calc
ltcalc
mfcalc
This manual is for GNU Bison (version 2.3, 30 May 2006), the GNU parser generator.
Copyright © 1988, 1989, 1990, 1991, 1992, 1993, 1995, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006 Free Software Foundation, Inc.
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, with the Front-Cover texts being “A GNU Manual,” and with the Back-Cover Texts as in (a) below. A copy of the license is included in the section entitled “GNU Free Documentation License.”(a) The FSF's Back-Cover Text is: “You have freedom to copy and modify this GNU Manual, like GNU software. Copies published by the Free Software Foundation raise funds for GNU development.”
Tutorial sections:
Reference sections:
--- The Detailed Node Listing ---
The Concepts of Bison
Writing GLR Parsers
Examples
Reverse Polish Notation Calculator
Grammar Rules for rpcalc
Location Tracking Calculator: ltcalc
Multi-Function Calculator: mfcalc
Bison Grammar Files
Outline of a Bison Grammar
Defining Language Semantics
Tracking Locations
Bison Declarations
Parser C-Language Interface
The Lexical Analyzer Function yylex
The Bison Parser Algorithm
Operator Precedence
Handling Context Dependencies
Debugging Your Parser
Invoking Bison
C++ Language Interface
C++ Parsers
A Complete C++ Example
Frequently Asked Questions
Copying This Manual
Bison is a general-purpose parser generator that converts an annotated context-free grammar into an LALR(1) or GLR parser for that grammar. Once you are proficient with Bison, you can use it to develop a wide range of language parsers, from those used in simple desk calculators to complex programming languages.
Bison is upward compatible with Yacc: all properly-written Yacc grammars ought to work with Bison with no change. Anyone familiar with Yacc should be able to use Bison with little trouble. You need to be fluent in C or C++ programming in order to use Bison or to understand this manual.
We begin with tutorial chapters that explain the basic concepts of using Bison and show three explained examples, each building on the last. If you don't know Bison or Yacc, start by reading these chapters. Reference chapters follow which describe specific aspects of Bison in detail.
Bison was written primarily by Robert Corbett; Richard Stallman made it Yacc-compatible. Wilfred Hansen of Carnegie Mellon University added multi-character string literals and other features.
This edition corresponds to version 2.3 of Bison.
The distribution terms for Bison-generated parsers permit using the parsers in nonfree programs. Before Bison version 2.2, these extra permissions applied only when Bison was generating LALR(1) parsers in C. And before Bison version 1.24, Bison-generated parsers could be used only in programs that were free software.
The other GNU programming tools, such as the GNU C compiler, have never had such a requirement. They could always be used for nonfree software. The reason Bison was different was not due to a special policy decision; it resulted from applying the usual General Public License to all of the Bison source code.
The output of the Bison utility—the Bison parser file—contains a verbatim copy of a sizable piece of Bison, which is the code for the parser's implementation. (The actions from your grammar are inserted into this implementation at one point, but most of the rest of the implementation is not changed.) When we applied the GPL terms to the skeleton code for the parser's implementation, the effect was to restrict the use of Bison output to free software.
We didn't change the terms because of sympathy for people who want to make software proprietary. Software should be free. But we concluded that limiting Bison's use to free software was doing little to encourage people to make other software free. So we decided to make the practical conditions for using Bison match the practical conditions for using the other GNU tools.
This exception applies when Bison is generating code for a parser. You can tell whether the exception applies to a Bison output file by inspecting the file for text beginning with “As a special exception...”. The text spells out the exact terms of the exception.
Copyright © 1989, 1991 Free Software Foundation, Inc.
51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA
Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.
The licenses for most software are designed to take away your freedom to share and change it. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change free software—to make sure the software is free for all its users. This General Public License applies to most of the Free Software Foundation's software and to any other program whose authors commit to using it. (Some other Free Software Foundation software is covered by the GNU Library General Public License instead.) You can apply it to your programs, too.
When we speak of free software, we are referring to freedom, not price. Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software (and charge for this service if you wish), that you receive source code or can get it if you want it, that you can change the software or use pieces of it in new free programs; and that you know you can do these things.
To protect your rights, we need to make restrictions that forbid anyone to deny you these rights or to ask you to surrender the rights. These restrictions translate to certain responsibilities for you if you distribute copies of the software, or if you modify it.
For example, if you distribute copies of such a program, whether gratis or for a fee, you must give the recipients all the rights that you have. You must make sure that they, too, receive or can get the source code. And you must show them these terms so they know their rights.
We protect your rights with two steps: (1) copyright the software, and (2) offer you this license which gives you legal permission to copy, distribute and/or modify the software.
Also, for each author's protection and ours, we want to make certain that everyone understands that there is no warranty for this free software. If the software is modified by someone else and passed on, we want its recipients to know that what they have is not the original, so that any problems introduced by others will not reflect on the original authors' reputations.
Finally, any free program is threatened constantly by software patents. We wish to avoid the danger that redistributors of a free program will individually obtain patent licenses, in effect making the program proprietary. To prevent this, we have made it clear that any patent must be licensed for everyone's free use or not licensed at all.
The precise terms and conditions for copying, distribution and modification follow.
Activities other than copying, distribution and modification are not covered by this License; they are outside its scope. The act of running the Program is not restricted, and the output from the Program is covered only if its contents constitute a work based on the Program (independent of having been made by running the Program). Whether that is true depends on what the Program does.
You may charge a fee for the physical act of transferring a copy, and you may at your option offer warranty protection in exchange for a fee.
These requirements apply to the modified work as a whole. If identifiable sections of that work are not derived from the Program, and can be reasonably considered independent and separate works in themselves, then this License, and its terms, do not apply to those sections when you distribute them as separate works. But when you distribute the same sections as part of a whole which is a work based on the Program, the distribution of the whole must be on the terms of this License, whose permissions for other licensees extend to the entire whole, and thus to each and every part regardless of who wrote it.
