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 <body>

 <h1>Kaleidoscope: Tutorial Introduction and the Lexer</h1>

 <ul>
 <li><a href="index.html">Up to Tutorial Index</a></li>
 <li>Chapter 1
   <ol>
     <li><a href="#intro">Tutorial Introduction</a></li>
     <li><a href="#language">The Basic Language</a></li>
     <li><a href="#lexer">The Lexer</a></li>
   </ol>
 </li>
 <li><a href="OCamlLangImpl2.html">Chapter 2</a>: Implementing a Parser and
 AST</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">Tutorial Introduction</a></h2>
 <!-- *********************************************************************** -->

 <div>

 <p>Welcome to the "Implementing a language with LLVM" tutorial.  This tutorial
 runs through the implementation of a simple language, showing how fun and
 easy it can be.  This tutorial will get you up and started as well as help to
 build a framework you can extend to other languages.  The code in this tutorial
 can also be used as a playground to hack on other LLVM specific things.
 </p>

 <p>
 The goal of this tutorial is to progressively unveil our language, describing
 how it is built up over time.  This will let us cover a fairly broad range of
 language design and LLVM-specific usage issues, showing and explaining the code
 for it all along the way, without overwhelming you with tons of details up
 front.</p>

 <p>It is useful to point out ahead of time that this tutorial is really about
 teaching compiler techniques and LLVM specifically, <em>not</em> about teaching
 modern and sane software engineering principles.  In practice, this means that
 we'll take a number of shortcuts to simplify the exposition.  For example, the
 code leaks memory, uses global variables all over the place, doesn't use nice
 design patterns like <a
 href="http://en.wikipedia.org/wiki/Visitor_pattern">visitors</a>, etc... but it
 is very simple.  If you dig in and use the code as a basis for future projects,
 fixing these deficiencies shouldn't be hard.</p>

 <p>I've tried to put this tutorial together in a way that makes chapters easy to
 skip over if you are already familiar with or are uninterested in the various
 pieces.  The structure of the tutorial is:
 </p>

 <ul>
 <li><b><a href="#language">Chapter #1</a>: Introduction to the Kaleidoscope
 language, and the definition of its Lexer</b> - This shows where we are going
 and the basic functionality that we want it to do.  In order to make this
 tutorial maximally understandable and hackable, we choose to implement
 everything in Objective Caml instead of using lexer and parser generators.
 LLVM obviously works just fine with such tools, feel free to use one if you
 prefer.</li>
 <li><b><a href="OCamlLangImpl2.html">Chapter #2</a>: Implementing a Parser and
 AST</b> - With the lexer in place, we can talk about parsing techniques and
 basic AST construction.  This tutorial describes recursive descent parsing and
 operator precedence parsing.  Nothing in Chapters 1 or 2 is LLVM-specific,
 the code doesn't even link in LLVM at this point. :)</li>
 <li><b><a href="OCamlLangImpl3.html">Chapter #3</a>: Code generation to LLVM
 IR</b> - With the AST ready, we can show off how easy generation of LLVM IR
 really is.</li>
 <li><b><a href="OCamlLangImpl4.html">Chapter #4</a>: Adding JIT and Optimizer
 Support</b> - Because a lot of people are interested in using LLVM as a JIT,
 we'll dive right into it and show you the 3 lines it takes to add JIT support.
 LLVM is also useful in many other ways, but this is one simple and "sexy" way
 to shows off its power. :)</li>
 <li><b><a href="OCamlLangImpl5.html">Chapter #5</a>: Extending the Language:
 Control Flow</b> - With the language up and running, we show how to extend it
 with control flow operations (if/then/else and a 'for' loop).  This gives us a
 chance to talk about simple SSA construction and control flow.</li>
 <li><b><a href="OCamlLangImpl6.html">Chapter #6</a>: Extending the Language:
 User-defined Operators</b> - This is a silly but fun chapter that talks about
 extending the language to let the user program define their own arbitrary
 unary and binary operators (with assignable precedence!).  This lets us build a
 significant piece of the "language" as library routines.</li>
 <li><b><a href="OCamlLangImpl7.html">Chapter #7</a>: Extending the Language:
 Mutable Variables</b> - This chapter talks about adding user-defined local
 variables along with an assignment operator.  The interesting part about this
 is how easy and trivial it is to construct SSA form in LLVM: no, LLVM does
 <em>not</em> require your front-end to construct SSA form!</li>
 <li><b><a href="OCamlLangImpl8.html">Chapter #8</a>: Conclusion and other
 useful LLVM tidbits</b> - This chapter wraps up the series by talking about
 potential ways to extend the language, but also includes a bunch of pointers to
 info about "special topics" like adding garbage collection support, exceptions,
 debugging, support for "spaghetti stacks", and a bunch of other tips and
 tricks.</li>

