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llvm/docs/tutorial/LangImpl06.rst
Sjoerd Meijer 5e6fce1693 [Kaleidoscope] Tiny typo fixes 
Fixes for "lets" references which should be "let's" in the Kaleidoscope
tutorial.

Patch by: Robin Dupret

Differential Revision: https://reviews.llvm.org/D44990


git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@328772 91177308-0d34-0410-b5e6-96231b3b80d8
2018-03-29 12:31:06 +00:00

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============================================================
Kaleidoscope: Extending the Language: User-defined Operators
============================================================
.. contents::
:local:
Chapter 6 Introduction
======================
Welcome to Chapter 6 of the "`Implementing a language with
LLVM <index.html>`_" tutorial. At this point in our tutorial, we now
have a fully functional language that is fairly minimal, but also
useful. There is still one big problem with it, however. Our language
doesn't have many useful operators (like division, logical negation, or
even any comparisons besides less-than).
This chapter of the tutorial takes a wild digression into adding
user-defined operators to the simple and beautiful Kaleidoscope
language. This digression now gives us a simple and ugly language in
some ways, but also a powerful one at the same time. One of the great
things about creating your own language is that you get to decide what
is good or bad. In this tutorial we'll assume that it is okay to use
this as a way to show some interesting parsing techniques.
At the end of this tutorial, we'll run through an example Kaleidoscope
application that `renders the Mandelbrot set <#kicking-the-tires>`_. This gives an
example of what you can build with Kaleidoscope and its feature set.
User-defined Operators: the Idea
================================
The "operator overloading" that we will add to Kaleidoscope is more
general than in languages like C++. In C++, you are only allowed to
redefine existing operators: you can't programmatically change the
grammar, introduce new operators, change precedence levels, etc. In this
chapter, we will add this capability to Kaleidoscope, which will let the
user round out the set of operators that are supported.
The point of going into user-defined operators in a tutorial like this
is to show the power and flexibility of using a hand-written parser.
Thus far, the parser we have been implementing uses recursive descent
for most parts of the grammar and operator precedence parsing for the
expressions. See `Chapter 2 <LangImpl02.html>`_ for details. By
using operator precedence parsing, it is very easy to allow
the programmer to introduce new operators into the grammar: the grammar
is dynamically extensible as the JIT runs.
The two specific features we'll add are programmable unary operators
(right now, Kaleidoscope has no unary operators at all) as well as
binary operators. An example of this is:
::
# Logical unary not.
def unary!(v)
if v then
0
else
1;
# Define > with the same precedence as <.
def binary> 10 (LHS RHS)
RHS < LHS;
# Binary "logical or", (note that it does not "short circuit")
def binary| 5 (LHS RHS)
if LHS then
1
else if RHS then
1
else
0;
# Define = with slightly lower precedence than relationals.
def binary= 9 (LHS RHS)
!(LHS < RHS | LHS > RHS);
Many languages aspire to being able to implement their standard runtime
library in the language itself. In Kaleidoscope, we can implement
significant parts of the language in the library!
We will break down implementation of these features into two parts:
implementing support for user-defined binary operators and adding unary
operators.
User-defined Binary Operators
=============================
Adding support for user-defined binary operators is pretty simple with
our current framework. We'll first add support for the unary/binary
keywords:
.. code-block:: c++
enum Token {
...
// operators
tok_binary = -11,
tok_unary = -12
};
...
static int gettok() {
...
if (IdentifierStr == "for")
return tok_for;
if (IdentifierStr == "in")
return tok_in;
if (IdentifierStr == "binary")
return tok_binary;
if (IdentifierStr == "unary")
return tok_unary;
return tok_identifier;
This just adds lexer support for the unary and binary keywords, like we
did in `previous chapters <LangImpl5.html#lexer-extensions-for-if-then-else>`_. One nice thing
about our current AST, is that we represent binary operators with full
generalisation by using their ASCII code as the opcode. For our extended
operators, we'll use this same representation, so we don't need any new
AST or parser support.