Thus, it is not the intent of this section to claim rights or contest your rights to work written entirely by you; rather, the intent is to exercise the right to control the distribution of derivative or collective works based on the Program.
In addition, mere aggregation of another work not based on the Program with the Program (or with a work based on the Program) on a volume of a storage or distribution medium does not bring the other work under the scope of this License.
The source code for a work means the preferred form of the work for making modifications to it. For an executable work, complete source code means all the source code for all modules it contains, plus any associated interface definition files, plus the scripts used to control compilation and installation of the executable. However, as a special exception, the source code distributed need not include anything that is normally distributed (in either source or binary form) with the major components (compiler, kernel, and so on) of the operating system on which the executable runs, unless that component itself accompanies the executable.
If distribution of executable or object code is made by offering access to copy from a designated place, then offering equivalent access to copy the source code from the same place counts as distribution of the source code, even though third parties are not compelled to copy the source along with the object code.
If any portion of this section is held invalid or unenforceable under any particular circumstance, the balance of the section is intended to apply and the section as a whole is intended to apply in other circumstances.
It is not the purpose of this section to induce you to infringe any patents or other property right claims or to contest validity of any such claims; this section has the sole purpose of protecting the integrity of the free software distribution system, which is implemented by public license practices. Many people have made generous contributions to the wide range of software distributed through that system in reliance on consistent application of that system; it is up to the author/donor to decide if he or she is willing to distribute software through any other system and a licensee cannot impose that choice.
This section is intended to make thoroughly clear what is believed to be a consequence of the rest of this License.
Each version is given a distinguishing version number. If the Program specifies a version number of this License which applies to it and “any later version”, you have the option of following the terms and conditions either of that version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of this License, you may choose any version ever published by the Free Software Foundation.
If you develop a new program, and you want it to be of the greatest possible use to the public, the best way to achieve this is to make it free software which everyone can redistribute and change under these terms.
To do so, attach the following notices to the program. It is safest to attach them to the start of each source file to most effectively convey the exclusion of warranty; and each file should have at least the “copyright” line and a pointer to where the full notice is found.
one line to give the program's name and a brief idea of what it does.
Copyright (C) yyyy name of author
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
Also add information on how to contact you by electronic and paper mail.
If the program is interactive, make it output a short notice like this when it starts in an interactive mode:
Gnomovision version 69, Copyright (C) 19yy name of author
Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
This is free software, and you are welcome to redistribute it
under certain conditions; type `show c' for details.
The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, the commands you use may be called something other than `show w' and `show c'; they could even be mouse-clicks or menu items—whatever suits your program.
You should also get your employer (if you work as a programmer) or your school, if any, to sign a “copyright disclaimer” for the program, if necessary. Here is a sample; alter the names:
Yoyodyne, Inc., hereby disclaims all copyright interest in the program
`Gnomovision' (which makes passes at compilers) written by James Hacker.
signature of Ty Coon, 1 April 1989
Ty Coon, President of Vice
This General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Library General Public License instead of this License.
This chapter introduces many of the basic concepts without which the details of Bison will not make sense. If you do not already know how to use Bison or Yacc, we suggest you start by reading this chapter carefully.
In order for Bison to parse a language, it must be described by a context-free grammar. This means that you specify one or more syntactic groupings and give rules for constructing them from their parts. For example, in the C language, one kind of grouping is called an `expression'. One rule for making an expression might be, “An expression can be made of a minus sign and another expression”. Another would be, “An expression can be an integer”. As you can see, rules are often recursive, but there must be at least one rule which leads out of the recursion.
The most common formal system for presenting such rules for humans to read is Backus-Naur Form or “BNF”, which was developed in order to specify the language Algol 60. Any grammar expressed in BNF is a context-free grammar. The input to Bison is essentially machine-readable BNF.
There are various important subclasses of context-free grammar. Although it can handle almost all context-free grammars, Bison is optimized for what are called LALR(1) grammars. In brief, in these grammars, it must be possible to tell how to parse any portion of an input string with just a single token of look-ahead. Strictly speaking, that is a description of an LR(1) grammar, and LALR(1) involves additional restrictions that are hard to explain simply; but it is rare in actual practice to find an LR(1) grammar that fails to be LALR(1). See Mysterious Reduce/Reduce Conflicts, for more information on this.
Parsers for LALR(1) grammars are deterministic, meaning roughly that the next grammar rule to apply at any point in the input is uniquely determined by the preceding input and a fixed, finite portion (called a look-ahead) of the remaining input. A context-free grammar can be ambiguous, meaning that there are multiple ways to apply the grammar rules to get the same inputs. Even unambiguous grammars can be nondeterministic, meaning that no fixed look-ahead always suffices to determine the next grammar rule to apply. With the proper declarations, Bison is also able to parse these more general context-free grammars, using a technique known as GLR parsing (for Generalized LR). Bison's GLR parsers are able to handle any context-free grammar for which the number of possible parses of any given string is finite.
In the formal grammatical rules for a language, each kind of syntactic unit or grouping is named by a symbol. Those which are built by grouping smaller constructs according to grammatical rules are called nonterminal symbols; those which can't be subdivided are called terminal symbols or token types. We call a piece of input corresponding to a single terminal symbol a token, and a piece corresponding to a single nonterminal symbol a grouping.
We can use the C language as an example of what symbols, terminal and nonterminal, mean. The tokens of C are identifiers, constants (numeric and string), and the various keywords, arithmetic operators and punctuation marks. So the terminal symbols of a grammar for C include `identifier', `number', `string', plus one symbol for each keyword, operator or punctuation mark: `if', `return', `const', `static', `int', `char', `plus-sign', `open-brace', `close-brace', `comma' and many more. (These tokens can be subdivided into characters, but that is a matter of lexicography, not grammar.)
