docs: Sphinxify `docs/tutorial/`

Sorry for the massive commit, but I just wanted to knock this one down
and it is really straightforward.

There are still a couple trivial (i.e. not related to the content)
things left to fix:

- Use of raw HTML links where :doc:`...` and :ref:`...` could be used
  instead. If you are a newbie and want to help fix this it would make
  for some good bite-sized patches; more experienced developers should
  be focusing on adding new content (to this tutorial or elsewhere, but
  please _do not_ waste your time on formatting when there is such dire
  need for documentation (see docs/SphinxQuickstartTemplate.rst to get
  started writing)).

- Highlighting of the kaleidoscope code blocks (currently left as bare
  `::`).  I will be working on writing a custom Pygments highlighter for
  this, mostly as training for maintaining the `llvm` code-block's lexer
  in-tree. I want to do this because I am extremely unhappy with how it
  just "gives up" on the slightest deviation from the expected syntax
  and leaves the whole code-block un-highlighted.

  More generally I am looking at writing some Sphinx extensions and
  keeping them in-tree as well, to support common use cases that
  currently have no good solution (like "monospace text inside a link").

git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@169343 91177308-0d34-0410-b5e6-96231b3b80d8

1 files changed, 1365 insertions, 0 deletions

diff --git a/docs/tutorial/OCamlLangImpl5.rst b/docs/tutorial/OCamlLangImpl5.rst
new file mode 100644
index 0000000000..203fb6f73b
--- /dev/null
+++ b/docs/tutorial/OCamlLangImpl5.rst
@@ -0,0 +1,1365 @@
+==================================================
+Kaleidoscope: Extending the Language: Control Flow
+==================================================
+
+.. contents::
+   :local:
+
+Written by `Chris Lattner <mailto:sabre@nondot.org>`_ and `Erick
+Tryzelaar <mailto:idadesub@users.sourceforge.net>`_
+
+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 lexer 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 variants for
+the relevant tokens:
+
+.. code-block:: ocaml
+
+      (* control *)
+      | If | Then | Else | For | In
+
+Once we have that, we recognize the new keywords in the lexer. This is
+pretty simple stuff:
+
+.. code-block:: ocaml
+
+          ...
+          match Buffer.contents buffer with
+          | "def" -> [< 'Token.Def; stream >]
+          | "extern" -> [< 'Token.Extern; stream >]
+          | "if" -> [< 'Token.If; stream >]
+          | "then" -> [< 'Token.Then; stream >]
+          | "else" -> [< 'Token.Else; stream >]
+          | "for" -> [< 'Token.For; stream >]
+          | "in" -> [< 'Token.In; stream >]
+          | id -> [< 'Token.Ident id; stream >]
+
+AST Extensions for If/Then/Else
+-------------------------------
+
+To represent the new expression we add a new AST variant for it:
+
+.. code-block:: ocaml
+
+    type expr =
+      ...
+      (* variant for if/then/else. *)
+      | If of expr * expr * expr
+
+The AST variant 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:: ocaml
+
+    let rec parse_primary = parser
+      ...
+      (* ifexpr ::= 'if' expr 'then' expr 'else' expr *)
+      | [< 'Token.If; c=parse_expr;
+           'Token.Then ?? "expected 'then'"; t=parse_expr;
+           'Token.Else ?? "expected 'else'"; e=parse_expr >] ->
+          Ast.If (c, t, e)
+
+Next we hook it up as a primary expression:
+
+.. code-block:: ocaml
+
+    let rec parse_primary = parser
+      ...
+      (* ifexpr ::= 'if' expr 'then' expr 'else' expr *)
+      | [< 'Token.If; c=parse_expr;
+           'Token.Then ?? "expected 'then'"; t=parse_expr;
+           'Token.Else ?? "expected 'else'"; e=parse_expr >] ->
+          Ast.If (c, t, e)
+
+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
+"``Llvm_analysis.view_function_cfg f``" or
+"``Llvm_analysis.view_function_cfg_only f``" (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 <OCamlLangImpl7.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
+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:: ocaml
+
+    let rec codegen_expr = function
+      ...
