Stop storing rules from 1 to nrules + 1.

[bison.git] / doc / bison.texinfo

\input texinfo @c -*-texinfo-*-
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@setfilename bison.info
@include version.texi
@settitle Bison @value{VERSION}
@setchapternewpage odd

@finalout

@c SMALL BOOK version
@c This edition has been formatted so that you can format and print it in
@c the smallbook format.
@c @smallbook

@c Set following if you have the new `shorttitlepage' command
@c @clear shorttitlepage-enabled
@c @set shorttitlepage-enabled

@c ISPELL CHECK: done, 14 Jan 1993 --bob

@c Check COPYRIGHT dates.  should be updated in the titlepage, ifinfo
@c titlepage; should NOT be changed in the GPL.  --mew

@c FIXME: I don't understand this `iftex'.  Obsolete? --akim.
@iftex
@syncodeindex fn cp
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@ifinfo
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@copying

This manual is for GNU Bison (version @value{VERSION}, @value{UPDATED}),
the GNU parser generator.

Copyright @copyright{} 1988, 1989, 1990, 1991, 1992, 1993, 1995, 1998,
1999, 2000, 2001, 2002 Free Software Foundation, Inc.

@quotation
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.''
@end quotation
@end copying

@dircategory GNU programming tools
@direntry
* bison: (bison).	GNU parser generator (yacc replacement).
@end direntry

@ifset shorttitlepage-enabled
@shorttitlepage Bison
@end ifset
@titlepage
@title Bison
@subtitle The YACC-compatible Parser Generator
@subtitle @value{UPDATED}, Bison Version @value{VERSION}

@author by Charles Donnelly and Richard Stallman

@page
@vskip 0pt plus 1filll
@insertcopying
@sp 2
Published by the Free Software Foundation @*
59 Temple Place, Suite 330 @*
Boston, MA  02111-1307  USA @*
Printed copies are available from the Free Software Foundation.@*
ISBN 1-882114-44-2
@sp 2
Cover art by Etienne Suvasa.
@end titlepage

@contents

@ifnottex
@node Top
@top Bison
@insertcopying
@end ifnottex

@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 @code{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.
* Copying This Manual::  License for copying this manual.
* Index::             Cross-references to the text.

@detailmenu --- 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.
* Location Tracking Calc:: Demonstrating the use of @@@var{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 @code{rpcalc}

* Rpcalc Input::
* Rpcalc Line::
* Rpcalc Expr::

Location Tracking Calculator: @code{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: @code{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

* Prologue::          Syntax and usage of the prologue (declarations section).
* 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 (additional 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 @code{yyparse} and what it returns.
* Lexical::           You must supply a function @code{yylex}
                        which reads tokens.
* Error Reporting::   You must supply a function @code{yyerror}.
* Action Features::   Special features for use in actions.

The Lexical Analyzer Function @code{yylex}

* Calling Convention::  How @code{yyparse} calls @code{yylex}.
* Token Values::      How @code{yylex} must return the semantic value
                        of the token it has read.
* Token Positions::   How @code{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 (@pxref{Pure Decl, ,A Pure (Reentrant) Parser}).

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.

Understanding or 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.
* VMS Invocation::    Bison command syntax on VMS.

Copying This Manual

* GNU Free Documentation License::  License for copying this manual.

@end detailmenu
@end menu

@node Introduction
@unnumbered Introduction
@cindex introduction

@dfn{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 @value{VERSION} of Bison.

@node Conditions
@unnumbered Conditions for Using Bison

As of Bison version 1.24, we have changed the distribution terms for
@code{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
@code{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 @code{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.  @strong{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.

@include gpl.texi

@node Concepts
@chapter 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.
@end menu

@node Language and Grammar
@section Languages and Context-Free Grammars

@cindex context-free grammar
@cindex grammar, context-free
In order for Bison to parse a language, it must be described by a
@dfn{context-free grammar}.  This means that you specify one or more
@dfn{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.

@cindex BNF
@cindex Backus-Naur form
The most common formal system for presenting such rules for humans to read
is @dfn{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.

@cindex LALR(1) grammars
@cindex LR(1) grammars
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).  @xref{Mystery Conflicts, ,
Mysterious Reduce/Reduce Conflicts}, for more information on this.

@cindex GLR parsing
@cindex generalized LR (GLR) parsing
@cindex ambiguous grammars
@cindex non-deterministic parsing
Parsers for LALR(1) grammars are @dfn{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 @dfn{look-ahead}) of the remaining input.
A context-free grammar can be @dfn{ambiguous}, meaning that
there are multiple ways to apply the grammar rules to get the some inputs.
Even unambiguous grammars can be @dfn{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.

@cindex symbols (abstract)
@cindex token
@cindex syntactic grouping
@cindex grouping, syntactic
In the formal grammatical rules for a language, each kind of syntactic unit
or grouping is named by a @dfn{symbol}.  Those which are built by grouping
smaller constructs according to grammatical rules are called
@dfn{nonterminal symbols}; those which can't be subdivided are called
@dfn{terminal symbols} or @dfn{token types}.  We call a piece of input
corresponding to a single terminal symbol a @dfn{token}, and a piece
corresponding to a single nonterminal symbol a @dfn{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:

@ifinfo
@example
int             /* @r{keyword `int'} */
square (int x)  /* @r{identifier, open-paren, identifier,}
                   @r{identifier, close-paren} */
@{               /* @r{open-brace} */
  return x * x; /* @r{keyword `return', identifier, asterisk,
                   identifier, semicolon} */
@}               /* @r{close-brace} */
@end example
@end ifinfo
@ifnotinfo
@example
int             /* @r{keyword `int'} */
square (int x)  /* @r{identifier, open-paren, identifier, identifier, close-paren} */
@{               /* @r{open-brace} */
  return x * x; /* @r{keyword `return', identifier, asterisk, identifier, semicolon} */
@}               /* @r{close-brace} */
@end example
@end ifnotinfo

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 @samp{x} is an expression and so is @samp{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
@code{return} statement; this would be described with a grammar rule which
reads informally as follows:

@quotation
A `statement' can be made of a `return' keyword, an `expression' and a
`semicolon'.
@end quotation

@noindent
There would be many other rules for `statement', one for each kind of
statement in C.

@cindex start symbol
One nonterminal symbol must be distinguished as the special one which
defines a complete utterance in the language.  It is called the @dfn{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, @samp{1 + 2} is a valid C expression---a valid part of a C
program---but it is not valid as an @emph{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.

@node Grammar in Bison
@section From Formal Rules to Bison Input
@cindex Bison grammar
@cindex grammar, Bison
@cindex formal grammar

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 @dfn{Bison grammar} file.  @xref{Grammar File, ,Bison Grammar Files}.

A nonterminal symbol in the formal grammar is represented in Bison input
as an identifier, like an identifier in C.  By convention, it should be
in lower case, such as @code{expr}, @code{stmt} or @code{declaration}.

The Bison representation for a terminal symbol is also called a @dfn{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, @code{INTEGER}, @code{IDENTIFIER}, @code{IF} or
@code{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 @code{error} is reserved for error recovery.
@xref{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.  @xref{Symbols}, for more information.

The grammar rules also have an expression in Bison syntax.  For example,
here is the Bison rule for a C @code{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.

@example
stmt:   RETURN expr ';'
        ;
@end example

@noindent
@xref{Rules, ,Syntax of Grammar Rules}.

@node Semantic Values
@section Semantic Values
@cindex semantic value
@cindex value, semantic

A formal grammar selects tokens only by their classifications: for example,
if a rule mentions the terminal symbol `integer constant', it means that
@emph{any} integer constant is grammatically valid in that position.  The
precise value of the constant is irrelevant to how to parse the input: if
@samp{x+4} is grammatical then @samp{x+1} or @samp{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 @dfn{semantic value}.  @xref{Semantics, ,Defining Language Semantics},
for details.

The token type is a terminal symbol defined in the grammar, such as
@code{INTEGER}, @code{IDENTIFIER} or @code{','}.  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 @code{','} which is just punctuation doesn't
need to have any semantic value.)

For example, an input token might be classified as token type
@code{INTEGER} and have the semantic value 4.  Another input token might
have the same token type @code{INTEGER} but value 3989.  When a grammar
rule says that @code{INTEGER} is allowed, either of these tokens is
acceptable because each is an @code{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.

@node Semantic Actions
@section Semantic Actions
@cindex semantic actions
@cindex actions, semantic

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 @dfn{action} made up of C statements.  Each time the
parser recognizes a match for that rule, the action is executed.
@xref{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:

@example
expr: expr '+' expr   @{ $$ = $1 + $3; @}
        ;
@end example

@noindent
The action says how to produce the semantic value of the sum expression
from the values of the two subexpressions.

@node GLR Parsers
@section Writing GLR Parsers
@cindex GLR parsing
@cindex generalized LR (GLR) parsing
@findex %glr-parser
@cindex conflicts
@cindex shift/reduce conflicts

In some grammars, there will be cases where 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 @dfn{reduce/reduce} conflicts (@pxref{Reduce/Reduce}),
and @dfn{shift/reduce} conflicts (@pxref{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
@code{%glr-parser} among the Bison declarations in your file
(@pxref{Grammar Outline}), the result will be 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.

Let's consider an example, vastly simplified from C++.

