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6  <title>Kaleidoscope: Implementing a Parser and AST</title>
7  <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
8  <meta name="author" content="Chris Lattner">
9  <meta name="author" content="Erick Tryzelaar">
10  <link rel="stylesheet" href="../llvm.css" type="text/css">
11</head>
12
13<body>
14
15<h1>Kaleidoscope: Implementing a Parser and AST</h1>
16
17<ul>
18<li><a href="index.html">Up to Tutorial Index</a></li>
19<li>Chapter 2
20  <ol>
21    <li><a href="#intro">Chapter 2 Introduction</a></li>
22    <li><a href="#ast">The Abstract Syntax Tree (AST)</a></li>
23    <li><a href="#parserbasics">Parser Basics</a></li>
24    <li><a href="#parserprimexprs">Basic Expression Parsing</a></li>
25    <li><a href="#parserbinops">Binary Expression Parsing</a></li>
26    <li><a href="#parsertop">Parsing the Rest</a></li>
27    <li><a href="#driver">The Driver</a></li>
28    <li><a href="#conclusions">Conclusions</a></li>
29    <li><a href="#code">Full Code Listing</a></li>
30  </ol>
31</li>
32<li><a href="OCamlLangImpl3.html">Chapter 3</a>: Code generation to LLVM IR</li>
33</ul>
34
35<div class="doc_author">
36	<p>
37		Written by <a href="mailto:sabre@nondot.org">Chris Lattner</a>
38		and <a href="mailto:idadesub@users.sourceforge.net">Erick Tryzelaar</a>
39	</p>
40</div>
41
42<!-- *********************************************************************** -->
43<h2><a name="intro">Chapter 2 Introduction</a></h2>
44<!-- *********************************************************************** -->
45
46<div>
47
48<p>Welcome to Chapter 2 of the "<a href="index.html">Implementing a language
49with LLVM in Objective Caml</a>" tutorial.  This chapter shows you how to use
50the lexer, built in <a href="OCamlLangImpl1.html">Chapter 1</a>, to build a
51full <a href="http://en.wikipedia.org/wiki/Parsing">parser</a> for our
52Kaleidoscope language.  Once we have a parser, we'll define and build an <a
53href="http://en.wikipedia.org/wiki/Abstract_syntax_tree">Abstract Syntax
54Tree</a> (AST).</p>
55
56<p>The parser we will build uses a combination of <a
57href="http://en.wikipedia.org/wiki/Recursive_descent_parser">Recursive Descent
58Parsing</a> and <a href=
59"http://en.wikipedia.org/wiki/Operator-precedence_parser">Operator-Precedence
60Parsing</a> to parse the Kaleidoscope language (the latter for
61binary expressions and the former for everything else).  Before we get to
62parsing though, lets talk about the output of the parser: the Abstract Syntax
63Tree.</p>
64
65</div>
66
67<!-- *********************************************************************** -->
68<h2><a name="ast">The Abstract Syntax Tree (AST)</a></h2>
69<!-- *********************************************************************** -->
70
71<div>
72
73<p>The AST for a program captures its behavior in such a way that it is easy for
74later stages of the compiler (e.g. code generation) to interpret.  We basically
75want one object for each construct in the language, and the AST should closely
76model the language.  In Kaleidoscope, we have expressions, a prototype, and a
77function object.  We'll start with expressions first:</p>
78
79<div class="doc_code">
80<pre>
81(* expr - Base type for all expression nodes. *)
82type expr =
83  (* variant for numeric literals like "1.0". *)
84  | Number of float
85</pre>
86</div>
87
88<p>The code above shows the definition of the base ExprAST class and one
89subclass which we use for numeric literals.  The important thing to note about
90this code is that the Number variant captures the numeric value of the
91literal as an instance variable. This allows later phases of the compiler to
92know what the stored numeric value is.</p>
93
94<p>Right now we only create the AST,  so there are no useful functions on
95them.  It would be very easy to add a function to pretty print the code,
96for example.  Here are the other expression AST node definitions that we'll use
97in the basic form of the Kaleidoscope language:
98</p>
99
100<div class="doc_code">
101<pre>
102  (* variant for referencing a variable, like "a". *)
103  | Variable of string
104
105  (* variant for a binary operator. *)
106  | Binary of char * expr * expr
107
108  (* variant for function calls. *)
109  | Call of string * expr array
110</pre>
111</div>
112
113<p>This is all (intentionally) rather straight-forward: variables capture the
114variable name, binary operators capture their opcode (e.g. '+'), and calls
115capture a function name as well as a list of any argument expressions.  One thing
116that is nice about our AST is that it captures the language features without
117talking about the syntax of the language.  Note that there is no discussion about
118precedence of binary operators, lexical structure, etc.</p>
119
120<p>For our basic language, these are all of the expression nodes we'll define.
121Because it doesn't have conditional control flow, it isn't Turing-complete;
122we'll fix that in a later installment.  The two things we need next are a way
123to talk about the interface to a function, and a way to talk about functions
124themselves:</p>
125
126<div class="doc_code">
127<pre>
128(* proto - This type represents the "prototype" for a function, which captures
129 * its name, and its argument names (thus implicitly the number of arguments the
130 * function takes). *)
131type proto = Prototype of string * string array
132
133(* func - This type represents a function definition itself. *)
134type func = Function of proto * expr
135</pre>
136</div>
137
138<p>In Kaleidoscope, functions are typed with just a count of their arguments.
