This is bison.info, produced by makeinfo version 4.7 from bison.texinfo.
This manual is for GNU Bison (version 2.0, 22 December 2004), the
GNU parser generator.
Copyright (C) 1988, 1989, 1990, 1991, 1992, 1993, 1995, 1998, 1999,
2000, 2001, 2002, 2003, 2004 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 1.1 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."
INFO-DIR-SECTION GNU programming tools
START-INFO-DIR-ENTRY
* bison: (bison). GNU parser generator (Yacc replacement).
END-INFO-DIR-ENTRY
File: bison.info, Node: Top, Next: Introduction, Up: (dir)
Bison
*****
This manual is for GNU Bison (version 2.0, 22 December 2004), the GNU
parser generator.
Copyright (C) 1988, 1989, 1990, 1991, 1992, 1993, 1995, 1998, 1999,
2000, 2001, 2002, 2003, 2004 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 1.1 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."
* Menu:
* Introduction::
* Conditions::
* Copying:: The GNU General Public License says
how you can copy and share Bison
Tutorial sections:
* Concepts:: Basic concepts for understanding Bison.
* Examples:: Three simple explained examples of using Bison.
Reference sections:
* Grammar File:: Writing Bison declarations and rules.
* Interface:: C-language interface to the parser function `yyparse'.
* Algorithm:: How the Bison parser works at run-time.
* Error Recovery:: Writing rules for error recovery.
* Context Dependency:: What to do if your language syntax is too
messy for Bison to handle straightforwardly.
* Debugging:: Understanding or debugging Bison parsers.
* Invocation:: How to run Bison (to produce the parser source file).
* Table of Symbols:: All the keywords of the Bison language are explained.
* Glossary:: Basic concepts are explained.
* FAQ:: Frequently Asked Questions
* Copying This Manual:: License for copying this manual.
* Index:: Cross-references to the text.
--- The Detailed Node Listing ---
The Concepts of Bison
* Language and Grammar:: Languages and context-free grammars,
as mathematical ideas.
* Grammar in Bison:: How we represent grammars for Bison's sake.
* Semantic Values:: Each token or syntactic grouping can have
a semantic value (the value of an integer,
the name of an identifier, etc.).
* Semantic Actions:: Each rule can have an action containing C code.
* GLR Parsers:: Writing parsers for general context-free languages.
* Locations Overview:: Tracking Locations.
* Bison Parser:: What are Bison's input and output,
how is the output used?
* Stages:: Stages in writing and running Bison grammars.
* Grammar Layout:: Overall structure of a Bison grammar file.
Writing GLR Parsers
* Simple GLR Parsers:: Using GLR parsers on unambiguous grammars
* Merging GLR Parses:: Using GLR parsers to resolve ambiguities
* Compiler Requirements:: GLR parsers require a modern C compiler
Examples
* RPN Calc:: Reverse polish notation calculator;
a first example with no operator precedence.
* Infix Calc:: Infix (algebraic) notation calculator.
Operator precedence is introduced.
* Simple Error Recovery:: Continuing after syntax errors.
* Location Tracking Calc:: Demonstrating the use of @N and @$.
* Multi-function Calc:: Calculator with memory and trig functions.
It uses multiple data-types for semantic values.
* Exercises:: Ideas for improving the multi-function calculator.
Reverse Polish Notation Calculator
* Decls: Rpcalc Decls. Prologue (declarations) for rpcalc.
* Rules: Rpcalc Rules. Grammar Rules for rpcalc, with explanation.
* Lexer: Rpcalc Lexer. The lexical analyzer.
* Main: Rpcalc Main. The controlling function.
* Error: Rpcalc Error. The error reporting function.
* Gen: Rpcalc Gen. Running Bison on the grammar file.
* Comp: Rpcalc Compile. Run the C compiler on the output code.
Grammar Rules for `rpcalc'
* Rpcalc Input::
* Rpcalc Line::
* Rpcalc Expr::
Location Tracking Calculator: `ltcalc'
* Decls: Ltcalc Decls. Bison and C declarations for ltcalc.
* Rules: Ltcalc Rules. Grammar rules for ltcalc, with explanations.
* Lexer: Ltcalc Lexer. The lexical analyzer.
Multi-Function Calculator: `mfcalc'
* Decl: Mfcalc Decl. Bison declarations for multi-function calculator.
* Rules: Mfcalc Rules. Grammar rules for the calculator.
* Symtab: Mfcalc Symtab. Symbol table management subroutines.
Bison Grammar Files
* Grammar Outline:: Overall layout of the grammar file.
* Symbols:: Terminal and nonterminal symbols.
* Rules:: How to write grammar rules.
* Recursion:: Writing recursive rules.
* Semantics:: Semantic values and actions.
* Locations:: Locations and actions.
* Declarations:: All kinds of Bison declarations are described here.
* Multiple Parsers:: Putting more than one Bison parser in one program.
Outline of a Bison Grammar
* Prologue:: Syntax and usage of the prologue.
* Bison Declarations:: Syntax and usage of the Bison declarations section.
* Grammar Rules:: Syntax and usage of the grammar rules section.
* Epilogue:: Syntax and usage of the epilogue.
Defining Language Semantics
* Value Type:: Specifying one data type for all semantic values.
* Multiple Types:: Specifying several alternative data types.
* Actions:: An action is the semantic definition of a grammar rule.
* Action Types:: Specifying data types for actions to operate on.
* Mid-Rule Actions:: Most actions go at the end of a rule.
This says when, why and how to use the exceptional
action in the middle of a rule.
Tracking Locations
* Location Type:: Specifying a data type for locations.
* Actions and Locations:: Using locations in actions.
* Location Default Action:: Defining a general way to compute locations.
Bison Declarations
* Token Decl:: Declaring terminal symbols.
* Precedence Decl:: Declaring terminals with precedence and associativity.
* Union Decl:: Declaring the set of all semantic value types.
* Type Decl:: Declaring the choice of type for a nonterminal symbol.
* Initial Action Decl:: Code run before parsing starts.
* Destructor Decl:: Declaring how symbols are freed.
* Expect Decl:: Suppressing warnings about parsing conflicts.
* Start Decl:: Specifying the start symbol.
* Pure Decl:: Requesting a reentrant parser.
* Decl Summary:: Table of all Bison declarations.
Parser C-Language Interface
* Parser Function:: How to call `yyparse' and what it returns.
* Lexical:: You must supply a function `yylex'
which reads tokens.
* Error Reporting:: You must supply a function `yyerror'.
* Action Features:: Special features for use in actions.
The Lexical Analyzer Function `yylex'
* Calling Convention:: How `yyparse' calls `yylex'.
* Token Values:: How `yylex' must return the semantic value
of the token it has read.
