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  <meta name="author" content="Chris Lattner">
  <meta name="author" content="Erick Tryzelaar">
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<h1>Kaleidoscope: Implementing a Parser and AST</h1>

<ul>
<li><a href="index.html">Up to Tutorial Index</a></li>
<li>Chapter 2
  <ol>
    <li><a href="#intro">Chapter 2 Introduction</a></li>
    <li><a href="#ast">The Abstract Syntax Tree (AST)</a></li>
    <li><a href="#parserbasics">Parser Basics</a></li>
    <li><a href="#parserprimexprs">Basic Expression Parsing</a></li>
    <li><a href="#parserbinops">Binary Expression Parsing</a></li>
    <li><a href="#parsertop">Parsing the Rest</a></li>
    <li><a href="#driver">The Driver</a></li>
    <li><a href="#conclusions">Conclusions</a></li>
    <li><a href="#code">Full Code Listing</a></li>
  </ol>
</li>
<li><a href="OCamlLangImpl3.html">Chapter 3</a>: Code generation to LLVM IR</li>
</ul>

<div class="doc_author">
	<p>
		Written by <a href="mailto:sabre@nondot.org">Chris Lattner</a>
		and <a href="mailto:idadesub@users.sourceforge.net">Erick Tryzelaar</a>
	</p>
</div>

<!-- *********************************************************************** -->
<h2><a name="intro">Chapter 2 Introduction</a></h2>
<!-- *********************************************************************** -->

<div>

<p>Welcome to Chapter 2 of the "<a href="index.html">Implementing a language
with LLVM in Objective Caml</a>" tutorial.  This chapter shows you how to use
the lexer, built in <a href="OCamlLangImpl1.html">Chapter 1</a>, to build a
full <a href="http://en.wikipedia.org/wiki/Parsing">parser</a> for our
Kaleidoscope language.  Once we have a parser, we'll define and build an <a
href="http://en.wikipedia.org/wiki/Abstract_syntax_tree">Abstract Syntax
Tree</a> (AST).</p>

<p>The parser we will build uses a combination of <a
href="http://en.wikipedia.org/wiki/Recursive_descent_parser">Recursive Descent
Parsing</a> and <a href=
"http://en.wikipedia.org/wiki/Operator-precedence_parser">Operator-Precedence
Parsing</a> to parse the Kaleidoscope language (the latter for
binary expressions and the former for everything else).  Before we get to
parsing though, lets talk about the output of the parser: the Abstract Syntax
Tree.</p>

</div>

<!-- *********************************************************************** -->
<h2><a name="ast">The Abstract Syntax Tree (AST)</a></h2>
<!-- *********************************************************************** -->

<div>

<p>The AST for a program captures its behavior in such a way that it is easy for
later stages of the compiler (e.g. code generation) to interpret.  We basically
want one object for each construct in the language, and the AST should closely
model the language.  In Kaleidoscope, we have expressions, a prototype, and a
function object.  We'll start with expressions first:</p>

<div class="doc_code">
<pre>
(* expr - Base type for all expression nodes. *)
type expr =
  (* variant for numeric literals like "1.0". *)
  | Number of float
</pre>
</div>

<p>The code above shows the definition of the base ExprAST class and one
subclass which we use for numeric literals.  The important thing to note about
this code is that the Number variant captures the numeric value of the
literal as an instance variable. This allows later phases of the compiler to
know what the stored numeric value is.</p>

<p>Right now we only create the AST,  so there are no useful functions on
them.  It would be very easy to add a function to pretty print the code,
for example.  Here are the other expression AST node definitions that we'll use
in the basic form of the Kaleidoscope language:
</p>

<div class="doc_code">
<pre>
  (* 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
</pre>
</div>

<p>This is all (intentionally) rather straight-forward: variables capture the
variable name, binary operators capture their opcode (e.g. '+'), and calls
capture a function name as well as a list of any argument expressions.  One thing
that is nice about our AST is that it captures the language features without
talking about the syntax of the language.  Note that there is no discussion about
precedence of binary operators, lexical structure, etc.</p>