Here is a simple C function subdivided into tokens:
int /* keyword `int' */ square (int x) /* identifier, open-paren, keyword `int', identifier, close-paren */ { /* open-brace */ return x * x; /* keyword `return', identifier, asterisk, identifier, semicolon */ } /* close-brace */
The syntactic groupings of C include the expression, the statement, the declaration, and the function definition. These are represented in the grammar of C by nonterminal symbols `expression', `statement', `declaration' and `function definition'. The full grammar uses dozens of additional language constructs, each with its own nonterminal symbol, in order to express the meanings of these four. The example above is a function definition; it contains one declaration, and one statement. In the statement, each `x' is an expression and so is `x * x'.
Each nonterminal symbol must have grammatical rules showing how it is made
out of simpler constructs. For example, one kind of C statement is the
return statement; this would be described with a grammar rule which
reads informally as follows:
A `statement' can be made of a `return' keyword, an `expression' and a `semicolon'.
There would be many other rules for `statement', one for each kind of statement in C.
One nonterminal symbol must be distinguished as the special one which defines a complete utterance in the language. It is called the start symbol. In a compiler, this means a complete input program. In the C language, the nonterminal symbol `sequence of definitions and declarations' plays this role.
For example, `1 + 2' is a valid C expression—a valid part of a C program—but it is not valid as an entire C program. In the context-free grammar of C, this follows from the fact that `expression' is not the start symbol.
The Bison parser reads a sequence of tokens as its input, and groups the tokens using the grammar rules. If the input is valid, the end result is that the entire token sequence reduces to a single grouping whose symbol is the grammar's start symbol. If we use a grammar for C, the entire input must be a `sequence of definitions and declarations'. If not, the parser reports a syntax error.
A formal grammar is a mathematical construct. To define the language for Bison, you must write a file expressing the grammar in Bison syntax: a Bison grammar file. See Bison Grammar Files.
A nonterminal symbol in the formal grammar is represented in Bison input
as an identifier, like an identifier in C. By convention, it should be
in lower case, such as expr, stmt or declaration.
The Bison representation for a terminal symbol is also called a token
type. Token types as well can be represented as C-like identifiers. By
convention, these identifiers should be upper case to distinguish them from
nonterminals: for example, INTEGER, IDENTIFIER, IF or
RETURN. A terminal symbol that stands for a particular keyword in
the language should be named after that keyword converted to upper case.
The terminal symbol error is reserved for error recovery.
See Symbols.
A terminal symbol can also be represented as a character literal, just like a C character constant. You should do this whenever a token is just a single character (parenthesis, plus-sign, etc.): use that same character in a literal as the terminal symbol for that token.
A third way to represent a terminal symbol is with a C string constant containing several characters. See Symbols, for more information.
The grammar rules also have an expression in Bison syntax. For example,
here is the Bison rule for a C return statement. The semicolon in
quotes is a literal character token, representing part of the C syntax for
the statement; the naked semicolon, and the colon, are Bison punctuation
used in every rule.
stmt: RETURN expr ';'
;
A formal grammar selects tokens only by their classifications: for example, if a rule mentions the terminal symbol `integer constant', it means that any integer constant is grammatically valid in that position. The precise value of the constant is irrelevant to how to parse the input: if `x+4' is grammatical then `x+1' or `x+3989' is equally grammatical.
But the precise value is very important for what the input means once it is parsed. A compiler is useless if it fails to distinguish between 4, 1 and 3989 as constants in the program! Therefore, each token in a Bison grammar has both a token type and a semantic value. See Defining Language Semantics, for details.
The token type is a terminal symbol defined in the grammar, such as
INTEGER, IDENTIFIER or ','. It tells everything
you need to know to decide where the token may validly appear and how to
group it with other tokens. The grammar rules know nothing about tokens
except their types.
The semantic value has all the rest of the information about the
meaning of the token, such as the value of an integer, or the name of an
identifier. (A token such as ',' which is just punctuation doesn't
need to have any semantic value.)
For example, an input token might be classified as token type
INTEGER and have the semantic value 4. Another input token might
have the same token type INTEGER but value 3989. When a grammar
rule says that INTEGER is allowed, either of these tokens is
acceptable because each is an INTEGER. When the parser accepts the
token, it keeps track of the token's semantic value.
Each grouping can also have a semantic value as well as its nonterminal symbol. For example, in a calculator, an expression typically has a semantic value that is a number. In a compiler for a programming language, an expression typically has a semantic value that is a tree structure describing the meaning of the expression.
In order to be useful, a program must do more than parse input; it must also produce some output based on the input. In a Bison grammar, a grammar rule can have an action made up of C statements. Each time the parser recognizes a match for that rule, the action is executed. See Actions.
Most of the time, the purpose of an action is to compute the semantic value of the whole construct from the semantic values of its parts. For example, suppose we have a rule which says an expression can be the sum of two expressions. When the parser recognizes such a sum, each of the subexpressions has a semantic value which describes how it was built up. The action for this rule should create a similar sort of value for the newly recognized larger expression.
For example, here is a rule that says an expression can be the sum of two subexpressions:
expr: expr '+' expr { $$ = $1 + $3; }
;
The action says how to produce the semantic value of the sum expression from the values of the two subexpressions.
In some grammars, Bison's standard LALR(1) parsing algorithm cannot decide whether to apply a certain grammar rule at a given point. That is, it may not be able to decide (on the basis of the input read so far) which of two possible reductions (applications of a grammar rule) applies, or whether to apply a reduction or read more of the input and apply a reduction later in the input. These are known respectively as reduce/reduce conflicts (see Reduce/Reduce), and shift/reduce conflicts (see Shift/Reduce).
To use a grammar that is not easily modified to be LALR(1), a
more general parsing algorithm is sometimes necessary. If you include
%glr-parser among the Bison declarations in your file
(see Grammar Outline), the result is a Generalized LR
(GLR) parser. These parsers handle Bison grammars that
contain no unresolved conflicts (i.e., after applying precedence
declarations) identically to LALR(1) parsers. However, when
faced with unresolved shift/reduce and reduce/reduce conflicts,
GLR parsers use the simple expedient of doing both,
effectively cloning the parser to follow both possibilities. Each of
the resulting parsers can again split, so that at any given time, there
can be any number of possible parses being explored. The parsers
proceed in lockstep; that is, all of them consume (shift) a given input
symbol before any of them proceed to the next. Each of the cloned
parsers eventually meets one of two possible fates: either it runs into
a parsing error, in which case it simply vanishes, or it merges with
another parser, because the two of them have reduced the input to an
identical set of symbols.
