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1351 lines
51 KiB
ReStructuredText
==================================================
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Kaleidoscope: Extending the Language: Control Flow
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==================================================
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.. contents::
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:local:
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Chapter 5 Introduction
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======================
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Welcome to Chapter 5 of the "`Implementing a language with
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LLVM <index.html>`_" tutorial. Parts 1-4 described the implementation of
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the simple Kaleidoscope language and included support for generating
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LLVM IR, followed by optimizations and a JIT compiler. Unfortunately, as
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presented, Kaleidoscope is mostly useless: it has no control flow other
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than call and return. This means that you can't have conditional
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branches in the code, significantly limiting its power. In this episode
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of "build that compiler", we'll extend Kaleidoscope to have an
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if/then/else expression plus a simple 'for' loop.
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If/Then/Else
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============
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Extending Kaleidoscope to support if/then/else is quite straightforward.
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It basically requires adding lexer support for this "new" concept to the
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lexer, parser, AST, and LLVM code emitter. This example is nice, because
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it shows how easy it is to "grow" a language over time, incrementally
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extending it as new ideas are discovered.
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Before we get going on "how" we add this extension, lets talk about
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"what" we want. The basic idea is that we want to be able to write this
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sort of thing:
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::
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def fib(x)
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if x < 3 then
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1
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else
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fib(x-1)+fib(x-2);
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In Kaleidoscope, every construct is an expression: there are no
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statements. As such, the if/then/else expression needs to return a value
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like any other. Since we're using a mostly functional form, we'll have
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it evaluate its conditional, then return the 'then' or 'else' value
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based on how the condition was resolved. This is very similar to the C
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"?:" expression.
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The semantics of the if/then/else expression is that it evaluates the
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condition to a boolean equality value: 0.0 is considered to be false and
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everything else is considered to be true. If the condition is true, the
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first subexpression is evaluated and returned, if the condition is
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false, the second subexpression is evaluated and returned. Since
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Kaleidoscope allows side-effects, this behavior is important to nail
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down.
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Now that we know what we "want", lets break this down into its
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constituent pieces.
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Lexer Extensions for If/Then/Else
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---------------------------------
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The lexer extensions are straightforward. First we add new variants for
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the relevant tokens:
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.. code-block:: ocaml
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(* control *)
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| If | Then | Else | For | In
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Once we have that, we recognize the new keywords in the lexer. This is
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pretty simple stuff:
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.. code-block:: ocaml
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...
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match Buffer.contents buffer with
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| "def" -> [< 'Token.Def; stream >]
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| "extern" -> [< 'Token.Extern; stream >]
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| "if" -> [< 'Token.If; stream >]
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| "then" -> [< 'Token.Then; stream >]
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| "else" -> [< 'Token.Else; stream >]
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| "for" -> [< 'Token.For; stream >]
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| "in" -> [< 'Token.In; stream >]
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| id -> [< 'Token.Ident id; stream >]
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AST Extensions for If/Then/Else
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-------------------------------
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To represent the new expression we add a new AST variant for it:
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.. code-block:: ocaml
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type expr =
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...
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(* variant for if/then/else. *)
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| If of expr * expr * expr
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The AST variant just has pointers to the various subexpressions.
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Parser Extensions for If/Then/Else
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----------------------------------
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Now that we have the relevant tokens coming from the lexer and we have
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the AST node to build, our parsing logic is relatively straightforward.
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Next we add a new case for parsing a if-expression as a primary expression:
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.. code-block:: ocaml
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let rec parse_primary = parser
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...
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(* ifexpr ::= 'if' expr 'then' expr 'else' expr *)
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| [< 'Token.If; c=parse_expr;
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'Token.Then ?? "expected 'then'"; t=parse_expr;
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'Token.Else ?? "expected 'else'"; e=parse_expr >] ->
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Ast.If (c, t, e)
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LLVM IR for If/Then/Else
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------------------------
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Now that we have it parsing and building the AST, the final piece is
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adding LLVM code generation support. This is the most interesting part
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of the if/then/else example, because this is where it starts to
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introduce new concepts. All of the code above has been thoroughly
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described in previous chapters.
