1 ===========================================
2 Kaleidoscope: Implementing a Parser and AST
3 ===========================================
11 Welcome to Chapter 2 of the "`Implementing a language with
12 LLVM <index.html>`_" tutorial. This chapter shows you how to use the
13 lexer, built in `Chapter 1 <LangImpl1.html>`_, to build a full
14 `parser <http://en.wikipedia.org/wiki/Parsing>`_ for our Kaleidoscope
15 language. Once we have a parser, we'll define and build an `Abstract
16 Syntax Tree <http://en.wikipedia.org/wiki/Abstract_syntax_tree>`_ (AST).
18 The parser we will build uses a combination of `Recursive Descent
19 Parsing <http://en.wikipedia.org/wiki/Recursive_descent_parser>`_ and
21 Parsing <http://en.wikipedia.org/wiki/Operator-precedence_parser>`_ to
22 parse the Kaleidoscope language (the latter for binary expressions and
23 the former for everything else). Before we get to parsing though, lets
24 talk about the output of the parser: the Abstract Syntax Tree.
26 The Abstract Syntax Tree (AST)
27 ==============================
29 The AST for a program captures its behavior in such a way that it is
30 easy for later stages of the compiler (e.g. code generation) to
31 interpret. We basically want one object for each construct in the
32 language, and the AST should closely model the language. In
33 Kaleidoscope, we have expressions, a prototype, and a function object.
34 We'll start with expressions first:
38 /// ExprAST - Base class for all expression nodes.
44 /// NumberExprAST - Expression class for numeric literals like "1.0".
45 class NumberExprAST : public ExprAST {
48 NumberExprAST(double val) : Val(val) {}
51 The code above shows the definition of the base ExprAST class and one
52 subclass which we use for numeric literals. The important thing to note
53 about this code is that the NumberExprAST class captures the numeric
54 value of the literal as an instance variable. This allows later phases
55 of the compiler to know what the stored numeric value is.
57 Right now we only create the AST, so there are no useful accessor
58 methods on them. It would be very easy to add a virtual method to pretty
59 print the code, for example. Here are the other expression AST node
60 definitions that we'll use in the basic form of the Kaleidoscope
65 /// VariableExprAST - Expression class for referencing a variable, like "a".
66 class VariableExprAST : public ExprAST {
69 VariableExprAST(const std::string &name) : Name(name) {}
72 /// BinaryExprAST - Expression class for a binary operator.
73 class BinaryExprAST : public ExprAST {
77 BinaryExprAST(char op, ExprAST *lhs, ExprAST *rhs)
78 : Op(op), LHS(lhs), RHS(rhs) {}
81 /// CallExprAST - Expression class for function calls.
82 class CallExprAST : public ExprAST {
84 std::vector<ExprAST*> Args;
86 CallExprAST(const std::string &callee, std::vector<ExprAST*> &args)
87 : Callee(callee), Args(args) {}
90 This is all (intentionally) rather straight-forward: variables capture
91 the variable name, binary operators capture their opcode (e.g. '+'), and
92 calls capture a function name as well as a list of any argument
93 expressions. One thing that is nice about our AST is that it captures
94 the language features without talking about the syntax of the language.
95 Note that there is no discussion about precedence of binary operators,
96 lexical structure, etc.
98 For our basic language, these are all of the expression nodes we'll
99 define. Because it doesn't have conditional control flow, it isn't
100 Turing-complete; we'll fix that in a later installment. The two things
101 we need next are a way to talk about the interface to a function, and a
102 way to talk about functions themselves:
106 /// PrototypeAST - This class represents the "prototype" for a function,
107 /// which captures its name, and its argument names (thus implicitly the number
108 /// of arguments the function takes).
111 std::vector<std::string> Args;
113 PrototypeAST(const std::string &name, const std::vector<std::string> &args)
114 : Name(name), Args(args) {}
117 /// FunctionAST - This class represents a function definition itself.
122 FunctionAST(PrototypeAST *proto, ExprAST *body)
123 : Proto(proto), Body(body) {}
126 In Kaleidoscope, functions are typed with just a count of their
127 arguments. Since all values are double precision floating point, the
128 type of each argument doesn't need to be stored anywhere. In a more
129 aggressive and realistic language, the "ExprAST" class would probably
132 With this scaffolding, we can now talk about parsing expressions and
133 function bodies in Kaleidoscope.
