mirror of
https://github.com/RPCS3/llvm-mirror.git
synced 2024-11-25 12:12:47 +01:00
8f03e98627
is done with the other html files in doc, to hopefully keep strings like "Last modified" current. llvm-svn: 95225
1234 lines
40 KiB
HTML
1234 lines
40 KiB
HTML
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN"
|
|
"http://www.w3.org/TR/html4/strict.dtd">
|
|
|
|
<html>
|
|
<head>
|
|
<title>Kaleidoscope: Implementing a Parser and AST</title>
|
|
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
|
|
<meta name="author" content="Chris Lattner">
|
|
<link rel="stylesheet" href="../llvm.css" type="text/css">
|
|
</head>
|
|
|
|
<body>
|
|
|
|
<div class="doc_title">Kaleidoscope: Implementing a Parser and AST</div>
|
|
|
|
<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="LangImpl3.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></p>
|
|
</div>
|
|
|
|
<!-- *********************************************************************** -->
|
|
<div class="doc_section"><a name="intro">Chapter 2 Introduction</a></div>
|
|
<!-- *********************************************************************** -->
|
|
|
|
<div class="doc_text">
|
|
|
|
<p>Welcome to Chapter 2 of the "<a href="index.html">Implementing a language
|
|
with LLVM</a>" tutorial. This chapter shows you how to use the lexer, built in
|
|
<a href="LangImpl1.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>
|
|
|
|
<!-- *********************************************************************** -->
|
|
<div class="doc_section"><a name="ast">The Abstract Syntax Tree (AST)</a></div>
|
|
<!-- *********************************************************************** -->
|
|
|
|
<div class="doc_text">
|
|
|
|
<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>
|
|
/// ExprAST - Base class for all expression nodes.
|
|
class ExprAST {
|
|
public:
|
|
virtual ~ExprAST() {}
|
|
};
|
|
|
|
/// NumberExprAST - Expression class for numeric literals like "1.0".
|
|
class NumberExprAST : public ExprAST {
|
|
double Val;
|
|
public:
|
|
NumberExprAST(double val) : Val(val) {}
|
|
};
|
|
</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 NumberExprAST class 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 accessor methods on
|
|
them. It would be very easy to add a virtual method 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>
|
|
/// VariableExprAST - Expression class for referencing a variable, like "a".
|
|
class VariableExprAST : public ExprAST {
|
|
std::string Name;
|
|
public:
|
|
VariableExprAST(const std::string &name) : Name(name) {}
|
|
};
|
|
|
|
/// BinaryExprAST - Expression class for a binary operator.
|
|
class BinaryExprAST : public ExprAST {
|
|
char Op;
|
|
ExprAST *LHS, *RHS;
|
|
public:
|
|
BinaryExprAST(char op, ExprAST *lhs, ExprAST *rhs)
|
|
: Op(op), LHS(lhs), RHS(rhs) {}
|
|
};
|
|
|
|
/// CallExprAST - Expression class for function calls.
|
|
class CallExprAST : public ExprAST {
|
|
std::string Callee;
|
|
std::vector<ExprAST*> Args;
|
|
public:
|
|
CallExprAST(const std::string &callee, std::vector<ExprAST*> &args)
|
|
: Callee(callee), Args(args) {}
|
|
};
|
|
</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>
|
|
/// PrototypeAST - This class represents the "prototype" for a function,
|
|
/// which captures its name, and its argument names (thus implicitly the number
|
|
/// of arguments the function takes).
|
|
class PrototypeAST {
|
|
std::string Name;
|
|
std::vector<std::string> Args;
|
|
public:
|
|
PrototypeAST(const std::string &name, const std::vector<std::string> &args)
|
|
: Name(name), Args(args) {}
|
|
};
|
|
|
|
/// FunctionAST - This class represents a function definition itself.