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To motivate the code we want to produce, lets take a look at a simple
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example. Consider:
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::
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extern foo();
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extern bar();
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def baz(x) if x then foo() else bar();
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If you disable optimizations, the code you'll (soon) get from
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Kaleidoscope looks like this:
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.. code-block:: llvm
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declare double @foo()
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declare double @bar()
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define double @baz(double %x) {
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entry:
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%ifcond = fcmp one double %x, 0.000000e+00
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br i1 %ifcond, label %then, label %else
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then: ; preds = %entry
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%calltmp = call double @foo()
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br label %ifcont
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else: ; preds = %entry
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%calltmp1 = call double @bar()
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br label %ifcont
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ifcont: ; preds = %else, %then
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%iftmp = phi double [ %calltmp, %then ], [ %calltmp1, %else ]
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ret double %iftmp
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}
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To visualize the control flow graph, you can use a nifty feature of the
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LLVM '`opt <http://llvm.org/cmds/opt.html>`_' tool. If you put this LLVM
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IR into "t.ll" and run "``llvm-as < t.ll | opt -analyze -view-cfg``", `a
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window will pop up <../ProgrammersManual.html#viewing-graphs-while-debugging-code>`_ and you'll
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see this graph:
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.. figure:: LangImpl05-cfg.png
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:align: center
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:alt: Example CFG
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Example CFG
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Another way to get this is to call
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"``Llvm_analysis.view_function_cfg f``" or
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"``Llvm_analysis.view_function_cfg_only f``" (where ``f`` is a
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"``Function``") either by inserting actual calls into the code and
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recompiling or by calling these in the debugger. LLVM has many nice
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features for visualizing various graphs.
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Getting back to the generated code, it is fairly simple: the entry block
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evaluates the conditional expression ("x" in our case here) and compares
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the result to 0.0 with the "``fcmp one``" instruction ('one' is "Ordered
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and Not Equal"). Based on the result of this expression, the code jumps
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to either the "then" or "else" blocks, which contain the expressions for
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the true/false cases.
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Once the then/else blocks are finished executing, they both branch back
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to the 'ifcont' block to execute the code that happens after the
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if/then/else. In this case the only thing left to do is to return to the
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caller of the function. The question then becomes: how does the code
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know which expression to return?
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The answer to this question involves an important SSA operation: the
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`Phi
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operation <http://en.wikipedia.org/wiki/Static_single_assignment_form>`_.
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If you're not familiar with SSA, `the wikipedia
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article <http://en.wikipedia.org/wiki/Static_single_assignment_form>`_
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is a good introduction and there are various other introductions to it
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available on your favorite search engine. The short version is that
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"execution" of the Phi operation requires "remembering" which block
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control came from. The Phi operation takes on the value corresponding to
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the input control block. In this case, if control comes in from the
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"then" block, it gets the value of "calltmp". If control comes from the
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"else" block, it gets the value of "calltmp1".
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At this point, you are probably starting to think "Oh no! This means my
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simple and elegant front-end will have to start generating SSA form in
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order to use LLVM!". Fortunately, this is not the case, and we strongly
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advise *not* implementing an SSA construction algorithm in your
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front-end unless there is an amazingly good reason to do so. In
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practice, there are two sorts of values that float around in code
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written for your average imperative programming language that might need
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Phi nodes:
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#. Code that involves user variables: ``x = 1; x = x + 1;``
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#. Values that are implicit in the structure of your AST, such as the
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Phi node in this case.
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In `Chapter 7 <OCamlLangImpl7.html>`_ of this tutorial ("mutable
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variables"), we'll talk about #1 in depth. For now, just believe me that
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you don't need SSA construction to handle this case. For #2, you have
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the choice of using the techniques that we will describe for #1, or you
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can insert Phi nodes directly, if convenient. In this case, it is really
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really easy to generate the Phi node, so we choose to do it directly.
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Okay, enough of the motivation and overview, lets generate code!
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Code Generation for If/Then/Else
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--------------------------------
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In order to generate code for this, we implement the ``Codegen`` method
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for ``IfExprAST``:
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.. code-block:: ocaml
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let rec codegen_expr = function
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...
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| Ast.If (cond, then_, else_) ->
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let cond = codegen_expr cond in
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(* Convert condition to a bool by comparing equal to 0.0 *)
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let zero = const_float double_type 0.0 in
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let cond_val = build_fcmp Fcmp.One cond zero "ifcond" builder in
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This code is straightforward and similar to what we saw before. We emit
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the expression for the condition, then compare that value to zero to get
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a truth value as a 1-bit (bool) value.