+      | Ast.If (cond, then_, else_) ->
+          let cond = codegen_expr cond in
+
+          (* Convert condition to a bool by comparing equal to 0.0 *)
+          let zero = const_float double_type 0.0 in
+          let cond_val = build_fcmp Fcmp.One cond zero "ifcond" builder in
+
+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:: ocaml
+
+          (* Grab the first block so that we might later add the conditional branch
+           * to it at the end of the function. *)
+          let start_bb = insertion_block builder in
+          let the_function = block_parent start_bb in
+
+          let then_bb = append_block context "then" the_function in
+          position_at_end then_bb builder;
+
+As opposed to the `C++ tutorial <LangImpl5.html>`_, we have to build our
+basic blocks bottom up since we can't have dangling BasicBlocks. We
+start off by saving a pointer to the first block (which might not be the
+entry block), which we'll need to build a conditional branch later. We
+do this by asking the ``builder`` for the current BasicBlock. The fourth
+line gets the current Function object that is being built. It gets this
+by the ``start_bb`` for its "parent" (the function it is currently
+embedded into).
+
+Once it has that, it creates one block. It is automatically appended
+into the function's list of blocks.
+
+.. code-block:: ocaml
+
+          (* Emit 'then' value. *)
+          position_at_end then_bb builder;
+          let then_val = codegen_expr then_ in
+
+          (* Codegen of 'then' can change the current block, update then_bb for the
+           * phi. We create a new name because one is used for the phi node, and the
+           * other is used for the conditional branch. *)
+          let new_then_bb = insertion_block builder in
+
+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.
+
+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:: ocaml
+
+          (* Emit 'else' value. *)
+          let else_bb = append_block context "else" the_function in
+          position_at_end else_bb builder;
+          let else_val = codegen_expr else_ in
+
+          (* Codegen of 'else' can change the current block, update else_bb for the
+           * phi. *)
+          let new_else_bb = insertion_block builder in
+
+Code generation for the 'else' block is basically identical to codegen
+for the 'then' block.
+
+.. code-block:: ocaml
+
+          (* Emit merge block. *)
+          let merge_bb = append_block context "ifcont" the_function in
+          position_at_end merge_bb builder;
+          let incoming = [(then_val, new_then_bb); (else_val, new_else_bb)] in
+          let phi = build_phi incoming "iftmp" builder in
+
+The first two lines here are now familiar: the first adds the "merge"
+block to the Function object. The second block 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.
+
+.. code-block:: ocaml
+
+          (* Return to the start block to add the conditional branch. *)
+          position_at_end start_bb builder;
+          ignore (build_cond_br cond_val then_bb else_bb builder);
+
+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. This is why we needed to save the "start" block.
+
+.. code-block:: ocaml
+
+          (* Set a unconditional branch at the end of the 'then' block and the
+           * 'else' block to the 'merge' block. *)
+          position_at_end new_then_bb builder; ignore (build_br merge_bb builder);
+          position_at_end new_else_bb builder; ignore (build_br merge_bb builder);
+
+          (* Finally, set the builder to the end of the merge block. *)
+          position_at_end merge_bb builder;
+
+          phi
+
+To finish off the blocks, 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.
+
+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:: ocaml
+
+      ... in Token.token ...
+      (* control *)
+      | If | Then | Else
+      | For | In
+
+      ... in Lexer.lex_ident...
+          match Buffer.contents buffer with
+          | "def" -> [< 'Token.Def; stream >]
+          | "extern" -> [< 'Token.Extern; stream >]
+          | "if" -> [< 'Token.If; stream >]
+          | "then" -> [< 'Token.Then; stream >]
+          | "else" -> [< 'Token.Else; stream >]
+          | "for" -> [< 'Token.For; stream >]
+          | "in" -> [< 'Token.In; stream >]
+          | id -> [< 'Token.Ident id; stream >]
+
+AST Extensions for the 'for' Loop
+---------------------------------
+
+The AST variant is just as simple. It basically boils down to capturing
+the variable name and the constituent expressions in the node.
+
+.. code-block:: ocaml
+
+    type expr =
+      ...
+      (* variant for for/in. *)
+      | For of string * expr * expr * expr option * expr
+
+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:: ocaml
+
+    let rec parse_primary = parser
+      ...
+      (* forexpr
+            ::= 'for' identifier '=' expr ',' expr (',' expr)? 'in' expression *)
+      | [< 'Token.For;
+           'Token.Ident id ?? "expected identifier after for";
+           'Token.Kwd '=' ?? "expected '=' after for";
+           stream >] ->
+          begin parser
+            | [<
+                 start=parse_expr;
+                 'Token.Kwd ',' ?? "expected ',' after for";
+                 end_=parse_expr;
+                 stream >] ->
+                let step =
+                  begin parser
+                  | [< 'Token.Kwd ','; step=parse_expr >] -> Some step
+                  | [< >] -> None
+                  end stream
+                in
+                begin parser
+                | [< 'Token.In; body=parse_expr >] ->
+                    Ast.For (id, start, end_, step, body)
+                | [< >] ->
+                    raise (Stream.Error "expected 'in' after for")
+                end stream
+            | [< >] ->
+                raise (Stream.Error "expected '=' after for")
+          end stream
+
+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:: ocaml
+
+    let rec codegen_expr = function
+      ...