|
|
class FunctionAST {
|
|
PrototypeAST *Proto;
|
|
ExprAST *Body;
|
|
public:
|
|
FunctionAST(PrototypeAST *proto, ExprAST *body)
|
|
: Proto(proto), Body(body) {}
|
|
};
|
|
</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 "ExprAST" class 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>
|
|
|
|
<!-- *********************************************************************** -->
|
|
<div class="doc_section"><a name="parserbasics">Parser Basics</a></div>
|
|
<!-- *********************************************************************** -->
|
|
|
|
<div class="doc_text">
|
|
|
|
<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>
|
|
ExprAST *X = new VariableExprAST("x");
|
|
ExprAST *Y = new VariableExprAST("y");
|
|
ExprAST *Result = new BinaryExprAST('+', X, Y);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>In order to do this, we'll start by defining some basic helper routines:</p>
|
|
|
|
<div class="doc_code">
|
|
<pre>
|
|
/// CurTok/getNextToken - Provide a simple token buffer. CurTok is the current
|
|
/// token the parser is looking at. getNextToken reads another token from the
|
|
/// lexer and updates CurTok with its results.
|
|
static int CurTok;
|
|
static int getNextToken() {
|
|
return CurTok = gettok();
|
|
}
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
This implements a simple token buffer around the lexer. This allows
|
|
us to look one token ahead at what the lexer is returning. Every function in
|
|
our parser will assume that CurTok is the current token that needs to be
|
|
parsed.</p>
|
|
|
|
<div class="doc_code">
|
|
<pre>
|
|
|
|
/// Error* - These are little helper functions for error handling.
|
|
ExprAST *Error(const char *Str) { fprintf(stderr, "Error: %s\n", Str);return 0;}
|
|
PrototypeAST *ErrorP(const char *Str) { Error(Str); return 0; }
|
|
FunctionAST *ErrorF(const char *Str) { Error(Str); return 0; }
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The <tt>Error</tt> routines are simple helper routines that our parser will use
|
|
to handle errors. 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
|
|
routines make it easier to handle errors in routines that have various return
|
|
types: they always return null.</p>
|
|
|
|
<p>With these basic helper functions, we can implement the first
|
|
piece of our grammar: numeric literals.</p>
|
|
|
|
</div>
|
|
|
|
<!-- *********************************************************************** -->
|
|
<div class="doc_section"><a name="parserprimexprs">Basic Expression
|
|
Parsing</a></div>
|
|
<!-- *********************************************************************** -->
|
|
|
|
<div class="doc_text">
|
|
|
|
<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. For numeric literals, we have:
|
|
</p>
|
|
|
|
<div class="doc_code">
|
|
<pre>
|
|
/// numberexpr ::= number
|
|
static ExprAST *ParseNumberExpr() {
|
|
ExprAST *Result = new NumberExprAST(NumVal);
|
|
getNextToken(); // consume the number
|
|
return Result;
|
|
}
|
|
</pre>
|
|
</div>
|
|
|
|
<p>This routine is very simple: it expects to be called when the current token
|
|
is a <tt>tok_number</tt> token. It takes the current number value, creates
|
|
a <tt>NumberExprAST</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 ')'
|
|
static ExprAST *ParseParenExpr() {
|
|
getNextToken(); // eat (.
|
|
ExprAST *V = ParseExpression();
|
|
if (!V) return 0;
|
|
|
|
if (CurTok != ')')
|
|
return Error("expected ')'");
|
|
getNextToken(); // eat ).
|
|
return V;
|
|
}
|
|
</pre>
|
|
</div>
|
|
|
|
<p>This function illustrates a number of interesting things about the
|
|
parser:</p>
|
|
|
|
<p>
|
|
1) It shows how we use the Error routines. 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
|
|
return null on an error.</p>
|
|
|
|
<p>2) Another interesting aspect of this function is that it uses recursion by
|
|
calling <tt>ParseExpression</tt> (we will soon see that <tt>ParseExpression</tt> can call
|
|
<tt>ParseParenExpr</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 '(' expression* ')'
|
|
static ExprAST *ParseIdentifierExpr() {
|
|
std::string IdName = IdentifierStr;
|
|
|
|
getNextToken(); // eat identifier.
|
|
|
|
if (CurTok != '(') // Simple variable ref.
|
|
return new VariableExprAST(IdName);
|
|
|
|
// Call.
|
|
getNextToken(); // eat (
|
|
std::vector<ExprAST*> Args;
|
|
if (CurTok != ')') {
|
|
while (1) {
|
|
ExprAST *Arg = ParseExpression();
|
|
if (!Arg) return 0;
|
|
Args.push_back(Arg);
|
|
|
|
if (CurTok == ')') break;
|
|
|
|
if (CurTok != ',')
|
|
return Error("Expected ')' or ',' in argument list");
|
|
getNextToken();
|
|
}
|
|
}
|
|
|
|
// Eat the ')'.
