such imprecision can be ties and the generated property descriptions, following prior work +refined, whether the resulting properties can help uncover new on functionality-level evaluation beyond structural coverage met- +functional bugs in real-world apps, and how PropGen compares rics [6, 69]. The manual evaluation mainly involves two annotators, +with existing functional testing techniques in uncovering such bugs. who are graduate students majoring in software engineering and +We formulate the following research questions: with at least four years of Android app development experience. Be- + fore the annotation, each annotator was given time (at least fifteen +• RQ1: How effective is PropGen in exploring app functionalities + minutes) to familiarize themselves with the overall functionalities + and generating valid properties? + of every subject app. During this process, annotators also referred +• RQ2: To what extent do generated properties suffer from im- + to the app’s official introduction page when available, so that the + precision that leads to false positives, and how effective is our + subsequent judgments were made with sufficient understanding of + refinement technique in refining them? + the app’s functionalities. In addition, during annotation, annotators +• RQ3: Can the generated properties help find new functional bugs + could interact with the running app at any time to verify uncertain + in real-world mobile apps? + cases. +• RQ4: How does PropGen compare with prior functional testing + For each inferred functionality, we evaluate two aspects. The + techniques in uncovering new functional bugs? + first is functionality validity, which examines whether the inferred + functionality actually exists in the app. Annotators are given the +5.1 Setup and Method inferred functionality description together with the GUI screenshot +App subjects. We selected 12 popular and representative open- from which it was inferred, and determine whether the described +source Android apps as experimental subjects. Among them, eight functionality is genuinely supported by the interface. The second +apps were adopted from prior studies on functional bug detection is execution correctness, which examines whether the system cor- +for Android apps [48, 52, 60, 66]. From the candidate apps used rectly executes the inferred functionality. For each inferred func- +in these studies, we excluded those that were either (1) no longer tionality, annotators are provided with the corresponding execution +runnable or actively maintained, or (2) highly similar in functional- screenshots and interaction events, and judge whether the executed +ity to apps already selected. To further improve subject diversity, we interaction sequence indeed realizes the intended functionality. +additionally included four popular open-source apps from Google For each generated property description, we assess its valid- +Play that provide different features. Table 1 summarizes the selected ity from three aspects: (1) whether the precondition appropriately +apps. In the table, App Feature denotes the primary functionality constrains the UI state in which the property should be applied, +of each app, #Downloads and #Stars report the number of Google (2) whether the interaction scenario accurately reflects the user in- +Play installations and GitHub stars, respectively, and LOC gives the teractions required to perform the functionality, and (3) whether +lines of code. the postcondition correctly captures the observable UI behavior +Experimental environment. All experiments were conducted on that should hold immediately after the scenario. At the same time, +a machine running Ubuntu 22.04 with 192 CPU cores (AMD EPYC because each property is abstracted from an original functional- +9654) and official Android emulators (Android 11, Pixel). We use ity execution trace, it should first hold on the source trace from +GPT-5.2 as the backend MLLM with default settings for PropGen which it is derived. Based on this principle, a property description +and baseline tools that involve LLM. For each app, we allocated 3 is considered valid if it faithfully reflects the behavior exhibited in + Conference’17, July 2017, Washington, DC, USA Yiheng Xiong, Shiwen Song, Bo Ma, Ting Su, and Xiaofei Xie + + +the source trace and can serve as a reasonable specification of the Table 2: Validity of behavioral evidence and synthesized prop- +intended functionality; otherwise, it is labeled as invalid. erties across subject apps (RQ1). + Two annotators independently performed the annotations. We +measured inter-rater agreement using Cohen’s 𝜅, obtaining 0.91, App Name + #Inferred Func #Valid Func #Correctly Executed + #Prop + #Valid + +0.82, and 0.81 for functionality validity, execution correctness, and D P D P D P Prop + + OmniNotes 53 108 53 (100.0%) 102 (94.4%) 18 (34.0%) 80 (74.1%) 81 80 (98.8%) +property validity, respectively. Disagreements