+      | Ast.For (var_name, start, end_, step, body) ->
+          (* Emit the start code first, without 'variable' in scope. *)
+          let start_val = codegen_expr start in
+
+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:: ocaml
+
+          (* Make the new basic block for the loop header, inserting after current
+           * block. *)
+          let preheader_bb = insertion_block builder in
+          let the_function = block_parent preheader_bb in
+          let loop_bb = append_block context "loop" the_function in
+
+          (* Insert an explicit fall through from the current block to the
+           * loop_bb. *)
+          ignore (build_br loop_bb builder);
+
+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:: ocaml
+
+          (* Start insertion in loop_bb. *)
+          position_at_end loop_bb builder;
+
+          (* Start the PHI node with an entry for start. *)
+          let variable = build_phi [(start_val, preheader_bb)] var_name builder in
+
+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:: ocaml
+
+          (* 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. *)
+          let old_val =
+            try Some (Hashtbl.find named_values var_name) with Not_found -> None
+          in
+          Hashtbl.add named_values var_name 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 *)
+          ignore (codegen_expr body);
+
+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 ``old_val`` (which will be None 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:: ocaml
+
+          (* Emit the step value. *)
+          let step_val =
+            match step with
+            | Some step -> codegen_expr step
+            (* If not specified, use 1.0. *)
+            | None -> const_float double_type 1.0
+          in
+
+          let next_var = build_add variable step_val "nextvar" builder in
+
+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.
+'``next_var``' will be the value of the loop variable on the next
+iteration of the loop.
+
+.. code-block:: ocaml
+
+          (* Compute the end condition. *)
+          let end_cond = codegen_expr end_ in
+
+          (* Convert condition to a bool by comparing equal to 0.0. *)
+          let zero = const_float double_type 0.0 in
+          let end_cond = build_fcmp Fcmp.One end_cond zero "loopcond" builder in
+
+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:: ocaml
+
+          (* Create the "after loop" block and insert it. *)
+          let loop_end_bb = insertion_block builder in
+          let after_bb = append_block context "afterloop" the_function in
+
+          (* Insert the conditional branch into the end of loop_end_bb. *)
+          ignore (build_cond_br end_cond loop_bb after_bb builder);
+
+          (* Any new code will be inserted in after_bb. *)
+          position_at_end after_bb builder;
+
+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:: ocaml
+
+          (* Add a new entry to the PHI node for the backedge. *)
+          add_incoming (next_var, loop_end_bb) variable;
+
+          (* Restore the unshadowed variable. *)
+          begin match old_val with
+          | Some old_val -> Hashtbl.add named_values var_name old_val
+          | None -> ()
+          end;
+
+          (* for expr always returns 0.0. *)
+          const_null double_type
+
+The final code handles various cleanups: now that we have the
+"``next_var``" 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
+``Codegen.codegen_expr``.