|
|
getNextToken();
|
|
|
|
return new CallExprAST(IdName, Args);
|
|
}
|
|
</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>tok_identifier</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>VariableExprAST</tt> or <tt>CallExprAST</tt> node as appropriate.
|
|
</p>
|
|
|
|
<p>Now that we have all of our simple expression-parsing logic in place, we can
|
|
define a helper function to wrap it together into one entry point. We call this
|
|
class of expressions "primary" expressions, for reasons that will become more
|
|
clear <a href="LangImpl6.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:</p>
|
|
|
|
<div class="doc_code">
|
|
<pre>
|
|
/// primary
|
|
/// ::= identifierexpr
|
|
/// ::= numberexpr
|
|
/// ::= parenexpr
|
|
static ExprAST *ParsePrimary() {
|
|
switch (CurTok) {
|
|
default: return Error("unknown token when expecting an expression");
|
|
case tok_identifier: return ParseIdentifierExpr();
|
|
case tok_number: return ParseNumberExpr();
|
|
case '(': return ParseParenExpr();
|
|
}
|
|
}
|
|
</pre>
|
|
</div>
|
|
|
|
<p>Now that you see the definition of this function, it is more obvious why we
|
|
can assume the state of CurTok in the various functions. This uses look-ahead
|
|
to determine which sort of expression is being inspected, and then parses it
|
|
with a function call.</p>
|
|
|
|
<p>Now that basic expressions are handled, we need to handle binary expressions.
|
|
They are a bit more complex.</p>
|
|
|
|
</div>
|
|
|
|
<!-- *********************************************************************** -->
|
|
<div class="doc_section"><a name="parserbinops">Binary Expression
|
|
Parsing</a></div>
|
|
<!-- *********************************************************************** -->
|
|
|
|
<div class="doc_text">
|
|
|
|
<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>
|
|
/// BinopPrecedence - This holds the precedence for each binary operator that is
|
|
/// defined.
|
|
static std::map<char, int> BinopPrecedence;
|
|
|
|
/// GetTokPrecedence - Get the precedence of the pending binary operator token.
|
|
static int GetTokPrecedence() {
|
|
if (!isascii(CurTok))
|
|
return -1;
|
|
|
|
// Make sure it's a declared binop.
|
|
int TokPrec = BinopPrecedence[CurTok];
|
|
if (TokPrec <= 0) return -1;
|
|
return TokPrec;
|
|
}
|
|
|
|
int main() {
|
|
// Install standard binary operators.
|
|
// 1 is lowest precedence.
|
|
BinopPrecedence['<'] = 10;
|
|
BinopPrecedence['+'] = 20;
|
|
BinopPrecedence['-'] = 20;
|
|
BinopPrecedence['*'] = 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>GetTokPrecedence</tt> function returns the precedence for the current token,
|
|
or -1 if the token is not a binary operator. Having a map 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 map
|
|
and do the comparisons in the <tt>GetTokPrecedence</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
|
|
///
|
|
static ExprAST *ParseExpression() {
|
|
ExprAST *LHS = ParsePrimary();
|
|
if (!LHS) return 0;
|
|
|
|
return ParseBinOpRHS(0, LHS);
|
|
}
|
|
</pre>
|
|
</div>
|
|
|
|
<p><tt>ParseBinOpRHS</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>ParseBinOpRHS</tt> and the current token is "+".</p>
|
|
|
|
<p>The precedence value passed into <tt>ParseBinOpRHS</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>ParseBinOpRHS</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>ParseBinOpRHS</tt> starts
|
|
with:</p>
|
|
|
|
<div class="doc_code">
|
|
<pre>
|
|
/// binoprhs
|
|
/// ::= ('+' primary)*
|
|
static ExprAST *ParseBinOpRHS(int ExprPrec, ExprAST *LHS) {
|
|
// If this is a binop, find its precedence.
|
|
while (1) {
|
|
int TokPrec = GetTokPrecedence();
|
|
|
|
// If this is a binop that binds at least as tightly as the current binop,
|
|
// consume it, otherwise we are done.
