llvm/docs/tutorial/LangImpl5.rst

==================================================
Kaleidoscope: Extending the Language: Control Flow
==================================================

.. contents::
   :local:

Chapter 5 Introduction
======================

Welcome to Chapter 5 of the "`Implementing a language with
LLVM <index.html>`_" tutorial. Parts 1-4 described the implementation of
the simple Kaleidoscope language and included support for generating
LLVM IR, followed by optimizations and a JIT compiler. Unfortunately, as
presented, Kaleidoscope is mostly useless: it has no control flow other
than call and return. This means that you can't have conditional
branches in the code, significantly limiting its power. In this episode
of "build that compiler", we'll extend Kaleidoscope to have an
if/then/else expression plus a simple 'for' loop.

If/Then/Else
============

Extending Kaleidoscope to support if/then/else is quite straightforward.
It basically requires adding support for this "new" concept to the
lexer, parser, AST, and LLVM code emitter. This example is nice, because
it shows how easy it is to "grow" a language over time, incrementally
extending it as new ideas are discovered.

Before we get going on "how" we add this extension, lets talk about
"what" we want. The basic idea is that we want to be able to write this
sort of thing:

::

    def fib(x)
      if x < 3 then
        1
      else
        fib(x-1)+fib(x-2);

In Kaleidoscope, every construct is an expression: there are no
statements. As such, the if/then/else expression needs to return a value
like any other. Since we're using a mostly functional form, we'll have
it evaluate its conditional, then return the 'then' or 'else' value
based on how the condition was resolved. This is very similar to the C
"?:" expression.

The semantics of the if/then/else expression is that it evaluates the
condition to a boolean equality value: 0.0 is considered to be false and
everything else is considered to be true. If the condition is true, the
first subexpression is evaluated and returned, if the condition is
false, the second subexpression is evaluated and returned. Since
Kaleidoscope allows side-effects, this behavior is important to nail
down.

Now that we know what we "want", lets break this down into its
constituent pieces.

Lexer Extensions for If/Then/Else
---------------------------------

The lexer extensions are straightforward. First we add new enum values
for the relevant tokens:

.. code-block:: c++

      // control
      tok_if = -6, tok_then = -7, tok_else = -8,

Once we have that, we recognize the new keywords in the lexer. This is
pretty simple stuff:

.. code-block:: c++

        ...
        if (IdentifierStr == "def") return tok_def;
        if (IdentifierStr == "extern") return tok_extern;
        if (IdentifierStr == "if") return tok_if;
        if (IdentifierStr == "then") return tok_then;
        if (IdentifierStr == "else") return tok_else;
        return tok_identifier;

AST Extensions for If/Then/Else
-------------------------------

To represent the new expression we add a new AST node for it:

.. code-block:: c++

    /// IfExprAST - Expression class for if/then/else.
    class IfExprAST : public ExprAST {
      std::unique<ExprAST> Cond, Then, Else;
    public:
      IfExprAST(std::unique_ptr<ExprAST> Cond, std::unique_ptr<ExprAST> Then,
                std::unique_ptr<ExprAST> Else)
        : Cond(std::move(Cond)), Then(std::move(Then)), Else(std::move(Else)) {}
      virtual Value *Codegen();
    };

The AST node just has pointers to the various subexpressions.

Parser Extensions for If/Then/Else
----------------------------------

Now that we have the relevant tokens coming from the lexer and we have
the AST node to build, our parsing logic is relatively straightforward.
First we define a new parsing function:

.. code-block:: c++

    /// ifexpr ::= 'if' expression 'then' expression 'else' expression
    static std::unique_ptr<ExprAST> ParseIfExpr() {
      getNextToken();  // eat the if.