+
+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 <OCamlLangImpl6.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
+    ocamlbuild toy.byte
+    # Run
+    ./toy.byte
+
+Here is the code:
+
+\_tags:
+    ::
+
+        <{lexer,parser}.ml>: use_camlp4, pp(camlp4of)
+        <*.{byte,native}>: g++, use_llvm, use_llvm_analysis
+        <*.{byte,native}>: use_llvm_executionengine, use_llvm_target
+        <*.{byte,native}>: use_llvm_scalar_opts, use_bindings
+
+myocamlbuild.ml:
+    .. code-block:: ocaml
+
+        open Ocamlbuild_plugin;;
+
+        ocaml_lib ~extern:true "llvm";;
+        ocaml_lib ~extern:true "llvm_analysis";;
+        ocaml_lib ~extern:true "llvm_executionengine";;
+        ocaml_lib ~extern:true "llvm_target";;
+        ocaml_lib ~extern:true "llvm_scalar_opts";;
+
+        flag ["link"; "ocaml"; "g++"] (S[A"-cc"; A"g++"]);;
+        dep ["link"; "ocaml"; "use_bindings"] ["bindings.o"];;
+
+token.ml:
+    .. code-block:: ocaml
+
+        (*===----------------------------------------------------------------------===
+         * Lexer Tokens
+         *===----------------------------------------------------------------------===*)
+
+        (* The lexer returns these 'Kwd' if it is an unknown character, otherwise one of
+         * these others for known things. *)
+        type token =
+          (* commands *)
+          | Def | Extern
+
+          (* primary *)
+          | Ident of string | Number of float
+
+          (* unknown *)
+          | Kwd of char
+
+          (* control *)
+          | If | Then | Else
+          | For | In
+
+lexer.ml:
+    .. code-block:: ocaml
+
+        (*===----------------------------------------------------------------------===
+         * Lexer
+         *===----------------------------------------------------------------------===*)
+
+        let rec lex = parser
+          (* Skip any whitespace. *)
+          | [< ' (' ' | '\n' | '\r' | '\t'); stream >] -> lex stream
+
+          (* identifier: [a-zA-Z][a-zA-Z0-9] *)
+          | [< ' ('A' .. 'Z' | 'a' .. 'z' as c); stream >] ->
+              let buffer = Buffer.create 1 in
+              Buffer.add_char buffer c;
+              lex_ident buffer stream
+
+          (* number: [0-9.]+ *)
+          | [< ' ('0' .. '9' as c); stream >] ->
+              let buffer = Buffer.create 1 in
+              Buffer.add_char buffer c;
+              lex_number buffer stream
+
+          (* Comment until end of line. *)
+          | [< ' ('#'); stream >] ->
+              lex_comment stream
+
+          (* Otherwise, just return the character as its ascii value. *)
+          | [< 'c; stream >] ->
+              [< 'Token.Kwd c; lex stream >]
+
+          (* end of stream. *)
+          | [< >] -> [< >]
+
+        and lex_number buffer = parser
+          | [< ' ('0' .. '9' | '.' as c); stream >] ->
+              Buffer.add_char buffer c;
+              lex_number buffer stream
+          | [< stream=lex >] ->
+              [< 'Token.Number (float_of_string (Buffer.contents buffer)); stream >]
+
+        and lex_ident buffer = parser
+          | [< ' ('A' .. 'Z' | 'a' .. 'z' | '0' .. '9' as c); stream >] ->
+              Buffer.add_char buffer c;
+              lex_ident buffer stream
+          | [< stream=lex >] ->
+              match Buffer.contents buffer with
+              | "def" -> [< 'Token.Def; stream >]
+              | "extern" -> [< 'Token.Extern; stream >]
+              | "if" -> [< 'Token.If; stream >]
+              | "then" -> [< 'Token.Then; stream >]
+              | "else" -> [< 'Token.Else; stream >]
+              | "for" -> [< 'Token.For; stream >]
+              | "in" -> [< 'Token.In; stream >]
+              | id -> [< 'Token.Ident id; stream >]
+
+        and lex_comment = parser
+          | [< ' ('\n'); stream=lex >] -> stream
+          | [< 'c; e=lex_comment >] -> e
+          | [< >] -> [< >]
+
+ast.ml:
+    .. code-block:: ocaml
+
+        (*===----------------------------------------------------------------------===
+         * Abstract Syntax Tree (aka Parse Tree)
+         *===----------------------------------------------------------------------===*)
+
+        (* expr - Base type for all expression nodes. *)
+        type expr =
+          (* variant for numeric literals like "1.0". *)
+          | Number of float
+
+          (* variant for referencing a variable, like "a". *)
+          | Variable of string
+
+          (* variant for a binary operator. *)
+          | Binary of char * expr * expr
+
+          (* variant for function calls. *)
+          | Call of string * expr array
+
+          (* variant for if/then/else. *)
+          | If of expr * expr * expr
+
+          (* variant for for/in. *)
+          | For of string * expr * expr * expr option * expr
+
+        (* proto - This type represents the "prototype" for a function, which captures
+         * its name, and its argument names (thus implicitly the number of arguments the
+         * function takes). *)
+        type proto = Prototype of string * string array
+
+        (* func - This type represents a function definition itself. *)
+        type func = Function of proto * expr
+
+parser.ml:
+    .. code-block:: ocaml
+