* Token Locations:: How `yylex' must return the text location
(line number, etc.) of the token, if the
actions want that.
* Pure Calling:: How the calling convention differs
in a pure parser (*note A Pure (Reentrant) Parser: Pure Decl.).
The Bison Parser Algorithm
* Look-Ahead:: Parser looks one token ahead when deciding what to do.
* Shift/Reduce:: Conflicts: when either shifting or reduction is valid.
* Precedence:: Operator precedence works by resolving conflicts.
* Contextual Precedence:: When an operator's precedence depends on context.
* Parser States:: The parser is a finite-state-machine with stack.
* Reduce/Reduce:: When two rules are applicable in the same situation.
* Mystery Conflicts:: Reduce/reduce conflicts that look unjustified.
* Generalized LR Parsing:: Parsing arbitrary context-free grammars.
* Stack Overflow:: What happens when stack gets full. How to avoid it.
Operator Precedence
* Why Precedence:: An example showing why precedence is needed.
* Using Precedence:: How to specify precedence in Bison grammars.
* Precedence Examples:: How these features are used in the previous example.
* How Precedence:: How they work.
Handling Context Dependencies
* Semantic Tokens:: Token parsing can depend on the semantic context.
* Lexical Tie-ins:: Token parsing can depend on the syntactic context.
* Tie-in Recovery:: Lexical tie-ins have implications for how
error recovery rules must be written.
Debugging Your Parser
* Understanding:: Understanding the structure of your parser.
* Tracing:: Tracing the execution of your parser.
Invoking Bison
* Bison Options:: All the options described in detail,
in alphabetical order by short options.
* Option Cross Key:: Alphabetical list of long options.
* Yacc Library:: Yacc-compatible `yylex' and `main'.
Frequently Asked Questions
* Parser Stack Overflow:: Breaking the Stack Limits
* How Can I Reset the Parser:: `yyparse' Keeps some State
* Strings are Destroyed:: `yylval' Loses Track of Strings
* C++ Parsers:: Compiling Parsers with C++ Compilers
* Implementing Gotos/Loops:: Control Flow in the Calculator
Copying This Manual
* GNU Free Documentation License:: License for copying this manual.
File: bison.info, Node: Introduction, Next: Conditions, Prev: Top, Up: Top
Introduction
************
"Bison" is a general-purpose parser generator that converts a grammar
description for an LALR(1) context-free grammar into a C program to
parse that grammar. Once you are proficient with Bison, you may 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 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 2.0 of Bison.
File: bison.info, Node: Conditions, Next: Copying, Prev: Introduction, Up: Top
Conditions for Using Bison
**************************
As of Bison version 1.24, we have changed the distribution terms for
`yyparse' to permit using Bison's output in nonfree programs when Bison
is generating C code for LALR(1) parsers. Formerly, these 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
`yyparse' function. (The actions from your grammar are inserted into
this function at one point, but the rest of the function is not
changed.) When we applied the GPL terms to the code for `yyparse', 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 only when Bison is generating C code for an
LALR(1) parser; otherwise, the GPL terms operate as usual. You can
tell whether the exception applies to your `.c' output file by
inspecting it to see whether it says "As a special exception, when this
file is copied by Bison into a Bison output file, you may use that
output file without restriction."
File: bison.info, Node: Copying, Next: Concepts, Prev: Conditions, Up: Top
GNU GENERAL PUBLIC LICENSE
**************************
Version 2, June 1991
Copyright (C) 1989, 1991 Free Software Foundation, Inc.
59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.
Preamble
========
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
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Finally, any free program is threatened constantly by software
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patent must be licensed for everyone's free use or not licensed at all.
The precise terms and conditions for copying, distribution and
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TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
0. This License applies to any program or other work which contains a
notice placed by the copyright holder saying it may be distributed
under the terms of this General Public License. The "Program",
below, refers to any such program or work, and a "work based on
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translated into another language. (Hereinafter, translation is
included without limitation in the term "modification".) Each
licensee is addressed as "you".
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.
1. You may copy and distribute verbatim copies of the Program's
source code as you receive it, in any medium, provided that you
conspicuously and appropriately publish on each copy an appropriate
copyright notice and disclaimer of warranty; keep intact all the
notices that refer to this License and to the absence of any
warranty; and give any other recipients of the Program a copy of
this License along with the Program.
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.
2. You may modify your copy or copies of the Program or any portion
of it, thus forming a work based on the Program, and copy and
distribute such modifications or work under the terms of Section 1
above, provided that you also meet all of these conditions:
a. You must cause the modified files to carry prominent notices
stating that you changed the files and the date of any change.
b. You must cause any work that you distribute or publish, that
in whole or in part contains or is derived from the Program
or any part thereof, to be licensed as a whole at no charge
to all third parties under the terms of this License.
c. If the modified program normally reads commands interactively
when run, you must cause it, when started running for such
interactive use in the most ordinary way, to print or display
an announcement including an appropriate copyright notice and
a notice that there is no warranty (or else, saying that you
provide a warranty) and that users may redistribute the
program under these conditions, and telling the user how to
view a copy of this License. (Exception: if the Program
itself is interactive but does not normally print such an
announcement, your work based on the Program is not required
to print an announcement.)
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.
3. You may copy and distribute the Program (or a work based on it,
under Section 2) in object code or executable form under the terms
of Sections 1 and 2 above provided that you also do one of the
following:
a. Accompany it with the complete corresponding machine-readable
source code, which must be distributed under the terms of
Sections 1 and 2 above on a medium customarily used for
software interchange; or,
b. Accompany it with a written offer, valid for at least three
years, to give any third party, for a charge no more than your
cost of physically performing source distribution, a complete
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distributed under the terms of Sections 1 and 2 above on a
medium customarily used for software interchange; or,
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allowed only for noncommercial distribution and only if you
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The source code for a work means the preferred form of the work for
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compelled to copy the source along with the object code.
4. You may not copy, modify, sublicense, or distribute the Program
except as expressly provided under this License. Any attempt
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entirely from distribution of the Program.
If any portion of this section is held invalid or unenforceable
under any particular circumstance, the balance of the section is
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It is not the purpose of this section to induce you to infringe any
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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.
8. If the distribution and/or use of the Program is restricted in
certain countries either by patents or by copyrighted interfaces,
the original copyright holder who places the Program under this
License may add an explicit geographical distribution limitation
excluding those countries, so that distribution is permitted only
in or among countries not thus excluded. In such case, this
License incorporates the limitation as if written in the body of
this License.