During the time that there are multiple parsers, semantic actions are recorded, but not performed. When a parser disappears, its recorded semantic actions disappear as well, and are never performed. When a reduction makes two parsers identical, causing them to merge, Bison records both sets of semantic actions. Whenever the last two parsers merge, reverting to the single-parser case, Bison resolves all the outstanding actions either by precedences given to the grammar rules involved, or by performing both actions, and then calling a designated user-defined function on the resulting values to produce an arbitrary merged result.
In the simplest cases, you can use the GLR algorithm to parse grammars that are unambiguous, but fail to be LALR(1). Such grammars typically require more than one symbol of look-ahead, or (in rare cases) fall into the category of grammars in which the LALR(1) algorithm throws away too much information (they are in LR(1), but not LALR(1), Mystery Conflicts).
Consider a problem that arises in the declaration of enumerated and subrange types in the programming language Pascal. Here are some examples:
type subrange = lo .. hi;
type enum = (a, b, c);
The original language standard allows only numeric literals and constant identifiers for the subrange bounds (`lo' and `hi'), but Extended Pascal (ISO/IEC 10206) and many other Pascal implementations allow arbitrary expressions there. This gives rise to the following situation, containing a superfluous pair of parentheses:
type subrange = (a) .. b;
Compare this to the following declaration of an enumerated type with only one value:
type enum = (a);
(These declarations are contrived, but they are syntactically valid, and more-complicated cases can come up in practical programs.)
These two declarations look identical until the `..' token. With normal LALR(1) one-token look-ahead it is not possible to decide between the two forms when the identifier `a' is parsed. It is, however, desirable for a parser to decide this, since in the latter case `a' must become a new identifier to represent the enumeration value, while in the former case `a' must be evaluated with its current meaning, which may be a constant or even a function call.
You could parse `(a)' as an “unspecified identifier in parentheses”, to be resolved later, but this typically requires substantial contortions in both semantic actions and large parts of the grammar, where the parentheses are nested in the recursive rules for expressions.
You might think of using the lexer to distinguish between the two forms by returning different tokens for currently defined and undefined identifiers. But if these declarations occur in a local scope, and `a' is defined in an outer scope, then both forms are possible—either locally redefining `a', or using the value of `a' from the outer scope. So this approach cannot work.
A simple solution to this problem is to declare the parser to use the GLR algorithm. When the GLR parser reaches the critical state, it merely splits into two branches and pursues both syntax rules simultaneously. Sooner or later, one of them runs into a parsing error. If there is a `..' token before the next `;', the rule for enumerated types fails since it cannot accept `..' anywhere; otherwise, the subrange type rule fails since it requires a `..' token. So one of the branches fails silently, and the other one continues normally, performing all the intermediate actions that were postponed during the split.
If the input is syntactically incorrect, both branches fail and the parser reports a syntax error as usual.
The effect of all this is that the parser seems to “guess” the correct branch to take, or in other words, it seems to use more look-ahead than the underlying LALR(1) algorithm actually allows for. In this example, LALR(2) would suffice, but also some cases that are not LALR(k) for any k can be handled this way.
In general, a GLR parser can take quadratic or cubic worst-case time, and the current Bison parser even takes exponential time and space for some grammars. In practice, this rarely happens, and for many grammars it is possible to prove that it cannot happen. The present example contains only one conflict between two rules, and the type-declaration context containing the conflict cannot be nested. So the number of branches that can exist at any time is limited by the constant 2, and the parsing time is still linear.
Here is a Bison grammar corresponding to the example above. It parses a vastly simplified form of Pascal type declarations.
%token TYPE DOTDOT ID
%left '+' '-'
%left '*' '/'
%%
type_decl : TYPE ID '=' type ';'
;
type : '(' id_list ')'
| expr DOTDOT expr
;
id_list : ID
| id_list ',' ID
;
expr : '(' expr ')'
| expr '+' expr
| expr '-' expr
| expr '*' expr
| expr '/' expr
| ID
;
When used as a normal LALR(1) grammar, Bison correctly complains about one reduce/reduce conflict. In the conflicting situation the parser chooses one of the alternatives, arbitrarily the one declared first. Therefore the following correct input is not recognized:
type t = (a) .. b;
The parser can be turned into a GLR parser, while also telling Bison to be silent about the one known reduce/reduce conflict, by adding these two declarations to the Bison input file (before the first `%%'):
%glr-parser
%expect-rr 1
No change in the grammar itself is required. Now the parser recognizes all valid declarations, according to the limited syntax above, transparently. In fact, the user does not even notice when the parser splits.
So here we have a case where we can use the benefits of GLR, almost without disadvantages. Even in simple cases like this, however, there are at least two potential problems to beware. First, always analyze the conflicts reported by Bison to make sure that GLR splitting is only done where it is intended. A GLR parser splitting inadvertently may cause problems less obvious than an LALR parser statically choosing the wrong alternative in a conflict. Second, consider interactions with the lexer (see Semantic Tokens) with great care. Since a split parser consumes tokens without performing any actions during the split, the lexer cannot obtain information via parser actions. Some cases of lexer interactions can be eliminated by using GLR to shift the complications from the lexer to the parser. You must check the remaining cases for correctness.
In our example, it would be safe for the lexer to return tokens based on their current meanings in some symbol table, because no new symbols are defined in the middle of a type declaration. Though it is possible for a parser to define the enumeration constants as they are parsed, before the type declaration is completed, it actually makes no difference since they cannot be used within the same enumerated type declaration.
Let's consider an example, vastly simplified from a C++ grammar.