@example
%@{
  #define YYSTYPE const char*
%@}

%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 ')'
     ;
@end example

@noindent
This models a problematic part of the C++ grammar---the ambiguity between
certain declarations and statements.  For example,

@example
T (x) = y+z;
@end example

@noindent
parses as either an @code{expr} or a @code{stmt}
(assuming that @samp{T} is recognized as a TYPENAME and @samp{x} as an ID).
Bison detects this as a reduce/reduce conflict between the rules
@code{expr : ID} and @code{declarator : ID}, which it cannot resolve at the
time it encounters @code{x} in the example above.  The two @code{%dprec}
declarations, however, give precedence to interpreting the example as a
@code{decl}, which implies that @code{x} is a declarator.
The parser therefore prints

@example
"x" y z + T <init-declare>
@end example

Consider a different input string for this parser:

@example
T (x) + y;
@end example

@noindent
Here, there is no ambiguity (this cannot be parsed as a declaration).
However, at the time the Bison parser encounters @code{x}, it does not
have enough information to resolve the reduce/reduce conflict (again,
between @code{x} as an @code{expr} or a @code{declarator}).  In this
case, no precedence declaration is used.  Instead, the parser splits
into two, one assuming that @code{x} is an @code{expr}, and the other
assuming @code{x} is a @code{declarator}.  The second of these parsers
then vanishes when it sees @code{+}, and the parser prints

@example
x T <cast> y +
@end example

Suppose that instead of resolving the ambiguity, you wanted to see all
the possibilities.  For this purpose, we must @dfn{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 @code{stmt} as
follows:

@example
stmt : expr ';'  %merge <stmtMerge>
     | decl      %merge <stmtMerge>
     ;
@end example

@noindent

and define the @code{stmtMerge} function as:

@example
static YYSTYPE stmtMerge (YYSTYPE x0, YYSTYPE x1)
@{
  printf ("<OR> ");
  return "";
@}
@end example

@noindent
with an accompanying forward declaration
in the C declarations at the beginning of the file:

@example
%@{
  #define YYSTYPE const char*
  static YYSTYPE stmtMerge (YYSTYPE x0, YYSTYPE x1);
%@}
@end example

@noindent
With these declarations, the resulting parser will parse the first example
as both an @code{expr} and a @code{decl}, and print

@example
"x" y z + T <init-declare> x T <cast> y z + = <OR>
@end example


@node Locations Overview
@section Locations
@cindex location
@cindex textual position
@cindex position, textual

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 @dfn{textual position}, or @dfn{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 (@pxref{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 @code{@@$}, while the locations of the subexpressions are @code{@@1} and
@code{@@3}.

When a rule is matched, a default action is used to compute the semantic value
of its left hand side (@pxref{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 @code{@@$} 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.

@node Bison Parser
@section Bison Output: the Parser File
@cindex Bison parser
@cindex Bison utility
@cindex lexical analyzer, purpose
@cindex parser

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 @dfn{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 @dfn{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.
@xref{Lexical, ,The Lexical Analyzer Function @code{yylex}}.

The Bison parser file is C code which defines a function named
@code{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 @code{main}; you have to provide this, and
arrange for it to call @code{yyparse} or the parser will never run.
@xref{Interface, ,Parser C-Language Interface}.

Aside from the token type names and the symbols in the actions you
write, all symbols defined in the Bison parser file itself
begin with @samp{yy} or @samp{YY}.  This includes interface functions
such as the lexical analyzer function @code{yylex}, the error reporting
function @code{yyerror} and the parser function @code{yyparse} itself.
This also includes numerous identifiers used for internal purposes.
Therefore, you should avoid using C identifiers starting with @samp{yy}
or @samp{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-@sc{gnu} hosts, @code{<alloca.h>},
@code{<stddef.h>}, and @code{<stdlib.h>} are included as needed to
declare memory allocators and related types.  Other system headers may
be included if you define @code{YYDEBUG} to a nonzero value
(@pxref{Tracing, ,Tracing Your Parser}).

@node Stages
@section Stages in Using Bison
@cindex stages in using Bison
@cindex using Bison

The actual language-design process using Bison, from grammar specification
to a working compiler or interpreter, has these parts:

@enumerate
@item
Formally specify the grammar in a form recognized by Bison
(@pxref{Grammar File, ,Bison Grammar Files}).  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.

@item
Write a lexical analyzer to process input and pass tokens to the parser.
The lexical analyzer may be written by hand in C (@pxref{Lexical, ,The
Lexical Analyzer Function @code{yylex}}).  It could also be produced
using Lex, but the use of Lex is not discussed in this manual.

@item
Write a controlling function that calls the Bison-produced parser.

@item
Write error-reporting routines.
@end enumerate

To turn this source code as written into a runnable program, you
must follow these steps:

@enumerate
@item
Run Bison on the grammar to produce the parser.

@item
Compile the code output by Bison, as well as any other source files.

@item
Link the object files to produce the finished product.
@end enumerate

@node Grammar Layout
@section The Overall Layout of a Bison Grammar
@cindex grammar file
@cindex file format
@cindex format of grammar file
@cindex layout of Bison grammar

The input file for the Bison utility is a @dfn{Bison grammar file}.  The
general form of a Bison grammar file is as follows:

@example
%@{
@var{Prologue}
%@}

@var{Bison declarations}

%%
@var{Grammar rules}
%%
@var{Epilogue}
@end example

@noindent
The @samp{%%}, @samp{%@{} and @samp{%@}} 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
@code{#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 epilogue can contain any code you want to use. Often the definition of
the lexical analyzer @code{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.

@node Examples
@chapter Examples
@cindex simple examples
@cindex examples, simple

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.
@ifinfo
You can copy these examples out of the Info file and into a source file
to try them.
@end ifinfo

@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 @@@var{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.
@end menu

@node RPN Calc
@section Reverse Polish Notation Calculator
@cindex reverse polish notation
@cindex polish notation calculator
@cindex @code{rpcalc}
@cindex calculator, simple

The first example is that of a simple double-precision @dfn{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 @file{rpcalc.y}.  The
@samp{.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.
@end menu

@node Rpcalc Decls
@subsection Declarations for @code{rpcalc}

Here are the C and Bison declarations for the reverse polish notation
calculator.  As in C, comments are placed between @samp{/*@dots{}*/}.

@example
/* Reverse polish notation calculator. */

%@{
#define YYSTYPE double
#include <math.h>
%@}

%token NUM

%% /* Grammar rules and actions follow */
@end example

The declarations section (@pxref{Prologue, , The prologue}) contains two
preprocessor directives.

The @code{#define} directive defines the macro @code{YYSTYPE}, thus
specifying the C data type for semantic values of both tokens and
groupings (@pxref{Value Type, ,Data Types of Semantic Values}).  The
Bison parser will use whatever type @code{YYSTYPE} is defined as; if you
don't define it, @code{int} is the default.  Because we specify
@code{double}, each token and each expression has an associated value,
which is a floating point number.

The @code{#include} directive is used to declare the exponentiation
function @code{pow}.

The second section, Bison declarations, provides information to Bison
about the token types (@pxref{Bison Declarations, ,The Bison
Declarations Section}).  Each terminal symbol that is not a
single-character literal must be declared here.  (Single-character
literals normally don't need to be declared.)  In this example, all the
arithmetic operators are designated by single-character literals, so the
only terminal symbol that needs to be declared is @code{NUM}, the token
type for numeric constants.

@node Rpcalc Rules
@subsection Grammar Rules for @code{rpcalc}

Here are the grammar rules for the reverse polish notation calculator.

@example
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;        @}
;
%%
@end example

The groupings of the rpcalc ``language'' defined here are the expression
(given the name @code{exp}), the line of input (@code{line}), and the
complete input transcript (@code{input}).  Each of these nonterminal
symbols has several alternate rules, joined by the @samp{|} 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.  @xref{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 @code{$$} stands for the semantic value for the grouping
that the rule is going to construct.  Assigning a value to @code{$$} is the
main job of most actions.  The semantic values of the components of the
rule are referred to as @code{$1}, @code{$2}, and so on.

@menu
* Rpcalc Input::
* Rpcalc Line::
* Rpcalc Expr::
@end menu

@node Rpcalc Input
@subsubsection Explanation of @code{input}

Consider the definition of @code{input}:

@example
input:    /* empty */
        | input line
;
@end example

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 @dfn{left recursive} since @code{input} appears always as the
leftmost symbol in the sequence.  @xref{Recursion, ,Recursive Rules}.

The first alternative is empty because there are no symbols between the
colon and the first @samp{|}; this means that @code{input} can match an
empty string of input (no tokens).  We write the rules this way because it
is legitimate to type @kbd{Ctrl-d} right after you start the calculator.
It's conventional to put an empty alternative first and write the comment
@samp{/* empty */} in it.

The second alternate rule (@code{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 @code{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 file.

@node Rpcalc Line
@subsubsection Explanation of @code{line}

Now consider the definition of @code{line}:

@example
line:     '\n'
        | exp '\n'  @{ printf ("\t%.10g\n", $1); @}
;
@end example

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 @code{exp} grouping is the value of @code{$1} because the @code{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 @code{$$}.  As
a consequence, the semantic value associated with the @code{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.

@node Rpcalc Expr
@subsubsection Explanation of @code{expr}

The @code{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.

@example
exp:      NUM
        | exp exp '+'     @{ $$ = $1 + $2;    @}
        | exp exp '-'     @{ $$ = $1 - $2;    @}
        @dots{}
        ;
@end example

We have used @samp{|} to join all the rules for @code{exp}, but we could
equally well have written them separately:

@example
exp:      NUM ;
exp:      exp exp '+'     @{ $$ = $1 + $2;    @} ;
exp:      exp exp '-'     @{ $$ = $1 - $2;    @} ;
        @dots{}
@end example

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,
@code{$1} refers to the first component @code{exp} and @code{$2} refers to
the second one.  The third component, @code{'+'}, has no meaningful
associated semantic value, but if it had one you could refer to it as
@code{$3}.  When @code{yyparse} recognizes a sum expression using this
rule, the sum of the two subexpressions' values is produced as the value of
the entire expression.  @xref{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 @code{$1} into @code{$$}.
This is what happens in the first rule (the one that uses @code{NUM}).