<p>For our basic language, these are all of the expression nodes we'll define.
Because it doesn't have conditional control flow, it isn't Turing-complete;
we'll fix that in a later installment.  The two things we need next are a way
to talk about the interface to a function, and a way to talk about functions
themselves:</p>

<div class="doc_code">
<pre>
(* 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
</pre>
</div>

<p>In Kaleidoscope, functions are typed with just a count of their arguments.
Since all values are double precision floating point, the type of each argument
doesn't need to be stored anywhere.  In a more aggressive and realistic
language, the "expr" variants would probably have a type field.</p>

<p>With this scaffolding, we can now talk about parsing expressions and function
bodies in Kaleidoscope.</p>

</div>

<!-- *********************************************************************** -->
<h2><a name="parserbasics">Parser Basics</a></h2>
<!-- *********************************************************************** -->

<div>

<p>Now that we have an AST to build, we need to define the parser code to build
it.  The idea here is that we want to parse something like "x+y" (which is
returned as three tokens by the lexer) into an AST that could be generated with
calls like this:</p>

<div class="doc_code">
<pre>
  let x = Variable "x" in
  let y = Variable "y" in
  let result = Binary ('+', x, y) in
  ...
</pre>
</div>

<p>
The error handling routines make use of the builtin <tt>Stream.Failure</tt> and
<tt>Stream.Error</tt>s.  <tt>Stream.Failure</tt> is raised when the parser is
unable to find any matching token in the first position of a pattern.
<tt>Stream.Error</tt> is raised when the first token matches, but the rest do
not.  The error recovery in our parser will not be the best and is not
particular user-friendly, but it will be enough for our tutorial.  These
exceptions make it easier to handle errors in routines that have various return
types.</p>

<p>With these basic types and exceptions, we can implement the first
piece of our grammar: numeric literals.</p>

</div>

<!-- *********************************************************************** -->
<h2><a name="parserprimexprs">Basic Expression Parsing</a></h2>
<!-- *********************************************************************** -->

<div>

<p>We start with numeric literals, because they are the simplest to process.
For each production in our grammar, we'll define a function which parses that
production.  We call this class of expressions "primary" expressions, for
reasons that will become more clear <a href="OCamlLangImpl6.html#unary">
later in the tutorial</a>.  In order to parse an arbitrary primary expression,
we need to determine what sort of expression it is.  For numeric literals, we
have:</p>

<div class="doc_code">
<pre>
(* primary
 *   ::= identifier
 *   ::= numberexpr
 *   ::= parenexpr *)
parse_primary = parser
  (* numberexpr ::= number *)
  | [&lt; 'Token.Number n &gt;] -&gt; Ast.Number n
</pre>
</div>

<p>This routine is very simple: it expects to be called when the current token
is a <tt>Token.Number</tt> token.  It takes the current number value, creates
a <tt>Ast.Number</tt> node, advances the lexer to the next token, and finally
returns.</p>

<p>There are some interesting aspects to this.  The most important one is that
this routine eats all of the tokens that correspond to the production and
returns the lexer buffer with the next token (which is not part of the grammar
production) ready to go.  This is a fairly standard way to go for recursive
descent parsers.  For a better example, the parenthesis operator is defined like
this:</p>

<div class="doc_code">
<pre>
  (* parenexpr ::= '(' expression ')' *)
  | [&lt; 'Token.Kwd '('; e=parse_expr; 'Token.Kwd ')' ?? "expected ')'" &gt;] -&gt; e
</pre>
</div>

<p>This function illustrates a number of interesting things about the
parser:</p>

<p>
1) It shows how we use the <tt>Stream.Error</tt> exception.  When called, this
function expects that the current token is a '(' token, but after parsing the
subexpression, it is possible that there is no ')' waiting.  For example, if
the user types in "(4 x" instead of "(4)", the parser should emit an error.
Because errors can occur, the parser needs a way to indicate that they
happened. In our parser, we use the camlp4 shortcut syntax <tt>token ?? "parse
error"</tt>, where if the token before the <tt>??</tt> does not match, then
<tt>Stream.Error "parse error"</tt> will be raised.</p>