|
|
if (TokPrec < ExprPrec)
|
|
return LHS;
|
|
</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>
|
|
// Okay, we know this is a binop.
|
|
int BinOp = CurTok;
|
|
getNextToken(); // eat binop
|
|
|
|
// Parse the primary expression after the binary operator.
|
|
ExprAST *RHS = ParsePrimary();
|
|
if (!RHS) return 0;
|
|
</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.
|
|
int NextPrec = GetTokPrecedence();
|
|
if (TokPrec < NextPrec) {
|
|
</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 ...
|
|
}
|
|
|
|
// Merge LHS/RHS.
|
|
LHS = new BinaryExprAST(BinOp, LHS, RHS);
|
|
} // loop around to the top of the while loop.
|
|
}
|
|
</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>
|
|
// If BinOp binds less tightly with RHS than the operator after RHS, let
|
|
// the pending operator take RHS as its LHS.
|
|
int NextPrec = GetTokPrecedence();
|
|
if (TokPrec < NextPrec) {
|
|
<b>RHS = ParseBinOpRHS(TokPrec+1, RHS);
|
|
if (RHS == 0) return 0;</b>
|
|
}
|
|
// Merge LHS/RHS.
|
|
LHS = new BinaryExprAST(BinOp, LHS, RHS);
|
|
} // loop around to the top of the while loop.
|
|
}
|
|
</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>ParseBinOpRHS</tt> function specifying "TokPrec+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>
|
|
|
|
<!-- *********************************************************************** -->
|
|
<div class="doc_section"><a name="parsertop">Parsing the Rest</a></div>
|
|
<!-- *********************************************************************** -->
|
|
|
|
<div class="doc_text">
|
|
|
|
<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* ')'
|
|
static PrototypeAST *ParsePrototype() {
|
|
if (CurTok != tok_identifier)
|
|
return ErrorP("Expected function name in prototype");
|
|
|
|
std::string FnName = IdentifierStr;
|
|
getNextToken();
|
|
|
|
if (CurTok != '(')
|
|
return ErrorP("Expected '(' in prototype");
|
|
|
|
// Read the list of argument names.
|
|
std::vector<std::string> ArgNames;
|
|
while (getNextToken() == tok_identifier)
|
|
ArgNames.push_back(IdentifierStr);
|
|
if (CurTok != ')')
|
|
return ErrorP("Expected ')' in prototype");
|
|
|
|
// success.
|
|
getNextToken(); // eat ')'.
|
|
|
|
return new PrototypeAST(FnName, ArgNames);
|
|
}
|
|
</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
|
|
static FunctionAST *ParseDefinition() {
|
|
getNextToken(); // eat def.
|
|
PrototypeAST *Proto = ParsePrototype();
|
|
if (Proto == 0) return 0;
|
|
|
|
if (ExprAST *E = ParseExpression())
|
|
return new FunctionAST(Proto, E);
|
|
return 0;
|
|
}
|
|
</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
|
|
static PrototypeAST *ParseExtern() {
|
|
getNextToken(); // eat extern.
|
|
return ParsePrototype();
|
|
}
|
|
</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
|
|
static FunctionAST *ParseTopLevelExpr() {
|
|
if (ExprAST *E = ParseExpression()) {
|
|
// Make an anonymous proto.
|
|
PrototypeAST *Proto = new PrototypeAST("", std::vector<std::string>());
|
|
return new FunctionAST(Proto, E);
|
|
}
|
|
return 0;
|
|
}
|
|
</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>
|
|
|
|
<!-- *********************************************************************** -->
|
|
<div class="doc_section"><a name="driver">The Driver</a></div>
|
|
<!-- *********************************************************************** -->
|
|
|
|
<div class="doc_text">
|
|
|
|
<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 | ';'
|
|
static void MainLoop() {
|
|
while (1) {
|
|
fprintf(stderr, "ready> ");
|
|
switch (CurTok) {
|
|
case tok_eof: return;
|
|
case ';': getNextToken(); break; // ignore top-level semicolons.