On the other hand, we have to be able to represent the definitions of
these new operators, in the "def binary\| 5" part of the function
definition. In our grammar so far, the "name" for the function
definition is parsed as the "prototype" production and into the
``PrototypeAST`` AST node. To represent our new user-defined operators
as prototypes, we have to extend the ``PrototypeAST`` AST node like
this:
.. code-block:: c++
/// PrototypeAST - This class represents the "prototype" for a function,
/// which captures its argument names as well as if it is an operator.
class PrototypeAST {
std::string Name;
std::vector<std::string> Args;
bool IsOperator;
unsigned Precedence; // Precedence if a binary op.
public:
PrototypeAST(const std::string &name, std::vector<std::string> Args,
bool IsOperator = false, unsigned Prec = 0)
: Name(name), Args(std::move(Args)), IsOperator(IsOperator),
Precedence(Prec) {}
Function *codegen();
const std::string &getName() const { return Name; }
bool isUnaryOp() const { return IsOperator && Args.size() == 1; }
bool isBinaryOp() const { return IsOperator && Args.size() == 2; }
char getOperatorName() const {
assert(isUnaryOp() || isBinaryOp());
return Name[Name.size() - 1];
}
unsigned getBinaryPrecedence() const { return Precedence; }
};
Basically, in addition to knowing a name for the prototype, we now keep
track of whether it was an operator, and if it was, what precedence
level the operator is at. The precedence is only used for binary
operators (as you'll see below, it just doesn't apply for unary
operators). Now that we have a way to represent the prototype for a
user-defined operator, we need to parse it:
.. code-block:: c++
/// prototype
/// ::= id '(' id* ')'
/// ::= binary LETTER number? (id, id)
static std::unique_ptr<PrototypeAST> ParsePrototype() {
std::string FnName;
unsigned Kind = 0; // 0 = identifier, 1 = unary, 2 = binary.
unsigned BinaryPrecedence = 30;
switch (CurTok) {
default:
return LogErrorP("Expected function name in prototype");
case tok_identifier:
FnName = IdentifierStr;
Kind = 0;
getNextToken();
break;
case tok_binary:
getNextToken();
if (!isascii(CurTok))
return LogErrorP("Expected binary operator");
FnName = "binary";
FnName += (char)CurTok;
Kind = 2;
getNextToken();
// Read the precedence if present.
if (CurTok == tok_number) {
if (NumVal < 1 || NumVal > 100)
return LogErrorP("Invalid precedence: must be 1..100");
BinaryPrecedence = (unsigned)NumVal;
getNextToken();
}
break;
}
if (CurTok != '(')
return LogErrorP("Expected '(' in prototype");
std::vector<std::string> ArgNames;
while (getNextToken() == tok_identifier)
ArgNames.push_back(IdentifierStr);
if (CurTok != ')')
return LogErrorP("Expected ')' in prototype");
// success.
getNextToken(); // eat ')'.
// Verify right number of names for operator.
if (Kind && ArgNames.size() != Kind)
return LogErrorP("Invalid number of operands for operator");
return llvm::make_unique<PrototypeAST>(FnName, std::move(ArgNames), Kind != 0,
BinaryPrecedence);
}
This is all fairly straightforward parsing code, and we have already
seen a lot of similar code in the past. One interesting part about the
code above is the couple lines that set up ``FnName`` for binary
operators. This builds names like "binary@" for a newly defined "@"
operator. It then takes advantage of the fact that symbol names in the
LLVM symbol table are allowed to have any character in them, including
embedded nul characters.
The next interesting thing to add, is codegen support for these binary
operators. Given our current structure, this is a simple addition of a
default case for our existing binary operator node:
.. code-block:: c++
Value *BinaryExprAST::codegen() {
Value *L = LHS->codegen();
Value *R = RHS->codegen();
if (!L || !R)
return nullptr;
switch (Op) {
case '+':
return Builder.CreateFAdd(L, R, "addtmp");
case '-':
return Builder.CreateFSub(L, R, "subtmp");
case '*':
return Builder.CreateFMul(L, R, "multmp");
case '<':
L = Builder.CreateFCmpULT(L, R, "cmptmp");
// Convert bool 0/1 to double 0.0 or 1.0
return Builder.CreateUIToFP(L, Type::getDoubleTy(TheContext),
"booltmp");
default:
break;
}
// If it wasn't a builtin binary operator, it must be a user defined one. Emit
// a call to it.
