Hopefully added to the repository all the distributed files.

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START-INFO-DIR-ENTRY
* bison: (bison).       GNU Project parser generator (yacc replacement).
END-INFO-DIR-ENTRY

   This file documents the Bison parser generator.

   Copyright (C) 1988, 1989, 1990, 1991, 1992, 1993, 1995, 1998, 1999,
2000 Free Software Foundation, Inc.

   Permission is granted to make and distribute verbatim copies of this
manual provided the copyright notice and this permission notice are
preserved on all copies.

   Permission is granted to copy and distribute modified versions of
this manual under the conditions for verbatim copying, provided also
that the sections entitled "GNU General Public License" and "Conditions
for Using Bison" are included exactly as in the original, and provided
that the entire resulting derived work is distributed under the terms
of a permission notice identical to this one.

   Permission is granted to copy and distribute translations of this
manual into another language, under the above conditions for modified
versions, except that the sections entitled "GNU General Public
License", "Conditions for Using Bison" and this permission notice may be
included in translations approved by the Free Software Foundation
instead of in the original English.

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File: bison.info,  Node: Top,  Next: Introduction,  Prev: (dir),  Up: (dir)

   This manual documents version 1.28a of Bison.

* 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::         Debugging Bison parsers that parse wrong.
* 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.
* 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.
* 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.

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.
* 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.  Bison and C 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::

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.
* 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

* C Declarations::    Syntax and usage of the C declarations section.
* Bison Declarations::  Syntax and usage of the Bison declarations section.
* Grammar Rules::     Syntax and usage of the grammar rules section.
* C Code::            Syntax and usage of the additional C code section.

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.

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.
* Expect Decl::       Suppressing warnings about shift/reduce 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 Positions::   How `yylex' must return the text position
                        (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.
* 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.

Invoking Bison

* Bison Options::     All the options described in detail,
                        in alphabetical order by short options.
* Option Cross Key::  Alphabetical list of long options.
* VMS Invocation::    Bison command syntax on VMS.

\1f
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 1.28a of Bison.

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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.
Formerly, Bison 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.

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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
that any problems introduced by others will not reflect on the original
authors' reputations.

   Finally, any free program is threatened constantly by software
patents.  We wish to avoid the danger that redistributors of a free
program will individually obtain patent licenses, in effect making the
program proprietary.  To prevent this, we have made it clear that any
patent must be licensed for everyone's free use or not licensed at all.

   The precise terms and conditions for copying, distribution and
modification follow.

    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
     the Program" means either the Program or any derivative work under
     copyright law: that is to say, a work containing the Program or a
     portion of it, either verbatim or with modifications and/or
     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
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       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
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          distributed under the terms of Sections 1 and 2 above on a
          medium customarily used for software interchange; or,

       c. Accompany it with the information you received as to the offer
          to distribute corresponding source code.  (This alternative is
          allowed only for noncommercial distribution and only if you
          received the program in object code or executable form with
          such an offer, in accord with Subsection b above.)

     The source code for a work means the preferred form of the work for
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     If distribution of executable or object code is made by offering
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     access to copy the source code from the same place counts as
     distribution of the source code, even though third parties are not
     compelled to copy the source along with the object code.

  4. You may not copy, modify, sublicense, or distribute the Program
     except as expressly provided under this License.  Any attempt
     otherwise to copy, modify, sublicense or distribute the Program is
     void, and will automatically terminate your rights under this
     License.  However, parties who have received copies, or rights,
     from you under this License will not have their licenses
     terminated so long as such parties remain in full compliance.

  5. You are not required to accept this License, since you have not
     signed it.  However, nothing else grants you permission to modify
     or distribute the Program or its derivative works.  These actions
     are prohibited by law if you do not accept this License.
     Therefore, by modifying or distributing the Program (or any work
     based on the Program), you indicate your acceptance of this
     License to do so, and all its terms and conditions for copying,
     distributing or modifying the Program or works based on it.