+        (*===---------------------------------------------------------------------===
+         * Parser
+         *===---------------------------------------------------------------------===*)
+
+        (* binop_precedence - This holds the precedence for each binary operator that is
+         * defined *)
+        let binop_precedence:(char, int) Hashtbl.t = Hashtbl.create 10
+
+        (* precedence - Get the precedence of the pending binary operator token. *)
+        let precedence c = try Hashtbl.find binop_precedence c with Not_found -> -1
+
+        (* primary
+         *   ::= identifier
+         *   ::= numberexpr
+         *   ::= parenexpr
+         *   ::= ifexpr
+         *   ::= forexpr *)
+        let rec parse_primary = parser
+          (* numberexpr ::= number *)
+          | [< 'Token.Number n >] -> Ast.Number n
+
+          (* parenexpr ::= '(' expression ')' *)
+          | [< 'Token.Kwd '('; e=parse_expr; 'Token.Kwd ')' ?? "expected ')'" >] -> e
+
+          (* identifierexpr
+           *   ::= identifier
+           *   ::= identifier '(' argumentexpr ')' *)
+          | [< 'Token.Ident id; stream >] ->
+              let rec parse_args accumulator = parser
+                | [< e=parse_expr; stream >] ->
+                    begin parser
+                      | [< 'Token.Kwd ','; e=parse_args (e :: accumulator) >] -> e
+                      | [< >] -> e :: accumulator
+                    end stream
+                | [< >] -> accumulator
+              in
+              let rec parse_ident id = parser
+                (* Call. *)
+                | [< 'Token.Kwd '(';
+                     args=parse_args [];
+                     'Token.Kwd ')' ?? "expected ')'">] ->
+                    Ast.Call (id, Array.of_list (List.rev args))
+
+                (* Simple variable ref. *)
+                | [< >] -> Ast.Variable id
+              in
+              parse_ident id stream
+
+          (* ifexpr ::= 'if' expr 'then' expr 'else' expr *)
+          | [< 'Token.If; c=parse_expr;
+               'Token.Then ?? "expected 'then'"; t=parse_expr;
+               'Token.Else ?? "expected 'else'"; e=parse_expr >] ->
+              Ast.If (c, t, e)
+
+          (* forexpr
+                ::= 'for' identifier '=' expr ',' expr (',' expr)? 'in' expression *)
+          | [< 'Token.For;
+               'Token.Ident id ?? "expected identifier after for";
+               'Token.Kwd '=' ?? "expected '=' after for";
+               stream >] ->
+              begin parser
+                | [<
+                     start=parse_expr;
+                     'Token.Kwd ',' ?? "expected ',' after for";
+                     end_=parse_expr;
+                     stream >] ->
+                    let step =
+                      begin parser
+                      | [< 'Token.Kwd ','; step=parse_expr >] -> Some step
+                      | [< >] -> None
+                      end stream
+                    in
+                    begin parser
+                    | [< 'Token.In; body=parse_expr >] ->
+                        Ast.For (id, start, end_, step, body)
+                    | [< >] ->
+                        raise (Stream.Error "expected 'in' after for")
+                    end stream
+                | [< >] ->
+                    raise (Stream.Error "expected '=' after for")
+              end stream
+
+          | [< >] -> raise (Stream.Error "unknown token when expecting an expression.")
+
+        (* binoprhs
+         *   ::= ('+' primary)* *)
+        and parse_bin_rhs expr_prec lhs stream =
+          match Stream.peek stream with
+          (* If this is a binop, find its precedence. *)
+          | Some (Token.Kwd c) when Hashtbl.mem binop_precedence c ->
+              let token_prec = precedence c in
+
+              (* If this is a binop that binds at least as tightly as the current binop,
+               * consume it, otherwise we are done. *)
+              if token_prec < expr_prec then lhs else begin
+                (* Eat the binop. *)
+                Stream.junk stream;
+
+                (* Parse the primary expression after the binary operator. *)
+                let rhs = parse_primary stream in
+
+                (* Okay, we know this is a binop. *)
+                let rhs =
+                  match Stream.peek stream with
+                  | Some (Token.Kwd c2) ->
+                      (* If BinOp binds less tightly with rhs than the operator after
+                       * rhs, let the pending operator take rhs as its lhs. *)
+                      let next_prec = precedence c2 in
+                      if token_prec < next_prec
+                      then parse_bin_rhs (token_prec + 1) rhs stream
+                      else rhs
+                  | _ -> rhs
+                in
+
+                (* Merge lhs/rhs. *)
+                let lhs = Ast.Binary (c, lhs, rhs) in
+                parse_bin_rhs expr_prec lhs stream
+              end
+          | _ -> lhs
+
+        (* expression
+         *   ::= primary binoprhs *)
+        and parse_expr = parser
+          | [< lhs=parse_primary; stream >] -> parse_bin_rhs 0 lhs stream
+
+        (* prototype
+         *   ::= id '(' id* ')' *)