      // condition.
      auto Cond = ParseExpression();
      if (!Cond) return nullptr;

      if (CurTok != tok_then)
        return Error("expected then");
      getNextToken();  // eat the then

      auto Then = ParseExpression();
      if (Then) return nullptr;

      if (CurTok != tok_else)
        return Error("expected else");

      getNextToken();

      auto Else = ParseExpression();
      if (!Else) return nullptr;

      return llvm::make_unique<IfExprAST>(std::move(Cond), std::move(Then),
                                          std::move(Else));
    }

Next we hook it up as a primary expression:

.. code-block:: c++

    static std::unique_ptr<ExprAST> ParsePrimary() {
      switch (CurTok) {
      default: return Error("unknown token when expecting an expression");
      case tok_identifier: return ParseIdentifierExpr();
      case tok_number:     return ParseNumberExpr();
      case '(':            return ParseParenExpr();
      case tok_if:         return ParseIfExpr();
      }
    }

LLVM IR for If/Then/Else
------------------------

Now that we have it parsing and building the AST, the final piece is
adding LLVM code generation support. This is the most interesting part
of the if/then/else example, because this is where it starts to
introduce new concepts. All of the code above has been thoroughly
described in previous chapters.

To motivate the code we want to produce, lets take a look at a simple
example. Consider:

::

    extern foo();
    extern bar();
    def baz(x) if x then foo() else bar();

If you disable optimizations, the code you'll (soon) get from
Kaleidoscope looks like this:

.. code-block:: llvm

    declare double @foo()

    declare double @bar()

    define double @baz(double %x) {
    entry:
      %ifcond = fcmp one double %x, 0.000000e+00
      br i1 %ifcond, label %then, label %else

    then:       ; preds = %entry
      %calltmp = call double @foo()
      br label %ifcont

    else:       ; preds = %entry
      %calltmp1 = call double @bar()
      br label %ifcont

    ifcont:     ; preds = %else, %then
      %iftmp = phi double [ %calltmp, %then ], [ %calltmp1, %else ]
      ret double %iftmp
    }

To visualize the control flow graph, you can use a nifty feature of the
LLVM '`opt <http://llvm.org/cmds/opt.html>`_' tool. If you put this LLVM
IR into "t.ll" and run "``llvm-as < t.ll | opt -analyze -view-cfg``", `a
window will pop up <../ProgrammersManual.html#ViewGraph>`_ and you'll
see this graph:

.. figure:: LangImpl5-cfg.png
   :align: center
   :alt: Example CFG

   Example CFG

Another way to get this is to call "``F->viewCFG()``" or
"``F->viewCFGOnly()``" (where F is a "``Function*``") either by
inserting actual calls into the code and recompiling or by calling these
in the debugger. LLVM has many nice features for visualizing various
graphs.

Getting back to the generated code, it is fairly simple: the entry block
evaluates the conditional expression ("x" in our case here) and compares
the result to 0.0 with the "``fcmp one``" instruction ('one' is "Ordered
and Not Equal"). Based on the result of this expression, the code jumps
to either the "then" or "else" blocks, which contain the expressions for
the true/false cases.

Once the then/else blocks are finished executing, they both branch back
to the 'ifcont' block to execute the code that happens after the
if/then/else. In this case the only thing left to do is to return to the
caller of the function. The question then becomes: how does the code
know which expression to return?

The answer to this question involves an important SSA operation: the
`Phi
operation <http://en.wikipedia.org/wiki/Static_single_assignment_form>`_.
If you're not familiar with SSA, `the wikipedia
article <http://en.wikipedia.org/wiki/Static_single_assignment_form>`_
is a good introduction and there are various other introductions to it
available on your favorite search engine. The short version is that
"execution" of the Phi operation requires "remembering" which block
control came from. The Phi operation takes on the value corresponding to
the input control block. In this case, if control comes in from the
"then" block, it gets the value of "calltmp". If control comes from the
"else" block, it gets the value of "calltmp1".

At this point, you are probably starting to think "Oh no! This means my
simple and elegant front-end will have to start generating SSA form in
order to use LLVM!". Fortunately, this is not the case, and we strongly
advise *not* implementing an SSA construction algorithm in your
front-end unless there is an amazingly good reason to do so. In
practice, there are two sorts of values that float around in code
written for your average imperative programming language that might need
Phi nodes:

#. Code that involves user variables: ``x = 1; x = x + 1;``
#. Values that are implicit in the structure of your AST, such as the
   Phi node in this case.

In `Chapter 7 <LangImpl7.html>`_ of this tutorial ("mutable variables"),
we'll talk about #1 in depth. For now, just believe me that you don't
need SSA construction to handle this case. For #2, you have the choice
of using the techniques that we will describe for #1, or you can insert
Phi nodes directly, if convenient. In this case, it is really
easy to generate the Phi node, so we choose to do it directly.