%{
#include <stdio.h>
#define YYSTYPE char const *
int yylex (void);
void yyerror (char const *);
%}
%token TYPENAME ID
%right '='
%left '+'
%glr-parser
%%
prog :
| prog stmt { printf ("\n"); }
;
stmt : expr ';' %dprec 1
| decl %dprec 2
;
expr : ID { printf ("%s ", $$); }
| TYPENAME '(' expr ')'
{ printf ("%s <cast> ", $1); }
| expr '+' expr { printf ("+ "); }
| expr '=' expr { printf ("= "); }
;
decl : TYPENAME declarator ';'
{ printf ("%s <declare> ", $1); }
| TYPENAME declarator '=' expr ';'
{ printf ("%s <init-declare> ", $1); }
;
declarator : ID { printf ("\"%s\" ", $1); }
| '(' declarator ')'
;
This models a problematic part of the C++ grammar—the ambiguity between certain declarations and statements. For example,
T (x) = y+z;
parses as either an expr or a stmt
(assuming that `T' is recognized as a TYPENAME and
`x' as an ID).
Bison detects this as a reduce/reduce conflict between the rules
expr : ID and declarator : ID, which it cannot resolve at the
time it encounters x in the example above. Since this is a
GLR parser, it therefore splits the problem into two parses, one for
each choice of resolving the reduce/reduce conflict.
Unlike the example from the previous section (see Simple GLR Parsers),
however, neither of these parses “dies,” because the grammar as it stands is
ambiguous. One of the parsers eventually reduces stmt : expr ';' and
the other reduces stmt : decl, after which both parsers are in an
identical state: they've seen `prog stmt' and have the same unprocessed
input remaining. We say that these parses have merged.
At this point, the GLR parser requires a specification in the
grammar of how to choose between the competing parses.
In the example above, the two %dprec
declarations specify that Bison is to give precedence
to the parse that interprets the example as a
decl, which implies that x is a declarator.
The parser therefore prints
"x" y z + T <init-declare>
The %dprec declarations only come into play when more than one
parse survives. Consider a different input string for this parser:
T (x) + y;
This is another example of using GLR to parse an unambiguous
construct, as shown in the previous section (see Simple GLR Parsers).
Here, there is no ambiguity (this cannot be parsed as a declaration).
However, at the time the Bison parser encounters x, it does not
have enough information to resolve the reduce/reduce conflict (again,
between x as an expr or a declarator). In this
case, no precedence declaration is used. Again, the parser splits
into two, one assuming that x is an expr, and the other
assuming x is a declarator. The second of these parsers
then vanishes when it sees +, and the parser prints
x T <cast> y +
Suppose that instead of resolving the ambiguity, you wanted to see all
the possibilities. For this purpose, you must merge the semantic
actions of the two possible parsers, rather than choosing one over the
other. To do so, you could change the declaration of stmt as
follows:
stmt : expr ';' %merge <stmtMerge>
| decl %merge <stmtMerge>
;
and define the stmtMerge function as:
static YYSTYPE
stmtMerge (YYSTYPE x0, YYSTYPE x1)
{
printf ("<OR> ");
return "";
}
with an accompanying forward declaration in the C declarations at the beginning of the file:
%{
#define YYSTYPE char const *
static YYSTYPE stmtMerge (YYSTYPE x0, YYSTYPE x1);
%}
With these declarations, the resulting parser parses the first example
as both an expr and a decl, and prints
"x" y z + T <init-declare> x T <cast> y z + = <OR>
Bison requires that all of the productions that participate in any particular merge have identical `%merge' clauses. Otherwise, the ambiguity would be unresolvable, and the parser will report an error during any parse that results in the offending merge.
By definition, a deferred semantic action is not performed at the same time as the associated reduction. This raises caveats for several Bison features you might use in a semantic action in a GLR parser.
In any semantic action, you can examine yychar to determine the type of
the look-ahead token present at the time of the associated reduction.
After checking that yychar is not set to YYEMPTY or YYEOF,
you can then examine yylval and yylloc to determine the
look-ahead token's semantic value and location, if any.
In a nondeferred semantic action, you can also modify any of these variables to
influence syntax analysis.
See Look-Ahead Tokens.
In a deferred semantic action, it's too late to influence syntax analysis.
In this case, yychar, yylval, and yylloc are set to
shallow copies of the values they had at the time of the associated reduction.
For this reason alone, modifying them is dangerous.
Moreover, the result of modifying them is undefined and subject to change with
future versions of Bison.
For example, if a semantic action might be deferred, you should never write it
to invoke yyclearin (see Action Features) or to attempt to free
memory referenced by yylval.
Another Bison feature requiring special consideration is YYERROR
(see Action Features), which you can invoke in a semantic action to
initiate error recovery.
During deterministic GLR operation, the effect of YYERROR is
the same as its effect in an LALR(1) parser.
In a deferred semantic action, its effect is undefined.
Also, see Default Action for Locations, which
describes a special usage of YYLLOC_DEFAULT in GLR parsers.
The GLR parsers require a compiler for ISO C89 or
later. In addition, they use the inline keyword, which is not
C89, but is C99 and is a common extension in pre-C99 compilers. It is
up to the user of these parsers to handle
portability issues. For instance, if using Autoconf and the Autoconf
macro AC_C_INLINE, a mere
%{
#include <config.h>
%}
will suffice. Otherwise, we suggest
%{
#if __STDC_VERSION__ < 199901 && ! defined __GNUC__ && ! defined inline
#define inline
#endif
%}
Many applications, like interpreters or compilers, have to produce verbose and useful error messages. To achieve this, one must be able to keep track of the textual location, or location, of each syntactic construct. Bison provides a mechanism for handling these locations.
Each token has a semantic value. In a similar fashion, each token has an associated location, but the type of locations is the same for all tokens and groupings. Moreover, the output parser is equipped with a default data structure for storing locations (see Locations, for more details).
Like semantic values, locations can be reached in actions using a dedicated
set of constructs. In the example above, the location of the whole grouping
is @$, while the locations of the subexpressions are @1 and
@3.