+        let parse_prototype =
+          let rec parse_args accumulator = parser
+            | [< 'Token.Ident id; e=parse_args (id::accumulator) >] -> e
+            | [< >] -> accumulator
+          in
+
+          parser
+          | [< 'Token.Ident id;
+               'Token.Kwd '(' ?? "expected '(' in prototype";
+               args=parse_args [];
+               'Token.Kwd ')' ?? "expected ')' in prototype" >] ->
+              (* success. *)
+              Ast.Prototype (id, Array.of_list (List.rev args))
+
+          | [< >] ->
+              raise (Stream.Error "expected function name in prototype")
+
+        (* definition ::= 'def' prototype expression *)
+        let parse_definition = parser
+          | [< 'Token.Def; p=parse_prototype; e=parse_expr >] ->
+              Ast.Function (p, e)
+
+        (* toplevelexpr ::= expression *)
+        let parse_toplevel = parser
+          | [< e=parse_expr >] ->
+              (* Make an anonymous proto. *)
+              Ast.Function (Ast.Prototype ("", [||]), e)
+
+        (*  external ::= 'extern' prototype *)
+        let parse_extern = parser
+          | [< 'Token.Extern; e=parse_prototype >] -> e
+
+codegen.ml:
+    .. code-block:: ocaml
+
+        (*===----------------------------------------------------------------------===
+         * Code Generation
+         *===----------------------------------------------------------------------===*)
+
+        open Llvm
+
+        exception Error of string
+
+        let context = global_context ()
+        let the_module = create_module context "my cool jit"
+        let builder = builder context
+        let named_values:(string, llvalue) Hashtbl.t = Hashtbl.create 10
+        let double_type = double_type context
+
+        let rec codegen_expr = function
+          | Ast.Number n -> const_float double_type n
+          | Ast.Variable name ->
+              (try Hashtbl.find named_values name with
+                | Not_found -> raise (Error "unknown variable name"))
+          | Ast.Binary (op, lhs, rhs) ->
+              let lhs_val = codegen_expr lhs in
+              let rhs_val = codegen_expr rhs in
+              begin
+                match op with
+                | '+' -> build_add lhs_val rhs_val "addtmp" builder
+                | '-' -> build_sub lhs_val rhs_val "subtmp" builder
+                | '*' -> build_mul lhs_val rhs_val "multmp" builder
+                | '<' ->
+                    (* Convert bool 0/1 to double 0.0 or 1.0 *)
+                    let i = build_fcmp Fcmp.Ult lhs_val rhs_val "cmptmp" builder in
+                    build_uitofp i double_type "booltmp" builder
+                | _ -> raise (Error "invalid binary operator")
+              end
+          | Ast.Call (callee, args) ->
+              (* Look up the name in the module table. *)
+              let callee =
+                match lookup_function callee the_module with
+                | Some callee -> callee
+                | None -> raise (Error "unknown function referenced")
+              in
+              let params = params callee in
+
+              (* If argument mismatch error. *)
+              if Array.length params == Array.length args then () else
+                raise (Error "incorrect # arguments passed");
+              let args = Array.map codegen_expr args in
+              build_call callee args "calltmp" builder
+          | Ast.If (cond, then_, else_) ->
+              let cond = codegen_expr cond in
+
+              (* Convert condition to a bool by comparing equal to 0.0 *)
+              let zero = const_float double_type 0.0 in
+              let cond_val = build_fcmp Fcmp.One cond zero "ifcond" builder in
+
+              (* Grab the first block so that we might later add the conditional branch
+               * to it at the end of the function. *)
+              let start_bb = insertion_block builder in
+              let the_function = block_parent start_bb in
+
+              let then_bb = append_block context "then" the_function in
+
+              (* Emit 'then' value. *)
+              position_at_end then_bb builder;
+              let then_val = codegen_expr then_ in
+
+              (* Codegen of 'then' can change the current block, update then_bb for the
+               * phi. We create a new name because one is used for the phi node, and the
+               * other is used for the conditional branch. *)
+              let new_then_bb = insertion_block builder in
+
+              (* Emit 'else' value. *)
+              let else_bb = append_block context "else" the_function in
+              position_at_end else_bb builder;
+              let else_val = codegen_expr else_ in
+
+              (* Codegen of 'else' can change the current block, update else_bb for the
+               * phi. *)
+              let new_else_bb = insertion_block builder in
+
+              (* Emit merge block. *)
+              let merge_bb = append_block context "ifcont" the_function in
+              position_at_end merge_bb builder;
+              let incoming = [(then_val, new_then_bb); (else_val, new_else_bb)] in
+              let phi = build_phi incoming "iftmp" builder in
+
+              (* Return to the start block to add the conditional branch. *)