<p>2) Another interesting aspect of this function is that it uses recursion by
calling <tt>Parser.parse_primary</tt> (we will soon see that
<tt>Parser.parse_primary</tt> can call <tt>Parser.parse_primary</tt>).  This is
powerful because it allows us to handle recursive grammars, and keeps each
production very simple.  Note that parentheses do not cause construction of AST
nodes themselves.  While we could do it this way, the most important role of
parentheses are to guide the parser and provide grouping.  Once the parser
constructs the AST, parentheses are not needed.</p>

<p>The next simple production is for handling variable references and function
calls:</p>

<div class="doc_code">
<pre>
  (* identifierexpr
   *   ::= identifier
   *   ::= identifier '(' argumentexpr ')' *)
  | [&lt; 'Token.Ident id; stream &gt;] -&gt;
      let rec parse_args accumulator = parser
        | [&lt; e=parse_expr; stream &gt;] -&gt;
            begin parser
              | [&lt; 'Token.Kwd ','; e=parse_args (e :: accumulator) &gt;] -&gt; e
              | [&lt; &gt;] -&gt; e :: accumulator
            end stream
        | [&lt; &gt;] -&gt; accumulator
      in
      let rec parse_ident id = parser
        (* Call. *)
        | [&lt; 'Token.Kwd '(';
             args=parse_args [];
             'Token.Kwd ')' ?? "expected ')'"&gt;] -&gt;
            Ast.Call (id, Array.of_list (List.rev args))

        (* Simple variable ref. *)
        | [&lt; &gt;] -&gt; Ast.Variable id
      in
      parse_ident id stream
</pre>
</div>

<p>This routine follows the same style as the other routines.  (It expects to be
called if the current token is a <tt>Token.Ident</tt> token).  It also has
recursion and error handling.  One interesting aspect of this is that it uses
<em>look-ahead</em> to determine if the current identifier is a stand alone
variable reference or if it is a function call expression.  It handles this by
checking to see if the token after the identifier is a '(' token, constructing
either a <tt>Ast.Variable</tt> or <tt>Ast.Call</tt> node as appropriate.
</p>

<p>We finish up by raising an exception if we received a token we didn't
expect:</p>

<div class="doc_code">
<pre>
  | [&lt; &gt;] -&gt; raise (Stream.Error "unknown token when expecting an expression.")
</pre>
</div>

<p>Now that basic expressions are handled, we need to handle binary expressions.
They are a bit more complex.</p>

</div>

<!-- *********************************************************************** -->
<h2><a name="parserbinops">Binary Expression Parsing</a></h2>
<!-- *********************************************************************** -->

<div>

<p>Binary expressions are significantly harder to parse because they are often
ambiguous.  For example, when given the string "x+y*z", the parser can choose
to parse it as either "(x+y)*z" or "x+(y*z)".  With common definitions from
mathematics, we expect the later parse, because "*" (multiplication) has
higher <em>precedence</em> than "+" (addition).</p>

<p>There are many ways to handle this, but an elegant and efficient way is to
use <a href=
"http://en.wikipedia.org/wiki/Operator-precedence_parser">Operator-Precedence
Parsing</a>.  This parsing technique uses the precedence of binary operators to
guide recursion.  To start with, we need a table of precedences:</p>

<div class="doc_code">
<pre>
(* 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 -&gt; -1

...

let main () =
  (* Install standard binary operators.
   * 1 is the lowest precedence. *)
  Hashtbl.add Parser.binop_precedence '&lt;' 10;
  Hashtbl.add Parser.binop_precedence '+' 20;
  Hashtbl.add Parser.binop_precedence '-' 20;
  Hashtbl.add Parser.binop_precedence '*' 40;    (* highest. *)
  ...
</pre>
</div>

<p>For the basic form of Kaleidoscope, we will only support 4 binary operators
(this can obviously be extended by you, our brave and intrepid reader).  The
<tt>Parser.precedence</tt> function returns the precedence for the current
token, or -1 if the token is not a binary operator.  Having a <tt>Hashtbl.t</tt>
makes it easy to add new operators and makes it clear that the algorithm doesn't
depend on the specific operators involved, but it would be easy enough to
eliminate the <tt>Hashtbl.t</tt> and do the comparisons in the
<tt>Parser.precedence</tt> function.  (Or just use a fixed-size array).</p>