Function *F = getFunction(std::string("binary") + Op);
assert(F && "binary operator not found!");
Value *Ops[2] = { L, R };
return Builder.CreateCall(F, Ops, "binop");
}
As you can see above, the new code is actually really simple. It just
does a lookup for the appropriate operator in the symbol table and
generates a function call to it. Since user-defined operators are just
built as normal functions (because the "prototype" boils down to a
function with the right name) everything falls into place.
The final piece of code we are missing, is a bit of top-level magic:
.. code-block:: c++
Function *FunctionAST::codegen() {
// Transfer ownership of the prototype to the FunctionProtos map, but keep a
// reference to it for use below.
auto &P = *Proto;
FunctionProtos[Proto->getName()] = std::move(Proto);
Function *TheFunction = getFunction(P.getName());
if (!TheFunction)
return nullptr;
// If this is an operator, install it.
if (P.isBinaryOp())
BinopPrecedence[P.getOperatorName()] = P.getBinaryPrecedence();
// Create a new basic block to start insertion into.
BasicBlock *BB = BasicBlock::Create(TheContext, "entry", TheFunction);
...
Basically, before codegening a function, if it is a user-defined
operator, we register it in the precedence table. This allows the binary
operator parsing logic we already have in place to handle it. Since we
are working on a fully-general operator precedence parser, this is all
we need to do to "extend the grammar".
Now we have useful user-defined binary operators. This builds a lot on
the previous framework we built for other operators. Adding unary
operators is a bit more challenging, because we don't have any framework
for it yet - let's see what it takes.
User-defined Unary Operators
============================
Since we don't currently support unary operators in the Kaleidoscope
language, we'll need to add everything to support them. Above, we added
simple support for the 'unary' keyword to the lexer. In addition to
that, we need an AST node:
.. code-block:: c++
/// UnaryExprAST - Expression class for a unary operator.
class UnaryExprAST : public ExprAST {
char Opcode;
std::unique_ptr<ExprAST> Operand;
public:
UnaryExprAST(char Opcode, std::unique_ptr<ExprAST> Operand)
: Opcode(Opcode), Operand(std::move(Operand)) {}
Value *codegen() override;
};
This AST node is very simple and obvious by now. It directly mirrors the
binary operator AST node, except that it only has one child. With this,
we need to add the parsing logic. Parsing a unary operator is pretty
simple: we'll add a new function to do it:
.. code-block:: c++
/// unary
/// ::= primary
/// ::= '!' unary
static std::unique_ptr<ExprAST> ParseUnary() {
// If the current token is not an operator, it must be a primary expr.
if (!isascii(CurTok) || CurTok == '(' || CurTok == ',')
return ParsePrimary();
// If this is a unary operator, read it.
int Opc = CurTok;
getNextToken();
if (auto Operand = ParseUnary())
return llvm::make_unique<UnaryExprAST>(Opc, std::move(Operand));
return nullptr;
}
The grammar we add is pretty straightforward here. If we see a unary
operator when parsing a primary operator, we eat the operator as a
prefix and parse the remaining piece as another unary operator. This
allows us to handle multiple unary operators (e.g. "!!x"). Note that
unary operators can't have ambiguous parses like binary operators can,
so there is no need for precedence information.
The problem with this function, is that we need to call ParseUnary from
somewhere. To do this, we change previous callers of ParsePrimary to
call ParseUnary instead:
.. code-block:: c++
/// binoprhs
/// ::= ('+' unary)*
static std::unique_ptr<ExprAST> ParseBinOpRHS(int ExprPrec,
std::unique_ptr<ExprAST> LHS) {
...
// Parse the unary expression after the binary operator.
auto RHS = ParseUnary();
if (!RHS)
return nullptr;
...
}
/// expression
/// ::= unary binoprhs
///
static std::unique_ptr<ExprAST> ParseExpression() {
auto LHS = ParseUnary();
if (!LHS)
return nullptr;
return ParseBinOpRHS(0, std::move(LHS));
}
With these two simple changes, we are now able to parse unary operators
and build the AST for them. Next up, we need to add parser support for
prototypes, to parse the unary operator prototype. We extend the binary
operator code above with:
.. code-block:: c++
/// prototype
/// ::= id '(' id* ')'
/// ::= binary LETTER number? (id, id)
/// ::= unary LETTER (id)
static std::unique_ptr<PrototypeAST> ParsePrototype() {
std::string FnName;
unsigned Kind = 0; // 0 = identifier, 1 = unary, 2 = binary.
unsigned BinaryPrecedence = 30;
switch (CurTok) {
default:
return LogErrorP("Expected function name in prototype");
case tok_identifier:
FnName = IdentifierStr;
Kind = 0;
getNextToken();
break;
case tok_unary:
getNextToken();
if (!isascii(CurTok))
return LogErrorP("Expected unary operator");
FnName = "unary";
FnName += (char)CurTok;
Kind = 1;
getNextToken();
break;
case tok_binary:
...