138 Now that we have an AST to build, we need to define the parser code to
139 build it. The idea here is that we want to parse something like "x+y"
140 (which is returned as three tokens by the lexer) into an AST that could
141 be generated with calls like this:
145 ExprAST *X = new VariableExprAST("x");
146 ExprAST *Y = new VariableExprAST("y");
147 ExprAST *Result = new BinaryExprAST('+', X, Y);
149 In order to do this, we'll start by defining some basic helper routines:
153 /// CurTok/getNextToken - Provide a simple token buffer. CurTok is the current
154 /// token the parser is looking at. getNextToken reads another token from the
155 /// lexer and updates CurTok with its results.
157 static int getNextToken() {
158 return CurTok = gettok();
161 This implements a simple token buffer around the lexer. This allows us
162 to look one token ahead at what the lexer is returning. Every function
163 in our parser will assume that CurTok is the current token that needs to
169 /// Error* - These are little helper functions for error handling.
170 ExprAST *Error(const char *Str) { fprintf(stderr, "Error: %s\n", Str);return 0;}
171 PrototypeAST *ErrorP(const char *Str) { Error(Str); return 0; }
172 FunctionAST *ErrorF(const char *Str) { Error(Str); return 0; }
174 The ``Error`` routines are simple helper routines that our parser will
175 use to handle errors. The error recovery in our parser will not be the
176 best and is not particular user-friendly, but it will be enough for our
177 tutorial. These routines make it easier to handle errors in routines
178 that have various return types: they always return null.
180 With these basic helper functions, we can implement the first piece of
181 our grammar: numeric literals.
183 Basic Expression Parsing
184 ========================
186 We start with numeric literals, because they are the simplest to
187 process. For each production in our grammar, we'll define a function
188 which parses that production. For numeric literals, we have:
192 /// numberexpr ::= number
193 static ExprAST *ParseNumberExpr() {
194 ExprAST *Result = new NumberExprAST(NumVal);
195 getNextToken(); // consume the number
199 This routine is very simple: it expects to be called when the current
200 token is a ``tok_number`` token. It takes the current number value,
201 creates a ``NumberExprAST`` node, advances the lexer to the next token,
204 There are some interesting aspects to this. The most important one is
205 that this routine eats all of the tokens that correspond to the
206 production and returns the lexer buffer with the next token (which is
207 not part of the grammar production) ready to go. This is a fairly
208 standard way to go for recursive descent parsers. For a better example,
209 the parenthesis operator is defined like this:
213 /// parenexpr ::= '(' expression ')'
214 static ExprAST *ParseParenExpr() {
215 getNextToken(); // eat (.
216 ExprAST *V = ParseExpression();
220 return Error("expected ')'");
221 getNextToken(); // eat ).
225 This function illustrates a number of interesting things about the
228 1) It shows how we use the Error routines. When called, this function
229 expects that the current token is a '(' token, but after parsing the
230 subexpression, it is possible that there is no ')' waiting. For example,
231 if the user types in "(4 x" instead of "(4)", the parser should emit an
232 error. Because errors can occur, the parser needs a way to indicate that
233 they happened: in our parser, we return null on an error.
235 2) Another interesting aspect of this function is that it uses recursion
236 by calling ``ParseExpression`` (we will soon see that
237 ``ParseExpression`` can call ``ParseParenExpr``). This is powerful
238 because it allows us to handle recursive grammars, and keeps each
239 production very simple. Note that parentheses do not cause construction
240 of AST nodes themselves. While we could do it this way, the most
241 important role of parentheses are to guide the parser and provide
242 grouping. Once the parser constructs the AST, parentheses are not
245 The next simple production is for handling variable references and
252 /// ::= identifier '(' expression* ')'
253 static ExprAST *ParseIdentifierExpr() {
254 std::string IdName = IdentifierStr;
256 getNextToken(); // eat identifier.
258 if (CurTok != '(') // Simple variable ref.
259 return new VariableExprAST(IdName);
262 getNextToken(); // eat (
263 std::vector<ExprAST*> Args;
266 ExprAST *Arg = ParseExpression();
270 if (CurTok == ')') break;
273 return Error("Expected ')' or ',' in argument list");
281 return new CallExprAST(IdName, Args);
284 This routine follows the same style as the other routines. (It expects
285 to be called if the current token is a ``tok_identifier`` token). It
286 also has recursion and error handling. One interesting aspect of this is
287 that it uses *look-ahead* to determine if the current identifier is a
288 stand alone variable reference or if it is a function call expression.
289 It handles this by checking to see if the token after the identifier is
290 a '(' token, constructing either a ``VariableExprAST`` or
291 ``CallExprAST`` node as appropriate.