Okay, enough of the motivation and overview, lets generate code!

Code Generation for If/Then/Else
--------------------------------

In order to generate code for this, we implement the ``Codegen`` method
for ``IfExprAST``:

.. code-block:: c++

    Value *IfExprAST::Codegen() {
      Value *CondV = Cond->Codegen();
      if (!CondV) return nullptr;

      // Convert condition to a bool by comparing equal to 0.0.
      CondV = Builder.CreateFCmpONE(CondV,
                                  ConstantFP::get(getGlobalContext(), APFloat(0.0)),
                                    "ifcond");

This code is straightforward and similar to what we saw before. We emit
the expression for the condition, then compare that value to zero to get
a truth value as a 1-bit (bool) value.

.. code-block:: c++

      Function *TheFunction = Builder.GetInsertBlock()->getParent();

      // Create blocks for the then and else cases.  Insert the 'then' block at the
      // end of the function.
      BasicBlock *ThenBB = BasicBlock::Create(getGlobalContext(), "then", TheFunction);
      BasicBlock *ElseBB = BasicBlock::Create(getGlobalContext(), "else");
      BasicBlock *MergeBB = BasicBlock::Create(getGlobalContext(), "ifcont");

      Builder.CreateCondBr(CondV, ThenBB, ElseBB);

This code creates the basic blocks that are related to the if/then/else
statement, and correspond directly to the blocks in the example above.
The first line gets the current Function object that is being built. It
gets this by asking the builder for the current BasicBlock, and asking
that block for its "parent" (the function it is currently embedded
into).

Once it has that, it creates three blocks. Note that it passes
"TheFunction" into the constructor for the "then" block. This causes the
constructor to automatically insert the new block into the end of the
specified function. The other two blocks are created, but aren't yet
inserted into the function.

Once the blocks are created, we can emit the conditional branch that
chooses between them. Note that creating new blocks does not implicitly
affect the IRBuilder, so it is still inserting into the block that the
condition went into. Also note that it is creating a branch to the
"then" block and the "else" block, even though the "else" block isn't
inserted into the function yet. This is all ok: it is the standard way
that LLVM supports forward references.

.. code-block:: c++

      // Emit then value.
      Builder.SetInsertPoint(ThenBB);

      Value *ThenV = Then->Codegen();
      if (ThenV == 0) return 0;

      Builder.CreateBr(MergeBB);
      // Codegen of 'Then' can change the current block, update ThenBB for the PHI.
      ThenBB = Builder.GetInsertBlock();

After the conditional branch is inserted, we move the builder to start
inserting into the "then" block. Strictly speaking, this call moves the
insertion point to be at the end of the specified block. However, since
the "then" block is empty, it also starts out by inserting at the
beginning of the block. :)

Once the insertion point is set, we recursively codegen the "then"
expression from the AST. To finish off the "then" block, we create an
unconditional branch to the merge block. One interesting (and very
important) aspect of the LLVM IR is that it `requires all basic blocks
to be "terminated" <../LangRef.html#functionstructure>`_ with a `control
flow instruction <../LangRef.html#terminators>`_ such as return or
branch. This means that all control flow, *including fall throughs* must
be made explicit in the LLVM IR. If you violate this rule, the verifier
will emit an error.

The final line here is quite subtle, but is very important. The basic
issue is that when we create the Phi node in the merge block, we need to
set up the block/value pairs that indicate how the Phi will work.
Importantly, the Phi node expects to have an entry for each predecessor
of the block in the CFG. Why then, are we getting the current block when
we just set it to ThenBB 5 lines above? The problem is that the "Then"
expression may actually itself change the block that the Builder is
emitting into if, for example, it contains a nested "if/then/else"
expression. Because calling Codegen recursively could arbitrarily change
the notion of the current block, we are required to get an up-to-date
value for code that will set up the Phi node.