When a rule is matched, a default action is used to compute the semantic value
of its left hand side (see Actions). In the same way, another default
action is used for locations. However, the action for locations is general
enough for most cases, meaning there is usually no need to describe for each
rule how @$ should be formed. When building a new location for a given
grouping, the default behavior of the output parser is to take the beginning
of the first symbol, and the end of the last symbol.
When you run Bison, you give it a Bison grammar file as input. The output is a C source file that parses the language described by the grammar. This file is called a Bison parser. Keep in mind that the Bison utility and the Bison parser are two distinct programs: the Bison utility is a program whose output is the Bison parser that becomes part of your program.
The job of the Bison parser is to group tokens into groupings according to the grammar rules—for example, to build identifiers and operators into expressions. As it does this, it runs the actions for the grammar rules it uses.
The tokens come from a function called the lexical analyzer that
you must supply in some fashion (such as by writing it in C). The Bison
parser calls the lexical analyzer each time it wants a new token. It
doesn't know what is “inside” the tokens (though their semantic values
may reflect this). Typically the lexical analyzer makes the tokens by
parsing characters of text, but Bison does not depend on this.
See The Lexical Analyzer Function yylex.
The Bison parser file is C code which defines a function named
yyparse which implements that grammar. This function does not make
a complete C program: you must supply some additional functions. One is
the lexical analyzer. Another is an error-reporting function which the
parser calls to report an error. In addition, a complete C program must
start with a function called main; you have to provide this, and
arrange for it to call yyparse or the parser will never run.
See Parser C-Language Interface.
Aside from the token type names and the symbols in the actions you
write, all symbols defined in the Bison parser file itself
begin with `yy' or `YY'. This includes interface functions
such as the lexical analyzer function yylex, the error reporting
function yyerror and the parser function yyparse itself.
This also includes numerous identifiers used for internal purposes.
Therefore, you should avoid using C identifiers starting with `yy'
or `YY' in the Bison grammar file except for the ones defined in
this manual. Also, you should avoid using the C identifiers
`malloc' and `free' for anything other than their usual
meanings.
In some cases the Bison parser file includes system headers, and in
those cases your code should respect the identifiers reserved by those
headers. On some non-GNU hosts, <alloca.h>, <malloc.h>,
<stddef.h>, and <stdlib.h> are included as needed to
declare memory allocators and related types. <libintl.h> is
included if message translation is in use
(see Internationalization). Other system headers may
be included if you define YYDEBUG to a nonzero value
(see Tracing Your Parser).
The actual language-design process using Bison, from grammar specification to a working compiler or interpreter, has these parts:
yylex). It could also be produced
using Lex, but the use of Lex is not discussed in this manual.
To turn this source code as written into a runnable program, you must follow these steps:
The input file for the Bison utility is a Bison grammar file. The general form of a Bison grammar file is as follows:
%{
Prologue
%}
Bison declarations
%%
Grammar rules
%%
Epilogue
The `%%', `%{' and `%}' are punctuation that appears in every Bison grammar file to separate the sections.
The prologue may define types and variables used in the actions. You can
also use preprocessor commands to define macros used there, and use
#include to include header files that do any of these things.
You need to declare the lexical analyzer yylex and the error
printer yyerror here, along with any other global identifiers
used by the actions in the grammar rules.
The Bison declarations declare the names of the terminal and nonterminal symbols, and may also describe operator precedence and the data types of semantic values of various symbols.
The grammar rules define how to construct each nonterminal symbol from its parts.
The epilogue can contain any code you want to use. Often the definitions of functions declared in the prologue go here. In a simple program, all the rest of the program can go here.
Now we show and explain three sample programs written using Bison: a reverse polish notation calculator, an algebraic (infix) notation calculator, and a multi-function calculator. All three have been tested under BSD Unix 4.3; each produces a usable, though limited, interactive desk-top calculator.
These examples are simple, but Bison grammars for real programming languages are written the same way. You can copy these examples into a source file to try them.
The first example is that of a simple double-precision reverse polish notation calculator (a calculator using postfix operators). This example provides a good starting point, since operator precedence is not an issue. The second example will illustrate how operator precedence is handled.
The source code for this calculator is named rpcalc.y. The `.y' extension is a convention used for Bison input files.
rpcalcHere are the C and Bison declarations for the reverse polish notation calculator. As in C, comments are placed between `/*...*/'.
/* Reverse polish notation calculator. */
%{
#define YYSTYPE double
#include <math.h>
int yylex (void);
void yyerror (char const *);
%}
%token NUM
%% /* Grammar rules and actions follow. */
The declarations section (see The prologue) contains two preprocessor directives and two forward declarations.
The #define directive defines the macro YYSTYPE, thus
specifying the C data type for semantic values of both tokens and
groupings (see Data Types of Semantic Values). The
Bison parser will use whatever type YYSTYPE is defined as; if you
don't define it, int is the default. Because we specify
double, each token and each expression has an associated value,
which is a floating point number.
The #include directive is used to declare the exponentiation
function pow.
The forward declarations for yylex and yyerror are
needed because the C language requires that functions be declared
before they are used. These functions will be defined in the
epilogue, but the parser calls them so they must be declared in the
prologue.
The second section, Bison declarations, provides information to Bison
about the token types (see The Bison Declarations Section). Each terminal symbol that is not a
single-character literal must be declared here. (Single-character
literals normally don't need to be declared.) In this example, all the
arithmetic operators are designated by single-character literals, so the
only terminal symbol that needs to be declared is NUM, the token
type for numeric constants.
rpcalcHere are the grammar rules for the reverse polish notation calculator.
input: /* empty */
| input line
;
line: '\n'
| exp '\n' { printf ("\t%.10g\n", $1); }
;
exp: NUM { $$ = $1; }
| exp exp '+' { $$ = $1 + $2; }
| exp exp '-' { $$ = $1 - $2; }
| exp exp '*' { $$ = $1 * $2; }
| exp exp '/' { $$ = $1 / $2; }
/* Exponentiation */
| exp exp '^' { $$ = pow ($1, $2); }
/* Unary minus */
| exp 'n' { $$ = -$1; }
;
%%
The groupings of the rpcalc “language” defined here are the expression
(given the name exp), the line of input (line), and the
complete input transcript (input). Each of these nonterminal
symbols has several alternate rules, joined by the vertical bar `|'
which is read as “or”. The following sections explain what these rules
mean.