The formatting shown here is the recommended convention, but Bison does
not require it.  You can add or change whitespace as much as you wish.
For example, this:

@example
exp   : NUM | exp exp '+' @{$$ = $1 + $2; @} | @dots{}
@end example

@noindent
means the same thing as this:

@example
exp:      NUM
        | exp exp '+'    @{ $$ = $1 + $2; @}
        | @dots{}
@end example

@noindent
The latter, however, is much more readable.

@node Rpcalc Lexer
@subsection The @code{rpcalc} Lexical Analyzer
@cindex writing a lexical analyzer
@cindex lexical analyzer, writing

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.  @xref{Lexical, ,The Lexical
Analyzer Function @code{yylex}}.

Only a simple lexical analyzer is needed for the RPN calculator.  This
lexical analyzer skips blanks and tabs, then reads in numbers as
@code{double} and returns them as @code{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, @code{NUM} becomes a macro for @code{yylex} to use.

The semantic value of the token (if it has one) is stored into the
global variable @code{yylval}, which is where the Bison parser will look
for it.  (The C data type of @code{yylval} is @code{YYSTYPE}, which was
defined at the beginning of the grammar; @pxref{Rpcalc Decls,
,Declarations for @code{rpcalc}}.)

A token type code of zero is returned if the end-of-file is encountered.
(Bison recognizes any nonpositive value as indicating the end of the
input.)

Here is the code for the lexical analyzer:

@example
@group
/* 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.  Skips all blanks
   and tabs, returns 0 for EOF. */

#include <ctype.h>
@end group

@group
int
yylex (void)
@{
  int c;

  /* skip white space  */
  while ((c = getchar ()) == ' ' || c == '\t')
    ;
@end group
@group
  /* process numbers   */
  if (c == '.' || isdigit (c))
    @{
      ungetc (c, stdin);
      scanf ("%lf", &yylval);
      return NUM;
    @}
@end group
@group
  /* return end-of-file  */
  if (c == EOF)
    return 0;
  /* return single chars */
  return c;
@}
@end group
@end example

@node Rpcalc Main
@subsection The Controlling Function
@cindex controlling function
@cindex main function in simple example

In keeping with the spirit of this example, the controlling function is
kept to the bare minimum.  The only requirement is that it call
@code{yyparse} to start the process of parsing.

@example
@group
int
main (void)
@{
  return yyparse ();
@}
@end group
@end example

@node Rpcalc Error
@subsection The Error Reporting Routine
@cindex error reporting routine

When @code{yyparse} detects a syntax error, it calls the error reporting
function @code{yyerror} to print an error message (usually but not
always @code{"parse error"}).  It is up to the programmer to supply
@code{yyerror} (@pxref{Interface, ,Parser C-Language Interface}), so
here is the definition we will use:

@example
@group
#include <stdio.h>

void
yyerror (const char *s)  /* Called by yyparse on error */
@{
  printf ("%s\n", s);
@}
@end group
@end example

After @code{yyerror} returns, the Bison parser may recover from the error
and continue parsing if the grammar contains a suitable error rule
(@pxref{Error Recovery}).  Otherwise, @code{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.

@node Rpcalc Gen
@subsection Running Bison to Make the Parser
@cindex running Bison (introduction)

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 @code{yylex}, @code{yyerror} and @code{main} go at the
end, in the epilogue of the file
(@pxref{Grammar Layout, ,The Overall Layout of a Bison Grammar}).

For a large project, you would probably have several source files, and use
@code{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:

@example
bison @var{file_name}.y
@end example

@noindent
In this example the file was called @file{rpcalc.y} (for ``Reverse Polish
CALCulator'').  Bison produces a file named @file{@var{file_name}.tab.c},
removing the @samp{.y} from the original file name. The file output by
Bison contains the source code for @code{yyparse}.  The additional
functions in the input file (@code{yylex}, @code{yyerror} and @code{main})
are copied verbatim to the output.

@node Rpcalc Compile
@subsection Compiling the Parser File
@cindex compiling the parser

Here is how to compile and run the parser file:

@example
@group
# @r{List files in current directory.}
$ @kbd{ls}
rpcalc.tab.c  rpcalc.y
@end group

@group
# @r{Compile the Bison parser.}
# @r{@samp{-lm} tells compiler to search math library for @code{pow}.}
$ @kbd{cc rpcalc.tab.c -lm -o rpcalc}
@end group

@group
# @r{List files again.}
$ @kbd{ls}
rpcalc  rpcalc.tab.c  rpcalc.y
@end group
@end example

The file @file{rpcalc} now contains the executable code.  Here is an
example session using @code{rpcalc}.

@example
$ @kbd{rpcalc}
@kbd{4 9 +}
13
@kbd{3 7 + 3 4 5 *+-}
-13
@kbd{3 7 + 3 4 5 * + - n}              @r{Note the unary minus, @samp{n}}
13
@kbd{5 6 / 4 n +}
-3.166666667
@kbd{3 4 ^}                            @r{Exponentiation}
81
@kbd{^D}                               @r{End-of-file indicator}
$
@end example

@node Infix Calc
@section Infix Notation Calculator: @code{calc}
@cindex infix notation calculator
@cindex @code{calc}
@cindex calculator, infix notation

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
@file{calc.y}, an infix desk-top calculator.

@example
/* Infix notation calculator--calc */

%@{
#define YYSTYPE double
#include <math.h>
%@}

/* BISON Declarations */
%token NUM
%left '-' '+'
%left '*' '/'
%left NEG     /* negation--unary minus */
%right '^'    /* exponentiation        */

/* Grammar follows */
%%
input:    /* empty string */
        | 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;         @}
;
%%
@end example

@noindent
The functions @code{yylex}, @code{yyerror} and @code{main} can be the
same as before.

There are two important new features shown in this code.

In the second section (Bison declarations), @code{%left} declares token
types and says they are left-associative operators.  The declarations
@code{%left} and @code{%right} (right associativity) take the place of
@code{%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 (@code{NEG}) is next, followed
by @samp{*} and @samp{/}, and so on.  @xref{Precedence, ,Operator
Precedence}.

The other important new feature is the @code{%prec} in the grammar
section for the unary minus operator.  The @code{%prec} simply instructs
Bison that the rule @samp{| '-' exp} has the same precedence as
@code{NEG}---in this case the next-to-highest.  @xref{Contextual
Precedence, ,Context-Dependent Precedence}.

Here is a sample run of @file{calc.y}:

@need 500
@example
$ @kbd{calc}
@kbd{4 + 4.5 - (34/(8*3+-3))}
6.880952381
@kbd{-56 + 2}
-54
@kbd{3 ^ 2}
9
@end example

@node Simple Error Recovery
@section Simple Error Recovery
@cindex error recovery, simple

Up to this point, this manual has not addressed the issue of @dfn{error
recovery}---how to continue parsing after the parser detects a syntax
error.  All we have handled is error reporting with @code{yyerror}.
Recall that by default @code{yyparse} returns after calling
@code{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 @code{error}, which
may be included in the grammar rules.  In the example below it has
been added to one of the alternatives for @code{line}:

@example
@group
line:     '\n'
        | exp '\n'   @{ printf ("\t%.10g\n", $1); @}
        | error '\n' @{ yyerrok;                  @}
;
@end group
@end example

This addition to the grammar allows for simple error recovery in the
event of a parse error.  If an expression that cannot be evaluated is
read, the error will be recognized by the third rule for @code{line},
and parsing will continue.  (The @code{yyerror} function is still called
upon to print its message as well.)  The action executes the statement
@code{yyerrok}, a macro defined automatically by Bison; its meaning is
that error recovery is complete (@pxref{Error Recovery}).  Note the
difference between @code{yyerrok} and @code{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 @code{longjmp} to return to @code{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.

@node Location Tracking Calc
@section Location Tracking Calculator: @code{ltcalc}
@cindex location tracking calculator
@cindex @code{ltcalc}
@cindex calculator, location tracking

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
analyser.

@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.
@end menu

@node Ltcalc Decls
@subsection Declarations for @code{ltcalc}

The C and Bison declarations for the location tracking calculator are
the same as the declarations for the infix notation calculator.

@example
/* Location tracking calculator.  */

%@{
#define YYSTYPE int
#include <math.h>
%@}

/* Bison declarations.  */
%token NUM

%left '-' '+'
%left '*' '/'
%left NEG
%right '^'

%% /* Grammar follows */
@end example

@noindent
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 (@pxref{Location Type, ,Data Types of Locations}), which is a
four member structure with the following integer fields:
@code{first_line}, @code{first_column}, @code{last_line} and
@code{last_column}.

@node Ltcalc Rules
@subsection Grammar Rules for @code{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.

@example
@group
input   : /* empty */
        | input line
;
@end group

@group
line    : '\n'
        | exp '\n' @{ printf ("%d\n", $1); @}
;
@end group

@group
exp     : NUM           @{ $$ = $1; @}
        | exp '+' exp   @{ $$ = $1 + $3; @}
        | exp '-' exp   @{ $$ = $1 - $3; @}
        | exp '*' exp   @{ $$ = $1 * $3; @}
@end group
@group
        | 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);
                @}
            @}
@end group
@group
        | '-' exp %preg NEG     @{ $$ = -$2; @}
        | exp '^' exp           @{ $$ = pow ($1, $3); @}
        | '(' exp ')'           @{ $$ = $2; @}
@end group
@end example

This code shows how to reach locations inside of semantic actions, by
using the pseudo-variables @code{@@@var{n}} for rule components, and the
pseudo-variable @code{@@$} for groupings.

We don't need to assign a value to @code{@@$}: the output parser does it
automatically.  By default, before executing the C code of each action,
@code{@@$} is set to range from the beginning of @code{@@1} to the end
of @code{@@@var{n}}, for a rule with @var{n} components.  This behavior
can be redefined (@pxref{Location Default Action, , Default Action for
Locations}), and for very specific rules, @code{@@$} can be computed by
hand.