|
|
case tok_def: HandleDefinition(); break;
|
|
case tok_extern: HandleExtern(); break;
|
|
default: HandleTopLevelExpression(); break;
|
|
}
|
|
}
|
|
}
|
|
</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>
|
|
|
|
<!-- *********************************************************************** -->
|
|
<div class="doc_section"><a name="conclusions">Conclusions</a></div>
|
|
<!-- *********************************************************************** -->
|
|
|
|
<div class="doc_text">
|
|
|
|
<p>With just under 400 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>./a.out</b>
|
|
ready> <b>def foo(x y) x+foo(y, 4.0);</b>
|
|
Parsed a function definition.
|
|
ready> <b>def foo(x y) x+y y;</b>
|
|
Parsed a function definition.
|
|
Parsed a top-level expr
|
|
ready> <b>def foo(x y) x+y );</b>
|
|
Parsed a function definition.
|
|
Error: unknown token when expecting an expression
|
|
ready> <b>extern sin(a);</b>
|
|
ready> Parsed an extern
|
|
ready> <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="LangImpl3.html">next
|
|
installment</a>, we will describe how to generate LLVM Intermediate
|
|
Representation (IR) from the AST.</p>
|
|
|
|
</div>
|
|
|
|
<!-- *********************************************************************** -->
|
|
<div class="doc_section"><a name="code">Full Code Listing</a></div>
|
|
<!-- *********************************************************************** -->
|
|
|
|
<div class="doc_text">
|
|
|
|
<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 C and C++ standard libraries, of
|
|
course.) To build this, just compile with:</p>
|
|
|
|
<div class="doc_code">
|
|
<pre>
|
|
# Compile
|
|
g++ -g -O3 toy.cpp
|
|
# Run
|
|
./a.out
|
|
</pre>
|
|
</div>
|
|
|
|
<p>Here is the code:</p>
|
|
|
|
<div class="doc_code">
|
|
<pre>
|
|
#include <cstdio>
|
|
#include <cstdlib>
|
|
#include <string>
|
|
#include <map>
|
|
#include <vector>
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// Lexer
|
|
//===----------------------------------------------------------------------===//
|
|
|
|
// The lexer returns tokens [0-255] if it is an unknown character, otherwise one
|
|
// of these for known things.
|
|
enum Token {
|
|
tok_eof = -1,
|
|
|
|
// commands
|
|
tok_def = -2, tok_extern = -3,
|
|
|
|
// primary
|
|
tok_identifier = -4, tok_number = -5
|
|
};
|
|
|
|
static std::string IdentifierStr; // Filled in if tok_identifier
|
|
static double NumVal; // Filled in if tok_number
|
|
|
|
/// gettok - Return the next token from standard input.
|
|
static int gettok() {
|
|
static int LastChar = ' ';
|
|
|
|
// Skip any whitespace.
|
|
while (isspace(LastChar))
|
|
LastChar = getchar();
|
|
|
|
if (isalpha(LastChar)) { // identifier: [a-zA-Z][a-zA-Z0-9]*
|
|
IdentifierStr = LastChar;
|
|
while (isalnum((LastChar = getchar())))
|
|
IdentifierStr += LastChar;
|
|
|
|
if (IdentifierStr == "def") return tok_def;
|
|
if (IdentifierStr == "extern") return tok_extern;
|
|
return tok_identifier;
|
|
}
|
|
|
|
if (isdigit(LastChar) || LastChar == '.') { // Number: [0-9.]+
|
|
std::string NumStr;
|
|
do {
|
|
NumStr += LastChar;
|
|
LastChar = getchar();
|
|
} while (isdigit(LastChar) || LastChar == '.');
|
|
|
|
NumVal = strtod(NumStr.c_str(), 0);
|
|
return tok_number;
|
|
}
|
|
|
|
if (LastChar == '#') {
|
|
// Comment until end of line.
|
|
do LastChar = getchar();
|
|
while (LastChar != EOF && LastChar != '\n' && LastChar != '\r');
|
|
|
|
if (LastChar != EOF)
|
|
return gettok();
|
|
}
|
|
|
|
// Check for end of file. Don't eat the EOF.
|
|
if (LastChar == EOF)
|
|
return tok_eof;
|
|
|
|
// Otherwise, just return the character as its ascii value.
|
|
int ThisChar = LastChar;
|
|
LastChar = getchar();
|
|
return ThisChar;
|
|
}
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// Abstract Syntax Tree (aka Parse Tree)
|
|
//===----------------------------------------------------------------------===//
|
|
|
|
/// ExprAST - Base class for all expression nodes.