293 Now that we have all of our simple expression-parsing logic in place, we
294 can define a helper function to wrap it together into one entry point.
295 We call this class of expressions "primary" expressions, for reasons
296 that will become more clear `later in the
297 tutorial <LangImpl6.html#unary>`_. In order to parse an arbitrary
298 primary expression, we need to determine what sort of expression it is:
303 /// ::= identifierexpr
306 static ExprAST *ParsePrimary() {
308 default: return Error("unknown token when expecting an expression");
309 case tok_identifier: return ParseIdentifierExpr();
310 case tok_number: return ParseNumberExpr();
311 case '(': return ParseParenExpr();
315 Now that you see the definition of this function, it is more obvious why
316 we can assume the state of CurTok in the various functions. This uses
317 look-ahead to determine which sort of expression is being inspected, and
318 then parses it with a function call.
320 Now that basic expressions are handled, we need to handle binary
321 expressions. They are a bit more complex.
323 Binary Expression Parsing
324 =========================
326 Binary expressions are significantly harder to parse because they are
327 often ambiguous. For example, when given the string "x+y\*z", the parser
328 can choose to parse it as either "(x+y)\*z" or "x+(y\*z)". With common
329 definitions from mathematics, we expect the later parse, because "\*"
330 (multiplication) has higher *precedence* than "+" (addition).
332 There are many ways to handle this, but an elegant and efficient way is
333 to use `Operator-Precedence
334 Parsing <http://en.wikipedia.org/wiki/Operator-precedence_parser>`_.
335 This parsing technique uses the precedence of binary operators to guide
336 recursion. To start with, we need a table of precedences:
340 /// BinopPrecedence - This holds the precedence for each binary operator that is
342 static std::map<char, int> BinopPrecedence;
344 /// GetTokPrecedence - Get the precedence of the pending binary operator token.
345 static int GetTokPrecedence() {
346 if (!isascii(CurTok))
349 // Make sure it's a declared binop.
350 int TokPrec = BinopPrecedence[CurTok];
351 if (TokPrec <= 0) return -1;
356 // Install standard binary operators.
357 // 1 is lowest precedence.
358 BinopPrecedence['<'] = 10;
359 BinopPrecedence['+'] = 20;
360 BinopPrecedence['-'] = 20;
361 BinopPrecedence['*'] = 40; // highest.
365 For the basic form of Kaleidoscope, we will only support 4 binary
366 operators (this can obviously be extended by you, our brave and intrepid
367 reader). The ``GetTokPrecedence`` function returns the precedence for
368 the current token, or -1 if the token is not a binary operator. Having a
369 map makes it easy to add new operators and makes it clear that the
370 algorithm doesn't depend on the specific operators involved, but it
371 would be easy enough to eliminate the map and do the comparisons in the
372 ``GetTokPrecedence`` function. (Or just use a fixed-size array).
374 With the helper above defined, we can now start parsing binary
375 expressions. The basic idea of operator precedence parsing is to break
376 down an expression with potentially ambiguous binary operators into
377 pieces. Consider ,for example, the expression "a+b+(c+d)\*e\*f+g".
378 Operator precedence parsing considers this as a stream of primary
379 expressions separated by binary operators. As such, it will first parse
380 the leading primary expression "a", then it will see the pairs [+, b]
381 [+, (c+d)] [\*, e] [\*, f] and [+, g]. Note that because parentheses are
382 primary expressions, the binary expression parser doesn't need to worry
383 about nested subexpressions like (c+d) at all.
385 To start, an expression is a primary expression potentially followed by
386 a sequence of [binop,primaryexpr] pairs:
391 /// ::= primary binoprhs
393 static ExprAST *ParseExpression() {
394 ExprAST *LHS = ParsePrimary();
397 return ParseBinOpRHS(0, LHS);
400 ``ParseBinOpRHS`` is the function that parses the sequence of pairs for
401 us. It takes a precedence and a pointer to an expression for the part
402 that has been parsed so far. Note that "x" is a perfectly valid
403 expression: As such, "binoprhs" is allowed to be empty, in which case it
404 returns the expression that is passed into it. In our example above, the
405 code passes the expression for "a" into ``ParseBinOpRHS`` and the
406 current token is "+".
408 The precedence value passed into ``ParseBinOpRHS`` indicates the
409 *minimal operator precedence* that the function is allowed to eat. For
410 example, if the current pair stream is [+, x] and ``ParseBinOpRHS`` is
411 passed in a precedence of 40, it will not consume any tokens (because
412 the precedence of '+' is only 20). With this in mind, ``ParseBinOpRHS``
418 /// ::= ('+' primary)*
419 static ExprAST *ParseBinOpRHS(int ExprPrec, ExprAST *LHS) {
420 // If this is a binop, find its precedence.