The semantics of the language is determined by the actions taken when a grouping is recognized. The actions are the C code that appears inside braces. See Actions.
You must specify these actions in C, but Bison provides the means for
passing semantic values between the rules. In each action, the
pseudo-variable $$ stands for the semantic value for the grouping
that the rule is going to construct. Assigning a value to $$ is the
main job of most actions. The semantic values of the components of the
rule are referred to as $1, $2, and so on.
inputConsider the definition of input:
input: /* empty */
| input line
;
This definition reads as follows: “A complete input is either an empty
string, or a complete input followed by an input line”. Notice that
“complete input” is defined in terms of itself. This definition is said
to be left recursive since input appears always as the
leftmost symbol in the sequence. See Recursive Rules.
The first alternative is empty because there are no symbols between the
colon and the first `|'; this means that input can match an
empty string of input (no tokens). We write the rules this way because it
is legitimate to type Ctrl-d right after you start the calculator.
It's conventional to put an empty alternative first and write the comment
`/* empty */' in it.
The second alternate rule (input line) handles all nontrivial input.
It means, “After reading any number of lines, read one more line if
possible.” The left recursion makes this rule into a loop. Since the
first alternative matches empty input, the loop can be executed zero or
more times.
The parser function yyparse continues to process input until a
grammatical error is seen or the lexical analyzer says there are no more
input tokens; we will arrange for the latter to happen at end-of-input.
lineNow consider the definition of line:
line: '\n'
| exp '\n' { printf ("\t%.10g\n", $1); }
;
The first alternative is a token which is a newline character; this means
that rpcalc accepts a blank line (and ignores it, since there is no
action). The second alternative is an expression followed by a newline.
This is the alternative that makes rpcalc useful. The semantic value of
the exp grouping is the value of $1 because the exp in
question is the first symbol in the alternative. The action prints this
value, which is the result of the computation the user asked for.
This action is unusual because it does not assign a value to $$. As
a consequence, the semantic value associated with the line is
uninitialized (its value will be unpredictable). This would be a bug if
that value were ever used, but we don't use it: once rpcalc has printed the
value of the user's input line, that value is no longer needed.
exprThe exp grouping has several rules, one for each kind of expression.
The first rule handles the simplest expressions: those that are just numbers.
The second handles an addition-expression, which looks like two expressions
followed by a plus-sign. The third handles subtraction, and so on.
exp: NUM
| exp exp '+' { $$ = $1 + $2; }
| exp exp '-' { $$ = $1 - $2; }
...
;
We have used `|' to join all the rules for exp, but we could
equally well have written them separately:
exp: NUM ;
exp: exp exp '+' { $$ = $1 + $2; } ;
exp: exp exp '-' { $$ = $1 - $2; } ;
...
Most of the rules have actions that compute the value of the expression in
terms of the value of its parts. For example, in the rule for addition,
$1 refers to the first component exp and $2 refers to
the second one. The third component, '+', has no meaningful
associated semantic value, but if it had one you could refer to it as
$3. When yyparse recognizes a sum expression using this
rule, the sum of the two subexpressions' values is produced as the value of
the entire expression. See Actions.
You don't have to give an action for every rule. When a rule has no
action, Bison by default copies the value of $1 into $$.
This is what happens in the first rule (the one that uses NUM).
The formatting shown here is the recommended convention, but Bison does not require it. You can add or change white space as much as you wish. For example, this:
exp : NUM | exp exp '+' {$$ = $1 + $2; } | ... ;
means the same thing as this:
exp: NUM
| exp exp '+' { $$ = $1 + $2; }
| ...
;
The latter, however, is much more readable.
rpcalc Lexical Analyzer
The lexical analyzer's job is low-level parsing: converting characters
or sequences of characters into tokens. The Bison parser gets its
tokens by calling the lexical analyzer. See The Lexical Analyzer Function yylex.
Only a simple lexical analyzer is needed for the RPN
calculator. This
lexical analyzer skips blanks and tabs, then reads in numbers as
double and returns them as NUM tokens. Any other character
that isn't part of a number is a separate token. Note that the token-code
for such a single-character token is the character itself.
The return value of the lexical analyzer function is a numeric code which
represents a token type. The same text used in Bison rules to stand for
this token type is also a C expression for the numeric code for the type.
This works in two ways. If the token type is a character literal, then its
numeric code is that of the character; you can use the same
character literal in the lexical analyzer to express the number. If the
token type is an identifier, that identifier is defined by Bison as a C
macro whose definition is the appropriate number. In this example,
therefore, NUM becomes a macro for yylex to use.
The semantic value of the token (if it has one) is stored into the
global variable yylval, which is where the Bison parser will look
for it. (The C data type of yylval is YYSTYPE, which was
defined at the beginning of the grammar; see Declarations for rpcalc.)
A token type code of zero is returned if the end-of-input is encountered. (Bison recognizes any nonpositive value as indicating end-of-input.)