  6. Each time you redistribute the Program (or any work based on the
     Program), the recipient automatically receives a license from the
     original licensor to copy, distribute or modify the Program
     subject to these terms and conditions.  You may not impose any
     further restrictions on the recipients' exercise of the rights
     granted herein.  You are not responsible for enforcing compliance
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  7. If, as a consequence of a court judgment or allegation of patent
     infringement or for any other reason (not limited to patent
     issues), conditions are imposed on you (whether by court order,
     agreement or otherwise) that contradict the conditions of this
     License, they do not excuse you from the conditions of this
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     royalty-free redistribution of the Program by all those who
     receive copies directly or indirectly through you, then the only
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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
     intended to apply and the section as a whole is intended to apply
     in other circumstances.

     It is not the purpose of this section to induce you to infringe any
     patents or other property right claims or to contest validity of
     any such claims; this section has the sole purpose of protecting
     the integrity of the free software distribution system, which is
     implemented by public license practices.  Many people have made
     generous contributions to the wide range of software distributed
     through that system in reliance on consistent application of that
     system; it is up to the author/donor to decide if he or she is
     willing to distribute software through any other system and a
     licensee cannot impose that choice.

     This section is intended to make thoroughly clear what is believed
     to be a consequence of the rest of this License.

  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
     new versions will be similar in spirit to the present version, but
     may differ in detail to address new problems or concerns.

     Each version is given a distinguishing version number.  If the
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     to it and "any later version", you have the option of following
     the terms and conditions either of that version or of any later
     version published by the Free Software Foundation.  If the Program
     does not specify a version number of this License, you may choose
     any version ever published by the Free Software Foundation.

 10. If you wish to incorporate parts of the Program into other free
     programs whose distribution conditions are different, write to the
     author to ask for permission.  For software which is copyrighted
     by the Free Software Foundation, write to the Free Software
     Foundation; we sometimes make exceptions for this.  Our decision
     will be guided by the two goals of preserving the free status of
     all derivatives of our free software and of promoting the sharing
     and reuse of software generally.

                                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
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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,
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     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

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) 19YY  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.

\1f
File: bison.info,  Node: Concepts,  Next: Examples,  Prev: Copying,  Up: Top

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.
* 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.

\1f
File: bison.info,  Node: Language and Grammar,  Next: Grammar in Bison,  Up: Concepts

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.

   Not all context-free languages can be handled by Bison, only those
that are LALR(1).  In brief, this means that 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.

   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 (x)      /* identifier, open-paren, */
                     /* identifier, close-paren */
          int x;     /* keyword `int', identifier, semicolon */
     {               /* 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.

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File: bison.info,  Node: Grammar in Bison,  Next: Semantic Values,  Prev: Language and Grammar,  Up: Concepts

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.

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File: bison.info,  Node: Semantic Values,  Next: Semantic Actions,  Prev: Grammar in Bison,  Up: Concepts

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.

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File: bison.info,  Node: Semantic Actions,  Next: Bison Parser,  Prev: Semantic Values,  Up: Concepts

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.

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File: bison.info,  Node: Bison Parser,  Next: Stages,  Prev: Semantic Actions,  Up: Concepts

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 variable and function names used in the Bison parser file
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.

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File: bison.info,  Node: Stages,  Next: Grammar Layout,  Prev: Bison Parser,  Up: Concepts

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.

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File: bison.info,  Node: Grammar Layout,  Prev: Stages,  Up: Concepts

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:

     %{
     C DECLARATIONS
     %}
     
     BISON DECLARATIONS
     
     %%
     GRAMMAR RULES
     %%
     ADDITIONAL C CODE

The `%%', `%{' and `%}' are punctuation that appears in every Bison
grammar file to separate the sections.

   The C declarations 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.

   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 additional C code can contain any C code you want to use.  Often
the definition of the lexical analyzer `yylex' goes here, plus
subroutines called by the actions in the grammar rules.  In a simple
program, all the rest of the program can go here.

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File: bison.info,  Node: Examples,  Next: Grammar File,  Prev: Concepts,  Up: Top

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.
* 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.

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File: bison.info,  Node: RPN Calc,  Next: Infix Calc,  Up: Examples

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.  Bison and C 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.

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File: bison.info,  Node: Rpcalc Decls,  Next: Rpcalc Rules,  Up: RPN Calc

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>
     %}
     
     %token NUM
     
     %% /* Grammar rules and actions follow */

   The C declarations section (*note The C Declarations Section: C
Declarations.) contains two preprocessor directives.

   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 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.