@node Ltcalc Lexer
@subsection The @code{ltcalc} Lexical Analyzer.

Until now, we relied on Bison's defaults to enable location
tracking. The next step is to rewrite the lexical analyser, 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:

@example
@group
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;
@end group

@group
  /* 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;
    @}
@end group

  /* return end-of-file */
  if (c == EOF)
    return 0;

  /* return single chars and update location */
  if (c == '\n')
    @{
      ++yylloc.last_line;
      yylloc.last_column = 0;
    @}
  else
    ++yylloc.last_column;
  return c;
@}
@end example

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 @code{yylloc}, the global variable (of type
@code{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 @code{yylloc}, for example in the
controlling function:

@example
@group
int
main (void)
@{
  yylloc.first_line = yylloc.last_line = 1;
  yylloc.first_column = yylloc.last_column = 0;
  return yyparse ();
@}
@end group
@end example

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.

@node Multi-function Calc
@section Multi-Function Calculator: @code{mfcalc}
@cindex multi-function calculator
@cindex @code{mfcalc}
@cindex calculator, multi-function

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, @samp{+}, @samp{-}, @samp{*}, @samp{/} and @samp{^}.  It would
be nice to have a calculator that provides other mathematical functions such
as @code{sin}, @code{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 @code{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:

@example
@var{function_name} (@var{argument})
@end example

@noindent
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:

@example
$ @kbd{mfcalc}
@kbd{pi = 3.141592653589}
3.1415926536
@kbd{sin(pi)}
0.0000000000
@kbd{alpha = beta1 = 2.3}
2.3000000000
@kbd{alpha}
2.3000000000
@kbd{ln(alpha)}
0.8329091229
@kbd{exp(ln(beta1))}
2.3000000000
$
@end example

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.
@end menu

@node Mfcalc Decl
@subsection Declarations for @code{mfcalc}

Here are the C and Bison declarations for the multi-function calculator.

@smallexample
%@{
#include <math.h>  /* For math functions, cos(), sin(), etc. */
#include "calc.h"  /* Contains definition of `symrec'        */
%@}
%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        */

/* Grammar follows */

%%
@end smallexample

The above grammar introduces only two new features of the Bison language.
These features allow semantic values to have various data types
(@pxref{Multiple Types, ,More Than One Value Type}).

The @code{%union} declaration specifies the entire list of possible types;
this is instead of defining @code{YYSTYPE}.  The allowable types are now
double-floats (for @code{exp} and @code{NUM}) and pointers to entries in
the symbol table.  @xref{Union Decl, ,The Collection of Value Types}.

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 @code{NUM}, @code{VAR}, @code{FNCT}, and @code{exp}.  Their
declarations are augmented with information about their data type (placed
between angle brackets).

The Bison construct @code{%type} is used for declaring nonterminal
symbols, just as @code{%token} is used for declaring token types.  We
have not used @code{%type} before because nonterminal symbols are
normally declared implicitly by the rules that define them.  But
@code{exp} must be declared explicitly so we can specify its value type.
@xref{Type Decl, ,Nonterminal Symbols}.

@node Mfcalc Rules
@subsection Grammar Rules for @code{mfcalc}

Here are the grammar rules for the multi-function calculator.
Most of them are copied directly from @code{calc}; three rules,
those which mention @code{VAR} or @code{FNCT}, are new.

@smallexample
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 */
%%
@end smallexample

@node Mfcalc Symtab
@subsection The @code{mfcalc} Symbol Table
@cindex symbol table example

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 @file{calc.h}, is as follows.  It
provides for either functions or variables to be placed in the table.

@smallexample
@group
/* Fonctions 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              */
@};
@end group

@group
typedef struct symrec symrec;

/* The symbol table: a chain of `struct symrec'.     */
extern symrec *sym_table;

symrec *putsym (const char *, func_t);
symrec *getsym (const char *);
@end group
@end smallexample

The new version of @code{main} includes a call to @code{init_table}, a
function that initializes the symbol table.  Here it is, and
@code{init_table} as well:

@smallexample
@group
#include <stdio.h>

int
main (void)
@{
  init_table ();
  return yyparse ();
@}
@end group

@group
void
yyerror (const char *s)  /* Called by yyparse on error */
@{
  printf ("%s\n", s);
@}

struct init
@{
  char *fname;
  double (*fnct)(double);
@};
@end group

@group
struct init 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 = (symrec *) 0;
@end group

@group
/* 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;
    @}
@}
@end group
@end smallexample

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 @code{putsym} is passed a name and the type
(@code{VAR} or @code{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 @code{getsym} is passed the name of the symbol to look up.  If
found, a pointer to that symbol is returned; otherwise zero is returned.

@smallexample
symrec *
putsym (char *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 (const char *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;
@}
@end smallexample

The function @code{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 @code{getsym} for look up in the symbol table.  If
the name appears in the table, a pointer to its location and its type
(@code{VAR} or @code{FNCT}) is returned to @code{yyparse}.  If it is not
already in the table, then it is installed as a @code{VAR} using
@code{putsym}.  Again, a pointer and its type (which must be @code{VAR}) is
returned to @code{yyparse}.

No change is needed in the handling of numeric values and arithmetic
operators in @code{yylex}.

@smallexample
@group
#include <ctype.h>

int
yylex (void)
@{
  int c;

  /* Ignore whitespace, get first nonwhite character.  */
  while ((c = getchar ()) == ' ' || c == '\t');

  if (c == EOF)
    return 0;
@end group

@group
  /* Char starts a number => parse the number.         */
  if (c == '.' || isdigit (c))
    @{
      ungetc (c, stdin);
      scanf ("%lf", &yylval.val);
      return NUM;
    @}
@end group

@group
  /* Char starts an identifier => read the name.       */
  if (isalpha (c))
    @{
      symrec *s;
      static char *symbuf = 0;
      static int length = 0;
      int i;
@end group

@group
      /* 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
@end group
@group
        @{
          /* 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 ();
        @}
@end group
@group
      while (c != EOF && isalnum (c));

      ungetc (c, stdin);
      symbuf[i] = '\0';
@end group

@group
      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;
@}
@end group
@end smallexample

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 @code{pi} or @code{e} as well.

@node Exercises
@section Exercises
@cindex exercises

@enumerate
@item
Add some new functions from @file{math.h} to the initialization list.

@item
Add another array that contains constants and their values.  Then
modify @code{init_table} to add these constants to the symbol table.
It will be easiest to give the constants type @code{VAR}.

@item
Make the program report an error if the user refers to an
uninitialized variable in any way except to store a value in it.
@end enumerate

@node Grammar File
@chapter 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 @samp{.y}.
@xref{Invocation, ,Invoking Bison}.

@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.
@end menu

@node Grammar Outline
@section Outline of a Bison Grammar

A Bison grammar file has four main sections, shown here with the
appropriate delimiters:

@example
%@{
@var{Prologue}
%@}

@var{Bison declarations}

%%
@var{Grammar rules}
%%

@var{Epilogue}
@end example

Comments enclosed in @samp{/* @dots{} */} may appear in any of the sections.

@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.
@end menu

@node Prologue, Bison Declarations,  , Grammar Outline
@subsection The prologue
@cindex declarations section
@cindex Prologue
@cindex declarations

The @var{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 @code{yyparse}.  You can use
@samp{#include} to get the declarations from a header file.  If you don't
need any C declarations, you may omit the @samp{%@{} and @samp{%@}}
delimiters that bracket this section.

You may have more than one @var{Prologue} section, intermixed with the
@var{Bison declarations}.  This allows you to have C and Bison
declarations that refer to each other.  For example, the @code{%union}
declaration may use types defined in a header file, and you may wish to
prototype functions that take arguments of type @code{YYSTYPE}.  This
can be done with two @var{Prologue} blocks, one before and one after the
@code{%union} declaration.

@smallexample
%@{
#include <stdio.h>
#include "ptypes.h"
%@}

%union @{
  long n;
  tree t;  /* @r{@code{tree} is defined in @file{ptypes.h}.} */
@}

%@{
static void yyprint(FILE *, int, YYSTYPE);
#define YYPRINT(F, N, L) yyprint(F, N, L)
%@}

@dots{}
@end smallexample

@node Bison Declarations
@subsection The Bison Declarations Section
@cindex Bison declarations (introduction)
@cindex declarations, Bison (introduction)

The @var{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.
@xref{Declarations, ,Bison Declarations}.

@node Grammar Rules
@subsection The Grammar Rules Section
@cindex grammar rules section
@cindex rules section for grammar

The @dfn{grammar rules} section contains one or more Bison grammar
rules, and nothing else.  @xref{Rules, ,Syntax of Grammar Rules}.

There must always be at least one grammar rule, and the first
@samp{%%} (which precedes the grammar rules) may never be omitted even
if it is the first thing in the file.

@node Epilogue,  , Grammar Rules, Grammar Outline
@subsection The epilogue
@cindex additional C code section
@cindex epilogue
@cindex C code, section for additional

The @var{Epilogue} is copied verbatim to the end of the parser file, just as
the @var{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 @code{yyparse}.  For example, the
definitions of @code{yylex} and @code{yyerror} often go here.
@xref{Interface, ,Parser C-Language Interface}.

If the last section is empty, you may omit the @samp{%%} that separates it
from the grammar rules.

The Bison parser itself contains many static variables whose names start
with @samp{yy} and many macros whose names start with @samp{YY}.  It is a
good idea to avoid using any such names (except those documented in this
manual) in the epilogue of the grammar file.

@node Symbols
@section Symbols, Terminal and Nonterminal
@cindex nonterminal symbol
@cindex terminal symbol
@cindex token type
@cindex symbol

@dfn{Symbols} in Bison grammars represent the grammatical classifications
of the language.