were resolved through Markor 48 117 36 (75.0%) 116 (99.1%) 12 (33.3%) 85 (72.6%) 88 83 (94.3%) +discussion with authors. Based on these annotations, we report RetroMusic 48 113 42 (87.5%) 104 (92.0%) 9 (21.4%) 88 (77.9%) 89 70 (78.7%) + +the proportions of inferred functionalities that are valid, inferred Amaze 37 84 24 (64.9%) 83 (98.8%) 8 (33.3%) 64 (76.2%) 57 52 (91.2%) + 54 106 54 (100.0%) 104 (98.1%) 21 (38.9%) 82 (77.4%) 81 78 (96.3%) +functionalities that are correctly executed, and generated property + MyExpenses + AntennaPod 47 142 38 (80.9%) 139 (97.9%) 28 (73.7%) 116 (81.7%) 120 111 (92.5%) +descriptions that are valid. AnkiDroid 50 116 28 (56.0%) 107 (92.2%) 9 (32.1%) 93 (80.2%) 91 85 (93.4%) + We note that, because mobile apps lack precise functional speci- OuterTune 41 76 41 (100.0%) 67 (88.2%) 9 (22.0%) 55 (72.4%) 48 44 (91.7%) + +fications, manual annotation in RQ1 mainly serves as a sanity check NewPipe 46 106 45 (97.8%) 92 (86.8%) 20 (44.4%) 81 (76.4%) 79 72 (91.1%) + MaterialFiles 47 110 44 (93.6%) 103 (93.6%) 23 (52.3%) 82 (74.5%) 86 82 (95.3%) +on the validity of the generated property descriptions. Whether Orgzly 49 124 48 (98.0%) 115 (92.7%) 14 (29.2%) 88 (71.0%) 96 91 (94.8%) +these properties are precise as executable specifications still needs uhabits 55 80 38 (69.1%) 78 (97.5%) 16 (42.1%) 63 (78.8%) 69 64 (92.8%) + +to be validated through execution. Therefore, RQ2 further examines Total 575 1282 491 (85.4%) 1210 (94.4%) 187 (35.2%) 977 (76.2%) 985 912 (92.6%) + +their precision by running the translated executable properties and +analyzing the reported violations. +Evaluation method of RQ2 and RQ3. RQ2 evaluates two aspects analysis to determine whether each of the 25 bugs uncovered by +of property refinement: (1) how many generated properties are im- PropGen theoretically falls within the detection scope of each prior +precise and thus lead to spurious violations during testing, and (2) technique. This analysis is performed manually based on bug char- +how many of these imprecise properties can be successfully refined acteristics and the detection capabilities claimed by each technique. +through refinement. RQ3 evaluates whether the generated proper- To improve reliability, we further consulted the authors of Genie, +ties can uncover new functional bugs. Specifically, for each app, we Odin, and PBFDroid to validate our analysis. For VisionDroid, we +load all initially generated executable properties into Kea [66] for do not perform a separate scope analysis, since its LLM-based de- +testing with 6 hours. Whenever Kea reports a property violation, sign makes its theoretical detection scope difficult to characterize +we manually inspect the property description, executable property precisely; instead, we focus only on its empirical bug-finding per- +code, violation-triggering execution trace, corresponding screen- formance. +shots and interaction events, and the assertion outcome. Based on Second, we empirically evaluate each tool by running it on the +this, we determine whether the violation is caused by a real app bug corresponding apps and checking whether it can rediscover the +or by non-bug factors, such as property imprecision or automation same bugs in practice. For Genie, Odin, and VisionDroid, we fol- +failures. low the default configurations described in their original papers. + For RQ2, we focus on the properties whose reported violations PBFDroid requires users to manually specify properties for data +are diagnosed as spurious. We apply refinement only to those caused manipulation functionalities (DMFs). Therefore, we manually de- +by property imprecision. For each such property, the refinement fined the required DMF properties for detecting the corresponding +module takes the original property description, executable property bugs. To ensure fairness, we align the time budget with each tool’s +code, and violation-triggering execution evidence as input, and workflow: PropGen uses 3 hours for property generation and 6 +produces a revised executable property. We then re-execute the hours for bug finding; accordingly, we allocate 9 hours per app to +refined property on the app and inspect the result. A refinement Genie, Odin, and VisionDroid, and 6 hours of automated testing to +is considered successful if the revised property no longer triggers PBFDroid after manual property construction. +the same spurious violation while preserving the original testing +intent. Based on this process, we report the number of properties 5.2 Results of RQ1 +sent to refinement due to property imprecision, the number and Table 2 reports the results of functionality inference, execution, +rate of successful refinements, and the breakdown of successfully and property synthesis on all subject apps, where #Inferred Func +refined properties by the modified component (i.e., precondition, denotes the number of functionalities identified by tools, #Valid +interaction, and