|
|
class ExprAST {
|
|
public:
|
|
virtual ~ExprAST() {}
|
|
};
|
|
|
|
/// NumberExprAST - Expression class for numeric literals like "1.0".
|
|
class NumberExprAST : public ExprAST {
|
|
double Val;
|
|
public:
|
|
NumberExprAST(double val) : Val(val) {}
|
|
};
|
|
|
|
/// VariableExprAST - Expression class for referencing a variable, like "a".
|
|
class VariableExprAST : public ExprAST {
|
|
std::string Name;
|
|
public:
|
|
VariableExprAST(const std::string &name) : Name(name) {}
|
|
};
|
|
|
|
/// BinaryExprAST - Expression class for a binary operator.
|
|
class BinaryExprAST : public ExprAST {
|
|
char Op;
|
|
ExprAST *LHS, *RHS;
|
|
public:
|
|
BinaryExprAST(char op, ExprAST *lhs, ExprAST *rhs)
|
|
: Op(op), LHS(lhs), RHS(rhs) {}
|
|
};
|
|
|
|
/// CallExprAST - Expression class for function calls.
|
|
class CallExprAST : public ExprAST {
|
|
std::string Callee;
|
|
std::vector<ExprAST*> Args;
|
|
public:
|
|
CallExprAST(const std::string &callee, std::vector<ExprAST*> &args)
|
|
: Callee(callee), Args(args) {}
|
|
};
|
|
|
|
/// PrototypeAST - This class represents the "prototype" for a function,
|
|
/// which captures its name, and its argument names (thus implicitly the number
|
|
/// of arguments the function takes).
|
|
class PrototypeAST {
|
|
std::string Name;
|
|
std::vector<std::string> Args;
|
|
public:
|
|
PrototypeAST(const std::string &name, const std::vector<std::string> &args)
|
|
: Name(name), Args(args) {}
|
|
|
|
};
|
|
|
|
/// FunctionAST - This class represents a function definition itself.
|
|
class FunctionAST {
|
|
PrototypeAST *Proto;
|
|
ExprAST *Body;
|
|
public:
|
|
FunctionAST(PrototypeAST *proto, ExprAST *body)
|
|
: Proto(proto), Body(body) {}
|
|
|
|
};
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// Parser
|
|
//===----------------------------------------------------------------------===//
|
|
|
|
/// CurTok/getNextToken - Provide a simple token buffer. CurTok is the current
|
|
/// token the parser is looking at. getNextToken reads another token from the
|
|
/// lexer and updates CurTok with its results.
|
|
static int CurTok;
|
|
static int getNextToken() {
|
|
return CurTok = gettok();
|
|
}
|
|
|
|
/// BinopPrecedence - This holds the precedence for each binary operator that is
|
|
/// defined.
|
|
static std::map<char, int> BinopPrecedence;
|
|
|
|
/// GetTokPrecedence - Get the precedence of the pending binary operator token.
|
|
static int GetTokPrecedence() {
|
|
if (!isascii(CurTok))
|
|
return -1;
|
|
|
|
// Make sure it's a declared binop.
|
|
int TokPrec = BinopPrecedence[CurTok];
|
|
if (TokPrec <= 0) return -1;
|
|
return TokPrec;
|
|
}
|
|
|
|
/// Error* - These are little helper functions for error handling.
|
|
ExprAST *Error(const char *Str) { fprintf(stderr, "Error: %s\n", Str);return 0;}
|
|
PrototypeAST *ErrorP(const char *Str) { Error(Str); return 0; }
|
|
FunctionAST *ErrorF(const char *Str) { Error(Str); return 0; }
|
|
|
|
static ExprAST *ParseExpression();
|
|
|
|
/// identifierexpr
|
|
/// ::= identifier
|
|
/// ::= identifier '(' expression* ')'
|
|
static ExprAST *ParseIdentifierExpr() {
|
|
std::string IdName = IdentifierStr;
|
|
|
|
getNextToken(); // eat identifier.
|
|
|
|
if (CurTok != '(') // Simple variable ref.
|
|
return new VariableExprAST(IdName);
|
|
|
|
// Call.