139Since all values are double precision floating point, the type of each argument
140doesn't need to be stored anywhere.  In a more aggressive and realistic
141language, the "expr" variants would probably have a type field.</p>
142
143<p>With this scaffolding, we can now talk about parsing expressions and function
144bodies in Kaleidoscope.</p>
145
146</div>
147
148<!-- *********************************************************************** -->
149<h2><a name="parserbasics">Parser Basics</a></h2>
150<!-- *********************************************************************** -->
151
152<div>
153
154<p>Now that we have an AST to build, we need to define the parser code to build
155it.  The idea here is that we want to parse something like "x+y" (which is
156returned as three tokens by the lexer) into an AST that could be generated with
157calls like this:</p>
158
159<div class="doc_code">
160<pre>
161  let x = Variable "x" in
162  let y = Variable "y" in
163  let result = Binary ('+', x, y) in
164  ...
165</pre>
166</div>
167
168<p>
169The error handling routines make use of the builtin <tt>Stream.Failure</tt> and
170<tt>Stream.Error</tt>s.  <tt>Stream.Failure</tt> is raised when the parser is
171unable to find any matching token in the first position of a pattern.
172<tt>Stream.Error</tt> is raised when the first token matches, but the rest do
173not.  The error recovery in our parser will not be the best and is not
174particular user-friendly, but it will be enough for our tutorial.  These
175exceptions make it easier to handle errors in routines that have various return
176types.</p>
177
178<p>With these basic types and exceptions, we can implement the first
179piece of our grammar: numeric literals.</p>
180
181</div>
182
183<!-- *********************************************************************** -->
184<h2><a name="parserprimexprs">Basic Expression Parsing</a></h2>
185<!-- *********************************************************************** -->
186
187<div>
188
189<p>We start with numeric literals, because they are the simplest to process.
190For each production in our grammar, we'll define a function which parses that
191production.  We call this class of expressions "primary" expressions, for
192reasons that will become more clear <a href="OCamlLangImpl6.html#unary">
193later in the tutorial</a>.  In order to parse an arbitrary primary expression,
194we need to determine what sort of expression it is.  For numeric literals, we
195have:</p>
196
197<div class="doc_code">
198<pre>
199(* primary
200 *   ::= identifier
201 *   ::= numberexpr
202 *   ::= parenexpr *)
203parse_primary = parser
204  (* numberexpr ::= number *)
205  | [&lt; 'Token.Number n &gt;] -&gt; Ast.Number n
206</pre>
207</div>
208
209<p>This routine is very simple: it expects to be called when the current token
210is a <tt>Token.Number</tt> token.  It takes the current number value, creates
211a <tt>Ast.Number</tt> node, advances the lexer to the next token, and finally
212returns.</p>
213
214<p>There are some interesting aspects to this.  The most important one is that
215this routine eats all of the tokens that correspond to the production and
216returns the lexer buffer with the next token (which is not part of the grammar
217production) ready to go.  This is a fairly standard way to go for recursive
218descent parsers.  For a better example, the parenthesis operator is defined like
219this:</p>
220
221<div class="doc_code">
222<pre>
223  (* parenexpr ::= '(' expression ')' *)
224  | [&lt; 'Token.Kwd '('; e=parse_expr; 'Token.Kwd ')' ?? "expected ')'" &gt;] -&gt; e
225</pre>
226</div>
227
228<p>This function illustrates a number of interesting things about the
229parser:</p>
230
231<p>
2321) It shows how we use the <tt>Stream.Error</tt> exception.  When called, this
233function expects that the current token is a '(' token, but after parsing the
234subexpression, it is possible that there is no ')' waiting.  For example, if
235the user types in "(4 x" instead of "(4)", the parser should emit an error.