<p>With the helper above defined, we can now start parsing binary expressions.
The basic idea of operator precedence parsing is to break down an expression
with potentially ambiguous binary operators into pieces.  Consider ,for example,
the expression "a+b+(c+d)*e*f+g".  Operator precedence parsing considers this
as a stream of primary expressions separated by binary operators.  As such,
it will first parse the leading primary expression "a", then it will see the
pairs [+, b] [+, (c+d)] [*, e] [*, f] and [+, g].  Note that because parentheses
are primary expressions, the binary expression parser doesn't need to worry
about nested subexpressions like (c+d) at all.
</p>

<p>
To start, an expression is a primary expression potentially followed by a
sequence of [binop,primaryexpr] pairs:</p>

<div class="doc_code">
<pre>
(* expression
 *   ::= primary binoprhs *)
and parse_expr = parser
  | [&lt; lhs=parse_primary; stream &gt;] -&gt; parse_bin_rhs 0 lhs stream
</pre>
</div>

<p><tt>Parser.parse_bin_rhs</tt> is the function that parses the sequence of
pairs for us.  It takes a precedence and a pointer to an expression for the part
that has been parsed so far.   Note that "x" is a perfectly valid expression: As
such, "binoprhs" is allowed to be empty, in which case it returns the expression
that is passed into it. In our example above, the code passes the expression for
"a" into <tt>Parser.parse_bin_rhs</tt> and the current token is "+".</p>

<p>The precedence value passed into <tt>Parser.parse_bin_rhs</tt> indicates the
<em>minimal operator precedence</em> that the function is allowed to eat.  For
example, if the current pair stream is [+, x] and <tt>Parser.parse_bin_rhs</tt>
is passed in a precedence of 40, it will not consume any tokens (because the
precedence of '+' is only 20).  With this in mind, <tt>Parser.parse_bin_rhs</tt>
starts with:</p>

<div class="doc_code">
<pre>
(* 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 -&gt;
      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 &lt; expr_prec then lhs else begin
</pre>
</div>

<p>This code gets the precedence of the current token and checks to see if if is
too low.  Because we defined invalid tokens to have a precedence of -1, this
check implicitly knows that the pair-stream ends when the token stream runs out
of binary operators.  If this check succeeds, we know that the token is a binary
operator and that it will be included in this expression:</p>

<div class="doc_code">
<pre>
        (* Eat the binop. *)
        Stream.junk stream;

        (* Okay, we know this is a binop. *)
        let rhs =
          match Stream.peek stream with
          | Some (Token.Kwd c2) -&gt;
</pre>
</div>

<p>As such, this code eats (and remembers) the binary operator and then parses
the primary expression that follows.  This builds up the whole pair, the first of
which is [+, b] for the running example.</p>

<p>Now that we parsed the left-hand side of an expression and one pair of the
RHS sequence, we have to decide which way the expression associates.  In
particular, we could have "(a+b) binop unparsed"  or "a + (b binop unparsed)".
To determine this, we look ahead at "binop" to determine its precedence and
compare it to BinOp's precedence (which is '+' in this case):</p>

<div class="doc_code">
<pre>
              (* 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 &lt; next_prec
</pre>
</div>

<p>If the precedence of the binop to the right of "RHS" is lower or equal to the
precedence of our current operator, then we know that the parentheses associate
as "(a+b) binop ...".  In our example, the current operator is "+" and the next
operator is "+", we know that they have the same precedence.  In this case we'll
create the AST node for "a+b", and then continue parsing:</p>

<div class="doc_code">
<pre>
          ... if body omitted ...
        in

        (* Merge lhs/rhs. *)
        let lhs = Ast.Binary (c, lhs, rhs) in
        parse_bin_rhs expr_prec lhs stream
      end
</pre>
</div>

<p>In our example above, this will turn "a+b+" into "(a+b)" and execute the next
iteration of the loop, with "+" as the current token.  The code above will eat,
remember, and parse "(c+d)" as the primary expression, which makes the
current pair equal to [+, (c+d)].  It will then evaluate the 'if' conditional above with
"*" as the binop to the right of the primary.  In this case, the precedence of "*" is
higher than the precedence of "+" so the if condition will be entered.</p>