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.. code-block:: ocaml
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(* Grab the first block so that we might later add the conditional branch
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* to it at the end of the function. *)
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let start_bb = insertion_block builder in
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let the_function = block_parent start_bb in
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let then_bb = append_block context "then" the_function in
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position_at_end then_bb builder;
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As opposed to the `C++ tutorial <LangImpl5.html>`_, we have to build our
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basic blocks bottom up since we can't have dangling BasicBlocks. We
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start off by saving a pointer to the first block (which might not be the
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entry block), which we'll need to build a conditional branch later. We
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do this by asking the ``builder`` for the current BasicBlock. The fourth
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line gets the current Function object that is being built. It gets this
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by the ``start_bb`` for its "parent" (the function it is currently
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embedded into).
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Once it has that, it creates one block. It is automatically appended
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into the function's list of blocks.
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.. code-block:: ocaml
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(* Emit 'then' value. *)
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position_at_end then_bb builder;
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let then_val = codegen_expr then_ in
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(* Codegen of 'then' can change the current block, update then_bb for the
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* phi. We create a new name because one is used for the phi node, and the
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* other is used for the conditional branch. *)
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let new_then_bb = insertion_block builder in
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We move the builder to start inserting into the "then" block. Strictly
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speaking, this call moves the insertion point to be at the end of the
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specified block. However, since the "then" block is empty, it also
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starts out by inserting at the beginning of the block. :)
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Once the insertion point is set, we recursively codegen the "then"
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expression from the AST.
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The final line here is quite subtle, but is very important. The basic
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issue is that when we create the Phi node in the merge block, we need to
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set up the block/value pairs that indicate how the Phi will work.
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Importantly, the Phi node expects to have an entry for each predecessor
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of the block in the CFG. Why then, are we getting the current block when
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we just set it to ThenBB 5 lines above? The problem is that the "Then"
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expression may actually itself change the block that the Builder is
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emitting into if, for example, it contains a nested "if/then/else"
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expression. Because calling Codegen recursively could arbitrarily change
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the notion of the current block, we are required to get an up-to-date
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value for code that will set up the Phi node.
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.. code-block:: ocaml
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(* Emit 'else' value. *)
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let else_bb = append_block context "else" the_function in
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position_at_end else_bb builder;
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let else_val = codegen_expr else_ in
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(* Codegen of 'else' can change the current block, update else_bb for the
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* phi. *)
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let new_else_bb = insertion_block builder in
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Code generation for the 'else' block is basically identical to codegen
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for the 'then' block.
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.. code-block:: ocaml
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(* Emit merge block. *)
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let merge_bb = append_block context "ifcont" the_function in
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position_at_end merge_bb builder;
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let incoming = [(then_val, new_then_bb); (else_val, new_else_bb)] in
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let phi = build_phi incoming "iftmp" builder in
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The first two lines here are now familiar: the first adds the "merge"
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block to the Function object. The second changes the insertion
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point so that newly created code will go into the "merge" block. Once
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that is done, we need to create the PHI node and set up the block/value
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pairs for the PHI.
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.. code-block:: ocaml
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(* Return to the start block to add the conditional branch. *)
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position_at_end start_bb builder;
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ignore (build_cond_br cond_val then_bb else_bb builder);
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Once the blocks are created, we can emit the conditional branch that
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chooses between them. Note that creating new blocks does not implicitly
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affect the IRBuilder, so it is still inserting into the block that the
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condition went into. This is why we needed to save the "start" block.
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.. code-block:: ocaml
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(* Set a unconditional branch at the end of the 'then' block and the
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* 'else' block to the 'merge' block. *)
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position_at_end new_then_bb builder; ignore (build_br merge_bb builder);
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position_at_end new_else_bb builder; ignore (build_br merge_bb builder);
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(* Finally, set the builder to the end of the merge block. *)
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position_at_end merge_bb builder;
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phi
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To finish off the blocks, we create an unconditional branch to the merge
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block. One interesting (and very important) aspect of the LLVM IR is
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that it `requires all basic blocks to be
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"terminated" <../LangRef.html#functionstructure>`_ with a `control flow
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instruction <../LangRef.html#terminators>`_ such as return or branch.