236Because errors can occur, the parser needs a way to indicate that they
237happened. In our parser, we use the camlp4 shortcut syntax <tt>token ?? "parse
238error"</tt>, where if the token before the <tt>??</tt> does not match, then
239<tt>Stream.Error "parse error"</tt> will be raised.</p>
240
241<p>2) Another interesting aspect of this function is that it uses recursion by
242calling <tt>Parser.parse_primary</tt> (we will soon see that
243<tt>Parser.parse_primary</tt> can call <tt>Parser.parse_primary</tt>).  This is
244powerful because it allows us to handle recursive grammars, and keeps each
245production very simple.  Note that parentheses do not cause construction of AST
246nodes themselves.  While we could do it this way, the most important role of
247parentheses are to guide the parser and provide grouping.  Once the parser
248constructs the AST, parentheses are not needed.</p>
249
250<p>The next simple production is for handling variable references and function
251calls:</p>
252
253<div class="doc_code">
254<pre>
255  (* identifierexpr
256   *   ::= identifier
257   *   ::= identifier '(' argumentexpr ')' *)
258  | [&lt; 'Token.Ident id; stream &gt;] -&gt;
259      let rec parse_args accumulator = parser
260        | [&lt; e=parse_expr; stream &gt;] -&gt;
261            begin parser
262              | [&lt; 'Token.Kwd ','; e=parse_args (e :: accumulator) &gt;] -&gt; e
263              | [&lt; &gt;] -&gt; e :: accumulator
264            end stream
265        | [&lt; &gt;] -&gt; accumulator
266      in
267      let rec parse_ident id = parser
268        (* Call. *)
269        | [&lt; 'Token.Kwd '(';
270             args=parse_args [];
271             'Token.Kwd ')' ?? "expected ')'"&gt;] -&gt;
272            Ast.Call (id, Array.of_list (List.rev args))
273
274        (* Simple variable ref. *)
275        | [&lt; &gt;] -&gt; Ast.Variable id
276      in
277      parse_ident id stream
278</pre>
279</div>
280
281<p>This routine follows the same style as the other routines.  (It expects to be
282called if the current token is a <tt>Token.Ident</tt> token).  It also has
283recursion and error handling.  One interesting aspect of this is that it uses
284<em>look-ahead</em> to determine if the current identifier is a stand alone
285variable reference or if it is a function call expression.  It handles this by
286checking to see if the token after the identifier is a '(' token, constructing
287either a <tt>Ast.Variable</tt> or <tt>Ast.Call</tt> node as appropriate.
288</p>
289
290<p>We finish up by raising an exception if we received a token we didn't
291expect:</p>
292
293<div class="doc_code">
294<pre>
295  | [&lt; &gt;] -&gt; raise (Stream.Error "unknown token when expecting an expression.")
296</pre>
297</div>
298
299<p>Now that basic expressions are handled, we need to handle binary expressions.
300They are a bit more complex.</p>
301
302</div>
303
304<!-- *********************************************************************** -->
305<h2><a name="parserbinops">Binary Expression Parsing</a></h2>
306<!-- *********************************************************************** -->
307
308<div>
309
310<p>Binary expressions are significantly harder to parse because they are often
311ambiguous.  For example, when given the string "x+y*z", the parser can choose
312to parse it as either "(x+y)*z" or "x+(y*z)".  With common definitions from
313mathematics, we expect the later parse, because "*" (multiplication) has
314higher <em>precedence</em> than "+" (addition).</p>
315
316<p>There are many ways to handle this, but an elegant and efficient way is to
317use <a href=
318"http://en.wikipedia.org/wiki/Operator-precedence_parser">Operator-Precedence
319Parsing</a>.  This parsing technique uses the precedence of binary operators to
320guide recursion.  To start with, we need a table of precedences:</p>
321
322<div class="doc_code">
323<pre>
324(* binop_precedence - This holds the precedence for each binary operator that is
325 * defined *)
326let binop_precedence:(char, int) Hashtbl.t = Hashtbl.create 10
327
328(* precedence - Get the precedence of the pending binary operator token. *)
329let precedence c = try Hashtbl.find binop_precedence c with Not_found -&gt; -1
330
331...
332
333let main () =
334  (* Install standard binary operators.
335   * 1 is the lowest precedence. *)
336  Hashtbl.add Parser.binop_precedence '&lt;' 10;
337  Hashtbl.add Parser.binop_precedence '+' 20;
338  Hashtbl.add Parser.binop_precedence '-' 20;
339  Hashtbl.add Parser.binop_precedence '*' 40;    (* highest. *)
340  ...
341</pre>
342</div>
343
344<p>For the basic form of Kaleidoscope, we will only support 4 binary operators
345(this can obviously be extended by you, our brave and intrepid reader).  The
346<tt>Parser.precedence</tt> function returns the precedence for the current
347token, or -1 if the token is not a binary operator.  Having a <tt>Hashtbl.t</tt>
348makes it easy to add new operators and makes it clear that the algorithm doesn't
349depend on the specific operators involved, but it would be easy enough to
350eliminate the <tt>Hashtbl.t</tt> and do the comparisons in the
351<tt>Parser.precedence</tt> function.  (Or just use a fixed-size array).</p>
352
353<p>With the helper above defined, we can now start parsing binary expressions.
354The basic idea of operator precedence parsing is to break down an expression
355with potentially ambiguous binary operators into pieces.  Consider ,for example,
356the expression "a+b+(c+d)*e*f+g".  Operator precedence parsing considers this
357as a stream of primary expressions separated by binary operators.  As such,
358it will first parse the leading primary expression "a", then it will see the
359pairs [+, b] [+, (c+d)] [*, e] [*, f] and [+, g].  Note that because parentheses
360are primary expressions, the binary expression parser doesn't need to worry
361about nested subexpressions like (c+d) at all.