|
|
getNextToken(); // eat (
|
|
std::vector<ExprAST*> Args;
|
|
if (CurTok != ')') {
|
|
while (1) {
|
|
ExprAST *Arg = ParseExpression();
|
|
if (!Arg) return 0;
|
|
Args.push_back(Arg);
|
|
|
|
if (CurTok == ')') break;
|
|
|
|
if (CurTok != ',')
|
|
return Error("Expected ')' or ',' in argument list");
|
|
getNextToken();
|
|
}
|
|
}
|
|
|
|
// Eat the ')'.
|
|
getNextToken();
|
|
|
|
return new CallExprAST(IdName, Args);
|
|
}
|
|
|
|
/// numberexpr ::= number
|
|
static ExprAST *ParseNumberExpr() {
|
|
ExprAST *Result = new NumberExprAST(NumVal);
|
|
getNextToken(); // consume the number
|
|
return Result;
|
|
}
|
|
|
|
/// parenexpr ::= '(' expression ')'
|
|
static ExprAST *ParseParenExpr() {
|
|
getNextToken(); // eat (.
|
|
ExprAST *V = ParseExpression();
|
|
if (!V) return 0;
|
|
|
|
if (CurTok != ')')
|
|
return Error("expected ')'");
|
|
getNextToken(); // eat ).
|
|
return V;
|
|
}
|
|
|
|
/// primary
|
|
/// ::= identifierexpr
|
|
/// ::= numberexpr
|
|
/// ::= parenexpr
|
|
static ExprAST *ParsePrimary() {
|
|
switch (CurTok) {
|
|
default: return Error("unknown token when expecting an expression");
|
|
case tok_identifier: return ParseIdentifierExpr();
|
|
case tok_number: return ParseNumberExpr();
|
|
case '(': return ParseParenExpr();
|
|
}
|
|
}
|
|
|
|
/// binoprhs
|
|
/// ::= ('+' primary)*
|
|
static ExprAST *ParseBinOpRHS(int ExprPrec, ExprAST *LHS) {
|
|
// If this is a binop, find its precedence.
|
|
while (1) {
|
|
int TokPrec = GetTokPrecedence();
|
|
|
|
// If this is a binop that binds at least as tightly as the current binop,
|
|
// consume it, otherwise we are done.
|
|
if (TokPrec < ExprPrec)
|
|
return LHS;
|
|
|
|
// Okay, we know this is a binop.
|
|
int BinOp = CurTok;
|
|
getNextToken(); // eat binop
|
|
|
|
// Parse the primary expression after the binary operator.
|
|
ExprAST *RHS = ParsePrimary();
|
|
if (!RHS) return 0;
|
|
|
|
// If BinOp binds less tightly with RHS than the operator after RHS, let
|
|
// the pending operator take RHS as its LHS.
|
|
int NextPrec = GetTokPrecedence();
|
|
if (TokPrec < NextPrec) {
|
|
RHS = ParseBinOpRHS(TokPrec+1, RHS);
|
|
if (RHS == 0) return 0;
|
|
}
|
|
|
|
// Merge LHS/RHS.
|
|
LHS = new BinaryExprAST(BinOp, LHS, RHS);
|
|
}
|
|
}
|
|
|
|
/// expression
|
|
/// ::= primary binoprhs
|
|
///
|
|
static ExprAST *ParseExpression() {
|
|
ExprAST *LHS = ParsePrimary();
|
|
if (!LHS) return 0;
|
|
|
|
return ParseBinOpRHS(0, LHS);
|
|
}
|
|
|
|
/// prototype
|
|
/// ::= id '(' id* ')'
|
|
static PrototypeAST *ParsePrototype() {
|
|
if (CurTok != tok_identifier)
|
|
return ErrorP("Expected function name in prototype");
|
|
|
|
std::string FnName = IdentifierStr;
|
|
getNextToken();
|
|
|
|
if (CurTok != '(')
|
|
return ErrorP("Expected '(' in prototype");
|
|
|
|
std::vector<std::string> ArgNames;
|
|
while (getNextToken() == tok_identifier)
|
|
ArgNames.push_back(IdentifierStr);
|
|
if (CurTok != ')')
|
|
return ErrorP("Expected ')' in prototype");
|
|
|
|
// success.