As with binary operators, we name unary operators with a name that
includes the operator character. This assists us at code generation
time. Speaking of, the final piece we need to add is codegen support for
unary operators. It looks like this:
.. code-block:: c++
Value *UnaryExprAST::codegen() {
Value *OperandV = Operand->codegen();
if (!OperandV)
return nullptr;
Function *F = getFunction(std::string("unary") + Opcode);
if (!F)
return LogErrorV("Unknown unary operator");
return Builder.CreateCall(F, OperandV, "unop");
}
This code is similar to, but simpler than, the code for binary
operators. It is simpler primarily because it doesn't need to handle any
predefined operators.
Kicking the Tires
=================
It is somewhat hard to believe, but with a few simple extensions we've
covered in the last chapters, we have grown a real-ish language. With
this, we can do a lot of interesting things, including I/O, math, and a
bunch of other things. For example, we can now add a nice sequencing
operator (printd is defined to print out the specified value and a
newline):
::
ready> extern printd(x);
Read extern:
declare double @printd(double)
ready> def binary : 1 (x y) 0; # Low-precedence operator that ignores operands.
...
ready> printd(123) : printd(456) : printd(789);
123.000000
456.000000
789.000000
Evaluated to 0.000000
We can also define a bunch of other "primitive" operations, such as:
::
# Logical unary not.
def unary!(v)
if v then
0
else
1;
# Unary negate.
def unary-(v)
0-v;
# Define > with the same precedence as <.
def binary> 10 (LHS RHS)
RHS < LHS;
# Binary logical or, which does not short circuit.
def binary| 5 (LHS RHS)
if LHS then
1
else if RHS then
1
else
0;
# Binary logical and, which does not short circuit.
def binary& 6 (LHS RHS)
if !LHS then
0
else
!!RHS;
# Define = with slightly lower precedence than relationals.
def binary = 9 (LHS RHS)
!(LHS < RHS | LHS > RHS);
# Define ':' for sequencing: as a low-precedence operator that ignores operands
# and just returns the RHS.
def binary : 1 (x y) y;
Given the previous if/then/else support, we can also define interesting
functions for I/O. For example, the following prints out a character
whose "density" reflects the value passed in: the lower the value, the
denser the character:
::
ready> extern putchard(char);
...
ready> def printdensity(d)
if d > 8 then
putchard(32) # ' '
else if d > 4 then
putchard(46) # '.'
else if d > 2 then
putchard(43) # '+'
else
putchard(42); # '*'
...
ready> printdensity(1): printdensity(2): printdensity(3):
printdensity(4): printdensity(5): printdensity(9):
putchard(10);
**++.
Evaluated to 0.000000
Based on these simple primitive operations, we can start to define more
interesting things. For example, here's a little function that determines
the number of iterations it takes for a certain function in the complex
plane to diverge:
::
# Determine whether the specific location diverges.
# Solve for z = z^2 + c in the complex plane.
def mandelconverger(real imag iters creal cimag)
if iters > 255 | (real*real + imag*imag > 4) then
iters
else
mandelconverger(real*real - imag*imag + creal,
2*real*imag + cimag,
iters+1, creal, cimag);
# Return the number of iterations required for the iteration to escape
def mandelconverge(real imag)
mandelconverger(real, imag, 0, real, imag);
This "``z = z2 + c``" function is a beautiful little creature that is
the basis for computation of the `Mandelbrot
Set <http://en.wikipedia.org/wiki/Mandelbrot_set>`_. Our
``mandelconverge`` function returns the number of iterations that it
takes for a complex orbit to escape, saturating to 255. This is not a
very useful function by itself, but if you plot its value over a
two-dimensional plane, you can see the Mandelbrot set. Given that we are
limited to using putchard here, our amazing graphical output is limited,
but we can whip together something using the density plotter above:
::