<p>The critical question left here is "how can the if condition parse the right
hand side in full"?  In particular, to build the AST correctly for our example,
it needs to get all of "(c+d)*e*f" as the RHS expression variable.  The code to
do this is surprisingly simple (code from the above two blocks duplicated for
context):</p>

<div class="doc_code">
<pre>
          match Stream.peek stream with
          | Some (Token.Kwd c2) -&gt;
              (* If BinOp binds less tightly with rhs than the operator after
               * rhs, let the pending operator take rhs as its lhs. *)
              if token_prec &lt; precedence c2
              then <b>parse_bin_rhs (token_prec + 1) rhs stream</b>
              else rhs
          | _ -&gt; rhs
        in

        (* Merge lhs/rhs. *)
        let lhs = Ast.Binary (c, lhs, rhs) in
        parse_bin_rhs expr_prec lhs stream
      end
</pre>
</div>

<p>At this point, we know that the binary operator to the RHS of our primary
has higher precedence than the binop we are currently parsing.  As such, we know
that any sequence of pairs whose operators are all higher precedence than "+"
should be parsed together and returned as "RHS".  To do this, we recursively
invoke the <tt>Parser.parse_bin_rhs</tt> function specifying "token_prec+1" as
the minimum precedence required for it to continue.  In our example above, this
will cause it to return the AST node for "(c+d)*e*f" as RHS, which is then set
as the RHS of the '+' expression.</p>

<p>Finally, on the next iteration of the while loop, the "+g" piece is parsed
and added to the AST.  With this little bit of code (14 non-trivial lines), we
correctly handle fully general binary expression parsing in a very elegant way.
This was a whirlwind tour of this code, and it is somewhat subtle.  I recommend
running through it with a few tough examples to see how it works.
</p>

<p>This wraps up handling of expressions.  At this point, we can point the
parser at an arbitrary token stream and build an expression from it, stopping
at the first token that is not part of the expression.  Next up we need to
handle function definitions, etc.</p>

</div>

<!-- *********************************************************************** -->
<h2><a name="parsertop">Parsing the Rest</a></h2>
<!-- *********************************************************************** -->

<div>

<p>
The next thing missing is handling of function prototypes.  In Kaleidoscope,
these are used both for 'extern' function declarations as well as function body
definitions.  The code to do this is straight-forward and not very interesting
(once you've survived expressions):
</p>

<div class="doc_code">
<pre>
(* prototype
 *   ::= id '(' id* ')' *)
let parse_prototype =
  let rec parse_args accumulator = parser
    | [&lt; 'Token.Ident id; e=parse_args (id::accumulator) &gt;] -&gt; e
    | [&lt; &gt;] -&gt; accumulator
  in

  parser
  | [&lt; 'Token.Ident id;
       'Token.Kwd '(' ?? "expected '(' in prototype";
       args=parse_args [];
       'Token.Kwd ')' ?? "expected ')' in prototype" &gt;] -&gt;
      (* success. *)
      Ast.Prototype (id, Array.of_list (List.rev args))

  | [&lt; &gt;] -&gt;
      raise (Stream.Error "expected function name in prototype")
</pre>
</div>

<p>Given this, a function definition is very simple, just a prototype plus
an expression to implement the body:</p>

<div class="doc_code">
<pre>
(* definition ::= 'def' prototype expression *)
let parse_definition = parser
  | [&lt; 'Token.Def; p=parse_prototype; e=parse_expr &gt;] -&gt;
      Ast.Function (p, e)
</pre>
</div>

<p>In addition, we support 'extern' to declare functions like 'sin' and 'cos' as
well as to support forward declaration of user functions.  These 'extern's are just
prototypes with no body:</p>

<div class="doc_code">
<pre>
(*  external ::= 'extern' prototype *)
let parse_extern = parser
  | [&lt; 'Token.Extern; e=parse_prototype &gt;] -&gt; e
</pre>
</div>

<p>Finally, we'll also let the user type in arbitrary top-level expressions and
evaluate them on the fly.  We will handle this by defining anonymous nullary
(zero argument) functions for them:</p>