.. code-block:: c++

      // Emit else block.
      TheFunction->getBasicBlockList().push_back(ElseBB);
      Builder.SetInsertPoint(ElseBB);

      Value *ElseV = Else->Codegen();
      if (ElseV == 0) return 0;

      Builder.CreateBr(MergeBB);
      // Codegen of 'Else' can change the current block, update ElseBB for the PHI.
      ElseBB = Builder.GetInsertBlock();

Code generation for the 'else' block is basically identical to codegen
for the 'then' block. The only significant difference is the first line,
which adds the 'else' block to the function. Recall previously that the
'else' block was created, but not added to the function. Now that the
'then' and 'else' blocks are emitted, we can finish up with the merge
code:

.. code-block:: c++

      // Emit merge block.
      TheFunction->getBasicBlockList().push_back(MergeBB);
      Builder.SetInsertPoint(MergeBB);
      PHINode *PN = Builder.CreatePHI(Type::getDoubleTy(getGlobalContext()), 2,
                                      "iftmp");

      PN->addIncoming(ThenV, ThenBB);
      PN->addIncoming(ElseV, ElseBB);
      return PN;
    }

The first two lines here are now familiar: the first adds the "merge"
block to the Function object (it was previously floating, like the else
block above). The second changes the insertion point so that newly
created code will go into the "merge" block. Once that is done, we need
to create the PHI node and set up the block/value pairs for the PHI.

Finally, the CodeGen function returns the phi node as the value computed
by the if/then/else expression. In our example above, this returned
value will feed into the code for the top-level function, which will
create the return instruction.

Overall, we now have the ability to execute conditional code in
Kaleidoscope. With this extension, Kaleidoscope is a fairly complete
language that can calculate a wide variety of numeric functions. Next up
we'll add another useful expression that is familiar from non-functional
languages...

'for' Loop Expression
=====================

Now that we know how to add basic control flow constructs to the
language, we have the tools to add more powerful things. Lets add
something more aggressive, a 'for' expression:

::

     extern putchard(char)
     def printstar(n)
       for i = 1, i < n, 1.0 in
         putchard(42);  # ascii 42 = '*'

     # print 100 '*' characters
     printstar(100);

This expression defines a new variable ("i" in this case) which iterates
from a starting value, while the condition ("i < n" in this case) is
true, incrementing by an optional step value ("1.0" in this case). If
the step value is omitted, it defaults to 1.0. While the loop is true,
it executes its body expression. Because we don't have anything better
to return, we'll just define the loop as always returning 0.0. In the
future when we have mutable variables, it will get more useful.

As before, lets talk about the changes that we need to Kaleidoscope to
support this.

Lexer Extensions for the 'for' Loop
-----------------------------------

The lexer extensions are the same sort of thing as for if/then/else:

.. code-block:: c++

      ... in enum Token ...
      // control
      tok_if = -6, tok_then = -7, tok_else = -8,
      tok_for = -9, tok_in = -10

      ... in gettok ...
      if (IdentifierStr == "def") return tok_def;
      if (IdentifierStr == "extern") return tok_extern;
      if (IdentifierStr == "if") return tok_if;
      if (IdentifierStr == "then") return tok_then;
      if (IdentifierStr == "else") return tok_else;
      if (IdentifierStr == "for") return tok_for;
      if (IdentifierStr == "in") return tok_in;
      return tok_identifier;

AST Extensions for the 'for' Loop
---------------------------------

The AST node is just as simple. It basically boils down to capturing the
variable name and the constituent expressions in the node.

.. code-block:: c++

    /// ForExprAST - Expression class for for/in.
    class ForExprAST : public ExprAST {
      std::string VarName;
      std::unique_ptr<ExprAST> Start, End, Step, Body;
    public:
      ForExprAST(const std::string &VarName, std::unique_ptr<ExprAST> Start,
                 std::unique_ptr<ExprAST> End, std::unique_ptr<ExprAST> Step,
                 std::unique_ptr<ExprAST> Body)
        : VarName(VarName), Start(std::move(Start)), End(std::move(End)),
          Step(std::move(Step)), Body(std::move(Body)) {}
      virtual Value *Codegen();
    };

Parser Extensions for the 'for' Loop
------------------------------------

The parser code is also fairly standard. The only interesting thing here
is handling of the optional step value. The parser code handles it by
checking to see if the second comma is present. If not, it sets the step
value to null in the AST node:

.. code-block:: c++

    /// forexpr ::= 'for' identifier '=' expr ',' expr (',' expr)? 'in' expression
    static std::unique_ptr<ExprAST> ParseForExpr() {
      getNextToken();  // eat the for.

      if (CurTok != tok_identifier)
        return Error("expected identifier after for");

      std::string IdName = IdentifierStr;
      getNextToken();  // eat identifier.