postcondition). Func, #Correctly Executed and #Valid Prop denote the numbers of + For RQ3, we focus on the violations diagnosed as real app bugs functionalities and properties validated by human annotators, and +through manual inspection. For each confirmed bug, we prepare #Prop denotes the number of generated properties. For functionality- +a bug report containing the bug description, reproduction steps, related evaluation, we compare DroidAgent (D) and our approach +expected and actual behaviors, and submit it to the corresponding (P). Overall, our approach consistently outperforms DroidAgent +app developers. in both functionality inference and execution. Across the 12 apps, +Evaluation method of RQ4. RQ4 evaluates whether existing our approach infers 1,282 functionalities, of which 1,210 are judged +functional testing techniques can find the bugs uncovered by Prop- valid, achieving 94.4% functionality validity, compared with 575 +Gen. We emphasize that this comparison is intended to assess inferred functionalities and 491 valid ones (85.4%) for DroidAgent. It +complementarity rather than replacement, i.e., whether PropGen also correctly executes 977 functionalities, yielding 76.2% execution +can uncover bugs that prior approaches may miss. correctness, substantially higher than DroidAgent’s 187 correctly + Following prior comparative analysis practice [66], we evalu- executed functionalities and 35.2% execution correctness. On aver- +ate these tools from two perspectives. First, we conduct a scope age, this corresponds to 101 valid functionalities and 81 correctly + From Exploration to Specification: LLM-Based Property Generation for Mobile App Testing Conference’17, July 2017, Washington, DC, USA + + +Table 3: Effectiveness of property refinement across subject Table 4: Statistics of the 25 new functional bugs found by the +apps (RQ2). generated properties. + + Modified Component App Name ID Violated Property + App Name #Imprecise Prop #Successful Refinements + Pre I Post 1 Note info dialog should contain statistical data + OmniNotes 12 11 (91.7%) 5 0 6 2 The date should appear on the selection page + Markor 15 12 (80.0%) 2 1 9 3 The category selection should be changeable + RetroMusic 15 14 (93.3%) 9 0 5 4 The category page should be accessible from the drawer + Amaze 11 10 (90.9%) 2 0 8 5 The captured photo should appeared in the note content + MyExpenses 8 8 (100.0%) 6 0 2 OmniNotes + 6 Returning from the sketch should display the note title + AntennaPod 20 18 (90.0%) 7 0 11 7 The reminder icon should be displayed after setting a reminder + AnkiDroid 9 9 (100.0%) 7 0 2 + 8 The attachment should appear after selection + OuterTune 3 3 (100.0%) 3 0 0 + 9 The image can be opened in the note content + NewPipe 11 10 (90.9%) 2 0 8 + 10 The FAB should appear after return + MaterialFiles 6 6 (100.0%) 2 0 4 + 11 The specific item should disappear from the list + Orgzly 12 12 (100.0%) 5 0 7 + 12 The lyrics should be displayed after saving + uhabits 5 5 (100.0%) 3 0 2 + 13 The item should not exist in the list + Total 127 118 (92.9%) 53 1 64 RetroMusic + 14 The image should be displayed after change + 15 The artist can be reset to default + 16 The metadata should remain consistent + Amaze 17 The item should be deleted successfully + 18 The song list should open from navigation menu +executed functionalities per app for our approach, compared with OuterTune + 19 The file can be successfully created +41 and 16, respectively, for DroidAgent. MaterialFiles 20 The item can be found + One likely reason for the performance gap is the difference in 21 Navigation to the sub-directory should succeed +functionality inference. DroidAgent infers functionalities without uhabits 22 The added number should keep consistent +explicitly grounding them to concrete GUI widgets, making some Orgzly 23 The imported file should be present +inferred results loosely related to the current interface context and Markor 24 Star and "Favourite" checkbox should stay in sync + 25 The insert image should be displayed after preview +thus more likely to be invalid or non-executable. In contrast, our +approach grounds functionality inference in the current GUI con- +text, which helps produce more valid functionality hypotheses and apps: six apps achieve a 100% refinement rate, while the remaining +makes subsequent execution more reliable. Also, we find DroidA- apps still achieve rates above 80%. +gent tends to repeatedly execute failed events during functionality We further analyze which property components are modified +execution. during refinement. Among the 118 successfully refined properties, + For property synthesis, our approach generates 985 property 53 involve precondition modifications, 64 involve postcondition +descriptions, among which 912 are judged valid, corresponding to modifications, and only 1 involves an interaction modification. This +92.6% property validity. Moreover, property validity exceeds 