362</p>
363
364<p>
365To start, an expression is a primary expression potentially followed by a
366sequence of [binop,primaryexpr] pairs:</p>
367
368<div class="doc_code">
369<pre>
370(* expression
371 *   ::= primary binoprhs *)
372and parse_expr = parser
373  | [&lt; lhs=parse_primary; stream &gt;] -&gt; parse_bin_rhs 0 lhs stream
374</pre>
375</div>
376
377<p><tt>Parser.parse_bin_rhs</tt> is the function that parses the sequence of
378pairs for us.  It takes a precedence and a pointer to an expression for the part
379that has been parsed so far.   Note that "x" is a perfectly valid expression: As
380such, "binoprhs" is allowed to be empty, in which case it returns the expression
381that is passed into it. In our example above, the code passes the expression for
382"a" into <tt>Parser.parse_bin_rhs</tt> and the current token is "+".</p>
383
384<p>The precedence value passed into <tt>Parser.parse_bin_rhs</tt> indicates the
385<em>minimal operator precedence</em> that the function is allowed to eat.  For
386example, if the current pair stream is [+, x] and <tt>Parser.parse_bin_rhs</tt>
387is passed in a precedence of 40, it will not consume any tokens (because the
388precedence of '+' is only 20).  With this in mind, <tt>Parser.parse_bin_rhs</tt>
389starts with:</p>
390
391<div class="doc_code">
392<pre>
393(* binoprhs
394 *   ::= ('+' primary)* *)
395and parse_bin_rhs expr_prec lhs stream =
396  match Stream.peek stream with
397  (* If this is a binop, find its precedence. *)
398  | Some (Token.Kwd c) when Hashtbl.mem binop_precedence c -&gt;
399      let token_prec = precedence c in
400
401      (* If this is a binop that binds at least as tightly as the current binop,
402       * consume it, otherwise we are done. *)
403      if token_prec &lt; expr_prec then lhs else begin
404</pre>
405</div>
406
407<p>This code gets the precedence of the current token and checks to see if if is
408too low.  Because we defined invalid tokens to have a precedence of -1, this
409check implicitly knows that the pair-stream ends when the token stream runs out
410of binary operators.  If this check succeeds, we know that the token is a binary
411operator and that it will be included in this expression:</p>
412
413<div class="doc_code">
414<pre>
415        (* Eat the binop. *)
416        Stream.junk stream;
417
418        (* Okay, we know this is a binop. *)
419        let rhs =
420          match Stream.peek stream with
421          | Some (Token.Kwd c2) -&gt;
422</pre>
423</div>
424
425<p>As such, this code eats (and remembers) the binary operator and then parses
426the primary expression that follows.  This builds up the whole pair, the first of
427which is [+, b] for the running example.</p>
428
429<p>Now that we parsed the left-hand side of an expression and one pair of the
430RHS sequence, we have to decide which way the expression associates.  In
431particular, we could have "(a+b) binop unparsed"  or "a + (b binop unparsed)".
432To determine this, we look ahead at "binop" to determine its precedence and
433compare it to BinOp's precedence (which is '+' in this case):</p>
434
435<div class="doc_code">
436<pre>
437              (* If BinOp binds less tightly with rhs than the operator after
438               * rhs, let the pending operator take rhs as its lhs. *)
439              let next_prec = precedence c2 in
440              if token_prec &lt; next_prec
441</pre>
442</div>
443
444<p>If the precedence of the binop to the right of "RHS" is lower or equal to the
445precedence of our current operator, then we know that the parentheses associate
446as "(a+b) binop ...".  In our example, the current operator is "+" and the next
447operator is "+", we know that they have the same precedence.  In this case we'll
448create the AST node for "a+b", and then continue parsing:</p>
449
450<div class="doc_code">
451<pre>
452          ... if body omitted ...
453        in
454
455        (* Merge lhs/rhs. *)
456        let lhs = Ast.Binary (c, lhs, rhs) in
457        parse_bin_rhs expr_prec lhs stream
458      end
459</pre>
460</div>
461
462<p>In our example above, this will turn "a+b+" into "(a+b)" and execute the next
463iteration of the loop, with "+" as the current token.  The code above will eat,
464remember, and parse "(c+d)" as the primary expression, which makes the
465current pair equal to [+, (c+d)].  It will then evaluate the 'if' conditional above with
466"*" as the binop to the right of the primary.  In this case, the precedence of "*" is
467higher than the precedence of "+" so the if condition will be entered.</p>
468
469<p>The critical question left here is "how can the if condition parse the right
470hand side in full"?  In particular, to build the AST correctly for our example,
471it needs to get all of "(c+d)*e*f" as the RHS expression variable.  The code to
472do this is surprisingly simple (code from the above two blocks duplicated for
473context):</p>
474
475<div class="doc_code">
476<pre>
477          match Stream.peek stream with
478          | Some (Token.Kwd c2) -&gt;
479              (* If BinOp binds less tightly with rhs than the operator after
480               * rhs, let the pending operator take rhs as its lhs. *)
481              if token_prec &lt; precedence c2
482              then <b>parse_bin_rhs (token_prec + 1) rhs stream</b>
483              else rhs
484          | _ -&gt; rhs
485        in
486
487        (* Merge lhs/rhs. *)
488        let lhs = Ast.Binary (c, lhs, rhs) in
489        parse_bin_rhs expr_prec lhs stream
490      end
491</pre>
492</div>
493
494<p>At this point, we know that the binary operator to the RHS of our primary
495has higher precedence than the binop we are currently parsing.  As such, we know
496that any sequence of pairs whose operators are all higher precedence than "+"
497should be parsed together and returned as "RHS".  To do this, we recursively
498invoke the <tt>Parser.parse_bin_rhs</tt> function specifying "token_prec+1" as
499the minimum precedence required for it to continue.  In our example above, this
500will cause it to return the AST node for "(c+d)*e*f" as RHS, which is then set
501as the RHS of the '+' expression.</p>
502
503<p>Finally, on the next iteration of the while loop, the "+g" piece is parsed
504and added to the AST.  With this little bit of code (14 non-trivial lines), we
505correctly handle fully general binary expression parsing in a very elegant way.