9. The Free Software Foundation may publish revised and/or new
versions of the General Public License from time to time. Such
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Each version is given a distinguishing version number. If the
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does not specify a version number of this License, you may choose
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10. If you wish to incorporate parts of the Program into other free
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Foundation; we sometimes make exceptions for this. Our decision
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NO WARRANTY
11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO
WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE
LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT
WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT
NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
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QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE
PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY
SERVICING, REPAIR OR CORRECTION.
12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN
WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY
MODIFY AND/OR REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE
LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL,
INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR
INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU
OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY
OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN
ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.
END OF TERMS AND CONDITIONS
Appendix: How to Apply These Terms to Your New Programs
=======================================================
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., 59 Temple Place - Suite 330, Boston, MA 02111-1307, 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.
File: bison.info, Node: Concepts, Next: Examples, Prev: Copying, Up: Top
1 The Concepts of Bison
***********************
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.
* Menu:
* Language and Grammar:: Languages and context-free grammars,
as mathematical ideas.
* Grammar in Bison:: How we represent grammars for Bison's sake.
* Semantic Values:: Each token or syntactic grouping can have
a semantic value (the value of an integer,
the name of an identifier, etc.).
* Semantic Actions:: Each rule can have an action containing C code.
* GLR Parsers:: Writing parsers for general context-free languages.
* Locations Overview:: Tracking Locations.
* Bison Parser:: What are Bison's input and output,
how is the output used?
* Stages:: Stages in writing and running Bison grammars.
* Grammar Layout:: Overall structure of a Bison grammar file.
File: bison.info, Node: Language and Grammar, Next: Grammar in Bison, Up: Concepts
1.1 Languages and Context-Free Grammars
=======================================
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). *Note Mysterious Reduce/Reduce Conflicts: Mystery 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 some inputs. Even unambiguous grammars can be
"non-deterministic", 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.
File: bison.info, Node: Grammar in Bison, Next: Semantic Values, Prev: Language and Grammar, Up: Concepts
1.2 From Formal Rules to Bison Input
====================================
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. *Note Bison Grammar Files: Grammar File.
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. *Note 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. *Note 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 ';'
;
*Note Syntax of Grammar Rules: Rules.
File: bison.info, Node: Semantic Values, Next: Semantic Actions, Prev: Grammar in Bison, Up: Concepts
1.3 Semantic Values
===================
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".
*Note Defining Language Semantics: 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.
File: bison.info, Node: Semantic Actions, Next: GLR Parsers, Prev: Semantic Values, Up: Concepts
1.4 Semantic Actions
====================
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.
*Note 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.
File: bison.info, Node: GLR Parsers, Next: Locations Overview, Prev: Semantic Actions, Up: Concepts
1.5 Writing GLR Parsers
=======================
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 (*note Reduce/Reduce::), and "shift/reduce"
conflicts (*note 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 (*note 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.
* Menu:
* Simple GLR Parsers:: Using GLR parsers on unambiguous grammars
* Merging GLR Parses:: Using GLR parsers to resolve ambiguities
* Compiler Requirements:: GLR parsers require a modern C compiler
File: bison.info, Node: Simple GLR Parsers, Next: Merging GLR Parses, Up: GLR Parsers
1.5.1 Using GLR on Unambiguous Grammars
---------------------------------------
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), *Note
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 (*note 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.
File: bison.info, Node: Merging GLR Parses, Next: Compiler Requirements, Prev: Simple GLR Parsers, Up: GLR Parsers
1.5.2 Using GLR to Resolve Ambiguities
--------------------------------------
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
(*note 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 (*note 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.
File: bison.info, Node: Compiler Requirements, Prev: Merging GLR Parses, Up: GLR Parsers
1.5.3 Considerations when Compiling 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
%}
File: bison.info, Node: Locations Overview, Next: Bison Parser, Prev: GLR Parsers, Up: Concepts
1.6 Locations
=============
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 (*note 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 (*note 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.
File: bison.info, Node: Bison Parser, Next: Stages, Prev: Locations Overview, Up: Concepts
1.7 Bison Output: the Parser File
=================================
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. *Note
The Lexical Analyzer Function `yylex': Lexical.
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. *Note
Parser C-Language Interface: 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.
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>', `<stddef.h>', and
`<stdlib.h>' are included as needed to declare memory allocators and
related types. Other system headers may be included if you define
`YYDEBUG' to a nonzero value (*note Tracing Your Parser: Tracing.).
File: bison.info, Node: Stages, Next: Grammar Layout, Prev: Bison Parser, Up: Concepts
1.8 Stages in Using Bison
=========================
The actual language-design process using Bison, from grammar
specification to a working compiler or interpreter, has these parts:
1. Formally specify the grammar in a form recognized by Bison (*note
Bison Grammar Files: Grammar File.). For each grammatical rule in
the language, describe the action that is to be taken when an
instance of that rule is recognized. The action is described by a
sequence of C statements.
2. Write a lexical analyzer to process input and pass tokens to the
parser. The lexical analyzer may be written by hand in C (*note
The Lexical Analyzer Function `yylex': Lexical.). It could also
be produced using Lex, but the use of Lex is not discussed in this
manual.
3. Write a controlling function that calls the Bison-produced parser.
4. Write error-reporting routines.
To turn this source code as written into a runnable program, you
must follow these steps:
1. Run Bison on the grammar to produce the parser.
2. Compile the code output by Bison, as well as any other source
files.
3. Link the object files to produce the finished product.
File: bison.info, Node: Grammar Layout, Prev: Stages, Up: Concepts
1.9 The Overall Layout of a Bison Grammar
=========================================
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.
File: bison.info, Node: Examples, Next: Grammar File, Prev: Concepts, Up: Top
2 Examples
**********
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 out of
the Info file and into a source file to try them.
* Menu:
* RPN Calc:: Reverse polish notation calculator;
a first example with no operator precedence.
* Infix Calc:: Infix (algebraic) notation calculator.
Operator precedence is introduced.
* Simple Error Recovery:: Continuing after syntax errors.
* Location Tracking Calc:: Demonstrating the use of @N and @$.
* Multi-function Calc:: Calculator with memory and trig functions.
It uses multiple data-types for semantic values.
* Exercises:: Ideas for improving the multi-function calculator.
File: bison.info, Node: RPN Calc, Next: Infix Calc, Up: Examples
2.1 Reverse Polish Notation Calculator
======================================
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.
* Menu:
* Decls: Rpcalc Decls. Prologue (declarations) for rpcalc.
* Rules: Rpcalc Rules. Grammar Rules for rpcalc, with explanation.
* Lexer: Rpcalc Lexer. The lexical analyzer.
* Main: Rpcalc Main. The controlling function.
* Error: Rpcalc Error. The error reporting function.
* Gen: Rpcalc Gen. Running Bison on the grammar file.
* Comp: Rpcalc Compile. Run the C compiler on the output code.
