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<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:
  explicit 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:
  explicit VariableExprAST(const std::string &amp;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&lt;ExprAST*&gt; Args;
public:
  CallExprAST(const std::string &amp;callee, std::vector&lt;ExprAST*&gt; &amp;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&lt;std::string&gt; Args;
public:
  PrototypeAST(const std::string &amp;name, const std::vector&lt;std::string&gt; &amp;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&lt;ExprAST*&gt; 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&lt;char, int&gt; 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 &lt;= 0) return -1;
  return TokPrec;
}

int main() {
  // Install standard binary operators.
  // 1 is lowest precedence.
  BinopPrecedence['&lt;'] = 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 &lt; 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 &lt; 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 &lt; 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&lt;std::string&gt; 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&lt;std::string&gt;());
    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&gt; ");
    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&gt; <b>def foo(x y) x+foo(y, 4.0);</b>
Parsed a function definition.
ready&gt; <b>def foo(x y) x+y y;</b>
Parsed a function definition.
Parsed a top-level expr
ready&gt; <b>def foo(x y) x+y );</b>
Parsed a function definition.
Error: unknown token when expecting an expression
ready&gt; <b>extern sin(a);</b>
ready&gt; Parsed an extern
ready&gt; <b>^D</b>
$ 
</pre>
</div>

<p>There is a lot of room for extension here.  You can define new AST nodes,
extend the language in many ways, etc.  In the <a href="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 &lt;cstdio&gt;
#include &lt;string&gt;
#include &lt;map&gt;
#include &lt;vector&gt;

//===----------------------------------------------------------------------===//
// 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 &amp;&amp; LastChar != '\n' &amp;&amp; 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:
  explicit NumberExprAST(double val) : Val(val) {}
};

/// VariableExprAST - Expression class for referencing a variable, like "a".
class VariableExprAST : public ExprAST {
  std::string Name;
public:
  explicit VariableExprAST(const std::string &amp;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&lt;ExprAST*&gt; Args;
public:
  CallExprAST(const std::string &amp;callee, std::vector&lt;ExprAST*&gt; &amp;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&lt;std::string&gt; Args;
public:
  PrototypeAST(const std::string &amp;name, const std::vector&lt;std::string&gt; &amp;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&lt;char, int&gt; 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 &lt;= 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&lt;ExprAST*&gt; 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 &lt; 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 &lt; 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&lt;std::string&gt; 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&lt;std::string&gt;());
    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 (FunctionAST *F = ParseDefinition()) {
    fprintf(stderr, "Parsed a function definition.\n");
  } else {
    // Skip token for error recovery.
    getNextToken();
  }
}

static void HandleExtern() {
  if (PrototypeAST *P = 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 (FunctionAST *F = 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&gt; ");
    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['&lt;'] = 10;
  BinopPrecedence['+'] = 20;
  BinopPrecedence['-'] = 20;
  BinopPrecedence['*'] = 40;  // highest.

  // Prime the first token.
  fprintf(stderr, "ready&gt; ");
  getNextToken();

  MainLoop();
  return 0;
}
</pre>
</div>
<a href="LangImpl3.html">Next: Implementing Code Generation to LLVM IR</a>
</div>

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