# Compute and plot the mandelbrot set with the specified 2 dimensional range
# info.
def mandelhelp(xmin xmax xstep ymin ymax ystep)
for y = ymin, y < ymax, ystep in (
(for x = xmin, x < xmax, xstep in
printdensity(mandelconverge(x,y)))
: putchard(10)
)
# mandel - This is a convenient helper function for plotting the mandelbrot set
# from the specified position with the specified Magnification.
def mandel(realstart imagstart realmag imagmag)
mandelhelp(realstart, realstart+realmag*78, realmag,
imagstart, imagstart+imagmag*40, imagmag);
Given this, we can try plotting out the mandelbrot set! Lets try it out:
::
ready> mandel(-2.3, -1.3, 0.05, 0.07);
*******************************+++++++++++*************************************
*************************+++++++++++++++++++++++*******************************
**********************+++++++++++++++++++++++++++++****************************
*******************+++++++++++++++++++++.. ...++++++++*************************
*****************++++++++++++++++++++++.... ...+++++++++***********************
***************+++++++++++++++++++++++..... ...+++++++++*********************
**************+++++++++++++++++++++++.... ....+++++++++********************
*************++++++++++++++++++++++...... .....++++++++*******************
************+++++++++++++++++++++....... .......+++++++******************
***********+++++++++++++++++++.... ... .+++++++*****************
**********+++++++++++++++++....... .+++++++****************
*********++++++++++++++........... ...+++++++***************
********++++++++++++............ ...++++++++**************
********++++++++++... .......... .++++++++**************
*******+++++++++..... .+++++++++*************
*******++++++++...... ..+++++++++*************
*******++++++....... ..+++++++++*************
*******+++++...... ..+++++++++*************
*******.... .... ...+++++++++*************
*******.... . ...+++++++++*************
*******+++++...... ...+++++++++*************
*******++++++....... ..+++++++++*************
*******++++++++...... .+++++++++*************
*******+++++++++..... ..+++++++++*************
********++++++++++... .......... .++++++++**************
********++++++++++++............ ...++++++++**************
*********++++++++++++++.......... ...+++++++***************
**********++++++++++++++++........ .+++++++****************
**********++++++++++++++++++++.... ... ..+++++++****************
***********++++++++++++++++++++++....... .......++++++++*****************
************+++++++++++++++++++++++...... ......++++++++******************
**************+++++++++++++++++++++++.... ....++++++++********************
***************+++++++++++++++++++++++..... ...+++++++++*********************
*****************++++++++++++++++++++++.... ...++++++++***********************
*******************+++++++++++++++++++++......++++++++*************************
*********************++++++++++++++++++++++.++++++++***************************
*************************+++++++++++++++++++++++*******************************
******************************+++++++++++++************************************
*******************************************************************************
*******************************************************************************
*******************************************************************************
Evaluated to 0.000000
ready> mandel(-2, -1, 0.02, 0.04);
**************************+++++++++++++++++++++++++++++++++++++++++++++++++++++
***********************++++++++++++++++++++++++++++++++++++++++++++++++++++++++
*********************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++.
*******************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++...
*****************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++.....
***************++++++++++++++++++++++++++++++++++++++++++++++++++++++++........
**************++++++++++++++++++++++++++++++++++++++++++++++++++++++...........
************+++++++++++++++++++++++++++++++++++++++++++++++++++++..............
***********++++++++++++++++++++++++++++++++++++++++++++++++++........ .
**********++++++++++++++++++++++++++++++++++++++++++++++.............
********+++++++++++++++++++++++++++++++++++++++++++..................
*******+++++++++++++++++++++++++++++++++++++++.......................
******+++++++++++++++++++++++++++++++++++...........................
*****++++++++++++++++++++++++++++++++............................
*****++++++++++++++++++++++++++++...............................
****++++++++++++++++++++++++++...... .........................
***++++++++++++++++++++++++......... ...... ...........
***++++++++++++++++++++++............
**+++++++++++++++++++++..............
**+++++++++++++++++++................
*++++++++++++++++++.................
*++++++++++++++++............ ...
*++++++++++++++..............
*+++....++++................