 </ul>

 <p>By the end of the tutorial, we'll have written a bit less than 700 lines of
 non-comment, non-blank, lines of code.  With this small amount of code, we'll
 have built up a very reasonable compiler for a non-trivial language including
 a hand-written lexer, parser, AST, as well as code generation support with a JIT
 compiler.  While other systems may have interesting "hello world" tutorials,
 I think the breadth of this tutorial is a great testament to the strengths of
 LLVM and why you should consider it if you're interested in language or compiler
 design.</p>

 <p>A note about this tutorial: we expect you to extend the language and play
 with it on your own.  Take the code and go crazy hacking away at it, compilers
 don't need to be scary creatures - it can be a lot of fun to play with
 languages!</p>

 </div>

 <!-- *********************************************************************** -->
 <h2><a name="language">The Basic Language</a></h2>
 <!-- *********************************************************************** -->

 <div>

 <p>This tutorial will be illustrated with a toy language that we'll call
 "<a href="http://en.wikipedia.org/wiki/Kaleidoscope">Kaleidoscope</a>" (derived
 from "meaning beautiful, form, and view").
 Kaleidoscope is a procedural language that allows you to define functions, use
 conditionals, math, etc.  Over the course of the tutorial, we'll extend
 Kaleidoscope to support the if/then/else construct, a for loop, user defined
 operators, JIT compilation with a simple command line interface, etc.</p>

 <p>Because we want to keep things simple, the only datatype in Kaleidoscope is a
 64-bit floating point type (aka 'float' in O'Caml parlance).  As such, all
 values are implicitly double precision and the language doesn't require type
 declarations.  This gives the language a very nice and simple syntax.  For
 example, the following simple example computes <a
 href="http://en.wikipedia.org/wiki/Fibonacci_number">Fibonacci numbers:</a></p>

 <div class="doc_code">
 <pre>
 # Compute the x'th fibonacci number.
 def fib(x)
   if x &lt; 3 then
     1
   else
     fib(x-1)+fib(x-2)

 # This expression will compute the 40th number.
 fib(40)
 </pre>
 </div>

 <p>We also allow Kaleidoscope to call into standard library functions (the LLVM
 JIT makes this completely trivial).  This means that you can use the 'extern'
 keyword to define a function before you use it (this is also useful for mutually
 recursive functions).  For example:</p>

 <div class="doc_code">
 <pre>
 extern sin(arg);
 extern cos(arg);
 extern atan2(arg1 arg2);

 atan2(sin(.4), cos(42))
 </pre>
 </div>

 <p>A more interesting example is included in Chapter 6 where we write a little
 Kaleidoscope application that <a href="OCamlLangImpl6.html#example">displays
 a Mandelbrot Set</a> at various levels of magnification.</p>

 <p>Lets dive into the implementation of this language!</p>

 </div>

 <!-- *********************************************************************** -->
 <h2><a name="lexer">The Lexer</a></h2>
 <!-- *********************************************************************** -->