90% on suggests that most false positives can be resolved by refining when +most apps, indicating that the synthesized properties are generally a property should be triggered or what outcome it should assert, +well aligned with observed app behaviors. rather than changing the core interaction sequence. Among the +LLM usage cost. For behavioral evidence construction and property 127 refined properties, 9 remain not refined. We find that 5 of them +synthesis, each LLM call consumes 6,198 tokens / $0.0145 on average. are caused by incorrect diagnosis of spurious violations, while the +Overall, our approach uses 6,364k tokens / $14.86 per app on average. others occur because the revised property can no longer remain +In comparison, DroidAgent uses 5,109k tokens / $13.01 per app on consistent with the original functionality. Note that for property +average. refinement, each property requires 8,768 tokens / $0.02 on average. + +5.3 Results of RQ2 5.4 Results of RQ3 +Table 3 reports the effectiveness of our property refinement tech- Table 4 summarizes the bug-finding results, including the app name, +nique across all subject apps, including how many generated prop- bug ID, and the brief description of the violated property. Overall, +erties produce false positives during property-based testing, how PropGen uncovered 25 unique previously unknown functional +many are successfully refined, and which property components are bugs in the latest app versions. Currently, 5 of the reported bugs +modified. have been fixed by developers, while the remaining reports are + Among all generated executable properties, 127 produce spuri- waiting for responses. +ous violations during testing and are thus identified as imprecise The discovered bugs cover diverse functionalities (e.g., note man- +properties that lead to false positives. This result shows that prop- agement, attachment insertion, content display), suggesting that +erty imprecision is not uncommon in LLM-generated properties, the generated properties can capture a broad range of behavioral +and therefore refinement is necessary to improve their practical us- constraints in mobile apps. These bugs typically arise when the +ability. Overall, our refinement technique is highly effective. Across actual app behavior deviates from the expected behavior encoded +all apps, 127 properties are sent to refinement, and 118 of them are by the generated properties. For example, Bug 5 in OmniNotes is +successfully refined, yielding an overall refinement rate of 92.9%. triggered by the property The captured photo should appear in the +Moreover, the refinement performance is consistently strong across note content. During testing, it generates a GUI event sequence that + Conference’17, July 2017, Washington, DC, USA Yiheng Xiong, Shiwen Song, Bo Ma, Ting Su, and Xiaofei Xie + + +Table 5: Results of prior functional testing tools for finding 7 Related Work +the new functional bugs. + Automated mobile app GUI testing. Automated testing for mo- + bile apps has been extensively studied. Choudhary et al. [4] con- + Tool #New Bugs in Scope #New Bugs Found ducted a systematic comparison of Android input-generation tools + Genie 1 (4.0%) 0 (0.0%) + ODIN 2 (8.0%) 0 (0.0%) + and highlighted both the promise and limitations of automated + PBFDroid 5 (17.9%) 2 (8.0%) mobile testing. Prior work has proposed a variety of techniques + VisionDroid - 1 (4.0%) to automatically explore app GUIs and generate event sequences + Total 7 (28.0%) 3 (12.0%) for detecting crash bugs [8, 17, 29, 31, 33, 38, 47, 58, 61]. For ex- + ample, Sapienz [33] uses multi-objective search to generate event + sequences for improving coverage and exposing crashes. To find + non-crash functional bugs, most of prior work [1, 18, 42, 48, 50, 51, + 60, 67, 71] designs automated oracles to overcome the oracle prob- +first opens audio recording and then checks this property. After lem. However, these work are limited to specific types of functional +executing the corresponding interaction sequence, the captured bugs (e.g., data losses [1, 18, 42, 71]). Some work leverages LLM to +photo fails to appear in the note content, thus violating the prop- analyze GUI pages during exploration to find data inconsistency +erty. This bug is difficult to uncover through conventional manual bugs [19], functional bugs [30], or inconsistencies between app +testing, as testers typically focus on the main interaction path and design and implementation [27]. +may not consider interleavings with other events. Property-based testing (PBT) is a powerful testing methodology + and have been adopted into many different software systems to + find logic bugs [2, 5, 20, 21, 23, 32, 35, 37, 43]. Recent work has +5.5 Results of RQ4 begun to bring property-based testing to mobile apps. Specifically, +Table 5 summarizes how many of the new bugs found by PropGen PBFDroid [49], PDTDroid [52], and Kea [66] have demonstrated +can also be