<div class="doc_code">
<pre>
(* toplevelexpr ::= expression *)
let parse_toplevel = parser
  | [&lt; e=parse_expr &gt;] -&gt;
      (* Make an anonymous proto. *)
      Ast.Function (Ast.Prototype ("", [||]), e)
</pre>
</div>

<p>Now that we have all the pieces, let's build a little driver that will let us
actually <em>execute</em> this code we've built!</p>

</div>

<!-- *********************************************************************** -->
<h2><a name="driver">The Driver</a></h2>
<!-- *********************************************************************** -->

<div>

<p>The driver for this simply invokes all of the parsing pieces with a top-level
dispatch loop.  There isn't much interesting here, so I'll just include the
top-level loop.  See <a href="#code">below</a> for full code in the "Top-Level
Parsing" section.</p>

<div class="doc_code">
<pre>
(* top ::= definition | external | expression | ';' *)
let rec main_loop stream =
  match Stream.peek stream with
  | None -&gt; ()

  (* ignore top-level semicolons. *)
  | Some (Token.Kwd ';') -&gt;
      Stream.junk stream;
      main_loop stream

  | Some token -&gt;
      begin
        try match token with
        | Token.Def -&gt;
            ignore(Parser.parse_definition stream);
            print_endline "parsed a function definition.";
        | Token.Extern -&gt;
            ignore(Parser.parse_extern stream);
            print_endline "parsed an extern.";
        | _ -&gt;
            (* Evaluate a top-level expression into an anonymous function. *)
            ignore(Parser.parse_toplevel stream);
            print_endline "parsed a top-level expr";
        with Stream.Error s -&gt;
          (* Skip token for error recovery. *)
          Stream.junk stream;
          print_endline s;
      end;
      print_string "ready&gt; "; flush stdout;
      main_loop stream
</pre>
</div>

<p>The most interesting part of this is that we ignore top-level semicolons.
Why is this, you ask?  The basic reason is that if you type "4 + 5" at the
command line, the parser doesn't know whether that is the end of what you will type
or not.  For example, on the next line you could type "def foo..." in which case
4+5 is the end of a top-level expression.  Alternatively you could type "* 6",
which would continue the expression.  Having top-level semicolons allows you to
type "4+5;", and the parser will know you are done.</p>

</div>

<!-- *********************************************************************** -->
<h2><a name="conclusions">Conclusions</a></h2>
<!-- *********************************************************************** -->

<div>

<p>With just under 300 lines of commented code (240 lines of non-comment,
non-blank code), we fully defined our minimal language, including a lexer,
parser, and AST builder.  With this done, the executable will validate
Kaleidoscope code and tell us if it is grammatically invalid.  For
example, here is a sample interaction:</p>

<div class="doc_code">
<pre>
$ <b>/toy.byte</b>
ready&gt; <b>def foo(x y) x+foo(y, 4.0);</b>
Parsed a function definition.
ready&gt; <b>def foo(x y) x+y y;</b>
Parsed a function definition.
Parsed a top-level expr
ready&gt; <b>def foo(x y) x+y );</b>
Parsed a function definition.
Error: unknown token when expecting an expression
ready&gt; <b>extern sin(a);</b>
ready&gt; Parsed an extern
ready&gt; <b>^D</b>
$
</pre>
</div>

<p>There is a lot of room for extension here.  You can define new AST nodes,
extend the language in many ways, etc.  In the <a href="OCamlLangImpl3.html">
next installment</a>, we will describe how to generate LLVM Intermediate
Representation (IR) from the AST.</p>

</div>

<!-- *********************************************************************** -->
<h2><a name="code">Full Code Listing</a></h2>
<!-- *********************************************************************** -->

<div>

<p>
Here is the complete code listing for this and the previous chapter.
Note that it is fully self-contained: you don't need LLVM or any external
libraries at all for this.  (Besides the ocaml standard libraries, of
course.)  To build this, just compile with:</p>

<div class="doc_code">
<pre>
# Compile
ocamlbuild toy.byte
# Run
/toy.byte
</pre>
</div>

<p>Here is the code:</p>

<dl>
<dt>_tags:</dt>
<dd class="doc_code">
<pre>
&lt;{lexer,parser}.ml&gt;: use_camlp4, pp(camlp4of)
</pre>
</dd>