 <div>

 <p>When it comes to implementing a language, the first thing needed is
 the ability to process a text file and recognize what it says.  The traditional
 way to do this is to use a "<a
 href="http://en.wikipedia.org/wiki/Lexical_analysis">lexer</a>" (aka 'scanner')
 to break the input up into "tokens".  Each token returned by the lexer includes
 a token code and potentially some metadata (e.g. the numeric value of a number).
 First, we define the possibilities:
 </p>

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

 <p>Each token returned by our lexer will be one of the token variant values.
 An unknown character like '+' will be returned as <tt>Token.Kwd '+'</tt>.  If
 the curr token is an identifier, the value will be <tt>Token.Ident s</tt>.  If
 the current token is a numeric literal (like 1.0), the value will be
 <tt>Token.Number 1.0</tt>.
 </p>

 <p>The actual implementation of the lexer is a collection of functions driven
 by a function named <tt>Lexer.lex</tt>.  The <tt>Lexer.lex</tt> function is
 called to return the next token from standard input.  We will use
 <a href="http://caml.inria.fr/pub/docs/manual-camlp4/index.html">Camlp4</a>
 to simplify the tokenization of the standard input.  Its definition starts
 as:</p>

 <div class="doc_code">
 <pre>
 (*===----------------------------------------------------------------------===
  * Lexer
  *===----------------------------------------------------------------------===*)

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

 <p>
 <tt>Lexer.lex</tt> works by recursing over a <tt>char Stream.t</tt> to read
 characters one at a time from the standard input.  It eats them as it recognizes
 them and stores them in in a <tt>Token.token</tt> variant.  The first thing that
 it has to do is ignore whitespace between tokens.  This is accomplished with the
 recursive call above.</p>

 <p>The next thing <tt>Lexer.lex</tt> needs to do is recognize identifiers and
 specific keywords like "def".  Kaleidoscope does this with a pattern match
 and a helper function.<p>

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

 ...

 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;]
 </pre>
 </div>

 <p>Numeric values are similar:</p>

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

 ...

 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;]
 </pre>
 </div>

 <p>This is all pretty straight-forward code for processing input.  When reading
 a numeric value from input, we use the ocaml <tt>float_of_string</tt> function
 to convert it to a numeric value that we store in <tt>Token.Number</tt>.  Note
 that this isn't doing sufficient error checking: it will raise <tt>Failure</tt>
 if the string "1.23.45.67".  Feel free to extend it :).  Next we handle
 comments:
 </p>

 <div class="doc_code">
 <pre>
   (* Comment until end of line. *)
   | [&lt; ' ('#'); stream &gt;] -&gt;
       lex_comment stream

 ...

 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>
 </div>

 <p>We handle comments by skipping to the end of the line and then return the
 next token.  Finally, if the input doesn't match one of the above cases, it is
 either an operator character like '+' or the end of the file.  These are handled
 with this code:</p>

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

 <p>With this, we have the complete lexer for the basic Kaleidoscope language
 (the <a href="OCamlLangImpl2.html#code">full code listing</a> for the Lexer is
 available in the <a href="OCamlLangImpl2.html">next chapter</a> of the
 tutorial).  Next we'll <a href="OCamlLangImpl2.html">build a simple parser that
 uses this to build an Abstract Syntax Tree</a>.  When we have that, we'll
 include a driver so that you can use the lexer and parser together.
 </p>

 <a href="OCamlLangImpl2.html">Next: Implementing a Parser and AST</a>
 </div>

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   <a href="mailto:sabre@nondot.org">Chris Lattner</a><br>
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	<html>
	<head>
	<title>Kaleidoscope: Tutorial Introduction and the Lexer</title>
	<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
	<meta name="author" content="Chris Lattner">
	<meta name="author" content="Erick Tryzelaar">
	<link rel="stylesheet" href="../llvm.css" type="text/css">
	</head>