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This means that all control flow, *including fall throughs* must be made
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explicit in the LLVM IR. If you violate this rule, the verifier will
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emit an error.
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Finally, the CodeGen function returns the phi node as the value computed
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by the if/then/else expression. In our example above, this returned
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value will feed into the code for the top-level function, which will
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create the return instruction.
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Overall, we now have the ability to execute conditional code in
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Kaleidoscope. With this extension, Kaleidoscope is a fairly complete
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language that can calculate a wide variety of numeric functions. Next up
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we'll add another useful expression that is familiar from non-functional
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languages...
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'for' Loop Expression
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=====================
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Now that we know how to add basic control flow constructs to the
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language, we have the tools to add more powerful things. Lets add
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something more aggressive, a 'for' expression:
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::
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extern putchard(char);
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def printstar(n)
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for i = 1, i < n, 1.0 in
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putchard(42); # ascii 42 = '*'
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# print 100 '*' characters
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printstar(100);
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This expression defines a new variable ("i" in this case) which iterates
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from a starting value, while the condition ("i < n" in this case) is
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true, incrementing by an optional step value ("1.0" in this case). If
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the step value is omitted, it defaults to 1.0. While the loop is true,
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it executes its body expression. Because we don't have anything better
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to return, we'll just define the loop as always returning 0.0. In the
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future when we have mutable variables, it will get more useful.
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As before, lets talk about the changes that we need to Kaleidoscope to
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support this.
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Lexer Extensions for the 'for' Loop
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-----------------------------------
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The lexer extensions are the same sort of thing as for if/then/else:
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.. code-block:: ocaml
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... in Token.token ...
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(* control *)
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| If | Then | Else
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| For | In
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... in Lexer.lex_ident...
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match Buffer.contents buffer with
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| "def" -> [< 'Token.Def; stream >]
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| "extern" -> [< 'Token.Extern; stream >]
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| "if" -> [< 'Token.If; stream >]
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| "then" -> [< 'Token.Then; stream >]
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| "else" -> [< 'Token.Else; stream >]
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| "for" -> [< 'Token.For; stream >]
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| "in" -> [< 'Token.In; stream >]
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| id -> [< 'Token.Ident id; stream >]
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AST Extensions for the 'for' Loop
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---------------------------------
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The AST variant is just as simple. It basically boils down to capturing
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the variable name and the constituent expressions in the node.
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.. code-block:: ocaml
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type expr =
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...
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(* variant for for/in. *)
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| For of string * expr * expr * expr option * expr
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Parser Extensions for the 'for' Loop
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------------------------------------
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The parser code is also fairly standard. The only interesting thing here
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is handling of the optional step value. The parser code handles it by
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checking to see if the second comma is present. If not, it sets the step
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value to null in the AST node:
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.. code-block:: ocaml
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let rec parse_primary = parser
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...
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(* forexpr
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::= 'for' identifier '=' expr ',' expr (',' expr)? 'in' expression *)
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| [< 'Token.For;
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'Token.Ident id ?? "expected identifier after for";
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'Token.Kwd '=' ?? "expected '=' after for";
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stream >] ->
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begin parser
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| [<
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start=parse_expr;
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'Token.Kwd ',' ?? "expected ',' after for";
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end_=parse_expr;
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stream >] ->
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let step =
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begin parser
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| [< 'Token.Kwd ','; step=parse_expr >] -> Some step
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| [< >] -> None
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end stream
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in
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begin parser
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| [< 'Token.In; body=parse_expr >] ->
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Ast.For (id, start, end_, step, body)
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| [< >] ->
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raise (Stream.Error "expected 'in' after for")
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end stream
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| [< >] ->
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raise (Stream.Error "expected '=' after for")
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end stream
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LLVM IR for the 'for' Loop
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--------------------------
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Now we get to the good part: the LLVM IR we want to generate for this
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thing. With the simple example above, we get this LLVM IR (note that
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this dump is generated with optimizations disabled for clarity):
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.. code-block:: llvm
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declare double @putchard(double)
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define double @printstar(double %n) {
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entry:
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; initial value = 1.0 (inlined into phi)
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br label %loop
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loop: ; preds = %loop, %entry
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%i = phi double [ 1.000000e+00, %entry ], [ %nextvar, %loop ]
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; body
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%calltmp = call double @putchard(double 4.200000e+01)
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; 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>`_
|
|
|