detected by Genie, Odin, PBFDroid, and VisionDroid. that PBT can be effectively applied to GUI-driven mobile apps +Among the 25 new bugs uncovered by PropGen, only 7 (28%) are and can find non-crashing functional bugs that are difficult for +within the scope of these prior techniques, and only 3 (12%) are traditional automated GUI testing tools to detect. However, these +actually found in practice. work still assumes that meaningful properties are manually written + This result suggests that PropGen provides complementary bug- by developers or testers. Our work complements these approaches +finding capability to existing functional testing techniques. We by automating the executable property generation. +further analysis why most of the bugs cannot be found by prior Automated test generation. Traditional automated test genera- +techniques. Genie, Odin, and PBFDroid are designed with specific tion techniques, such as fuzzing [34], symbolic execution [14, 45, 54], +types of functional bugs, relying on predefined automated oracles or and search-based testing [12, 36], mainly aim to improve coverage, +manually specified DMF properties. As a result, they can only find but often struggle to generate effective assertions [39, 46]. Learning- +the bug categories emphasized in their original designs, whereas based approaches leverage pre-trained language models to generate +PropGen targets more broadly through generated properties. Vi- tests from code [25, 55, 68, 70]. Recently, LLMs have shown strong +sionDroid, in contrast, is a more general LLM-based functional promise in test generation [3, 7, 9, 11, 13, 22, 25, 44, 59, 70]. Beyond +testing approach. Its exploration strategy typically validates a func- unit test generation, several recent studies have explored the use +tionality by following one plausible interaction path at a time. In of LLMs in property-related testing tasks. For example, prior work +contrast, most bugs uncovered by PropGen do not appear on such has investigated generating postconditions for individual functions +a straightforward execution path. Instead, they are exposed only from their comments [10], synthesizing property-based tests from +when the property is checked under specific event sequences. In specifications for Python libraries [57], and generating properties +other words, these bugs are triggered not by whether the main func- for smart contracts [28]. In contrast, our work investigates how +tionality can be completed, but by whether the expected behavior LLMs can be used to automatically generate properties for property- +still holds under varied runtime conditions. based testing of mobile apps. Recently, different agents have been + proposed to automatically perform tasks on mobile apps [40, 41, 62– + 64, 69, 72]. These works focus on executing user-provided tasks, +6 Threats to Validity + whereas our work centers on automatically exploring app function- +First, our evaluation involves manual inspection to assess the cor- alities and generating executable properties. +rectness of inferred functionalities and generated properties, which +may introduce subjectivity and potential bias. To mitigate this +threat, each case is independently labeled by two experienced grad- 8 Conclusion +uate students following consistent evaluation criteria; disagree- In this paper, we present PropGen, an automated approach for +ments are further discussed until agreement is reached. Second, the constructing properties of mobile apps. By exploring app function- +apps used in our evaluation may not fully represent the diversity alities and deriving properties from behavioral evidence, PropGen +of real-world mobile apps. To mitigate this threat, most of the apps reduces the need for manual property specification. We further +are selected from prior relevant studies, and we further include propose a feedback-driven refinement technique to refine impre- +four additional apps to improve diversity. In the future, we plan to cise properties exposed during testing. Experiments on real-world +evaluate PropGen on a larger and broader set of apps. Android apps show that PropGen can effectively generate correct + From Exploration to Specification: LLM-Based Property Generation for Mobile App Testing Conference’17, July 2017, Washington, DC, USA + + +executable properties. These results demonstrate the practical value [22] Zongze Jiang, Ming Wen, Jialun Cao, Xuanhua Shi, and Hai Jin. 2024. 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Autodroid: Llm-powered + task automation in android. In Proceedings of the 30th Annual International Con- + ference on Mobile Computing and Networking. 