File: bison.info, Node: Rpcalc Decls, Next: Rpcalc Rules, Up: RPN Calc
2.1.1 Declarations for `rpcalc'
-------------------------------
Here 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 (*note The prologue: 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 (*note
Data Types of Semantic Values: Value Type.). 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 (*note The Bison Declarations Section: Bison
Declarations.). 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.
File: bison.info, Node: Rpcalc Rules, Next: Rpcalc Lexer, Prev: Rpcalc Decls, Up: RPN Calc
2.1.2 Grammar Rules for `rpcalc'
--------------------------------
Here 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' { $$ = -$1; }
;
%%
The groupings of the rpcalc "language" defined here are the
expression (given the name `exp'), the line of input (`line'), and the
complete input transcript (`input'). Each of these nonterminal symbols
has several alternate rules, joined by the `|' punctuator which is read
as "or". The following sections explain what these rules mean.
The semantics of the language is determined by the actions taken
when a grouping is recognized. The actions are the C code that appears
inside braces. *Note Actions::.
You must specify these actions in C, but Bison provides the means for
passing semantic values between the rules. In each action, the
pseudo-variable `$$' 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.
* Menu:
* Rpcalc Input::
* Rpcalc Line::
* Rpcalc Expr::
File: bison.info, Node: Rpcalc Input, Next: Rpcalc Line, Up: Rpcalc Rules
2.1.2.1 Explanation of `input'
..............................
Consider 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. *Note Recursive Rules: Recursion.
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.
File: bison.info, Node: Rpcalc Line, Next: Rpcalc Expr, Prev: Rpcalc Input, Up: Rpcalc Rules
2.1.2.2 Explanation of `line'
.............................
Now 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.
File: bison.info, Node: Rpcalc Expr, Prev: Rpcalc Line, Up: Rpcalc Rules
2.1.2.3 Explanation of `expr'
.............................
The `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. *Note 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.
File: bison.info, Node: Rpcalc Lexer, Next: Rpcalc Main, Prev: Rpcalc Rules, Up: RPN Calc
2.1.3 The `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. *Note The Lexical Analyzer
Function `yylex': Lexical.
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; *note Declarations for `rpcalc': Rpcalc
Decls.)
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;
}
File: bison.info, Node: Rpcalc Main, Next: Rpcalc Error, Prev: Rpcalc Lexer, Up: RPN Calc
2.1.4 The Controlling Function
------------------------------
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 ();
}
File: bison.info, Node: Rpcalc Error, Next: Rpcalc Gen, Prev: Rpcalc Main, Up: RPN Calc
2.1.5 The Error Reporting Routine
---------------------------------
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'
(*note Parser C-Language Interface: 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
(*note 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.
File: bison.info, Node: Rpcalc Gen, Next: Rpcalc Compile, Prev: Rpcalc Error, Up: RPN Calc
2.1.6 Running Bison to Make the Parser
--------------------------------------
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 (*note The Overall Layout of a Bison Grammar:
Grammar Layout.).
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_NAME.y
In this example the file was called `rpcalc.y' (for "Reverse Polish
CALCulator"). Bison produces a file named `FILE_NAME.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.
File: bison.info, Node: Rpcalc Compile, Prev: Rpcalc Gen, Up: RPN Calc
2.1.7 Compiling the Parser File
-------------------------------
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
$
File: bison.info, Node: Infix Calc, Next: Simple Error Recovery, Prev: RPN Calc, Up: Examples
2.2 Infix Notation Calculator: `calc'
=====================================
We 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. *Note Operator Precedence: 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. *Note Context-Dependent Precedence:
Contextual 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
File: bison.info, Node: Simple Error Recovery, Next: Location Tracking Calc, Prev: Infix Calc, Up: Examples
2.3 Simple Error Recovery
=========================
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 (*note 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.
File: bison.info, Node: Location Tracking Calc, Next: Multi-function Calc, Prev: Simple Error Recovery, Up: Examples
2.4 Location Tracking Calculator: `ltcalc'
==========================================
This 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.
* Menu:
* Decls: Ltcalc Decls. Bison and C declarations for ltcalc.
* Rules: Ltcalc Rules. Grammar rules for ltcalc, with explanations.
* Lexer: Ltcalc Lexer. The lexical analyzer.
File: bison.info, Node: Ltcalc Decls, Next: Ltcalc Rules, Up: Location Tracking Calc
2.4.1 Declarations for `ltcalc'
-------------------------------
The C and Bison declarations for the location tracking calculator are
the same as the declarations for the infix notation calculator.
/* Location tracking calculator. */
%{
#define YYSTYPE int
#include <math.h>
int yylex (void);
void yyerror (char const *);
%}
/* Bison declarations. */
%token NUM
%left '-' '+'
%left '*' '/'
%left NEG
%right '^'
%% /* The grammar follows. */
Note there are no declarations specific to locations. Defining a data
type for storing locations is not needed: we will use the type provided
by default (*note Data Types of Locations: Location Type.), which is a
four member structure with the following integer fields: `first_line',
`first_column', `last_line' and `last_column'.
File: bison.info, Node: Ltcalc Rules, Next: Ltcalc Lexer, Prev: Ltcalc Decls, Up: Location Tracking Calc
2.4.2 Grammar Rules for `ltcalc'
--------------------------------
Whether handling locations or not has no effect on the syntax of your
language. Therefore, grammar rules for this example will be very close
to those of the previous example: we will only modify them to benefit
from the new information.
Here, we will use locations to report divisions by zero, and locate
the wrong expressions or subexpressions.
input : /* empty */
| input line
;
line : '\n'
| exp '\n' { printf ("%d\n", $1); }
;
exp : NUM { $$ = $1; }
| exp '+' exp { $$ = $1 + $3; }
| exp '-' exp { $$ = $1 - $3; }
| exp '*' exp { $$ = $1 * $3; }
| exp '/' exp
{
if ($3)
$$ = $1 / $3;
else
{
$$ = 1;
fprintf (stderr, "%d.%d-%d.%d: division by zero",
@3.first_line, @3.first_column,
@3.last_line, @3.last_column);
}
}
| '-' exp %preg NEG { $$ = -$2; }
| exp '^' exp { $$ = pow ($1, $3); }
| '(' exp ')' { $$ = $2; }
This code shows how to reach locations inside of semantic actions, by
using the pseudo-variables `@N' for rule components, and the
pseudo-variable `@$' for groupings.
We don't need to assign a value to `@$': the output parser does it
automatically. By default, before executing the C code of each action,
`@$' is set to range from the beginning of `@1' to the end of `@N', for
a rule with N components. This behavior can be redefined (*note
Default Action for Locations: Location Default Action.), and for very
specific rules, `@$' can be computed by hand.