A @dfn{terminal symbol} (also known as a @dfn{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 @code{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 @dfn{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:

@itemize @bullet
@item
A @dfn{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
@code{%token}.  @xref{Token Decl, ,Token Type Names}.

@item
@cindex character token
@cindex literal token
@cindex single-character literal
A @dfn{character token type} (or @dfn{literal character token}) is
written in the grammar using the same syntax used in C for character
constants; for example, @code{'+'} 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 (@pxref{Value Type, ,Data Types of
Semantic Values}), associativity, or precedence (@pxref{Precedence,
,Operator Precedence}).

By convention, a character token type is used only to represent a
token that consists of that particular character.  Thus, the token
type @code{'+'} is used to represent the character @samp{+} 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, is the code @code{yylex}
returns for end-of-input (@pxref{Calling Convention, ,Calling Convention
for @code{yylex}}).

@item
@cindex string token
@cindex literal string token
@cindex multicharacter literal
A @dfn{literal string token} is written like a C string constant; for
example, @code{"<="} 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 (@pxref{Value Type}), associativity, or precedence
(@pxref{Precedence}).

You can associate the literal string token with a symbolic name as an
alias, using the @code{%token} declaration (@pxref{Token Decl, ,Token
Declarations}).  If you don't do that, the lexical analyzer has to
retrieve the token number for the literal string token from the
@code{yytname} table (@pxref{Calling Convention}).

@strong{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 @code{"<="} to represent the string @samp{<=} 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.  A literal string token must contain two or more
characters; for a token containing just one character, use a character
token (see above).
@end itemize

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 @code{yylex} is always one of the terminal symbols
(or 0 for end-of-input).  Whichever way you write the token type in the
grammar rules, you write it the same way in the definition of @code{yylex}.
The numeric code for a character token type is simply the numeric code of
the character, so @code{yylex} can use the identical character constant to
generate the requisite code.  Each named token type becomes a C macro in
the parser file, so @code{yylex} can use the name to stand for the code.
(This is why periods don't make sense in terminal symbols.)
@xref{Calling Convention, ,Calling Convention for @code{yylex}}.

If @code{yylex} is defined in a separate file, you need to arrange for the
token-type macro definitions to be available there.  Use the @samp{-d}
option when you run Bison, so that it will write these macro definitions
into a separate header file @file{@var{name}.tab.h} which you can include
in the other source files that need it.  @xref{Invocation, ,Invoking Bison}.

The @code{yylex} function must use the same character set and encoding
that was used by Bison.  For example, if you run Bison in an
@sc{ascii} environment, but then compile and run the resulting program
in an environment that uses an incompatible character set like
@sc{ebcdic}, the resulting program will probably not work because the
tables generated by Bison will assume @sc{ascii} numeric values for
character tokens.  Portable grammars should avoid non-@sc{ascii}
character tokens, as implementations in practice often use different
and incompatible extensions in this area.  However, it is standard
practice for software distributions to contain C source files that
were generated by Bison in an @sc{ascii} environment, so installers on
platforms that are incompatible with @sc{ascii} must rebuild those
files before compiling them.

The symbol @code{error} is a terminal symbol reserved for error recovery
(@pxref{Error Recovery}); you shouldn't use it for any other purpose.
In particular, @code{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 @code{%token} declaration.

@node Rules
@section Syntax of Grammar Rules
@cindex rule syntax
@cindex grammar rule syntax
@cindex syntax of grammar rules

A Bison grammar rule has the following general form:

@example
@group
@var{result}: @var{components}@dots{}
        ;
@end group
@end example

@noindent
where @var{result} is the nonterminal symbol that this rule describes,
and @var{components} are various terminal and nonterminal symbols that
are put together by this rule (@pxref{Symbols}).

For example,

@example
@group
exp:      exp '+' exp
        ;
@end group
@end example

@noindent
says that two groupings of type @code{exp}, with a @samp{+} token in between,
can be combined into a larger grouping of type @code{exp}.

Whitespace in rules is significant only to separate symbols.  You can add
extra whitespace as you wish.

Scattered among the components can be @var{actions} that determine
the semantics of the rule.  An action looks like this:

@example
@{@var{C statements}@}
@end example

@noindent
Usually there is only one action and it follows the components.
@xref{Actions}.

@findex |
Multiple rules for the same @var{result} can be written separately or can
be joined with the vertical-bar character @samp{|} as follows:

@ifinfo
@example
@var{result}:   @var{rule1-components}@dots{}
        | @var{rule2-components}@dots{}
        @dots{}
        ;
@end example
@end ifinfo
@iftex
@example
@group
@var{result}:    @var{rule1-components}@dots{}
        | @var{rule2-components}@dots{}
        @dots{}
        ;
@end group
@end example
@end iftex

@noindent
They are still considered distinct rules even when joined in this way.

If @var{components} in a rule is empty, it means that @var{result} can
match the empty string.  For example, here is how to define a
comma-separated sequence of zero or more @code{exp} groupings:

@example
@group
expseq:   /* empty */
        | expseq1
        ;
@end group

@group
expseq1:  exp
        | expseq1 ',' exp
        ;
@end group
@end example

@noindent
It is customary to write a comment @samp{/* empty */} in each rule
with no components.

@node Recursion
@section Recursive Rules
@cindex recursive rule

A rule is called @dfn{recursive} when its @var{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:

@example
@group
expseq1:  exp
        | expseq1 ',' exp
        ;
@end group
@end example

@cindex left recursion
@cindex right recursion
@noindent
Since the recursive use of @code{expseq1} is the leftmost symbol in the
right hand side, we call this @dfn{left recursion}.  By contrast, here
the same construct is defined using @dfn{right recursion}:

@example
@group
expseq1:  exp
        | exp ',' expseq1
        ;
@end group
@end example

@noindent
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.
@xref{Algorithm, ,The Bison Parser Algorithm}, for further explanation
of this.

@cindex mutual recursion
@dfn{Indirect} or @dfn{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:

@example
@group
expr:     primary
        | primary '+' primary
        ;
@end group

@group
primary:  constant
        | '(' expr ')'
        ;
@end group
@end example

@noindent
defines two mutually-recursive nonterminals, since each refers to the
other.

@node Semantics
@section Defining Language Semantics
@cindex defining language semantics
@cindex language semantics, defining

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 @w{@samp{@var{x} + @var{y}}} is to add
the numbers associated with @var{x} and @var{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.
@end menu

@node Value Type
@subsection Data Types of Semantic Values
@cindex semantic value type
@cindex value type, semantic
@cindex data types of semantic values
@cindex default data type

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 (@pxref{RPN Calc, ,Reverse Polish
Notation Calculator}).

Bison's default is to use type @code{int} for all semantic values.  To
specify some other type, define @code{YYSTYPE} as a macro, like this:

@example
#define YYSTYPE double
@end example

@noindent
This macro definition must go in the prologue of the grammar file
(@pxref{Grammar Outline, ,Outline of a Bison Grammar}).

@node Multiple Types
@subsection 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
@code{int} or @code{long}, while a string constant needs type @code{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:

@itemize @bullet
@item
Specify the entire collection of possible data types, with the
@code{%union} Bison declaration (@pxref{Union Decl, ,The Collection of
Value Types}).

@item
Choose one of those types for each symbol (terminal or nonterminal) for
which semantic values are used.  This is done for tokens with the
@code{%token} Bison declaration (@pxref{Token Decl, ,Token Type Names})
and for groupings with the @code{%type} Bison declaration (@pxref{Type
Decl, ,Nonterminal Symbols}).
@end itemize

@node Actions
@subsection Actions
@cindex action
@vindex $$
@vindex $@var{n}

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.  It 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 (@pxref{Mid-Rule
Actions, ,Actions in Mid-Rule}).

The C code in an action can refer to the semantic values of the components
matched by the rule with the construct @code{$@var{n}}, which stands for
the value of the @var{n}th component.  The semantic value for the grouping
being constructed is @code{$$}.  (Bison translates both of these constructs
into array element references when it copies the actions into the parser
file.)

Here is a typical example:

@example
@group
exp:    @dots{}
        | exp '+' exp
            @{ $$ = $1 + $3; @}
@end group
@end example

@noindent
This rule constructs an @code{exp} from two smaller @code{exp} groupings
connected by a plus-sign token.  In the action, @code{$1} and @code{$3}
refer to the semantic values of the two component @code{exp} groupings,
which are the first and third symbols on the right hand side of the rule.
The sum is stored into @code{$$} so that it becomes the semantic value of
the addition-expression just recognized by the rule.  If there were a
useful semantic value associated with the @samp{+} token, it could be
referred to as @code{$2}.

Note that the vertical-bar character @samp{|} is really a rule
separator, and actions are attached to a single rule.  This is a
difference with tools like Flex, for which @samp{|} stands for either
``or'', or ``the same action as that of the next rule''.  In the
following example, the action is triggered only when @samp{b} is found:

@example
@group
a-or-b: 'a'|'b'   @{ a_or_b_found = 1; @};
@end group
@end example

@cindex default action
If you don't specify an action for a rule, Bison supplies a default:
@w{@code{$$ = $1}.}  Thus, the value of the first symbol in the rule becomes
the value of the whole rule.  Of course, the default rule is valid only
if the two data types match.  There is no meaningful default action for
an empty rule; every empty rule must have an explicit action unless the
rule's value does not matter.

@code{$@var{n}} with @var{n} zero or negative is allowed for reference
to tokens and groupings on the stack @emph{before} those that match the
current rule.  This is a very risky practice, and to use it reliably
you must be certain of the context in which the rule is applied.  Here
is a case in which you can use this reliably:

@example
@group
foo:      expr bar '+' expr  @{ @dots{} @}
        | expr bar '-' expr  @{ @dots{} @}
        ;
@end group

@group
bar:      /* empty */
        @{ previous_expr = $0; @}
        ;
@end group
@end example

As long as @code{bar} is used only in the fashion shown here, @code{$0}
always refers to the @code{expr} which precedes @code{bar} in the
definition of @code{foo}.