      if (CurTok != '=')
        return Error("expected '=' after for");
      getNextToken();  // eat '='.


      auto Start = ParseExpression();
      if (!Start) return nullptr;
      if (CurTok != ',')
        return Error("expected ',' after for start value");
      getNextToken();

      auto End = ParseExpression();
      if (!End) return nullptr;

      // The step value is optional.
      std::unique_ptr<ExprAST> Step;
      if (CurTok == ',') {
        getNextToken();
        Step = ParseExpression();
        if (!Step) return nullptr;
      }

      if (CurTok != tok_in)
        return Error("expected 'in' after for");
      getNextToken();  // eat 'in'.

      auto Body = ParseExpression();
      if (!Body) return nullptr;

      return llvm::make_unique<ForExprAST>(IdName, std::move(Start),
                                           std::move(End), std::move(Step),
                                           std::move(Body));
    }

LLVM IR for the 'for' Loop
--------------------------

Now we get to the good part: the LLVM IR we want to generate for this
thing. With the simple example above, we get this LLVM IR (note that
this dump is generated with optimizations disabled for clarity):

.. code-block:: llvm

    declare double @putchard(double)

    define double @printstar(double %n) {
    entry:
      ; initial value = 1.0 (inlined into phi)
      br label %loop

    loop:       ; preds = %loop, %entry
      %i = phi double [ 1.000000e+00, %entry ], [ %nextvar, %loop ]
      ; body
      %calltmp = call double @putchard(double 4.200000e+01)
      ; increment
      %nextvar = fadd double %i, 1.000000e+00

      ; termination test
      %cmptmp = fcmp ult double %i, %n
      %booltmp = uitofp i1 %cmptmp to double
      %loopcond = fcmp one double %booltmp, 0.000000e+00
      br i1 %loopcond, label %loop, label %afterloop

    afterloop:      ; preds = %loop
      ; loop always returns 0.0
      ret double 0.000000e+00
    }

This loop contains all the same constructs we saw before: a phi node,
several expressions, and some basic blocks. Lets see how this fits
together.

Code Generation for the 'for' Loop
----------------------------------

The first part of Codegen is very simple: we just output the start
expression for the loop value:

.. code-block:: c++

    Value *ForExprAST::Codegen() {
      // Emit the start code first, without 'variable' in scope.
      Value *StartVal = Start->Codegen();
      if (StartVal == 0) return 0;

With this out of the way, the next step is to set up the LLVM basic
block for the start of the loop body. In the case above, the whole loop
body is one block, but remember that the body code itself could consist
of multiple blocks (e.g. if it contains an if/then/else or a for/in
expression).

.. code-block:: c++

      // Make the new basic block for the loop header, inserting after current
      // block.
      Function *TheFunction = Builder.GetInsertBlock()->getParent();
      BasicBlock *PreheaderBB = Builder.GetInsertBlock();
      BasicBlock *LoopBB = BasicBlock::Create(getGlobalContext(), "loop", TheFunction);

      // Insert an explicit fall through from the current block to the LoopBB.
      Builder.CreateBr(LoopBB);

This code is similar to what we saw for if/then/else. Because we will
need it to create the Phi node, we remember the block that falls through
into the loop. Once we have that, we create the actual block that starts
the loop and create an unconditional branch for the fall-through between
the two blocks.

.. code-block:: c++

      // Start insertion in LoopBB.
      Builder.SetInsertPoint(LoopBB);

      // Start the PHI node with an entry for Start.
      PHINode *Variable = Builder.CreatePHI(Type::getDoubleTy(getGlobalContext()), 2, VarName.c_str());
      Variable->addIncoming(StartVal, PreheaderBB);

Now that the "preheader" for the loop is set up, we switch to emitting
code for the loop body. To begin with, we move the insertion point and
create the PHI node for the loop induction variable. Since we already
know the incoming value for the starting value, we add it to the Phi
node. Note that the Phi will eventually get a second value for the
backedge, but we can't set it up yet (because it doesn't exist!).