File: bison.info, Node: Ltcalc Lexer, Prev: Ltcalc Rules, Up: Location Tracking Calc
2.4.3 The `ltcalc' Lexical Analyzer.
------------------------------------
Until now, we relied on Bison's defaults to enable location tracking.
The next step is to rewrite the lexical analyzer, and make it able to
feed the parser with the token locations, as it already does for
semantic values.
To this end, we must take into account every single character of the
input text, to avoid the computed locations of being fuzzy or wrong:
int
yylex (void)
{
int c;
/* Skip white space. */
while ((c = getchar ()) == ' ' || c == '\t')
++yylloc.last_column;
/* Step. */
yylloc.first_line = yylloc.last_line;
yylloc.first_column = yylloc.last_column;
/* Process numbers. */
if (isdigit (c))
{
yylval = c - '0';
++yylloc.last_column;
while (isdigit (c = getchar ()))
{
++yylloc.last_column;
yylval = yylval * 10 + c - '0';
}
ungetc (c, stdin);
return NUM;
}
/* Return end-of-input. */
if (c == EOF)
return 0;
/* Return a single char, and update location. */
if (c == '\n')
{
++yylloc.last_line;
yylloc.last_column = 0;
}
else
++yylloc.last_column;
return c;
}
Basically, the lexical analyzer performs the same processing as
before: it skips blanks and tabs, and reads numbers or single-character
tokens. In addition, it updates `yylloc', the global variable (of type
`YYLTYPE') containing the token's location.
Now, each time this function returns a token, the parser has its
number as well as its semantic value, and its location in the text.
The last needed change is to initialize `yylloc', for example in the
controlling function:
int
main (void)
{
yylloc.first_line = yylloc.last_line = 1;
yylloc.first_column = yylloc.last_column = 0;
return yyparse ();
}
Remember that computing locations is not a matter of syntax. Every
character must be associated to a location update, whether it is in
valid input, in comments, in literal strings, and so on.
File: bison.info, Node: Multi-function Calc, Next: Exercises, Prev: Location Tracking Calc, Up: Examples
2.5 Multi-Function Calculator: `mfcalc'
=======================================
Now that the basics of Bison have been discussed, it is time to move on
to a more advanced problem. The above calculators provided only five
functions, `+', `-', `*', `/' and `^'. It would be nice to have a
calculator that provides other mathematical functions such as `sin',
`cos', etc.
It is easy to add new operators to the infix calculator as long as
they are only single-character literals. The lexical analyzer `yylex'
passes back all nonnumber characters as tokens, so new grammar rules
suffice for adding a new operator. But we want something more
flexible: built-in functions whose syntax has this form:
FUNCTION_NAME (ARGUMENT)
At the same time, we will add memory to the calculator, by allowing you
to create named variables, store values in them, and use them later.
Here is a sample session with the multi-function calculator:
$ mfcalc
pi = 3.141592653589
3.1415926536
sin(pi)
0.0000000000
alpha = beta1 = 2.3
2.3000000000
alpha
2.3000000000
ln(alpha)
0.8329091229
exp(ln(beta1))
2.3000000000
$
Note that multiple assignment and nested function calls are
permitted.
* Menu:
* Decl: Mfcalc Decl. Bison declarations for multi-function calculator.
* Rules: Mfcalc Rules. Grammar rules for the calculator.
* Symtab: Mfcalc Symtab. Symbol table management subroutines.
File: bison.info, Node: Mfcalc Decl, Next: Mfcalc Rules, Up: Multi-function Calc
2.5.1 Declarations for `mfcalc'
-------------------------------
Here are the C and Bison declarations for the multi-function calculator.
%{
#include <math.h> /* For math functions, cos(), sin(), etc. */
#include "calc.h" /* Contains definition of `symrec'. */
int yylex (void);
void yyerror (char const *);
%}
%union {
double val; /* For returning numbers. */
symrec *tptr; /* For returning symbol-table pointers. */
}
%token <val> NUM /* Simple double precision number. */
%token <tptr> VAR FNCT /* Variable and Function. */
%type <val> exp
%right '='
%left '-' '+'
%left '*' '/'
%left NEG /* negation--unary minus */
%right '^' /* exponentiation */
%% /* The grammar follows. */
The above grammar introduces only two new features of the Bison
language. These features allow semantic values to have various data
types (*note More Than One Value Type: Multiple Types.).
The `%union' declaration specifies the entire list of possible types;
this is instead of defining `YYSTYPE'. The allowable types are now
double-floats (for `exp' and `NUM') and pointers to entries in the
symbol table. *Note The Collection of Value Types: Union Decl.
Since values can now have various types, it is necessary to
associate a type with each grammar symbol whose semantic value is used.
These symbols are `NUM', `VAR', `FNCT', and `exp'. Their declarations
are augmented with information about their data type (placed between
angle brackets).
The Bison construct `%type' is used for declaring nonterminal
symbols, just as `%token' is used for declaring token types. We have
not used `%type' before because nonterminal symbols are normally
declared implicitly by the rules that define them. But `exp' must be
declared explicitly so we can specify its value type. *Note
Nonterminal Symbols: Type Decl.
File: bison.info, Node: Mfcalc Rules, Next: Mfcalc Symtab, Prev: Mfcalc Decl, Up: Multi-function Calc
2.5.2 Grammar Rules for `mfcalc'
--------------------------------
Here are the grammar rules for the multi-function calculator. Most of
them are copied directly from `calc'; three rules, those which mention
`VAR' or `FNCT', are new.
input: /* empty */
| input line
;
line:
'\n'
| exp '\n' { printf ("\t%.10g\n", $1); }
| error '\n' { yyerrok; }
;
exp: NUM { $$ = $1; }
| VAR { $$ = $1->value.var; }
| VAR '=' exp { $$ = $3; $1->value.var = $3; }
| FNCT '(' exp ')' { $$ = (*($1->value.fnctptr))($3); }
| 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; }
;
/* End of grammar. */
%%
File: bison.info, Node: Mfcalc Symtab, Prev: Mfcalc Rules, Up: Multi-function Calc
2.5.3 The `mfcalc' Symbol Table
-------------------------------
The multi-function calculator requires a symbol table to keep track of
the names and meanings of variables and functions. This doesn't affect
the grammar rules (except for the actions) or the Bison declarations,
but it requires some additional C functions for support.
The symbol table itself consists of a linked list of records. Its
definition, which is kept in the header `calc.h', is as follows. It
provides for either functions or variables to be placed in the table.