543–557. +[64] Hao Wen, Hongming Wang, Jiaxuan Liu, and Yuanchun Li. 2023. Droidbot-gpt: + Gpt-powered ui automation for android. arXiv preprint arXiv:2304.07061 (2023). + \ No newline at end of file diff --git a/packages/opencode/specs/simulation.md b/packages/opencode/specs/simulation.md new file mode 100644 index 00000000000..08ee29547a9 --- /dev/null +++ b/packages/opencode/specs/simulation.md @@ -0,0 +1,375 @@ +# Opencode Simulation Architecture + +Status: first milestone architecture draft. + +## Goal + +Build a simulation environment for exploring opencode through the real app, primarily through the TUI, while replacing only the lowest foundational layers needed to make runs controlled, observable, and safe. + +The first milestone is an interactive exploration and model-based testing environment. It should be enough to start opencode normally, put the app into generated states, drive real user-level TUI actions, observe what happened, and record an in-memory trace that can later be exported into deterministic replay tests. + +This is not intended to be a custom simulated app or a separate `simulate` command. The normal app should run, with simulation enabled by one required flag: + +```sh +OPENCODE_SIMULATION=1 bun run dev +``` + +## Non-Goals + +- Do not reimplement the app. +- Do not replace mid-level services like session processing, tool registry, provider orchestration, route trees, or TUI components unless a foundational seam proves impossible. +- Do not build shrinking in the first milestone. +- Do not make generated randomized runs part of CI yet. +- Do not build differential testing in the first milestone. +- Do not expose simulation controls when `OPENCODE_SIMULATION` is not set. + +## Design Principles + +- Run the real app through normal commands. +- Drive the TUI using real user-level input: typing, keypresses, focus, click, and mouse actions. +- Keep simulation code isolated under a simulation/testing area. +- Touch production app code only at narrow activation points: builders, TUI startup, foundational layers, and simulation-gated backend routes. +- Swap foundational layers, not app logic. +- Make observations rich enough for humans and models. +- Treat traces as first-class artifacts. +- Use a lightweight model of expected high-level behavior, not a clone of opencode internals. +- Generate valid commands from current observed state rather than blindly fuzzing impossible actions. + +## Activation + +`OPENCODE_SIMULATION=1` is the only required flag. + +Optional flags can be added later, but should stay minimal. Reasonable optional parameters later include renderer mode, trace output path, seed, or port override. + +When enabled: + +- The app builds with simulation layer replacements. +- The TUI process starts a loopback WebSocket control server. +- Simulation-gated backend control routes become available only to the frontend/control path. +- In-memory trace recording starts automatically. + +## Control Server + +The external control surface lives in the TUI/frontend process, not the backend API server. + +This is important because the frontend has direct access to the renderer, screen state, focus state, interactable elements, and user input APIs. The backend remains the normal backend, with only simulation-gated control routes used internally by the frontend when needed. + +Protocol: + +- JSON-RPC 2.0 over WebSocket. +- Loopback only. +- Start at `127.0.0.1:40900`. +- If occupied, scan upward and report the actual URL. +- External drivers connect only to this frontend WebSocket. + +The app should not send JSON-RPC requests back to the driver in the first milestone. The driver sends requests; the app responds and emits notifications/events as useful. + +Initial method groups: + +- `ui.state`: return screen, elements, focus, and generated possible actions. +- `ui.action`: execute one real user-level action. +- `ui.render`: force or wait for a render and return state. +- `backend.filesystem.seed`: seed project files. +- `backend.filesystem.write`: write one file. +- `backend.network.register`: register a fake network response. +- `backend.llm.enqueue`: queue scripted LLM behavior. +- `backend.snapshot`: return backend simulation state. +- `trace.list`: return trace records. +- `trace.clear`: clear in-memory trace. +- `trace.export`: export trace JSON for replay/test generation. +- `run.stabilize`: wait for frontend/backend quiescence and return observations. + +## TUI Actions + +The old simulation branch had the right basic shape: observe OpenTUI renderables, derive executable actions, and execute those actions through OpenTUI input/mouse APIs. + +The first action vocabulary should stay close to that work: + +```ts +type UIAction = + | { type: "typeText"; text: string } + | { type: "pressKey"; key: string; modifiers?: KeyModifiers } + | { type: "pressEnter" } + | { type: "pressArrow"; direction: "up" | "down" | "left" | "right" } + | { type: "focus"; target: number } + | { type: "click"; target: number; x: number; y: number } +``` + +`ui.state` should return: + +- Current screen text. +- Focused renderable/editor state. +- Interactable elements. +- Generated actions valid for the current UI state. + +Elements should include stable-enough semantic data