Here is the code for the lexical analyzer:
/* The lexical analyzer returns a double floating point
number on the stack and the token NUM, or the numeric code
of the character read if not a number. It skips all blanks
and tabs, and returns 0 for end-of-input. */
#include <ctype.h>
int
yylex (void)
{
int c;
/* Skip white space. */
while ((c = getchar ()) == ' ' || c == '\t')
;
/* Process numbers. */
if (c == '.' || isdigit (c))
{
ungetc (c, stdin);
scanf ("%lf", &yylval);
return NUM;
}
/* Return end-of-input. */
if (c == EOF)
return 0;
/* Return a single char. */
return c;
}
In keeping with the spirit of this example, the controlling function is
kept to the bare minimum. The only requirement is that it call
yyparse to start the process of parsing.
int
main (void)
{
return yyparse ();
}
When yyparse detects a syntax error, it calls the error reporting
function yyerror to print an error message (usually but not
always "syntax error"). It is up to the programmer to supply
yyerror (see Parser C-Language Interface), so
here is the definition we will use:
#include <stdio.h>
/* Called by yyparse on error. */
void
yyerror (char const *s)
{
fprintf (stderr, "%s\n", s);
}
After yyerror returns, the Bison parser may recover from the error
and continue parsing if the grammar contains a suitable error rule
(see Error Recovery). Otherwise, yyparse returns nonzero. We
have not written any error rules in this example, so any invalid input will
cause the calculator program to exit. This is not clean behavior for a
real calculator, but it is adequate for the first example.
Before running Bison to produce a parser, we need to decide how to
arrange all the source code in one or more source files. For such a
simple example, the easiest thing is to put everything in one file. The
definitions of yylex, yyerror and main go at the
end, in the epilogue of the file
(see The Overall Layout of a Bison Grammar).
For a large project, you would probably have several source files, and use
make to arrange to recompile them.
With all the source in a single file, you use the following command to convert it into a parser file:
bison file.y
In this example the file was called rpcalc.y (for “Reverse Polish
calculator”). Bison produces a file named file.tab.c,
removing the `.y' from the original file name. The file output by
Bison contains the source code for yyparse. The additional
functions in the input file (yylex, yyerror and main)
are copied verbatim to the output.
Here is how to compile and run the parser file:
# List files in current directory.
$ ls
rpcalc.tab.c rpcalc.y
# Compile the Bison parser.
# `-lm' tells compiler to search math library for pow.
$ cc -lm -o rpcalc rpcalc.tab.c
# List files again.
$ ls
rpcalc rpcalc.tab.c rpcalc.y
The file rpcalc now contains the executable code. Here is an
example session using rpcalc.
$ rpcalc
4 9 +
13
3 7 + 3 4 5 *+-
-13
3 7 + 3 4 5 * + - n Note the unary minus, `n'
13
5 6 / 4 n +
-3.166666667
3 4 ^ Exponentiation
81
^D End-of-file indicator
$
calcWe now modify rpcalc to handle infix operators instead of postfix. Infix notation involves the concept of operator precedence and the need for parentheses nested to arbitrary depth. Here is the Bison code for calc.y, an infix desk-top calculator.
/* Infix notation calculator. */
%{
#define YYSTYPE double
#include <math.h>
#include <stdio.h>
int yylex (void);
void yyerror (char const *);
%}
/* Bison declarations. */
%token NUM
%left '-' '+'
%left '*' '/'
%left NEG /* negation--unary minus */
%right '^' /* exponentiation */
%% /* The grammar follows. */
input: /* empty */
| input line
;
line: '\n'
| exp '\n' { printf ("\t%.10g\n", $1); }
;
exp: NUM { $$ = $1; }
| exp '+' exp { $$ = $1 + $3; }
| exp '-' exp { $$ = $1 - $3; }
| exp '*' exp { $$ = $1 * $3; }
| exp '/' exp { $$ = $1 / $3; }
| '-' exp %prec NEG { $$ = -$2; }
| exp '^' exp { $$ = pow ($1, $3); }
| '(' exp ')' { $$ = $2; }
;
%%
The functions yylex, yyerror and main can be the
same as before.
There are two important new features shown in this code.
In the second section (Bison declarations), %left declares token
types and says they are left-associative operators. The declarations
%left and %right (right associativity) take the place of
%token which is used to declare a token type name without
associativity. (These tokens are single-character literals, which
ordinarily don't need to be declared. We declare them here to specify
the associativity.)
Operator precedence is determined by the line ordering of the
declarations; the higher the line number of the declaration (lower on
the page or screen), the higher the precedence. Hence, exponentiation
has the highest precedence, unary minus (NEG) is next, followed
by `*' and `/', and so on. See Operator Precedence.
The other important new feature is the %prec in the grammar
section for the unary minus operator. The %prec simply instructs
Bison that the rule `| '-' exp' has the same precedence as
NEG—in this case the next-to-highest. See Context-Dependent Precedence.
Here is a sample run of calc.y:
$ calc
4 + 4.5 - (34/(8*3+-3))
6.880952381
-56 + 2
-54
3 ^ 2
9
Up to this point, this manual has not addressed the issue of error
recovery—how to continue parsing after the parser detects a syntax
error. All we have handled is error reporting with yyerror.
Recall that by default yyparse returns after calling
yyerror. This means that an erroneous input line causes the
calculator program to exit. Now we show how to rectify this deficiency.
The Bison language itself includes the reserved word error, which
may be included in the grammar rules. In the example below it has
been added to one of the alternatives for line:
line: '\n'
| exp '\n' { printf ("\t%.10g\n", $1); }
| error '\n' { yyerrok; }
;
This addition to the grammar allows for simple error recovery in the
event of a syntax error. If an expression that cannot be evaluated is
read, the error will be recognized by the third rule for line,
and parsing will continue. (The yyerror function is still called
upon to print its message as well.) The action executes the statement
yyerrok, a macro defined automatically by Bison; its meaning is
that error recovery is complete (see Error Recovery). Note the
difference between yyerrok and yyerror; neither one is a
misprint.
This form of error recovery deals with syntax errors. There are other
kinds of errors; for example, division by zero, which raises an exception
signal that is normally fatal. A real calculator program must handle this
signal and use longjmp to return to main and resume parsing
input lines; it would also have to discard the rest of the current line of
input. We won't discuss this issue further because it is not specific to
Bison programs.
ltcalcThis example extends the infix notation calculator with location tracking. This feature will be used to improve the error messages. For the sake of clarity, this example is a simple integer calculator, since most of the work needed to use locations will be done in the lexical analyzer.
ltcalcThe C and Bison declarations for the location tracking calculator are the same as the declarations for the infix notation calcu