506This was a whirlwind tour of this code, and it is somewhat subtle.  I recommend
507running through it with a few tough examples to see how it works.
508</p>
509
510<p>This wraps up handling of expressions.  At this point, we can point the
511parser at an arbitrary token stream and build an expression from it, stopping
512at the first token that is not part of the expression.  Next up we need to
513handle function definitions, etc.</p>
514
515</div>
516
517<!-- *********************************************************************** -->
518<h2><a name="parsertop">Parsing the Rest</a></h2>
519<!-- *********************************************************************** -->
520
521<div>
522
523<p>
524The next thing missing is handling of function prototypes.  In Kaleidoscope,
525these are used both for 'extern' function declarations as well as function body
526definitions.  The code to do this is straight-forward and not very interesting
527(once you've survived expressions):
528</p>
529
530<div class="doc_code">
531<pre>
532(* prototype
533 *   ::= id '(' id* ')' *)
534let parse_prototype =
535  let rec parse_args accumulator = parser
536    | [&lt; 'Token.Ident id; e=parse_args (id::accumulator) &gt;] -&gt; e
537    | [&lt; &gt;] -&gt; accumulator
538  in
539
540  parser
541  | [&lt; 'Token.Ident id;
542       'Token.Kwd '(' ?? "expected '(' in prototype";
543       args=parse_args [];
544       'Token.Kwd ')' ?? "expected ')' in prototype" &gt;] -&gt;
545      (* success. *)
546      Ast.Prototype (id, Array.of_list (List.rev args))
547
548  | [&lt; &gt;] -&gt;
549      raise (Stream.Error "expected function name in prototype")
550</pre>
551</div>
552
553<p>Given this, a function definition is very simple, just a prototype plus
554an expression to implement the body:</p>
555
556<div class="doc_code">
557<pre>
558(* definition ::= 'def' prototype expression *)
559let parse_definition = parser
560  | [&lt; 'Token.Def; p=parse_prototype; e=parse_expr &gt;] -&gt;
561      Ast.Function (p, e)
562</pre>
563</div>
564
565<p>In addition, we support 'extern' to declare functions like 'sin' and 'cos' as
566well as to support forward declaration of user functions.  These 'extern's are just
567prototypes with no body:</p>
568
569<div class="doc_code">
570<pre>
571(*  external ::= 'extern' prototype *)
572let parse_extern = parser
573  | [&lt; 'Token.Extern; e=parse_prototype &gt;] -&gt; e
574</pre>
575</div>
576
577<p>Finally, we'll also let the user type in arbitrary top-level expressions and
578evaluate them on the fly.  We will handle this by defining anonymous nullary
579(zero argument) functions for them:</p>
580
581<div class="doc_code">
582<pre>
583(* toplevelexpr ::= expression *)
584let parse_toplevel = parser
585  | [&lt; e=parse_expr &gt;] -&gt;
586      (* Make an anonymous proto. *)
587      Ast.Function (Ast.Prototype ("", [||]), e)
588</pre>
589</div>
590
591<p>Now that we have all the pieces, let's build a little driver that will let us
592actually <em>execute</em> this code we've built!</p>
593
594</div>
595
596<!-- *********************************************************************** -->
597<h2><a name="driver">The Driver</a></h2>
598<!-- *********************************************************************** -->
599
600<div>
601
602<p>The driver for this simply invokes all of the parsing pieces with a top-level
603dispatch loop.  There isn't much interesting here, so I'll just include the
604top-level loop.  See <a href="#code">below</a> for full code in the "Top-Level
605Parsing" section.</p>
606
607<div class="doc_code">
608<pre>
609(* top ::= definition | external | expression | ';' *)
610let rec main_loop stream =
611  match Stream.peek stream with
612  | None -&gt; ()
613
614  (* ignore top-level semicolons. *)
615  | Some (Token.Kwd ';') -&gt;
616      Stream.junk stream;
617      main_loop stream
618
619  | Some token -&gt;
620      begin
621        try match token with
622        | Token.Def -&gt;
623            ignore(Parser.parse_definition stream);
624            print_endline "parsed a function definition.";
625        | Token.Extern -&gt;
626            ignore(Parser.parse_extern stream);
627            print_endline "parsed an extern.";
628        | _ -&gt;
629            (* Evaluate a top-level expression into an anonymous function. *)
630            ignore(Parser.parse_toplevel stream);
631            print_endline "parsed a top-level expr";
632        with Stream.Error s -&gt;
633          (* Skip token for error recovery. *)
634          Stream.junk stream;
635          print_endline s;
636      end;
637      print_string "ready&gt; "; flush stdout;
638      main_loop stream
639</pre>
640</div>
641
642<p>The most interesting part of this is that we ignore top-level semicolons.