+              position_at_end start_bb builder;
+              ignore (build_cond_br cond_val then_bb else_bb builder);
+
+              (* Set a unconditional branch at the end of the 'then' block and the
+               * 'else' block to the 'merge' block. *)
+              position_at_end new_then_bb builder; ignore (build_br merge_bb builder);
+              position_at_end new_else_bb builder; ignore (build_br merge_bb builder);
+
+              (* Finally, set the builder to the end of the merge block. *)
+              position_at_end merge_bb builder;
+
+              phi
+          | Ast.For (var_name, start, end_, step, body) ->
+              (* Emit the start code first, without 'variable' in scope. *)
+              let start_val = codegen_expr start in
+
+              (* Make the new basic block for the loop header, inserting after current
+               * block. *)
+              let preheader_bb = insertion_block builder in
+              let the_function = block_parent preheader_bb in
+              let loop_bb = append_block context "loop" the_function in
+
+              (* Insert an explicit fall through from the current block to the
+               * loop_bb. *)
+              ignore (build_br loop_bb builder);
+
+              (* Start insertion in loop_bb. *)
+              position_at_end loop_bb builder;
+
+              (* Start the PHI node with an entry for start. *)
+              let variable = build_phi [(start_val, preheader_bb)] var_name builder in
+
+              (* 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. *)
+              let old_val =
+                try Some (Hashtbl.find named_values var_name) with Not_found -> None
+              in
+              Hashtbl.add named_values var_name 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 *)
+              ignore (codegen_expr body);
+
+              (* Emit the step value. *)
+              let step_val =
+                match step with
+                | Some step -> codegen_expr step
+                (* If not specified, use 1.0. *)
+                | None -> const_float double_type 1.0
+              in
+
+              let next_var = build_add variable step_val "nextvar" builder in
+
+              (* Compute the end condition. *)
+              let end_cond = codegen_expr end_ in
+
+              (* Convert condition to a bool by comparing equal to 0.0. *)
+              let zero = const_float double_type 0.0 in
+              let end_cond = build_fcmp Fcmp.One end_cond zero "loopcond" builder in
+
+              (* Create the "after loop" block and insert it. *)
+              let loop_end_bb = insertion_block builder in
+              let after_bb = append_block context "afterloop" the_function in
+
+              (* Insert the conditional branch into the end of loop_end_bb. *)
+              ignore (build_cond_br end_cond loop_bb after_bb builder);
+
+              (* Any new code will be inserted in after_bb. *)
+              position_at_end after_bb builder;
+
+              (* Add a new entry to the PHI node for the backedge. *)
+              add_incoming (next_var, loop_end_bb) variable;
+
+              (* Restore the unshadowed variable. *)
+              begin match old_val with
+              | Some old_val -> Hashtbl.add named_values var_name old_val
+              | None -> ()
+              end;
+
+              (* for expr always returns 0.0. *)
+              const_null double_type
+
+        let codegen_proto = function
+          | Ast.Prototype (name, args) ->
+              (* Make the function type: double(double,double) etc. *)
+              let doubles = Array.make (Array.length args) double_type in
+              let ft = function_type double_type doubles in
+              let f =
+                match lookup_function name the_module with
+                | None -> declare_function name ft the_module
+
+                (* If 'f' conflicted, there was already something named 'name'. If it
+                 * has a body, don't allow redefinition or reextern. *)
+                | Some f ->
+                    (* If 'f' already has a body, reject this. *)
+                    if block_begin f <> At_end f then
+                      raise (Error "redefinition of function");
+
+                    (* If 'f' took a different number of arguments, reject. *)
+                    if element_type (type_of f) <> ft then
+                      raise (Error "redefinition of function with different # args");
+                    f
+              in
+
+              (* Set names for all arguments. *)
+              Array.iteri (fun i a ->
+                let n = args.(i) in
+                set_value_name n a;
+                Hashtbl.add named_values n a;
+              ) (params f);
+              f
+
+        let codegen_func the_fpm = function
+          | Ast.Function (proto, body) ->
+              Hashtbl.clear named_values;
+              let the_function = codegen_proto proto in
+
+              (* Create a new basic block to start insertion into. *)
+              let bb = append_block context "entry" the_function in
+              position_at_end bb builder;
+
+              try