.. code-block:: c++

      // Within the loop, the variable is defined equal to the PHI node.  If it
      // shadows an existing variable, we have to restore it, so save it now.
      Value *OldVal = NamedValues[VarName];
      NamedValues[VarName] = Variable;

      // Emit the body of the loop.  This, like any other expr, can change the
      // current BB.  Note that we ignore the value computed by the body, but don't
      // allow an error.
      if (Body->Codegen() == 0)
        return 0;

Now the code starts to get more interesting. Our 'for' loop introduces a
new variable to the symbol table. This means that our symbol table can
now contain either function arguments or loop variables. To handle this,
before we codegen the body of the loop, we add the loop variable as the
current value for its name. Note that it is possible that there is a
variable of the same name in the outer scope. It would be easy to make
this an error (emit an error and return null if there is already an
entry for VarName) but we choose to allow shadowing of variables. In
order to handle this correctly, we remember the Value that we are
potentially shadowing in ``OldVal`` (which will be null if there is no
shadowed variable).

Once the loop variable is set into the symbol table, the code
recursively codegen's the body. This allows the body to use the loop
variable: any references to it will naturally find it in the symbol
table.

.. code-block:: c++

      // Emit the step value.
      Value *StepVal;
      if (Step) {
        StepVal = Step->Codegen();
        if (StepVal == 0) return 0;
      } else {
        // If not specified, use 1.0.
        StepVal = ConstantFP::get(getGlobalContext(), APFloat(1.0));
      }

      Value *NextVar = Builder.CreateFAdd(Variable, StepVal, "nextvar");

Now that the body is emitted, we compute the next value of the iteration
variable by adding the step value, or 1.0 if it isn't present.
'``NextVar``' will be the value of the loop variable on the next
iteration of the loop.

.. code-block:: c++

      // Compute the end condition.
      Value *EndCond = End->Codegen();
      if (EndCond == 0) return EndCond;

      // Convert condition to a bool by comparing equal to 0.0.
      EndCond = Builder.CreateFCmpONE(EndCond,
                                  ConstantFP::get(getGlobalContext(), APFloat(0.0)),
                                      "loopcond");

Finally, we evaluate the exit value of the loop, to determine whether
the loop should exit. This mirrors the condition evaluation for the
if/then/else statement.

.. code-block:: c++

      // Create the "after loop" block and insert it.
      BasicBlock *LoopEndBB = Builder.GetInsertBlock();
      BasicBlock *AfterBB = BasicBlock::Create(getGlobalContext(), "afterloop", TheFunction);

      // Insert the conditional branch into the end of LoopEndBB.
      Builder.CreateCondBr(EndCond, LoopBB, AfterBB);

      // Any new code will be inserted in AfterBB.
      Builder.SetInsertPoint(AfterBB);

With the code for the body of the loop complete, we just need to finish
up the control flow for it. This code remembers the end block (for the
phi node), then creates the block for the loop exit ("afterloop"). Based
on the value of the exit condition, it creates a conditional branch that
chooses between executing the loop again and exiting the loop. Any
future code is emitted in the "afterloop" block, so it sets the
insertion position to it.

.. code-block:: c++

      // Add a new entry to the PHI node for the backedge.
      Variable->addIncoming(NextVar, LoopEndBB);

      // Restore the unshadowed variable.
      if (OldVal)
        NamedValues[VarName] = OldVal;
      else
        NamedValues.erase(VarName);

      // for expr always returns 0.0.
      return Constant::getNullValue(Type::getDoubleTy(getGlobalContext()));
    }

The final code handles various cleanups: now that we have the "NextVar"
value, we can add the incoming value to the loop PHI node. After that,
we remove the loop variable from the symbol table, so that it isn't in
scope after the for loop. Finally, code generation of the for loop
always returns 0.0, so that is what we return from
``ForExprAST::Codegen``.

With this, we conclude the "adding control flow to Kaleidoscope" chapter
of the tutorial. In this chapter we added two control flow constructs,
and used them to motivate a couple of aspects of the LLVM IR that are
important for front-end implementors to know. In the next chapter of our
saga, we will get a bit crazier and add `user-defined
operators <LangImpl6.html>`_ to our poor innocent language.

Full Code Listing
=================

Here is the complete code listing for our running example, enhanced with
the if/then/else and for expressions.. 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

Here is the code:

.. literalinclude:: ../../examples/Kaleidoscope/Chapter5/toy.cpp
   :language: c++

`Next: Extending the language: user-defined operators <LangImpl6.html>`_