<dt>token.ml:</dt>
<dd class="doc_code">
<pre>
(*===----------------------------------------------------------------------===
 * 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
</pre>
</dd>

<dt>lexer.ml:</dt>
<dd class="doc_code">
<pre>
(*===----------------------------------------------------------------------===
 * Lexer
 *===----------------------------------------------------------------------===*)

let rec lex = parser
  (* Skip any whitespace. *)
  | [&lt; ' (' ' | '\n' | '\r' | '\t'); stream &gt;] -&gt; lex stream

  (* identifier: [a-zA-Z][a-zA-Z0-9] *)
  | [&lt; ' ('A' .. 'Z' | 'a' .. 'z' as c); stream &gt;] -&gt;
      let buffer = Buffer.create 1 in
      Buffer.add_char buffer c;
      lex_ident buffer stream

  (* number: [0-9.]+ *)
  | [&lt; ' ('0' .. '9' as c); stream &gt;] -&gt;
      let buffer = Buffer.create 1 in
      Buffer.add_char buffer c;
      lex_number buffer stream

  (* Comment until end of line. *)
  | [&lt; ' ('#'); stream &gt;] -&gt;
      lex_comment stream

  (* Otherwise, just return the character as its ascii value. *)
  | [&lt; 'c; stream &gt;] -&gt;
      [&lt; 'Token.Kwd c; lex stream &gt;]

  (* end of stream. *)
  | [&lt; &gt;] -&gt; [&lt; &gt;]

and lex_number buffer = parser
  | [&lt; ' ('0' .. '9' | '.' as c); stream &gt;] -&gt;
      Buffer.add_char buffer c;
      lex_number buffer stream
  | [&lt; stream=lex &gt;] -&gt;
      [&lt; 'Token.Number (float_of_string (Buffer.contents buffer)); stream &gt;]

and lex_ident buffer = parser
  | [&lt; ' ('A' .. 'Z' | 'a' .. 'z' | '0' .. '9' as c); stream &gt;] -&gt;
      Buffer.add_char buffer c;
      lex_ident buffer stream
  | [&lt; stream=lex &gt;] -&gt;
      match Buffer.contents buffer with
      | "def" -&gt; [&lt; 'Token.Def; stream &gt;]
      | "extern" -&gt; [&lt; 'Token.Extern; stream &gt;]
      | id -&gt; [&lt; 'Token.Ident id; stream &gt;]

and lex_comment = parser
  | [&lt; ' ('\n'); stream=lex &gt;] -&gt; stream
  | [&lt; 'c; e=lex_comment &gt;] -&gt; e
  | [&lt; &gt;] -&gt; [&lt; &gt;]
</pre>
</dd>

<dt>ast.ml:</dt>
<dd class="doc_code">
<pre>
(*===----------------------------------------------------------------------===
 * 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

(* 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
</pre>
</dd>

<dt>parser.ml:</dt>
<dd class="doc_code">
<pre>
(*===---------------------------------------------------------------------===
 * 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 -&gt; -1

(* primary
 *   ::= identifier
 *   ::= numberexpr
 *   ::= parenexpr *)
let rec parse_primary = parser
  (* numberexpr ::= number *)
  | [&lt; 'Token.Number n &gt;] -&gt; Ast.Number n

  (* parenexpr ::= '(' expression ')' *)
  | [&lt; 'Token.Kwd '('; e=parse_expr; 'Token.Kwd ')' ?? "expected ')'" &gt;] -&gt; e

  (* identifierexpr
   *   ::= identifier
   *   ::= identifier '(' argumentexpr ')' *)
  | [&lt; 'Token.Ident id; stream &gt;] -&gt;
      let rec parse_args accumulator = parser
        | [&lt; e=parse_expr; stream &gt;] -&gt;
            begin parser
              | [&lt; 'Token.Kwd ','; e=parse_args (e :: accumulator) &gt;] -&gt; e
              | [&lt; &gt;] -&gt; e :: accumulator
            end stream
        | [&lt; &gt;] -&gt; accumulator
      in
      let rec parse_ident id = parser
        (* Call. *)
        | [&lt; 'Token.Kwd '(';
             args=parse_args [];
             'Token.Kwd ')' ?? "expected ')'"&gt;] -&gt;
            Ast.Call (id, Array.of_list (List.rev args))