	<body>

	<h1>Kaleidoscope: Tutorial Introduction and the Lexer</h1>

	<ul>
	<li><a href="index.html">Up to Tutorial Index</a></li>
	<li>Chapter 1
	<ol>
	<li><a href="#intro">Tutorial Introduction</a></li>
	<li><a href="#language">The Basic Language</a></li>
	<li><a href="#lexer">The Lexer</a></li>
	</ol>
	</li>
	<li><a href="OCamlLangImpl2.html">Chapter 2</a>: Implementing a Parser and
	AST</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">Tutorial Introduction</a></h2>
	<!-- *********************************************************************** -->

	<div>

	<p>Welcome to the "Implementing a language with LLVM" tutorial. This tutorial
	runs through the implementation of a simple language, showing how fun and
	easy it can be. This tutorial will get you up and started as well as help to
	build a framework you can extend to other languages. The code in this tutorial
	can also be used as a playground to hack on other LLVM specific things.
	</p>

	<p>
	The goal of this tutorial is to progressively unveil our language, describing
	how it is built up over time. This will let us cover a fairly broad range of
	language design and LLVM-specific usage issues, showing and explaining the code
	for it all along the way, without overwhelming you with tons of details up
	front.</p>

	<p>It is useful to point out ahead of time that this tutorial is really about
	teaching compiler techniques and LLVM specifically, <em>not</em> about teaching
	modern and sane software engineering principles. In practice, this means that
	we'll take a number of shortcuts to simplify the exposition. For example, the
	code leaks memory, uses global variables all over the place, doesn't use nice
	design patterns like <a
	href="http://en.wikipedia.org/wiki/Visitor_pattern">visitors</a>, etc... but it
	is very simple. If you dig in and use the code as a basis for future projects,
	fixing these deficiencies shouldn't be hard.</p>

	<p>I've tried to put this tutorial together in a way that makes chapters easy to
	skip over if you are already familiar with or are uninterested in the various
	pieces. The structure of the tutorial is:
	</p>

	<ul>
	<li><b><a href="#language">Chapter #1</a>: Introduction to the Kaleidoscope
	language, and the definition of its Lexer</b> - This shows where we are going
	and the basic functionality that we want it to do. In order to make this
	tutorial maximally understandable and hackable, we choose to implement
	everything in Objective Caml instead of using lexer and parser generators.
	LLVM obviously works just fine with such tools, feel free to use one if you
	prefer.</li>
	<li><b><a href="OCamlLangImpl2.html">Chapter #2</a>: Implementing a Parser and
	AST</b> - With the lexer in place, we can talk about parsing techniques and
	basic AST construction. This tutorial describes recursive descent parsing and
	operator precedence parsing. Nothing in Chapters 1 or 2 is LLVM-specific,
	the code doesn't even link in LLVM at this point. :)</li>
	<li><b><a href="OCamlLangImpl3.html">Chapter #3</a>: Code generation to LLVM
	IR</b> - With the AST ready, we can show off how easy generation of LLVM IR
	really is.</li>
	<li><b><a href="OCamlLangImpl4.html">Chapter #4</a>: Adding JIT and Optimizer
	Support</b> - Because a lot of people are interested in using LLVM as a JIT,
	we'll dive right into it and show you the 3 lines it takes to add JIT support.
	LLVM is also useful in many other ways, but this is one simple and "sexy" way
	to shows off its power. :)</li>
	<li><b><a href="OCamlLangImpl5.html">Chapter #5</a>: Extending the Language:
	Control Flow</b> - With the language up and running, we show how to extend it
	with control flow operations (if/then/else and a 'for' loop). This gives us a
	chance to talk about simple SSA construction and control flow.</li>
	<li><b><a href="OCamlLangImpl6.html">Chapter #6</a>: Extending the Language:
	User-defined Operators</b> - This is a silly but fun chapter that talks about
	extending the language to let the user program define their own arbitrary
	unary and binary operators (with assignable precedence!). This lets us build a
	significant piece of the "language" as library routines.</li>
	<li><b><a href="OCamlLangImpl7.html">Chapter #7</a>: Extending the Language:
	Mutable Variables</b> - This chapter talks about adding user-defined local
	variables along with an assignment operator. The interesting part about this
	is how easy and trivial it is to construct SSA form in LLVM: no, LLVM does
	<em>not</em> require your front-end to construct SSA form!</li>
	<li><b><a href="OCamlLangImpl8.html">Chapter #8</a>: Conclusion and other
	useful LLVM tidbits</b> - This chapter wraps up the series by talking about
	potential ways to extend the language, but also includes a bunch of pointers to
	info about "special topics" like adding garbage collection support, exceptions,
	debugging, support for "spaghetti stacks", and a bunch of other tips and
	tricks.</li>