@node Action Types
@subsection Data Types of Values in Actions
@cindex action data types
@cindex data types in actions

If you have chosen a single data type for semantic values, the @code{$$}
and @code{$@var{n}} constructs always have that data type.

If you have used @code{%union} to specify a variety of data types, then you
must declare a choice among these types for each terminal or nonterminal
symbol that can have a semantic value.  Then each time you use @code{$$} or
@code{$@var{n}}, its data type is determined by which symbol it refers to
in the rule.  In this example,

@example
@group
exp:    @dots{}
        | exp '+' exp
            @{ $$ = $1 + $3; @}
@end group
@end example

@noindent
@code{$1} and @code{$3} refer to instances of @code{exp}, so they all
have the data type declared for the nonterminal symbol @code{exp}.  If
@code{$2} were used, it would have the data type declared for the
terminal symbol @code{'+'}, whatever that might be.

Alternatively, you can specify the data type when you refer to the value,
by inserting @samp{<@var{type}>} after the @samp{$} at the beginning of the
reference.  For example, if you have defined types as shown here:

@example
@group
%union @{
  int itype;
  double dtype;
@}
@end group
@end example

@noindent
then you can write @code{$<itype>1} to refer to the first subunit of the
rule as an integer, or @code{$<dtype>1} to refer to it as a double.

@node Mid-Rule Actions
@subsection Actions in Mid-Rule
@cindex actions in mid-rule
@cindex mid-rule actions

Occasionally it is useful to put an action in the middle of a rule.
These actions are written just like usual end-of-rule actions, but they
are executed before the parser even recognizes the following components.

A mid-rule action may refer to the components preceding it using
@code{$@var{n}}, but it may not refer to subsequent components because
it is run before they are parsed.

The mid-rule action itself counts as one of the components of the rule.
This makes a difference when there is another action later in the same rule
(and usually there is another at the end): you have to count the actions
along with the symbols when working out which number @var{n} to use in
@code{$@var{n}}.

The mid-rule action can also have a semantic value.  The action can set
its value with an assignment to @code{$$}, and actions later in the rule
can refer to the value using @code{$@var{n}}.  Since there is no symbol
to name the action, there is no way to declare a data type for the value
in advance, so you must use the @samp{$<@dots{}>@var{n}} construct to
specify a data type each time you refer to this value.

There is no way to set the value of the entire rule with a mid-rule
action, because assignments to @code{$$} do not have that effect.  The
only way to set the value for the entire rule is with an ordinary action
at the end of the rule.

Here is an example from a hypothetical compiler, handling a @code{let}
statement that looks like @samp{let (@var{variable}) @var{statement}} and
serves to create a variable named @var{variable} temporarily for the
duration of @var{statement}.  To parse this construct, we must put
@var{variable} into the symbol table while @var{statement} is parsed, then
remove it afterward.  Here is how it is done:

@example
@group
stmt:   LET '(' var ')'
                @{ $<context>$ = push_context ();
                  declare_variable ($3); @}
        stmt    @{ $$ = $6;
                  pop_context ($<context>5); @}
@end group
@end example

@noindent
As soon as @samp{let (@var{variable})} has been recognized, the first
action is run.  It saves a copy of the current semantic context (the
list of accessible variables) as its semantic value, using alternative
@code{context} in the data-type union.  Then it calls
@code{declare_variable} to add the new variable to that list.  Once the
first action is finished, the embedded statement @code{stmt} can be
parsed.  Note that the mid-rule action is component number 5, so the
@samp{stmt} is component number 6.

After the embedded statement is parsed, its semantic value becomes the
value of the entire @code{let}-statement.  Then the semantic value from the
earlier action is used to restore the prior list of variables.  This
removes the temporary @code{let}-variable from the list so that it won't
appear to exist while the rest of the program is parsed.

Taking action before a rule is completely recognized often leads to
conflicts since the parser must commit to a parse in order to execute the
action.  For example, the following two rules, without mid-rule actions,
can coexist in a working parser because the parser can shift the open-brace
token and look at what follows before deciding whether there is a
declaration or not:

@example
@group
compound: '@{' declarations statements '@}'
        | '@{' statements '@}'
        ;
@end group
@end example

@noindent
But when we add a mid-rule action as follows, the rules become nonfunctional:

@example
@group
compound: @{ prepare_for_local_variables (); @}
          '@{' declarations statements '@}'
@end group
@group
        | '@{' statements '@}'
        ;
@end group
@end example

@noindent
Now the parser is forced to decide whether to run the mid-rule action
when it has read no farther than the open-brace.  In other words, it
must commit to using one rule or the other, without sufficient
information to do it correctly.  (The open-brace token is what is called
the @dfn{look-ahead} token at this time, since the parser is still
deciding what to do about it.  @xref{Look-Ahead, ,Look-Ahead Tokens}.)

You might think that you could correct the problem by putting identical
actions into the two rules, like this:

@example
@group
compound: @{ prepare_for_local_variables (); @}
          '@{' declarations statements '@}'
        | @{ prepare_for_local_variables (); @}
          '@{' statements '@}'
        ;
@end group
@end example

@noindent
But this does not help, because Bison does not realize that the two actions
are identical.  (Bison never tries to understand the C code in an action.)

If the grammar is such that a declaration can be distinguished from a
statement by the first token (which is true in C), then one solution which
does work is to put the action after the open-brace, like this:

@example
@group
compound: '@{' @{ prepare_for_local_variables (); @}
          declarations statements '@}'
        | '@{' statements '@}'
        ;
@end group
@end example

@noindent
Now the first token of the following declaration or statement,
which would in any case tell Bison which rule to use, can still do so.

Another solution is to bury the action inside a nonterminal symbol which
serves as a subroutine:

@example
@group
subroutine: /* empty */
          @{ prepare_for_local_variables (); @}
        ;

@end group

@group
compound: subroutine
          '@{' declarations statements '@}'
        | subroutine
          '@{' statements '@}'
        ;
@end group
@end example

@noindent
Now Bison can execute the action in the rule for @code{subroutine} without
deciding which rule for @code{compound} it will eventually use.  Note that
the action is now at the end of its rule.  Any mid-rule action can be
converted to an end-of-rule action in this way, and this is what Bison
actually does to implement mid-rule actions.

@node Locations
@section Tracking Locations
@cindex location
@cindex textual position
@cindex position, textual

Though grammar rules and semantic actions are enough to write a fully
functional parser, it can be useful to process some additionnal informations,
especially symbol locations.

@c (terminal or not) ?

The way locations are handled is defined by providing a data type, and
actions to take when rules are matched.

@menu
* 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.
@end menu

@node Location Type
@subsection Data Type of Locations
@cindex data type of locations
@cindex default location type

Defining a data type for locations is much simpler than for semantic values,
since all tokens and groupings always use the same type.

The type of locations is specified by defining a macro called @code{YYLTYPE}.
When @code{YYLTYPE} is not defined, Bison uses a default structure type with
four members:

@example
struct
@{
  int first_line;
  int first_column;
  int last_line;
  int last_column;
@}
@end example

@node Actions and Locations
@subsection Actions and Locations
@cindex location actions
@cindex actions, location
@vindex @@$
@vindex @@@var{n}

Actions are not only useful for defining language semantics, but also for
describing the behavior of the output parser with locations.

The most obvious way for building locations of syntactic groupings is very
similar to the way semantic values are computed. In a given rule, several
constructs can be used to access the locations of the elements being matched.
The location of the @var{n}th component of the right hand side is
@code{@@@var{n}}, while the location of the left hand side grouping is
@code{@@$}.

Here is a basic example using the default data type for locations:

@example
@group
exp:    @dots{}
        | exp '/' exp
            @{
              @@$.first_column = @@1.first_column;
              @@$.first_line = @@1.first_line;
              @@$.last_column = @@3.last_column;
              @@$.last_line = @@3.last_line;
              if ($3)
                $$ = $1 / $3;
              else
                @{
                  $$ = 1;
                  printf("Division by zero, l%d,c%d-l%d,c%d",
                         @@3.first_line, @@3.first_column,
                         @@3.last_line, @@3.last_column);
                @}
            @}
@end group
@end example

As for semantic values, there is a default action for locations that is
run each time a rule is matched. It sets the beginning of @code{@@$} to the
beginning of the first symbol, and the end of @code{@@$} to the end of the
last symbol.

With this default action, the location tracking can be fully automatic. The
example above simply rewrites this way:

@example
@group
exp:    @dots{}
        | exp '/' exp
            @{
              if ($3)
                $$ = $1 / $3;
              else
                @{
                  $$ = 1;
                  printf("Division by zero, l%d,c%d-l%d,c%d",
                         @@3.first_line, @@3.first_column,
                         @@3.last_line, @@3.last_column);
                @}
            @}
@end group
@end example

@node Location Default Action
@subsection Default Action for Locations
@vindex YYLLOC_DEFAULT

Actually, actions are not the best place to compute locations. Since
locations are much more general than semantic values, there is room in
the output parser to redefine the default action to take for each
rule. The @code{YYLLOC_DEFAULT} macro is invoked each time a rule is
matched, before the associated action is run.

Most of the time, this macro is general enough to suppress location
dedicated code from semantic actions.

The @code{YYLLOC_DEFAULT} macro takes three parameters. The first one is
the location of the grouping (the result of the computation). The second one
is an array holding locations of all right hand side elements of the rule
being matched. The last one is the size of the right hand side rule.