643Why is this, you ask?  The basic reason is that if you type "4 + 5" at the
644command line, the parser doesn't know whether that is the end of what you will type
645or not.  For example, on the next line you could type "def foo..." in which case
6464+5 is the end of a top-level expression.  Alternatively you could type "* 6",
647which would continue the expression.  Having top-level semicolons allows you to
648type "4+5;", and the parser will know you are done.</p>
649
650</div>
651
652<!-- *********************************************************************** -->
653<h2><a name="conclusions">Conclusions</a></h2>
654<!-- *********************************************************************** -->
655
656<div>
657
658<p>With just under 300 lines of commented code (240 lines of non-comment,
659non-blank code), we fully defined our minimal language, including a lexer,
660parser, and AST builder.  With this done, the executable will validate
661Kaleidoscope code and tell us if it is grammatically invalid.  For
662example, here is a sample interaction:</p>
663
664<div class="doc_code">
665<pre>
666$ <b>./toy.byte</b>
667ready&gt; <b>def foo(x y) x+foo(y, 4.0);</b>
668Parsed a function definition.
669ready&gt; <b>def foo(x y) x+y y;</b>
670Parsed a function definition.
671Parsed a top-level expr
672ready&gt; <b>def foo(x y) x+y );</b>
673Parsed a function definition.
674Error: unknown token when expecting an expression
675ready&gt; <b>extern sin(a);</b>
676ready&gt; Parsed an extern
677ready&gt; <b>^D</b>
678$
679</pre>
680</div>
681
682<p>There is a lot of room for extension here.  You can define new AST nodes,
683extend the language in many ways, etc.  In the <a href="OCamlLangImpl3.html">
684next installment</a>, we will describe how to generate LLVM Intermediate
685Representation (IR) from the AST.</p>
686
687</div>
688
689<!-- *********************************************************************** -->
690<h2><a name="code">Full Code Listing</a></h2>
691<!-- *********************************************************************** -->
692
693<div>
694
695<p>
696Here is the complete code listing for this and the previous chapter.
697Note that it is fully self-contained: you don't need LLVM or any external
698libraries at all for this.  (Besides the ocaml standard libraries, of
699course.)  To build this, just compile with:</p>
700
701<div class="doc_code">
702<pre>
703# Compile
704ocamlbuild toy.byte
705# Run
706./toy.byte
707</pre>
708</div>
709
710<p>Here is the code:</p>
711
712<dl>
713<dt>_tags:</dt>
714<dd class="doc_code">
715<pre>
716&lt;{lexer,parser}.ml&gt;: use_camlp4, pp(camlp4of)
717</pre>
718</dd>
719
720<dt>token.ml:</dt>
721<dd class="doc_code">
722<pre>
723(*===----------------------------------------------------------------------===
724 * Lexer Tokens
725 *===----------------------------------------------------------------------===*)
726
727(* The lexer returns these 'Kwd' if it is an unknown character, otherwise one of
728 * these others for known things. *)
729type token =
730  (* commands *)
731  | Def | Extern
732
733  (* primary *)
734  | Ident of string | Number of float
735
736  (* unknown *)
737  | Kwd of char
738</pre>
739</dd>
740
741<dt>lexer.ml:</dt>
742<dd class="doc_code">
743<pre>
744(*===----------------------------------------------------------------------===
745 * Lexer
746 *===----------------------------------------------------------------------===*)
747
748let rec lex = parser
749  (* Skip any whitespace. *)
750  | [&lt; ' (' ' | '\n' | '\r' | '\t'); stream &gt;] -&gt; lex stream
751
752  (* identifier: [a-zA-Z][a-zA-Z0-9] *)
753  | [&lt; ' ('A' .. 'Z' | 'a' .. 'z' as c); stream &gt;] -&gt;
754      let buffer = Buffer.create 1 in
755      Buffer.add_char buffer c;
756      lex_ident buffer stream
757
758  (* number: [0-9.]+ *)
759  | [&lt; ' ('0' .. '9' as c); stream &gt;] -&gt;
760      let buffer = Buffer.create 1 in
761      Buffer.add_char buffer c;
762      lex_number buffer stream
763
764  (* Comment until end of line. *)
765  | [&lt; ' ('#'); stream &gt;] -&gt;