+                let ret_val = codegen_expr body in
+
+                (* Finish off the function. *)
+                let _ = build_ret ret_val builder in
+
+                (* Validate the generated code, checking for consistency. *)
+                Llvm_analysis.assert_valid_function the_function;
+
+                (* Optimize the function. *)
+                let _ = PassManager.run_function the_function the_fpm in
+
+                the_function
+              with e ->
+                delete_function the_function;
+                raise e
+
+toplevel.ml:
+    .. code-block:: ocaml
+
+        (*===----------------------------------------------------------------------===
+         * Top-Level parsing and JIT Driver
+         *===----------------------------------------------------------------------===*)
+
+        open Llvm
+        open Llvm_executionengine
+
+        (* top ::= definition | external | expression | ';' *)
+        let rec main_loop the_fpm the_execution_engine stream =
+          match Stream.peek stream with
+          | None -> ()
+
+          (* ignore top-level semicolons. *)
+          | Some (Token.Kwd ';') ->
+              Stream.junk stream;
+              main_loop the_fpm the_execution_engine stream
+
+          | Some token ->
+              begin
+                try match token with
+                | Token.Def ->
+                    let e = Parser.parse_definition stream in
+                    print_endline "parsed a function definition.";
+                    dump_value (Codegen.codegen_func the_fpm e);
+                | Token.Extern ->
+                    let e = Parser.parse_extern stream in
+                    print_endline "parsed an extern.";
+                    dump_value (Codegen.codegen_proto e);
+                | _ ->
+                    (* Evaluate a top-level expression into an anonymous function. *)
+                    let e = Parser.parse_toplevel stream in
+                    print_endline "parsed a top-level expr";
+                    let the_function = Codegen.codegen_func the_fpm e in
+                    dump_value the_function;
+
+                    (* JIT the function, returning a function pointer. *)
+                    let result = ExecutionEngine.run_function the_function [||]
+                      the_execution_engine in
+
+                    print_string "Evaluated to ";
+                    print_float (GenericValue.as_float Codegen.double_type result);
+                    print_newline ();
+                with Stream.Error s | Codegen.Error s ->
+                  (* Skip token for error recovery. *)
+                  Stream.junk stream;
+                  print_endline s;
+              end;
+              print_string "ready> "; flush stdout;
+              main_loop the_fpm the_execution_engine stream
+
+toy.ml:
+    .. code-block:: ocaml
+
+        (*===----------------------------------------------------------------------===
+         * Main driver code.
+         *===----------------------------------------------------------------------===*)
+
+        open Llvm
+        open Llvm_executionengine
+        open Llvm_target
+        open Llvm_scalar_opts
+
+        let main () =
+          ignore (initialize_native_target ());
+
+          (* Install standard binary operators.
+           * 1 is the lowest precedence. *)
+          Hashtbl.add Parser.binop_precedence '<' 10;
+          Hashtbl.add Parser.binop_precedence '+' 20;
+          Hashtbl.add Parser.binop_precedence '-' 20;
+          Hashtbl.add Parser.binop_precedence '*' 40;    (* highest. *)
+
+          (* Prime the first token. *)
+          print_string "ready> "; flush stdout;
+          let stream = Lexer.lex (Stream.of_channel stdin) in
+
+          (* Create the JIT. *)
+          let the_execution_engine = ExecutionEngine.create Codegen.the_module in
+          let the_fpm = PassManager.create_function Codegen.the_module in
+
+          (* Set up the optimizer pipeline.  Start with registering info about how the
+           * target lays out data structures. *)
+          DataLayout.add (ExecutionEngine.target_data the_execution_engine) the_fpm;
+
+          (* Do simple "peephole" optimizations and bit-twiddling optzn. *)
+          add_instruction_combination the_fpm;
+
+          (* reassociate expressions. *)
+          add_reassociation the_fpm;
+
+          (* Eliminate Common SubExpressions. *)
+          add_gvn the_fpm;
+
+          (* Simplify the control flow graph (deleting unreachable blocks, etc). *)
+          add_cfg_simplification the_fpm;
+
+          ignore (PassManager.initialize the_fpm);
+
+          (* Run the main "interpreter loop" now. *)
+          Toplevel.main_loop the_fpm the_execution_engine stream;
+
+          (* Print out all the generated code. *)
+          dump_module Codegen.the_module
+        ;;
+
+        main ()
+
+bindings.c
+    .. code-block:: c
+
+        #include <stdio.h>
+
+        /* putchard - putchar that takes a double and returns 0. */
+        extern double putchard(double X) {
+          putchar((char)X);
+          return 0;
+        }
+
+`Next: Extending the language: user-defined
+operators <OCamlLangImpl6.html>`_
+