where available: + +- Renderable ID and numeric target. +- Position and dimensions. +- Focusable/clickable/editor flags. +- Focused flag. +- Text or label when available. +- Role/capability when available. + +Both fake OpenTUI renderer and visible terminal renderer should share this protocol. The architecture should support both; the default can be decided later. + +## Backend Control + +The backend server should be exactly the normal backend server. + +Simulation-only backend routes may exist, but only when `OPENCODE_SIMULATION=1`. They are private implementation details for the frontend simulation server to proxy commands like filesystem seeding, LLM scripting, network registration, and snapshots. + +External drivers should not use backend simulation routes directly. + +## Foundational Layer Replacement + +Current `origin/dev` has the right seam: `AppNodeBuilder.build(...)` and `AppNodeBuilderV1.build(...)` accept replacements over `LayerNode`s. Simulation should use those seams instead of adding large alternate app assemblies. + +First milestone replacements: + +- Filesystem. +- Network / HTTP client. +- LLM boundary. +- Process spawner. + +Likely later replacements: + +- Clock/random. +- Database path/isolation. +- Global paths/temp paths. + +The goal is to swap things at the bottom of the app. Everything above these foundational services should behave as production code. + +## Filesystem + +The first filesystem simulation should be temp-directory backed. + +Rationale: + +- It is easier to inspect while debugging. +- It avoids reimplementing all filesystem semantics immediately. +- It makes generated scenarios concrete and replayable. +- It keeps the path open to tool behavior that expects real files. + +The temp filesystem is still controlled and isolated: + +- Each run gets its own temp root. +- Project files, config, data, state, cache, and temp paths should resolve inside that root. +- Host filesystem escapes should fail loudly. +- Trace should record seeded files and file diffs/observations needed for replay. + +## Network + +Unknown external network should fail loudly by default. + +The simulation network should support explicit response registration: + +- JSON response. +- Text response. +- Bytes response later if needed. +- Status-only response. +- Handler-style response later if needed. + +Loopback traffic needed by the app/frontend/backend may be allowed explicitly. + +All network calls should be traceable: + +- Method. +- URL. +- Request headers/body where safe. +- Matched simulation route. +- Status. +- Response summary. +- Error if denied. + +## LLM + +The LLM boundary should be scriptable. + +The driver can enqueue scripts that describe model behavior: + +- Text chunks. +- Thinking/reasoning chunks if relevant. +- Tool calls. +- Errors. +- Finish reason. + +The real session and tool pipeline should consume this behavior through the normal app path. The simulation should not bypass `SessionPrompt`, `SessionProcessor`, or tool execution. + +Missing scripted LLM behavior should fail with a clear simulation error unless a default response is explicitly configured. + +## Process Spawning + +External process spawning should be denied by default. + +The first milestone should provide a simulated process registry. This should be inspired by the old branch: + +- Shell commands can run through `just-bash` against the simulated filesystem. +- A small fake `git` command set can support project discovery/status paths needed by the app. +- Unsupported process spawns fail loudly. + +This preserves the rule that simulation does not spawn arbitrary external programs while still allowing useful shell/tool flows. + +## Trace + +Trace recording is always on in simulation mode, in memory for the first milestone. + +Trace entries should be append-only JSON-compatible records. They do not need to be written to disk initially, but `trace.export` should return a structure suitable for later replay and test generation. + +Trace should include: + +- Run metadata: seed, app version, renderer mode, WebSocket URL. +- Initial world setup. +- UI observations. +- Generated UI actions. +- Executed UI actions. +- Backend control requests. +- Backend snapshots. +- Network requests and matches/denials. +- LLM scripts enqueued and consumed. +- Tool calls and results. +- Permission decisions. +- Filesystem seed/write/diff summaries. +- Stabilization boundaries. +- Errors and crashes. +- Model command execution and postcondition results. + +The trace is the bridge between exploratory simulation and deterministic tests. + +## Model-Based Runner + +The first runner is an external driver connecting to the frontend WebSocket. + +Use a custom runner for now, not `fast-check`. It should still follow the core shape used by property/model-based testing libraries: + +```ts +interface Command { + readonly name: string + check(model: Model): boolean + run(model: Model, app: SimulationClient): Promise +} +``` + +Basic runner responsibilities: + +- Keep a lightweight model of high-level expected state. +- Generate commands whose preconditions match the model and current app observations. +- Execute commands through the WebSocket. +- Update the model. +- Check postconditions/invariants. +- Record all steps in the trace. +- Support seed/replay. +- Track simple distribution stats. + +The model should track high-level, observational state only, such as: + +- Current screen/route category. +- Whether prompt editor is available. +- Known sessions. +- Known files and expected file contents/diffs. +- Queued LLM scripts. +- Recent backend/session status. +- Whether app is expected to be idle. + +The model must not track implementation internals like fibers, exact runner loop state, cache internals, or database implementation details. + +Initial command families: + +- Seed filesystem. +- Register network response. +- Enqueue LLM script. +- Observe UI state. +- Execute one generated UI action. +- Type prompt text. +- Press enter. +- Stabilize. +- Assert no crash. +- Assert visible response or file effect. +- Export trace. + +## Generators + +The first milestone should include generation, but not shrinking. + +Generation should be model-based and state-aware: + +- Generate from currently valid `ui.state.actions`. +- Generate backend setup commands from scenario/model state. +- Generate LLM scripts that match likely user prompts and tool flows. +- Generate short command sequences using preconditions. +- Use a seed so runs can be replayed. +- Use simple weights to avoid degenerate action selection. + +The generator should not attempt to produce arbitrary full app states upfront. It should build state by executing commands through the real app and observing the result. + +Important stats to record: + +- Seed. +- Command counts. +- Action type distribution. +- Rejected command/precondition counts. +- UI element/action coverage. +- Backend event type coverage where available. +- Errors and stabilization failures. + +## Properties + +First milestone properties should be simple and high-signal: + +- App does not crash. +- Backend does not crash. +- Unknown network is denied. +- Host filesystem escape is denied. +- Prompt submission can reach a scripted LLM response. +- Stabilization eventually reaches a coherent idle state for the demo flow. +- File effects from scripted tool behavior are observable in the simulated filesystem. +- Trace contains enough information to replay the run. + +More advanced model/refinement, metamorphic, and differential properties are future work. + +## First Demo Flow + +The first major demo should show this system as a real environment for exploring the app in controlled states: + +1. Start opencode normally with `OPENCODE_SIMULATION=1`. +2. TUI starts and exposes the simulation WebSocket on `127.0.0.1:40900+`. +3. External runner connects. +4. Runner seeds a temp-backed project filesystem. +5. Runner queues a scripted LLM response. +6. Runner observes `ui.state` and generated actions. +7. Runner drives real TUI input to type and submit a prompt. +8. App processes the prompt through the real backend/session/tool path. +9. Scripted LLM response appears or executes a file-affecting tool flow. +10. Runner stabilizes the app. +11. Runner inspects trace, backend snapshot, UI state, and filesystem state. +12. Runner exports a deterministic replay trace. + +## Done-When Checklist + +- `OPENCODE_SIMULATION=1` starts the normal app with simulation wiring. +- Simulation code is isolated under a dedicated simulation/testing area. +- App changes outside simulation are limited to activation hooks, builder replacements, TUI startup, and gated backend routes. +- TUI exposes JSON-RPC WebSocket on `127.0.0.1:40900+`. +- Driver can call `ui.state`. +- Driver can execute generated UI actions. +- Fake and visible renderer paths use the same action protocol. +- Driver can seed filesystem state. +- Driver can register network responses and observe denied unknown network. +- Driver can enqueue LLM scripts. +- External process spawning is denied by default, with shell via `just-bash` and minimal fake process registry support. +- Driver can run a basic model-based generated command sequence. +- In-memory trace records observations/actions/backend interactions. +- Driver can list, clear, and export trace. +- Demo flow succeeds end-to-end. + +## Future Directions + +- Shrinking failed traces. +- Promote minimized traces into normal committed tests. +- Coverage-guided corpus and structured trace mutation. +- Richer semantic UI grounding for model-driven exploration. +- LLM-generated property proposals with validity/soundness checks. +- Differential testing across app versions, renderers, or storage modes. +- Deterministic scheduler/clock/random control. +- Parallel campaigns with isolated workers. +- File-backed trace persistence and replay CLI.

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