/* Function type. */
typedef double (*func_t) (double);
/* Data type for links in the chain of symbols. */
struct symrec
{
char *name; /* name of symbol */
int type; /* type of symbol: either VAR or FNCT */
union
{
double var; /* value of a VAR */
func_t fnctptr; /* value of a FNCT */
} value;
struct symrec *next; /* link field */
};
typedef struct symrec symrec;
/* The symbol table: a chain of `struct symrec'. */
extern symrec *sym_table;
symrec *putsym (char const *, func_t);
symrec *getsym (char const *);
The new version of `main' includes a call to `init_table', a
function that initializes the symbol table. Here it is, and
`init_table' as well:
#include <stdio.h>
/* Called by yyparse on error. */
void
yyerror (char const *s)
{
printf ("%s\n", s);
}
struct init
{
char const *fname;
double (*fnct) (double);
};
struct init const arith_fncts[] =
{
"sin", sin,
"cos", cos,
"atan", atan,
"ln", log,
"exp", exp,
"sqrt", sqrt,
0, 0
};
/* The symbol table: a chain of `struct symrec'. */
symrec *sym_table;
/* Put arithmetic functions in table. */
void
init_table (void)
{
int i;
symrec *ptr;
for (i = 0; arith_fncts[i].fname != 0; i++)
{
ptr = putsym (arith_fncts[i].fname, FNCT);
ptr->value.fnctptr = arith_fncts[i].fnct;
}
}
int
main (void)
{
init_table ();
return yyparse ();
}
By simply editing the initialization list and adding the necessary
include files, you can add additional functions to the calculator.
Two important functions allow look-up and installation of symbols in
the symbol table. The function `putsym' is passed a name and the type
(`VAR' or `FNCT') of the object to be installed. The object is linked
to the front of the list, and a pointer to the object is returned. The
function `getsym' is passed the name of the symbol to look up. If
found, a pointer to that symbol is returned; otherwise zero is returned.
symrec *
putsym (char const *sym_name, int sym_type)
{
symrec *ptr;
ptr = (symrec *) malloc (sizeof (symrec));
ptr->name = (char *) malloc (strlen (sym_name) + 1);
strcpy (ptr->name,sym_name);
ptr->type = sym_type;
ptr->value.var = 0; /* Set value to 0 even if fctn. */
ptr->next = (struct symrec *)sym_table;
sym_table = ptr;
return ptr;
}
symrec *
getsym (char const *sym_name)
{
symrec *ptr;
for (ptr = sym_table; ptr != (symrec *) 0;
ptr = (symrec *)ptr->next)
if (strcmp (ptr->name,sym_name) == 0)
return ptr;
return 0;
}
The function `yylex' must now recognize variables, numeric values,
and the single-character arithmetic operators. Strings of alphanumeric
characters with a leading non-digit are recognized as either variables
or functions depending on what the symbol table says about them.
The string is passed to `getsym' for look up in the symbol table. If
the name appears in the table, a pointer to its location and its type
(`VAR' or `FNCT') is returned to `yyparse'. If it is not already in
the table, then it is installed as a `VAR' using `putsym'. Again, a
pointer and its type (which must be `VAR') is returned to `yyparse'.
No change is needed in the handling of numeric values and arithmetic
operators in `yylex'.
#include <ctype.h>
int
yylex (void)
{
int c;
/* Ignore white space, get first nonwhite character. */
while ((c = getchar ()) == ' ' || c == '\t');
if (c == EOF)
return 0;
/* Char starts a number => parse the number. */
if (c == '.' || isdigit (c))
{
ungetc (c, stdin);
scanf ("%lf", &yylval.val);
return NUM;
}
/* Char starts an identifier => read the name. */
if (isalpha (c))
{
symrec *s;
static char *symbuf = 0;
static int length = 0;
int i;
/* Initially make the buffer long enough
for a 40-character symbol name. */
if (length == 0)
length = 40, symbuf = (char *)malloc (length + 1);
i = 0;
do
{
/* If buffer is full, make it bigger. */
if (i == length)
{
length *= 2;
symbuf = (char *) realloc (symbuf, length + 1);
}
/* Add this character to the buffer. */
symbuf[i++] = c;
/* Get another character. */
c = getchar ();
}
while (isalnum (c));
ungetc (c, stdin);
symbuf[i] = '\0';
s = getsym (symbuf);
if (s == 0)
s = putsym (symbuf, VAR);
yylval.tptr = s;
return s->type;
}
/* Any other character is a token by itself. */
return c;
}
This program is both powerful and flexible. You may easily add new
functions, and it is a simple job to modify this code to install
predefined variables such as `pi' or `e' as well.
File: bison.info, Node: Exercises, Prev: Multi-function Calc, Up: Examples
2.6 Exercises
=============
1. Add some new functions from `math.h' to the initialization list.
2. Add another array that contains constants and their values. Then
modify `init_table' to add these constants to the symbol table.
It will be easiest to give the constants type `VAR'.
3. Make the program report an error if the user refers to an
uninitialized variable in any way except to store a value in it.
File: bison.info, Node: Grammar File, Next: Interface, Prev: Examples, Up: Top
3 Bison Grammar Files
*********************
Bison takes as input a context-free grammar specification and produces a
C-language function that recognizes correct instances of the grammar.
The Bison grammar input file conventionally has a name ending in
`.y'. *Note Invoking Bison: Invocation.
* Menu:
* Grammar Outline:: Overall layout of the grammar file.
* Symbols:: Terminal and nonterminal symbols.
* Rules:: How to write grammar rules.
* Recursion:: Writing recursive rules.
* Semantics:: Semantic values and actions.
* Locations:: Locations and actions.
* Declarations:: All kinds of Bison declarations are described here.
* Multiple Parsers:: Putting more than one Bison parser in one program.
File: bison.info, Node: Grammar Outline, Next: Symbols, Up: Grammar File
3.1 Outline of a Bison Grammar
==============================
A Bison grammar file has four main sections, shown here with the
appropriate delimiters:
%{
PROLOGUE
%}
BISON DECLARATIONS
%%
GRAMMAR RULES
%%
EPILOGUE
Comments enclosed in `/* ... */' may appear in any of the sections.
As a GNU extension, `//' introduces a comment that continues until end
of line.
* Menu:
* Prologue:: Syntax and usage of the prologue.
* Bison Declarations:: Syntax and usage of the Bison declarations section.
* Grammar Rules:: Syntax and usage of the grammar rules section.
* Epilogue:: Syntax and usage of the epilogue.
File: bison.info, Node: Prologue, Next: Bison Declarations, Up: Grammar Outline
3.1.1 The prologue
------------------
The PROLOGUE section contains macro definitions and declarations of
functions and variables that are used in the actions in the grammar
rules. These are copied to the beginning of the parser file so that
they precede the definition of `yyparse'. You can use `#include' to
get the declarations from a header file. If you don't need any C
declarations, you may omit the `%{' and `%}' delimiters that bracket
this section.