By default, it is defined this way for simple LALR(1) parsers:

@example
@group
#define YYLLOC_DEFAULT(Current, Rhs, N)          \
  Current.first_line   = Rhs[1].first_line;      \
  Current.first_column = Rhs[1].first_column;    \
  Current.last_line    = Rhs[N].last_line;       \
  Current.last_column  = Rhs[N].last_column;
@end group
@end example

@noindent
and like this for GLR parsers:

@example
@group
#define YYLLOC_DEFAULT(Current, Rhs, N)          \
  Current.first_line   = YYRHSLOC(Rhs,1).first_line;      \
  Current.first_column = YYRHSLOC(Rhs,1).first_column;    \
  Current.last_line    = YYRHSLOC(Rhs,N).last_line;       \
  Current.last_column  = YYRHSLOC(Rhs,N).last_column;
@end group
@end example

When defining @code{YYLLOC_DEFAULT}, you should consider that:

@itemize @bullet
@item
All arguments are free of side-effects. However, only the first one (the
result) should be modified by @code{YYLLOC_DEFAULT}.

@item
For consistency with semantic actions, valid indexes for the location
array range from 1 to @var{n}.
@end itemize

@node Declarations
@section Bison Declarations
@cindex declarations, Bison
@cindex Bison declarations

The @dfn{Bison declarations} section of a Bison grammar defines the symbols
used in formulating the grammar and the data types of semantic values.
@xref{Symbols}.

All token type names (but not single-character literal tokens such as
@code{'+'} and @code{'*'}) must be declared.  Nonterminal symbols must be
declared if you need to specify which data type to use for the semantic
value (@pxref{Multiple Types, ,More Than One Value Type}).

The first rule in the file also specifies the start symbol, by default.
If you want some other symbol to be the start symbol, you must declare
it explicitly (@pxref{Language and Grammar, ,Languages and Context-Free
Grammars}).

@menu
* 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.
@end menu

@node Token Decl
@subsection Token Type Names
@cindex declaring token type names
@cindex token type names, declaring
@cindex declaring literal string tokens
@findex %token

The basic way to declare a token type name (terminal symbol) is as follows:

@example
%token @var{name}
@end example

Bison will convert this into a @code{#define} directive in
the parser, so that the function @code{yylex} (if it is in this file)
can use the name @var{name} to stand for this token type's code.

Alternatively, you can use @code{%left}, @code{%right}, or
@code{%nonassoc} instead of @code{%token}, if you wish to specify
associativity and precedence.  @xref{Precedence Decl, ,Operator
Precedence}.

You can explicitly specify the numeric code for a token type by appending
an integer value in the field immediately following the token name:

@example
%token NUM 300
@end example

@noindent
It is generally best, however, to let Bison choose the numeric codes for
all token types.  Bison will automatically select codes that don't conflict
with each other or with normal characters.

In the event that the stack type is a union, you must augment the
@code{%token} or other token declaration to include the data type
alternative delimited by angle-brackets (@pxref{Multiple Types, ,More
Than One Value Type}).

For example:

@example
@group
%union @{              /* define stack type */
  double val;
  symrec *tptr;
@}
%token <val> NUM      /* define token NUM and its type */
@end group
@end example

You can associate a literal string token with a token type name by
writing the literal string at the end of a @code{%token}
declaration which declares the name.  For example:

@example
%token arrow "=>"
@end example

@noindent
For example, a grammar for the C language might specify these names with
equivalent literal string tokens:

@example
%token  <operator>  OR      "||"
%token  <operator>  LE 134  "<="
%left  OR  "<="
@end example

@noindent
Once you equate the literal string and the token name, you can use them
interchangeably in further declarations or the grammar rules.  The
@code{yylex} function can use the token name or the literal string to
obtain the token type code number (@pxref{Calling Convention}).

@node Precedence Decl
@subsection Operator Precedence
@cindex precedence declarations
@cindex declaring operator precedence
@cindex operator precedence, declaring

Use the @code{%left}, @code{%right} or @code{%nonassoc} declaration to
declare a token and specify its precedence and associativity, all at
once.  These are called @dfn{precedence declarations}.
@xref{Precedence, ,Operator Precedence}, for general information on
operator precedence.

The syntax of a precedence declaration is the same as that of
@code{%token}: either

@example
%left @var{symbols}@dots{}
@end example

@noindent
or

@example
%left <@var{type}> @var{symbols}@dots{}
@end example

And indeed any of these declarations serves the purposes of @code{%token}.
But in addition, they specify the associativity and relative precedence for
all the @var{symbols}:

@itemize @bullet
@item
The associativity of an operator @var{op} determines how repeated uses
of the operator nest: whether @samp{@var{x} @var{op} @var{y} @var{op}
@var{z}} is parsed by grouping @var{x} with @var{y} first or by
grouping @var{y} with @var{z} first.  @code{%left} specifies
left-associativity (grouping @var{x} with @var{y} first) and
@code{%right} specifies right-associativity (grouping @var{y} with
@var{z} first).  @code{%nonassoc} specifies no associativity, which
means that @samp{@var{x} @var{op} @var{y} @var{op} @var{z}} is
considered a syntax error.

@item
The precedence of an operator determines how it nests with other operators.
All the tokens declared in a single precedence declaration have equal
precedence and nest together according to their associativity.
When two tokens declared in different precedence declarations associate,
the one declared later has the higher precedence and is grouped first.
@end itemize

@node Union Decl
@subsection The Collection of Value Types
@cindex declaring value types
@cindex value types, declaring
@findex %union

The @code{%union} declaration specifies the entire collection of possible
data types for semantic values.  The keyword @code{%union} is followed by a
pair of braces containing the same thing that goes inside a @code{union} in
C.

For example:

@example
@group
%union @{
  double val;
  symrec *tptr;
@}
@end group
@end example

@noindent
This says that the two alternative types are @code{double} and @code{symrec
*}.  They are given names @code{val} and @code{tptr}; these names are used
in the @code{%token} and @code{%type} declarations to pick one of the types
for a terminal or nonterminal symbol (@pxref{Type Decl, ,Nonterminal Symbols}).

Note that, unlike making a @code{union} declaration in C, you do not write
a semicolon after the closing brace.

@node Type Decl
@subsection Nonterminal Symbols
@cindex declaring value types, nonterminals
@cindex value types, nonterminals, declaring
@findex %type

@noindent
When you use @code{%union} to specify multiple value types, you must
declare the value type of each nonterminal symbol for which values are
used.  This is done with a @code{%type} declaration, like this:

@example
%type <@var{type}> @var{nonterminal}@dots{}
@end example

@noindent
Here @var{nonterminal} is the name of a nonterminal symbol, and
@var{type} is the name given in the @code{%union} to the alternative
that you want (@pxref{Union Decl, ,The Collection of Value Types}).  You
can give any number of nonterminal symbols in the same @code{%type}
declaration, if they have the same value type.  Use spaces to separate
the symbol names.

You can also declare the value type of a terminal symbol.  To do this,
use the same @code{<@var{type}>} construction in a declaration for the
terminal symbol.  All kinds of token declarations allow
@code{<@var{type}>}.

@node Expect Decl
@subsection Suppressing Conflict Warnings
@cindex suppressing conflict warnings
@cindex preventing warnings about conflicts
@cindex warnings, preventing
@cindex conflicts, suppressing warnings of
@findex %expect

Bison normally warns if there are any conflicts in the grammar
(@pxref{Shift/Reduce, ,Shift/Reduce Conflicts}), but most real grammars
have harmless shift/reduce conflicts which are resolved in a predictable
way and would be difficult to eliminate.  It is desirable to suppress
the warning about these conflicts unless the number of conflicts
changes.  You can do this with the @code{%expect} declaration.

The declaration looks like this:

@example
%expect @var{n}
@end example

Here @var{n} is a decimal integer.  The declaration says there should be
no warning if there are @var{n} shift/reduce conflicts and no
reduce/reduce conflicts.  An error, instead of the usual warning, is
given if there are either more or fewer conflicts, or if there are any
reduce/reduce conflicts.

In general, using @code{%expect} involves these steps:

@itemize @bullet
@item
Compile your grammar without @code{%expect}.  Use the @samp{-v} option
to get a verbose list of where the conflicts occur.  Bison will also
print the number of conflicts.

@item
Check each of the conflicts to make sure that Bison's default
resolution is what you really want.  If not, rewrite the grammar and
go back to the beginning.

@item
Add an @code{%expect} declaration, copying the number @var{n} from the
number which Bison printed.
@end itemize

Now Bison will stop annoying you about the conflicts you have checked, but
it will warn you again if changes in the grammar result in additional
conflicts.

@node Start Decl
@subsection The Start-Symbol
@cindex declaring the start symbol
@cindex start symbol, declaring
@cindex default start symbol
@findex %start

Bison assumes by default that the start symbol for the grammar is the first
nonterminal specified in the grammar specification section.  The programmer
may override this restriction with the @code{%start} declaration as follows:

@example
%start @var{symbol}
@end example

@node Pure Decl
@subsection A Pure (Reentrant) Parser
@cindex reentrant parser
@cindex pure parser
@findex %pure-parser

A @dfn{reentrant} program is one which does not alter in the course of
execution; in other words, it consists entirely of @dfn{pure} (read-only)
code.  Reentrancy is important whenever asynchronous execution is possible;
for example, a non-reentrant program may not be safe to call from a signal
handler.  In systems with multiple threads of control, a non-reentrant
program must be called only within interlocks.

Normally, Bison generates a parser which is not reentrant.  This is
suitable for most uses, and it permits compatibility with YACC.  (The
standard YACC interfaces are inherently nonreentrant, because they use
statically allocated variables for communication with @code{yylex},
including @code{yylval} and @code{yylloc}.)