*.......... ...........
*
*.......... ...........
*+++....++++................
*++++++++++++++..............
*++++++++++++++++............ ...
*++++++++++++++++++.................
**+++++++++++++++++++................
**+++++++++++++++++++++..............
***++++++++++++++++++++++............
***++++++++++++++++++++++++......... ...... ...........
****++++++++++++++++++++++++++...... .........................
*****++++++++++++++++++++++++++++...............................
*****++++++++++++++++++++++++++++++++............................
******+++++++++++++++++++++++++++++++++++...........................
*******+++++++++++++++++++++++++++++++++++++++.......................
********+++++++++++++++++++++++++++++++++++++++++++..................
Evaluated to 0.000000
ready> mandel(-0.9, -1.4, 0.02, 0.03);
*******************************************************************************
*******************************************************************************
*******************************************************************************
**********+++++++++++++++++++++************************************************
*+++++++++++++++++++++++++++++++++++++++***************************************
+++++++++++++++++++++++++++++++++++++++++++++**********************************
++++++++++++++++++++++++++++++++++++++++++++++++++*****************************
++++++++++++++++++++++++++++++++++++++++++++++++++++++*************************
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++**********************
+++++++++++++++++++++++++++++++++.........++++++++++++++++++*******************
+++++++++++++++++++++++++++++++.... ......+++++++++++++++++++****************
+++++++++++++++++++++++++++++....... ........+++++++++++++++++++**************
++++++++++++++++++++++++++++........ ........++++++++++++++++++++************
+++++++++++++++++++++++++++......... .. ...+++++++++++++++++++++**********
++++++++++++++++++++++++++........... ....++++++++++++++++++++++********
++++++++++++++++++++++++............. .......++++++++++++++++++++++******
+++++++++++++++++++++++............. ........+++++++++++++++++++++++****
++++++++++++++++++++++........... ..........++++++++++++++++++++++***
++++++++++++++++++++........... .........++++++++++++++++++++++*
++++++++++++++++++............ ...........++++++++++++++++++++
++++++++++++++++............... .............++++++++++++++++++
++++++++++++++................. ...............++++++++++++++++
++++++++++++.................. .................++++++++++++++
+++++++++.................. .................+++++++++++++
++++++........ . ......... ..++++++++++++
++............ ...... ....++++++++++
.............. ...++++++++++
.............. ....+++++++++
.............. .....++++++++
............. ......++++++++
........... .......++++++++
......... ........+++++++
......... ........+++++++
......... ....+++++++
........ ...+++++++
....... ...+++++++
....+++++++
.....+++++++
....+++++++
....+++++++
....+++++++
Evaluated to 0.000000
ready> ^D
At this point, you may be starting to realize that Kaleidoscope is a
real and powerful language. It may not be self-similar :), but it can be
used to plot things that are!
With this, we conclude the "adding user-defined operators" chapter of
the tutorial. We have successfully augmented our language, adding the
ability to extend the language in the library, and we have shown how
this can be used to build a simple but interesting end-user application
in Kaleidoscope. At this point, Kaleidoscope can build a variety of
applications that are functional and can call functions with
side-effects, but it can't actually define and mutate a variable itself.
Strikingly, variable mutation is an important feature of some languages,
and it is not at all obvious how to `add support for mutable
variables <LangImpl07.html>`_ without having to add an "SSA construction"
phase to your front-end. In the next chapter, we will describe how you
can add variable mutation without building SSA in your front-end.
Full Code Listing
=================
Here is the complete code listing for our running example, enhanced with
the support for user-defined operators. To build this example, use:
.. code-block:: bash
# Compile
clang++ -g toy.cpp `llvm-config --cxxflags --ldflags --system-libs --libs core mcjit native` -O3 -o toy
# Run
./toy
On some platforms, you will need to specify -rdynamic or
-Wl,--export-dynamic when linking. This ensures that symbols defined in
the main executable are exported to the dynamic linker and so are
available for symbol resolution at run time. This is not needed if you
compile your support code into a shared library, although doing that
will cause problems on Windows.
Here is the code:
.. literalinclude:: ../../examples/Kaleidoscope/Chapter6/toy.cpp
:language: c++
`Next: Extending the language: mutable variables / SSA
construction <LangImpl07.html>`_
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