You may have more than one PROLOGUE section, intermixed with the
BISON DECLARATIONS. This allows you to have C and Bison declarations
that refer to each other. For example, the `%union' declaration may
use types defined in a header file, and you may wish to prototype
functions that take arguments of type `YYSTYPE'. This can be done with
two PROLOGUE blocks, one before and one after the `%union' declaration.
%{
#include <stdio.h>
#include "ptypes.h"
%}
%union {
long int n;
tree t; /* `tree' is defined in `ptypes.h'. */
}
%{
static void print_token_value (FILE *, int, YYSTYPE);
#define YYPRINT(F, N, L) print_token_value (F, N, L)
%}
...
File: bison.info, Node: Bison Declarations, Next: Grammar Rules, Prev: Prologue, Up: Grammar Outline
3.1.2 The Bison Declarations Section
------------------------------------
The BISON DECLARATIONS section contains declarations that define
terminal and nonterminal symbols, specify precedence, and so on. In
some simple grammars you may not need any declarations. *Note Bison
Declarations: Declarations.
File: bison.info, Node: Grammar Rules, Next: Epilogue, Prev: Bison Declarations, Up: Grammar Outline
3.1.3 The Grammar Rules Section
-------------------------------
The "grammar rules" section contains one or more Bison grammar rules,
and nothing else. *Note Syntax of Grammar Rules: Rules.
There must always be at least one grammar rule, and the first `%%'
(which precedes the grammar rules) may never be omitted even if it is
the first thing in the file.
File: bison.info, Node: Epilogue, Prev: Grammar Rules, Up: Grammar Outline
3.1.4 The epilogue
------------------
The EPILOGUE is copied verbatim to the end of the parser file, just as
the PROLOGUE is copied to the beginning. This is the most convenient
place to put anything that you want to have in the parser file but
which need not come before the definition of `yyparse'. For example,
the definitions of `yylex' and `yyerror' often go here. Because C
requires functions to be declared before being used, you often need to
declare functions like `yylex' and `yyerror' in the Prologue, even if
you define them int he Epilogue. *Note Parser C-Language Interface:
Interface.
If the last section is empty, you may omit the `%%' that separates it
from the grammar rules.
The Bison parser itself contains many macros and identifiers whose
names start with `yy' or `YY', so it is a good idea to avoid using any
such names (except those documented in this manual) in the epilogue of
the grammar file.
File: bison.info, Node: Symbols, Next: Rules, Prev: Grammar Outline, Up: Grammar File
3.2 Symbols, Terminal and Nonterminal
=====================================
"Symbols" in Bison grammars represent the grammatical classifications
of the language.
A "terminal symbol" (also known as a "token type") represents a
class of syntactically equivalent tokens. You use the symbol in grammar
rules to mean that a token in that class is allowed. The symbol is
represented in the Bison parser by a numeric code, and the `yylex'
function returns a token type code to indicate what kind of token has
been read. You don't need to know what the code value is; you can use
the symbol to stand for it.
A "nonterminal symbol" stands for a class of syntactically equivalent
groupings. The symbol name is used in writing grammar rules. By
convention, it should be all lower case.
Symbol names can contain letters, digits (not at the beginning),
underscores and periods. Periods make sense only in nonterminals.
There are three ways of writing terminal symbols in the grammar:
* A "named token type" is written with an identifier, like an
identifier in C. By convention, it should be all upper case. Each
such name must be defined with a Bison declaration such as
`%token'. *Note Token Type Names: Token Decl.
* A "character token type" (or "literal character token") is written
in the grammar using the same syntax used in C for character
constants; for example, `'+'' is a character token type. A
character token type doesn't need to be declared unless you need to
specify its semantic value data type (*note Data Types of Semantic
Values: Value Type.), associativity, or precedence (*note Operator
Precedence: Precedence.).
By convention, a character token type is used only to represent a
token that consists of that particular character. Thus, the token
type `'+'' is used to represent the character `+' as a token.
Nothing enforces this convention, but if you depart from it, your
program will confuse other readers.
All the usual escape sequences used in character literals in C can
be used in Bison as well, but you must not use the null character
as a character literal because its numeric code, zero, signifies
end-of-input (*note Calling Convention for `yylex': Calling
Convention.). Also, unlike standard C, trigraphs have no special
meaning in Bison character literals, nor is backslash-newline
allowed.
* A "literal string token" is written like a C string constant; for
example, `"<="' is a literal string token. A literal string token
doesn't need to be declared unless you need to specify its semantic
value data type (*note Value Type::), associativity, or precedence
(*note Precedence::).
You can associate the literal string token with a symbolic name as
an alias, using the `%token' declaration (*note Token
Declarations: Token Decl.). If you don't do that, the lexical
analyzer has to retrieve the token number for the literal string
token from the `yytname' table (*note Calling Convention::).
*Warning*: literal string tokens do not work in Yacc.
By convention, a literal string token is used only to represent a
token that consists of that particular string. Thus, you should
use the token type `"<="' to represent the string `<=' as a token.
Bison does not enforce this convention, but if you depart from
it, people who read your program will be confused.
All the escape sequences used in string literals in C can be used
in Bison as well, except that you must not use a null character
within a string literal. Also, unlike Standard C, trigraphs have
no special meaning in Bison string literals, nor is
backslash-newline allowed. A literal string token must contain
two or more characters; for a token containing just one character,
use a character token (see above).
How you choose to write a terminal symbol has no effect on its
grammatical meaning. That depends only on where it appears in rules and
on when the parser function returns that symbol.
The value returned by `yylex' is always one of the terminal symbols,
except that a zero or negative value signifies end-of-input. Whichever
way you write the token type in the grammar rules, you write it the
same way in the definition of `yylex'. The numeric code for a
character token type is simply the positive numeric code of the
character, so `yylex' can use the identical value to generate the
requisite code, though you may need to convert it to `unsigned char' to
avoid sign-extension on hosts where `char' is signed. Each named token
type becomes a C macro in the parser file, so `yylex' can use the name
to stand for the code. (This is why periods don't make sense in
terminal symbols.) *Note Calling Convention for `yylex': Calling
Convention.
If `yylex' is defined in a separate file, you need to arrange for the
token-type macro definitions to be available there. Use the `-d'
option when you run Bison, so that it will write these macro definitions
into a separate header file `NAME.tab.h' which you can include in the
other source files that need it. *Note Invoking Bison: Invocation.