422 int TokPrec = GetTokPrecedence();
424 // If this is a binop that binds at least as tightly as the current binop,
425 // consume it, otherwise we are done.
426 if (TokPrec < ExprPrec)
429 This code gets the precedence of the current token and checks to see if
430 if is too low. Because we defined invalid tokens to have a precedence of
431 -1, this check implicitly knows that the pair-stream ends when the token
432 stream runs out of binary operators. If this check succeeds, we know
433 that the token is a binary operator and that it will be included in this
438 // Okay, we know this is a binop.
440 getNextToken(); // eat binop
442 // Parse the primary expression after the binary operator.
443 ExprAST *RHS = ParsePrimary();
446 As such, this code eats (and remembers) the binary operator and then
447 parses the primary expression that follows. This builds up the whole
448 pair, the first of which is [+, b] for the running example.
450 Now that we parsed the left-hand side of an expression and one pair of
451 the RHS sequence, we have to decide which way the expression associates.
452 In particular, we could have "(a+b) binop unparsed" or "a + (b binop
453 unparsed)". To determine this, we look ahead at "binop" to determine its
454 precedence and compare it to BinOp's precedence (which is '+' in this
459 // If BinOp binds less tightly with RHS than the operator after RHS, let
460 // the pending operator take RHS as its LHS.
461 int NextPrec = GetTokPrecedence();
462 if (TokPrec < NextPrec) {
464 If the precedence of the binop to the right of "RHS" is lower or equal
465 to the precedence of our current operator, then we know that the
466 parentheses associate as "(a+b) binop ...". In our example, the current
467 operator is "+" and the next operator is "+", we know that they have the
468 same precedence. In this case we'll create the AST node for "a+b", and
469 then continue parsing:
473 ... if body omitted ...
477 LHS = new BinaryExprAST(BinOp, LHS, RHS);
478 } // loop around to the top of the while loop.
481 In our example above, this will turn "a+b+" into "(a+b)" and execute the
482 next iteration of the loop, with "+" as the current token. The code
483 above will eat, remember, and parse "(c+d)" as the primary expression,
484 which makes the current pair equal to [+, (c+d)]. It will then evaluate
485 the 'if' conditional above with "\*" as the binop to the right of the
486 primary. In this case, the precedence of "\*" is higher than the
487 precedence of "+" so the if condition will be entered.
489 The critical question left here is "how can the if condition parse the
490 right hand side in full"? In particular, to build the AST correctly for
491 our example, it needs to get all of "(c+d)\*e\*f" as the RHS expression
492 variable. The code to do this is surprisingly simple (code from the
493 above two blocks duplicated for context):
497 // If BinOp binds less tightly with RHS than the operator after RHS, let
498 // the pending operator take RHS as its LHS.
499 int NextPrec = GetTokPrecedence();
500 if (TokPrec < NextPrec) {
501 RHS = ParseBinOpRHS(TokPrec+1, RHS);
502 if (RHS == 0) return 0;
505 LHS = new BinaryExprAST(BinOp, LHS, RHS);
506 } // loop around to the top of the while loop.
509 At this point, we know that the binary operator to the RHS of our
510 primary has higher precedence than the binop we are currently parsing.
511 As such, we know that any sequence of pairs whose operators are all
512 higher precedence than "+" should be parsed together and returned as
513 "RHS". To do this, we recursively invoke the ``ParseBinOpRHS`` function
514 specifying "TokPrec+1" as the minimum precedence required for it to
515 continue. In our example above, this will cause it to return the AST
516 node for "(c+d)\*e\*f" as RHS, which is then set as the RHS of the '+'
519 Finally, on the next iteration of the while loop, the "+g" piece is
520 parsed and added to the AST. With this little bit of code (14
521 non-trivial lines), we correctly handle fully general binary expression
522 parsing in a very elegant way. This was a whirlwind tour of this code,
523 and it is somewhat subtle. I recommend running through it with a few
524 tough examples to see how it works.
526 This wraps up handling of expressions. At this point, we can point the
527 parser at an arbitrary token stream and build an expression from it,
528 stopping at the first token that is not part of the expression. Next up
529 we need to handle function definitions, etc.