|
|
getNextToken(); // eat ')'.
|
|
|
|
return new PrototypeAST(FnName, ArgNames);
|
|
}
|
|
|
|
/// definition ::= 'def' prototype expression
|
|
static FunctionAST *ParseDefinition() {
|
|
getNextToken(); // eat def.
|
|
PrototypeAST *Proto = ParsePrototype();
|
|
if (Proto == 0) return 0;
|
|
|
|
if (ExprAST *E = ParseExpression())
|
|
return new FunctionAST(Proto, E);
|
|
return 0;
|
|
}
|
|
|
|
/// toplevelexpr ::= expression
|
|
static FunctionAST *ParseTopLevelExpr() {
|
|
if (ExprAST *E = ParseExpression()) {
|
|
// Make an anonymous proto.
|
|
PrototypeAST *Proto = new PrototypeAST("", std::vector<std::string>());
|
|
return new FunctionAST(Proto, E);
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
/// external ::= 'extern' prototype
|
|
static PrototypeAST *ParseExtern() {
|
|
getNextToken(); // eat extern.
|
|
return ParsePrototype();
|
|
}
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// Top-Level parsing
|
|
//===----------------------------------------------------------------------===//
|
|
|
|
static void HandleDefinition() {
|
|
if (ParseDefinition()) {
|
|
fprintf(stderr, "Parsed a function definition.\n");
|
|
} else {
|
|
// Skip token for error recovery.
|
|
getNextToken();
|
|
}
|
|
}
|
|
|
|
static void HandleExtern() {
|
|
if (ParseExtern()) {
|
|
fprintf(stderr, "Parsed an extern\n");
|
|
} else {
|
|
// Skip token for error recovery.
|
|
getNextToken();
|
|
}
|
|
}
|
|
|
|
static void HandleTopLevelExpression() {
|
|
// Evaluate a top-level expression into an anonymous function.
|
|
if (ParseTopLevelExpr()) {
|
|
fprintf(stderr, "Parsed a top-level expr\n");
|
|
} else {
|
|
// Skip token for error recovery.
|
|
getNextToken();
|
|
}
|
|
}
|
|
|
|
/// top ::= definition | external | expression | ';'
|
|
static void MainLoop() {
|
|
while (1) {
|
|
fprintf(stderr, "ready> ");
|
|
switch (CurTok) {
|
|
case tok_eof: return;
|
|
case ';': getNextToken(); break; // ignore top-level semicolons.
|
|
case tok_def: HandleDefinition(); break;
|
|
case tok_extern: HandleExtern(); break;
|
|
default: HandleTopLevelExpression(); break;
|
|
}
|
|
}
|
|
}
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// Main driver code.
|
|
//===----------------------------------------------------------------------===//
|
|
|
|
int main() {
|
|
// Install standard binary operators.
|
|
// 1 is lowest precedence.
|
|
BinopPrecedence['<'] = 10;
|
|
BinopPrecedence['+'] = 20;
|
|
BinopPrecedence['-'] = 20;
|
|
BinopPrecedence['*'] = 40; // highest.
|
|
|
|
// Prime the first token.
|
|
fprintf(stderr, "ready> ");
|
|
getNextToken();
|
|
|
|
// Run the main "interpreter loop" now.
|
|
MainLoop();
|
|
|
|
return 0;
|
|
}
|
|
</pre>
|
|
</div>
|
|
<a href="LangImpl3.html">Next: Implementing Code Generation to LLVM IR</a>
|
|
</div>
|
|
|
|
<!-- *********************************************************************** -->
|
|
<hr>
|
|
<address>
|
|
<a href="http://jigsaw.w3.org/css-validator/check/referer"><img
|
|
src="http://jigsaw.w3.org/css-validator/images/vcss" alt="Valid CSS!"></a>
|
|
<a href="http://validator.w3.org/check/referer"><img
|
|
src="http://www.w3.org/Icons/valid-html401" alt="Valid HTML 4.01!"></a>
|
|
|
|
<a href="mailto:sabre@nondot.org">Chris Lattner</a><br>
|
|
<a href="http://llvm.org">The LLVM Compiler Infrastructure</a><br>
|
|
Last modified: $Date$
|
|
</address>
|
|
</body>
|
|
</html>
|