If you want to write a grammar that is portable to any Standard C
host, you must use only non-null character tokens taken from the basic
execution character set of Standard C. This set consists of the ten
digits, the 52 lower- and upper-case English letters, and the
characters in the following C-language string:
"\a\b\t\n\v\f\r !\"#%&'()*+,-./:;<=>?[\\]^_{|}~"
The `yylex' function and Bison must use a consistent character set
and encoding for character tokens. For example, if you run Bison in an
ASCII environment, but then compile and run the resulting program in an
environment that uses an incompatible character set like EBCDIC, the
resulting program may not work because the tables generated by Bison
will assume ASCII numeric values for character tokens. It is standard
practice for software distributions to contain C source files that were
generated by Bison in an ASCII environment, so installers on platforms
that are incompatible with ASCII must rebuild those files before
compiling them.
The symbol `error' is a terminal symbol reserved for error recovery
(*note Error Recovery::); you shouldn't use it for any other purpose.
In particular, `yylex' should never return this value. The default
value of the error token is 256, unless you explicitly assigned 256 to
one of your tokens with a `%token' declaration.
File: bison.info, Node: Rules, Next: Recursion, Prev: Symbols, Up: Grammar File
3.3 Syntax of Grammar Rules
===========================
A Bison grammar rule has the following general form:
RESULT: COMPONENTS...
;
where RESULT is the nonterminal symbol that this rule describes, and
COMPONENTS are various terminal and nonterminal symbols that are put
together by this rule (*note Symbols::).
For example,
exp: exp '+' exp
;
says that two groupings of type `exp', with a `+' token in between, can
be combined into a larger grouping of type `exp'.
White space in rules is significant only to separate symbols. You
can add extra white space as you wish.
Scattered among the components can be ACTIONS that determine the
semantics of the rule. An action looks like this:
{C STATEMENTS}
Usually there is only one action and it follows the components. *Note
Actions::.
Multiple rules for the same RESULT can be written separately or can
be joined with the vertical-bar character `|' as follows:
RESULT: RULE1-COMPONENTS...
| RULE2-COMPONENTS...
...
;
They are still considered distinct rules even when joined in this way.
If COMPONENTS in a rule is empty, it means that RESULT can match the
empty string. For example, here is how to define a comma-separated
sequence of zero or more `exp' groupings:
expseq: /* empty */
| expseq1
;
expseq1: exp
| expseq1 ',' exp
;
It is customary to write a comment `/* empty */' in each rule with no
components.
File: bison.info, Node: Recursion, Next: Semantics, Prev: Rules, Up: Grammar File
3.4 Recursive Rules
===================
A rule is called "recursive" when its RESULT nonterminal appears also
on its right hand side. Nearly all Bison grammars need to use
recursion, because that is the only way to define a sequence of any
number of a particular thing. Consider this recursive definition of a
comma-separated sequence of one or more expressions:
expseq1: exp
| expseq1 ',' exp
;
Since the recursive use of `expseq1' is the leftmost symbol in the
right hand side, we call this "left recursion". By contrast, here the
same construct is defined using "right recursion":
expseq1: exp
| exp ',' expseq1
;
Any kind of sequence can be defined using either left recursion or right
recursion, but you should always use left recursion, because it can
parse a sequence of any number of elements with bounded stack space.
Right recursion uses up space on the Bison stack in proportion to the
number of elements in the sequence, because all the elements must be
shifted onto the stack before the rule can be applied even once. *Note
The Bison Parser Algorithm: Algorithm, for further explanation of this.
"Indirect" or "mutual" recursion occurs when the result of the rule
does not appear directly on its right hand side, but does appear in
rules for other nonterminals which do appear on its right hand side.
For example:
expr: primary
| primary '+' primary
;
primary: constant
| '(' expr ')'
;
defines two mutually-recursive nonterminals, since each refers to the
other.
File: bison.info, Node: Semantics, Next: Locations, Prev: Recursion, Up: Grammar File
3.5 Defining Language Semantics
===============================
The grammar rules for a language determine only the syntax. The
semantics are determined by the semantic values associated with various
tokens and groupings, and by the actions taken when various groupings
are recognized.
For example, the calculator calculates properly because the value
associated with each expression is the proper number; it adds properly
because the action for the grouping `X + Y' is to add the numbers
associated with X and Y.
* Menu:
* Value Type:: Specifying one data type for all semantic values.
* Multiple Types:: Specifying several alternative data types.
* Actions:: An action is the semantic definition of a grammar rule.
* Action Types:: Specifying data types for actions to operate on.
* Mid-Rule Actions:: Most actions go at the end of a rule.
This says when, why and how to use the exceptional
action in the middle of a rule.
File: bison.info, Node: Value Type, Next: Multiple Types, Up: Semantics
3.5.1 Data Types of Semantic Values
-----------------------------------
In a simple program it may be sufficient to use the same data type for
the semantic values of all language constructs. This was true in the
RPN and infix calculator examples (*note Reverse Polish Notation
Calculator: RPN Calc.).
Bison's default is to use type `int' for all semantic values. To
specify some other type, define `YYSTYPE' as a macro, like this:
#define YYSTYPE double
This macro definition must go in the prologue of the grammar file
(*note Outline of a Bison Grammar: Grammar Outline.).
File: bison.info, Node: Multiple Types, Next: Actions, Prev: Value Type, Up: Semantics
3.5.2 More Than One Value Type
------------------------------
In most programs, you will need different data types for different kinds
of tokens and groupings. For example, a numeric constant may need type
`int' or `long int', while a string constant needs type `char *', and
an identifier might need a pointer to an entry in the symbol table.
To use more than one data type for semantic values in one parser,
Bison requires you to do two things:
* Specify the entire collection of possible data types, with the
`%union' Bison declaration (*note The Collection of Value Types:
Union Decl.).
* Choose one of those types for each symbol (terminal or
nonterminal) for which semantic values are used. This is done for
tokens with the `%token' Bison declaration (*note Token Type
Names: Token Decl.) and for groupings with the `%type' Bison
declaration (*note Nonterminal Symbols: Type Decl.).
File: bison.info, Node: Actions, Next: Action Types, Prev: Multiple Types, Up: Semantics
3.5.3 Actions
-------------
An action accompanies a syntactic rule and contains C code to be
executed each time an instance of that rule is recognized. The task of
most actions is to compute a semantic value for the grouping built by
the rule from the semantic values associated with tokens or smaller
groupings.
An action consists of C statements surrounded by braces, much like a
compound statement in C. An action can contain any sequence of C
statements. Bison does not look for trigraphs, though, so if your C
code uses trigraphs you should ensure that they do not affect the
nesting of braces or the boundaries of comments, strings, or character
literals.
An action can be placed at any position in the rule; it is executed
at that position. Most rules have just one action at the end of the
rule, following all the components. Actions in the middle of a rule
are tricky and used only for special purposes (*note Actions in
Mid-Rule: Mid-Rule Actions.).
The C code in an action can refer to the semantic values of the
components matched by the rule wi