        (* Simple variable ref. *)
        | [&lt; &gt;] -&gt; Ast.Variable id
      in
      parse_ident id stream

  | [&lt; &gt;] -&gt; 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 -&gt;
      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 &lt; 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) -&gt;
              (* 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 &lt; next_prec
              then parse_bin_rhs (token_prec + 1) rhs stream
              else rhs
          | _ -&gt; rhs
        in

        (* Merge lhs/rhs. *)
        let lhs = Ast.Binary (c, lhs, rhs) in
        parse_bin_rhs expr_prec lhs stream
      end
  | _ -&gt; lhs

(* expression
 *   ::= primary binoprhs *)
and parse_expr = parser
  | [&lt; lhs=parse_primary; stream &gt;] -&gt; parse_bin_rhs 0 lhs stream

(* prototype
 *   ::= id '(' id* ')' *)
let parse_prototype =
  let rec parse_args accumulator = parser
    | [&lt; 'Token.Ident id; e=parse_args (id::accumulator) &gt;] -&gt; e
    | [&lt; &gt;] -&gt; accumulator
  in

  parser
  | [&lt; 'Token.Ident id;
       'Token.Kwd '(' ?? "expected '(' in prototype";
       args=parse_args [];
       'Token.Kwd ')' ?? "expected ')' in prototype" &gt;] -&gt;
      (* success. *)
      Ast.Prototype (id, Array.of_list (List.rev args))

  | [&lt; &gt;] -&gt;
      raise (Stream.Error "expected function name in prototype")

(* definition ::= 'def' prototype expression *)
let parse_definition = parser
  | [&lt; 'Token.Def; p=parse_prototype; e=parse_expr &gt;] -&gt;
      Ast.Function (p, e)

(* toplevelexpr ::= expression *)
let parse_toplevel = parser
  | [&lt; e=parse_expr &gt;] -&gt;
      (* Make an anonymous proto. *)
      Ast.Function (Ast.Prototype ("", [||]), e)

(*  external ::= 'extern' prototype *)
let parse_extern = parser
  | [&lt; 'Token.Extern; e=parse_prototype &gt;] -&gt; e
</pre>
</dd>

<dt>toplevel.ml:</dt>
<dd class="doc_code">
<pre>
(*===----------------------------------------------------------------------===
 * Top-Level parsing and JIT Driver
 *===----------------------------------------------------------------------===*)

(* top ::= definition | external | expression | ';' *)
let rec main_loop stream =
  match Stream.peek stream with
  | None -&gt; ()

  (* ignore top-level semicolons. *)
  | Some (Token.Kwd ';') -&gt;
      Stream.junk stream;
      main_loop stream

  | Some token -&gt;
      begin
        try match token with
        | Token.Def -&gt;
            ignore(Parser.parse_definition stream);
            print_endline "parsed a function definition.";
        | Token.Extern -&gt;
            ignore(Parser.parse_extern stream);
            print_endline "parsed an extern.";
        | _ -&gt;
            (* Evaluate a top-level expression into an anonymous function. *)
            ignore(Parser.parse_toplevel stream);
            print_endline "parsed a top-level expr";
        with Stream.Error s -&gt;
          (* Skip token for error recovery. *)
          Stream.junk stream;
          print_endline s;
      end;
      print_string "ready&gt; "; flush stdout;
      main_loop stream
</pre>
</dd>

<dt>toy.ml:</dt>
<dd class="doc_code">
<pre>
(*===----------------------------------------------------------------------===
 * Main driver code.
 *===----------------------------------------------------------------------===*)

let main () =
  (* Install standard binary operators.
   * 1 is the lowest precedence. *)
  Hashtbl.add Parser.binop_precedence '&lt;' 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&gt; "; flush stdout;
  let stream = Lexer.lex (Stream.of_channel stdin) in

  (* Run the main "interpreter loop" now. *)
  Toplevel.main_loop stream;
;;

main ()
</pre>
</dd>
</dl>

<a href="OCamlLangImpl3.html">Next: Implementing Code Generation to LLVM IR</a>
</div>

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