766      lex_comment stream
767
768  (* Otherwise, just return the character as its ascii value. *)
769  | [&lt; 'c; stream &gt;] -&gt;
770      [&lt; 'Token.Kwd c; lex stream &gt;]
771
772  (* end of stream. *)
773  | [&lt; &gt;] -&gt; [&lt; &gt;]
774
775and lex_number buffer = parser
776  | [&lt; ' ('0' .. '9' | '.' as c); stream &gt;] -&gt;
777      Buffer.add_char buffer c;
778      lex_number buffer stream
779  | [&lt; stream=lex &gt;] -&gt;
780      [&lt; 'Token.Number (float_of_string (Buffer.contents buffer)); stream &gt;]
781
782and lex_ident buffer = parser
783  | [&lt; ' ('A' .. 'Z' | 'a' .. 'z' | '0' .. '9' as c); stream &gt;] -&gt;
784      Buffer.add_char buffer c;
785      lex_ident buffer stream
786  | [&lt; stream=lex &gt;] -&gt;
787      match Buffer.contents buffer with
788      | "def" -&gt; [&lt; 'Token.Def; stream &gt;]
789      | "extern" -&gt; [&lt; 'Token.Extern; stream &gt;]
790      | id -&gt; [&lt; 'Token.Ident id; stream &gt;]
791
792and lex_comment = parser
793  | [&lt; ' ('\n'); stream=lex &gt;] -&gt; stream
794  | [&lt; 'c; e=lex_comment &gt;] -&gt; e
795  | [&lt; &gt;] -&gt; [&lt; &gt;]
796</pre>
797</dd>
798
799<dt>ast.ml:</dt>
800<dd class="doc_code">
801<pre>
802(*===----------------------------------------------------------------------===
803 * Abstract Syntax Tree (aka Parse Tree)
804 *===----------------------------------------------------------------------===*)
805
806(* expr - Base type for all expression nodes. *)
807type expr =
808  (* variant for numeric literals like "1.0". *)
809  | Number of float
810
811  (* variant for referencing a variable, like "a". *)
812  | Variable of string
813
814  (* variant for a binary operator. *)
815  | Binary of char * expr * expr
816
817  (* variant for function calls. *)
818  | Call of string * expr array
819
820(* proto - This type represents the "prototype" for a function, which captures
821 * its name, and its argument names (thus implicitly the number of arguments the
822 * function takes). *)
823type proto = Prototype of string * string array
824
825(* func - This type represents a function definition itself. *)
826type func = Function of proto * expr
827</pre>
828</dd>
829
830<dt>parser.ml:</dt>
831<dd class="doc_code">
832<pre>
833(*===---------------------------------------------------------------------===
834 * Parser
835 *===---------------------------------------------------------------------===*)
836
837(* binop_precedence - This holds the precedence for each binary operator that is
838 * defined *)
839let binop_precedence:(char, int) Hashtbl.t = Hashtbl.create 10
840
841(* precedence - Get the precedence of the pending binary operator token. *)
842let precedence c = try Hashtbl.find binop_precedence c with Not_found -&gt; -1
843
844(* primary
845 *   ::= identifier
846 *   ::= numberexpr
847 *   ::= parenexpr *)
848let rec parse_primary = parser
849  (* numberexpr ::= number *)
850  | [&lt; 'Token.Number n &gt;] -&gt; Ast.Number n
851
852  (* parenexpr ::= '(' expression ')' *)
853  | [&lt; 'Token.Kwd '('; e=parse_expr; 'Token.Kwd ')' ?? "expected ')'" &gt;] -&gt; e
854
855  (* identifierexpr
856   *   ::= identifier
857   *   ::= identifier '(' argumentexpr ')' *)
858  | [&lt; 'Token.Ident id; stream &gt;] -&gt;
859      let rec parse_args accumulator = parser
860        | [&lt; e=parse_expr; stream &gt;] -&gt;
861            begin parser
862              | [&lt; 'Token.Kwd ','; e=parse_args (e :: accumulator) &gt;] -&gt; e
863              | [&lt; &gt;] -&gt; e :: accumulator
864            end stream
865        | [&lt; &gt;] -&gt; accumulator
866      in
867      let rec parse_ident id = parser
868        (* Call. *)
869        | [&lt; 'Token.Kwd '(';
870             args=parse_args [];
871             'Token.Kwd ')' ?? "expected ')'"&gt;] -&gt;
872            Ast.Call (id, Array.of_list (List.rev args))
873
874        (* Simple variable ref. *)
875        | [&lt; &gt;] -&gt; Ast.Variable id
876      in
877      parse_ident id stream
878
879  | [&lt; &gt;] -&gt; raise (Stream.Error "unknown token when expecting an expression.")