534 The next thing missing is handling of function prototypes. In
535 Kaleidoscope, these are used both for 'extern' function declarations as
536 well as function body definitions. The code to do this is
537 straight-forward and not very interesting (once you've survived
543 /// ::= id '(' id* ')'
544 static PrototypeAST *ParsePrototype() {
545 if (CurTok != tok_identifier)
546 return ErrorP("Expected function name in prototype");
548 std::string FnName = IdentifierStr;
552 return ErrorP("Expected '(' in prototype");
554 // Read the list of argument names.
555 std::vector<std::string> ArgNames;
556 while (getNextToken() == tok_identifier)
557 ArgNames.push_back(IdentifierStr);
559 return ErrorP("Expected ')' in prototype");
562 getNextToken(); // eat ')'.
564 return new PrototypeAST(FnName, ArgNames);
567 Given this, a function definition is very simple, just a prototype plus
568 an expression to implement the body:
572 /// definition ::= 'def' prototype expression
573 static FunctionAST *ParseDefinition() {
574 getNextToken(); // eat def.
575 PrototypeAST *Proto = ParsePrototype();
576 if (Proto == 0) return 0;
578 if (ExprAST *E = ParseExpression())
579 return new FunctionAST(Proto, E);
583 In addition, we support 'extern' to declare functions like 'sin' and
584 'cos' as well as to support forward declaration of user functions. These
585 'extern's are just prototypes with no body:
589 /// external ::= 'extern' prototype
590 static PrototypeAST *ParseExtern() {
591 getNextToken(); // eat extern.
592 return ParsePrototype();
595 Finally, we'll also let the user type in arbitrary top-level expressions
596 and evaluate them on the fly. We will handle this by defining anonymous
597 nullary (zero argument) functions for them:
601 /// toplevelexpr ::= expression
602 static FunctionAST *ParseTopLevelExpr() {
603 if (ExprAST *E = ParseExpression()) {
604 // Make an anonymous proto.
605 PrototypeAST *Proto = new PrototypeAST("", std::vector<std::string>());
606 return new FunctionAST(Proto, E);
611 Now that we have all the pieces, let's build a little driver that will
612 let us actually *execute* this code we've built!
617 The driver for this simply invokes all of the parsing pieces with a
618 top-level dispatch loop. There isn't much interesting here, so I'll just
619 include the top-level loop. See `below <#code>`_ for full code in the
620 "Top-Level Parsing" section.
624 /// top ::= definition | external | expression | ';'
625 static void MainLoop() {
627 fprintf(stderr, "ready> ");
629 case tok_eof: return;
630 case ';': getNextToken(); break; // ignore top-level semicolons.
631 case tok_def: HandleDefinition(); break;
632 case tok_extern: HandleExtern(); break;
633 default: HandleTopLevelExpression(); break;
638 The most interesting part of this is that we ignore top-level
639 semicolons. Why is this, you ask? The basic reason is that if you type
640 "4 + 5" at the command line, the parser doesn't know whether that is the
641 end of what you will type or not. For example, on the next line you
642 could type "def foo..." in which case 4+5 is the end of a top-level
643 expression. Alternatively you could type "\* 6", which would continue
644 the expression. Having top-level semicolons allows you to type "4+5;",
645 and the parser will know you are done.
650 With just under 400 lines of commented code (240 lines of non-comment,
651 non-blank code), we fully defined our minimal language, including a
652 lexer, parser, and AST builder. With this done, the executable will
653 validate Kaleidoscope code and tell us if it is grammatically invalid.
654 For example, here is a sample interaction:
659 ready> def foo(x y) x+foo(y, 4.0);
660 Parsed a function definition.
661 ready> def foo(x y) x+y y;
662 Parsed a function definition.
663 Parsed a top-level expr
664 ready> def foo(x y) x+y );
665 Parsed a function definition.
666 Error: unknown token when expecting an expression
667 ready> extern sin(a);
668 ready> Parsed an extern
672 There is a lot of room for extension here. You can define new AST nodes,
673 extend the language in many ways, etc. In the `next
674 installment <LangImpl3.html>`_, we will describe how to generate LLVM
675 Intermediate Representation (IR) from the AST.
680 Here is the complete code listing for this and the previous chapter.
681 Note that it is fully self-contained: you don't need LLVM or any
682 external libraries at all for this. (Besides the C and C++ standard
683 libraries, of course.) To build this, just compile with:
688 clang++ -g -O3 toy.cpp
694 .. literalinclude:: ../../examples/Kaleidoscope/Chapter2/toy.cpp
697 `Next: Implementing Code Generation to LLVM IR <LangImpl3.html>`_