	</ul>

	<p>By the end of the tutorial, we'll have written a bit less than 700 lines of
	non-comment, non-blank, lines of code. With this small amount of code, we'll
	have built up a very reasonable compiler for a non-trivial language including
	a hand-written lexer, parser, AST, as well as code generation support with a JIT
	compiler. While other systems may have interesting "hello world" tutorials,
	I think the breadth of this tutorial is a great testament to the strengths of
	LLVM and why you should consider it if you're interested in language or compiler
	design.</p>

	<p>A note about this tutorial: we expect you to extend the language and play
	with it on your own. Take the code and go crazy hacking away at it, compilers
	don't need to be scary creatures - it can be a lot of fun to play with
	languages!</p>

	</div>

	<!-- *********************************************************************** -->
	<h2><a name="language">The Basic Language</a></h2>
	<!-- *********************************************************************** -->

	<div>

	<p>This tutorial will be illustrated with a toy language that we'll call
	"<a href="http://en.wikipedia.org/wiki/Kaleidoscope">Kaleidoscope</a>" (derived
	from "meaning beautiful, form, and view").
	Kaleidoscope is a procedural language that allows you to define functions, use
	conditionals, math, etc. Over the course of the tutorial, we'll extend
	Kaleidoscope to support the if/then/else construct, a for loop, user defined
	operators, JIT compilation with a simple command line interface, etc.</p>

	<p>Because we want to keep things simple, the only datatype in Kaleidoscope is a
	64-bit floating point type (aka 'float' in O'Caml parlance). As such, all
	values are implicitly double precision and the language doesn't require type
	declarations. This gives the language a very nice and simple syntax. For
	example, the following simple example computes <a
	href="http://en.wikipedia.org/wiki/Fibonacci_number">Fibonacci numbers:</a></p>

	<div class="doc_code">
	<pre>
	# Compute the x'th fibonacci number.
	def fib(x)
	if x < 3 then
	1
	else
	fib(x-1)+fib(x-2)

	# This expression will compute the 40th number.
	fib(40)
	</pre>
	</div>

	<p>We also allow Kaleidoscope to call into standard library functions (the LLVM
	JIT makes this completely trivial). This means that you can use the 'extern'
	keyword to define a function before you use it (this is also useful for mutually
	recursive functions). For example:</p>

	<div class="doc_code">
	<pre>
	extern sin(arg);
	extern cos(arg);
	extern atan2(arg1 arg2);

	atan2(sin(.4), cos(42))
	</pre>
	</div>

	<p>A more interesting example is included in Chapter 6 where we write a little
	Kaleidoscope application that <a href="OCamlLangImpl6.html#example">displays
	a Mandelbrot Set</a> at various levels of magnification.</p>

	<p>Lets dive into the implementation of this language!</p>

	</div>

	<!-- *********************************************************************** -->
	<h2><a name="lexer">The Lexer</a></h2>
	<!-- *********************************************************************** -->

	<div>

	<p>When it comes to implementing a language, the first thing needed is
	the ability to process a text file and recognize what it says. The traditional
	way to do this is to use a "<a
	href="http://en.wikipedia.org/wiki/Lexical_analysis">lexer</a>" (aka 'scanner')
	to break the input up into "tokens". Each token returned by the lexer includes
	a token code and potentially some metadata (e.g. the numeric value of a number).
	First, we define the possibilities:
	</p>