880
881(* binoprhs
882 *   ::= ('+' primary)* *)
883and parse_bin_rhs expr_prec lhs stream =
884  match Stream.peek stream with
885  (* If this is a binop, find its precedence. *)
886  | Some (Token.Kwd c) when Hashtbl.mem binop_precedence c -&gt;
887      let token_prec = precedence c in
888
889      (* If this is a binop that binds at least as tightly as the current binop,
890       * consume it, otherwise we are done. *)
891      if token_prec &lt; expr_prec then lhs else begin
892        (* Eat the binop. *)
893        Stream.junk stream;
894
895        (* Parse the primary expression after the binary operator. *)
896        let rhs = parse_primary stream in
897
898        (* Okay, we know this is a binop. *)
899        let rhs =
900          match Stream.peek stream with
901          | Some (Token.Kwd c2) -&gt;
902              (* If BinOp binds less tightly with rhs than the operator after
903               * rhs, let the pending operator take rhs as its lhs. *)
904              let next_prec = precedence c2 in
905              if token_prec &lt; next_prec
906              then parse_bin_rhs (token_prec + 1) rhs stream
907              else rhs
908          | _ -&gt; rhs
909        in
910
911        (* Merge lhs/rhs. *)
912        let lhs = Ast.Binary (c, lhs, rhs) in
913        parse_bin_rhs expr_prec lhs stream
914      end
915  | _ -&gt; lhs
916
917(* expression
918 *   ::= primary binoprhs *)
919and parse_expr = parser
920  | [&lt; lhs=parse_primary; stream &gt;] -&gt; parse_bin_rhs 0 lhs stream
921
922(* prototype
923 *   ::= id '(' id* ')' *)
924let parse_prototype =
925  let rec parse_args accumulator = parser
926    | [&lt; 'Token.Ident id; e=parse_args (id::accumulator) &gt;] -&gt; e
927    | [&lt; &gt;] -&gt; accumulator
928  in
929
930  parser
931  | [&lt; 'Token.Ident id;
932       'Token.Kwd '(' ?? "expected '(' in prototype";
933       args=parse_args [];
934       'Token.Kwd ')' ?? "expected ')' in prototype" &gt;] -&gt;
935      (* success. *)
936      Ast.Prototype (id, Array.of_list (List.rev args))
937
938  | [&lt; &gt;] -&gt;
939      raise (Stream.Error "expected function name in prototype")
940
941(* definition ::= 'def' prototype expression *)
942let parse_definition = parser
943  | [&lt; 'Token.Def; p=parse_prototype; e=parse_expr &gt;] -&gt;
944      Ast.Function (p, e)
945
946(* toplevelexpr ::= expression *)
947let parse_toplevel = parser
948  | [&lt; e=parse_expr &gt;] -&gt;
949      (* Make an anonymous proto. *)
950      Ast.Function (Ast.Prototype ("", [||]), e)
951
952(*  external ::= 'extern' prototype *)
953let parse_extern = parser
954  | [&lt; 'Token.Extern; e=parse_prototype &gt;] -&gt; e
955</pre>
956</dd>
957
958<dt>toplevel.ml:</dt>
959<dd class="doc_code">
960<pre>
961(*===----------------------------------------------------------------------===
962 * Top-Level parsing and JIT Driver
963 *===----------------------------------------------------------------------===*)
964
965(* top ::= definition | external | expression | ';' *)
966let rec main_loop stream =
967  match Stream.peek stream with
968  | None -&gt; ()
969
970  (* ignore top-level semicolons. *)
971  | Some (Token.Kwd ';') -&gt;
972      Stream.junk stream;
973      main_loop stream
974
975  | Some token -&gt;
976      begin
977        try match token with
978        | Token.Def -&gt;
979            ignore(Parser.parse_definition stream);
980            print_endline "parsed a function definition.";
981        | Token.Extern -&gt;
982            ignore(Parser.parse_extern stream);
983            print_endline "parsed an extern.";
984        | _ -&gt;
985            (* Evaluate a top-level expression into an anonymous function. *)
986            ignore(Parser.parse_toplevel stream);
987            print_endline "parsed a top-level expr";
988        with Stream.Error s -&gt;
989          (* Skip token for error recovery. *)
990          Stream.junk stream;
991          print_endline s;
992      end;
993      print_string "ready&gt; "; flush stdout;
994      main_loop stream
995</pre>
996</dd>
997
998<dt>toy.ml:</dt>
999<dd class="doc_code">
1000<pre>
1001(*===----------------------------------------------------------------------===
1002 * Main driver code.
1003 *===----------------------------------------------------------------------===*)
1004
1005let main () =
1006  (* Install standard binary operators.
1007   * 1 is the lowest precedence. *)
1008  Hashtbl.add Parser.binop_precedence '&lt;' 10;
1009  Hashtbl.add Parser.binop_precedence '+' 20;
1010  Hashtbl.add Parser.binop_precedence '-' 20;
1011  Hashtbl.add Parser.binop_precedence '*' 40;    (* highest. *)
1012
1013  (* Prime the first token. *)
1014  print_string "ready&gt; "; flush stdout;
1015  let stream = Lexer.lex (Stream.of_channel stdin) in
1016
1017  (* Run the main "interpreter loop" now. *)
1018  Toplevel.main_loop stream;
1019;;
1020
1021main ()
1022</pre>
1023</dd>
1024</dl>
1025
1026<a href="OCamlLangImpl3.html">Next: Implementing Code Generation to LLVM IR</a>
1027</div>
1028
1029<!-- *********************************************************************** -->
1030<hr>
1031<address>
1032  <a href="http://jigsaw.w3.org/css-validator/check/referer"><img
1033  src="http://jigsaw.w3.org/css-validator/images/vcss" alt="Valid CSS!"></a>
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1036
1037  <a href="mailto:sabre@nondot.org">Chris Lattner</a>
1038  <a href="mailto:erickt@users.sourceforge.net">Erick Tryzelaar</a><br>
1039  <a href="http://llvm.org/">The LLVM Compiler Infrastructure</a><br>
1040  Last modified: $Date: 2011-04-22 20:30:22 -0400 (Fri, 22 Apr 2011) $
1041</address>
1042</body>
1043</html>
1044