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

	<p>Each token returned by our lexer will be one of the token variant values.
	An unknown character like '+' will be returned as <tt>Token.Kwd '+'</tt>. If
	the curr token is an identifier, the value will be <tt>Token.Ident s</tt>. If
	the current token is a numeric literal (like 1.0), the value will be
	<tt>Token.Number 1.0</tt>.
	</p>

	<p>The actual implementation of the lexer is a collection of functions driven
	by a function named <tt>Lexer.lex</tt>. The <tt>Lexer.lex</tt> function is
	called to return the next token from standard input. We will use
	<a href="http://caml.inria.fr/pub/docs/manual-camlp4/index.html">Camlp4</a>
	to simplify the tokenization of the standard input. Its definition starts
	as:</p>

	<div class="doc_code">
	<pre>
	(*===----------------------------------------------------------------------===
	* Lexer
	===----------------------------------------------------------------------===)

	let rec lex = parser
	(* Skip any whitespace. *)
	\| [< ' (' ' \| '\n' \| '\r' \| '\t'); stream >] -> lex stream
	</pre>
	</div>

	<p>
	<tt>Lexer.lex</tt> works by recursing over a <tt>char Stream.t</tt> to read
	characters one at a time from the standard input. It eats them as it recognizes
	them and stores them in in a <tt>Token.token</tt> variant. The first thing that
	it has to do is ignore whitespace between tokens. This is accomplished with the
	recursive call above.</p>

	<p>The next thing <tt>Lexer.lex</tt> needs to do is recognize identifiers and
	specific keywords like "def". Kaleidoscope does this with a pattern match
	and a helper function.<p>

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

	...

	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 >]
	\| id -> [< 'Token.Ident id; stream >]
	</pre>
	</div>

	<p>Numeric values are similar:</p>

	<div class="doc_code">
	<pre>
	(* number: [0-9.]+ *)
	\| [< ' ('0' .. '9' as c); stream >] ->
	let buffer = Buffer.create 1 in
	Buffer.add_char buffer c;
	lex_number buffer 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 >]
	</pre>
	</div>

	<p>This is all pretty straight-forward code for processing input. When reading
	a numeric value from input, we use the ocaml <tt>float_of_string</tt> function
	to convert it to a numeric value that we store in <tt>Token.Number</tt>. Note
	that this isn't doing sufficient error checking: it will raise <tt>Failure</tt>
	if the string "1.23.45.67". Feel free to extend it :). Next we handle
	comments:
	</p>

	<div class="doc_code">
	<pre>
	(* Comment until end of line. *)
	\| [< ' ('#'); stream >] ->
	lex_comment stream

	...

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

	<p>We handle comments by skipping to the end of the line and then return the
	next token. Finally, if the input doesn't match one of the above cases, it is
	either an operator character like '+' or the end of the file. These are handled
	with this code:</p>

	<div class="doc_code">
	<pre>
	(* Otherwise, just return the character as its ascii value. *)
	\| [< 'c; stream >] ->
	[< 'Token.Kwd c; lex stream >]

	(* end of stream. *)
	\| [< >] -> [< >]
	</pre>
	</div>

	<p>With this, we have the complete lexer for the basic Kaleidoscope language
	(the <a href="OCamlLangImpl2.html#code">full code listing</a> for the Lexer is
	available in the <a href="OCamlLangImpl2.html">next chapter</a> of the
	tutorial). Next we'll <a href="OCamlLangImpl2.html">build a simple parser that
	uses this to build an Abstract Syntax Tree</a>. When we have that, we'll
	include a driver so that you can use the lexer and parser together.
	</p>

	<a href="OCamlLangImpl2.html">Next: Implementing a Parser and AST</a>
	</div>

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	<a href="mailto:sabre@nondot.org">Chris Lattner</a><br>
	<a href="mailto:idadesub@users.sourceforge.net">Erick Tryzelaar</a><br>
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