Alternatively, you can generate a pure, reentrant parser.  The Bison
declaration @code{%pure-parser} says that you want the parser to be
reentrant.  It looks like this:

@example
%pure-parser
@end example

The result is that the communication variables @code{yylval} and
@code{yylloc} become local variables in @code{yyparse}, and a different
calling convention is used for the lexical analyzer function
@code{yylex}.  @xref{Pure Calling, ,Calling Conventions for Pure
Parsers}, for the details of this.  The variable @code{yynerrs} also
becomes local in @code{yyparse} (@pxref{Error Reporting, ,The Error
Reporting Function @code{yyerror}}).  The convention for calling
@code{yyparse} itself is unchanged.

Whether the parser is pure has nothing to do with the grammar rules.
You can generate either a pure parser or a nonreentrant parser from any
valid grammar.

@node Decl Summary
@subsection Bison Declaration Summary
@cindex Bison declaration summary
@cindex declaration summary
@cindex summary, Bison declaration

Here is a summary of the declarations used to define a grammar:

@table @code
@item %union
Declare the collection of data types that semantic values may have
(@pxref{Union Decl, ,The Collection of Value Types}).

@item %token
Declare a terminal symbol (token type name) with no precedence
or associativity specified (@pxref{Token Decl, ,Token Type Names}).

@item %right
Declare a terminal symbol (token type name) that is right-associative
(@pxref{Precedence Decl, ,Operator Precedence}).

@item %left
Declare a terminal symbol (token type name) that is left-associative
(@pxref{Precedence Decl, ,Operator Precedence}).

@item %nonassoc
Declare a terminal symbol (token type name) that is nonassociative
(using it in a way that would be associative is a syntax error)
(@pxref{Precedence Decl, ,Operator Precedence}).

@item %type
Declare the type of semantic values for a nonterminal symbol
(@pxref{Type Decl, ,Nonterminal Symbols}).

@item %start
Specify the grammar's start symbol (@pxref{Start Decl, ,The
Start-Symbol}).

@item %expect
Declare the expected number of shift-reduce conflicts
(@pxref{Expect Decl, ,Suppressing Conflict Warnings}).
@end table

@sp 1
@noindent
In order to change the behavior of @command{bison}, use the following
directives:

@table @code
@item %debug
In the parser file, define the macro @code{YYDEBUG} to 1 if it is not
already defined, so that the debugging facilities are compiled.
@xref{Tracing, ,Tracing Your Parser}.

@item %defines
Write an extra output file containing macro definitions for the token
type names defined in the grammar and the semantic value type
@code{YYSTYPE}, as well as a few @code{extern} variable declarations.

If the parser output file is named @file{@var{name}.c} then this file
is named @file{@var{name}.h}.

This output file is essential if you wish to put the definition of
@code{yylex} in a separate source file, because @code{yylex} needs to
be able to refer to token type codes and the variable
@code{yylval}.  @xref{Token Values, ,Semantic Values of Tokens}.

@item %file-prefix="@var{prefix}"
Specify a prefix to use for all Bison output file names.  The names are
chosen as if the input file were named @file{@var{prefix}.y}.

@c @item %header-extension
@c Specify the extension of the parser header file generated when
@c @code{%define} or @samp{-d} are used.
@c
@c For example, a grammar file named @file{foo.ypp} and containing a
@c @code{%header-extension .hh} directive will produce a header file
@c named @file{foo.tab.hh}

@item %locations
Generate the code processing the locations (@pxref{Action Features,
,Special Features for Use in Actions}).  This mode is enabled as soon as
the grammar uses the special @samp{@@@var{n}} tokens, but if your
grammar does not use it, using @samp{%locations} allows for more
accurate parse error messages.

@item %name-prefix="@var{prefix}"
Rename the external symbols used in the parser so that they start with
@var{prefix} instead of @samp{yy}.  The precise list of symbols renamed
is @code{yyparse}, @code{yylex}, @code{yyerror}, @code{yynerrs},
@code{yylval}, @code{yychar}, @code{yydebug}, and possible
@code{yylloc}.  For example, if you use @samp{%name-prefix="c_"}, the
names become @code{c_parse}, @code{c_lex}, and so on.  @xref{Multiple
Parsers, ,Multiple Parsers in the Same Program}.

@item %no-parser
Do not include any C code in the parser file; generate tables only.  The
parser file contains just @code{#define} directives and static variable
declarations.

This option also tells Bison to write the C code for the grammar actions
into a file named @file{@var{filename}.act}, in the form of a
brace-surrounded body fit for a @code{switch} statement.

@item %no-lines
Don't generate any @code{#line} preprocessor commands in the parser
file.  Ordinarily Bison writes these commands in the parser file so that
the C compiler and debuggers will associate errors and object code with
your source file (the grammar file).  This directive causes them to
associate errors with the parser file, treating it an independent source
file in its own right.

@item %output="@var{filename}"
Specify the @var{filename} for the parser file.

@item %pure-parser
Request a pure (reentrant) parser program (@pxref{Pure Decl, ,A Pure
(Reentrant) Parser}).

@c @item %source-extension
@c Specify the extension of the parser output file.
@c
@c For example, a grammar file named @file{foo.yy} and containing a
@c @code{%source-extension .cpp} directive will produce a parser file
@c named @file{foo.tab.cpp}

@item %token-table
Generate an array of token names in the parser file.  The name of the
array is @code{yytname}; @code{yytname[@var{i}]} is the name of the
token whose internal Bison token code number is @var{i}.  The first three
elements of @code{yytname} are always @code{"$"}, @code{"error"}, and
@code{"$illegal"}; after these come the symbols defined in the grammar
file.

For single-character literal tokens and literal string tokens, the name
in the table includes the single-quote or double-quote characters: for
example, @code{"'+'"} is a single-character literal and @code{"\"<=\""}
is a literal string token.  All the characters of the literal string
token appear verbatim in the string found in the table; even
double-quote characters are not escaped.  For example, if the token
consists of three characters @samp{*"*}, its string in @code{yytname}
contains @samp{"*"*"}.  (In C, that would be written as
@code{"\"*\"*\""}).

When you specify @code{%token-table}, Bison also generates macro
definitions for macros @code{YYNTOKENS}, @code{YYNNTS}, and
@code{YYNRULES}, and @code{YYNSTATES}:

@table @code
@item YYNTOKENS
The highest token number, plus one.
@item YYNNTS
The number of nonterminal symbols.
@item YYNRULES
The number of grammar rules,
@item YYNSTATES
The number of parser states (@pxref{Parser States}).
@end table

@item %verbose
Write an extra output file containing verbose descriptions of the
parser states and what is done for each type of look-ahead token in
that state. @xref{Understanding, , Understanding Your Parser}, for more
information.



@item %yacc
Pretend the option @option{--yacc} was given, i.e., imitate Yacc,
including its naming conventions.  @xref{Bison Options}, for more.
@end table




@node Multiple Parsers
@section Multiple Parsers in the Same Program

Most programs that use Bison parse only one language and therefore contain
only one Bison parser.  But what if you want to parse more than one
language with the same program?  Then you need to avoid a name conflict
between different definitions of @code{yyparse}, @code{yylval}, and so on.

The easy way to do this is to use the option @samp{-p @var{prefix}}
(@pxref{Invocation, ,Invoking Bison}).  This renames the interface
functions and variables of the Bison parser to start with @var{prefix}
instead of @samp{yy}.  You can use this to give each parser distinct
names that do not conflict.

The precise list of symbols renamed is @code{yyparse}, @code{yylex},
@code{yyerror}, @code{yynerrs}, @code{yylval}, @code{yychar} and
@code{yydebug}.  For example, if you use @samp{-p c}, the names become
@code{cparse}, @code{clex}, and so on.

@strong{All the other variables and macros associated with Bison are not
renamed.} These others are not global; there is no conflict if the same
name is used in different parsers.  For example, @code{YYSTYPE} is not
renamed, but defining this in different ways in different parsers causes
no trouble (@pxref{Value Type, ,Data Types of Semantic Values}).

The @samp{-p} option works by adding macro definitions to the beginning
of the parser source file, defining @code{yyparse} as
@code{@var{prefix}parse}, and so on.  This effectively substitutes one
name for the other in the entire parser file.

@node Interface
@chapter Parser C-Language Interface
@cindex C-language interface
@cindex interface

The Bison parser is actually a C function named @code{yyparse}.  Here we
describe the interface conventions of @code{yyparse} and the other
functions that it needs to use.

Keep in mind that the parser uses many C identifiers starting with
@samp{yy} and @samp{YY} for internal purposes.  If you use such an
identifier (aside from those in this manual) in an action or in epilogue
in the grammar file, you are likely to run into trouble.

@menu
* Parser Function::   How to call @code{yyparse} and what it returns.
* Lexical::           You must supply a function @code{yylex}
                        which reads tokens.
* Error Reporting::   You must supply a function @code{yyerror}.
* Action Features::   Special features for use in actions.
@end menu

@node Parser Function
@section The Parser Function @code{yyparse}
@findex yyparse

You call the function @code{yyparse} to cause parsing to occur.  This
function reads tokens, executes actions, and ultimately returns when it
encounters end-of-input or an unrecoverable syntax error.  You can also
write an action which directs @code{yyparse} to return immediately
without reading further.

The value returned by @code{yyparse} is 0 if parsing was successful (return
is due to end-of-input).

The value is 1 if parsing failed (return is due to a syntax error).

In an action, you can cause immediate return from @code{yyparse} by using
these macros:

@table @code
@item YYACCEPT
@findex YYACCEPT
Return immediately with value 0 (to report success).

@item YYABORT
@findex YYABORT
Return immediately with value 1 (to report failure).
@end table

@node Lexical
@section The Lexical Analyzer Function @code{yylex}
@findex yylex
@cindex lexical analyzer

The @dfn{lexical analyzer} function, @code{yylex}, recognizes tokens from
the input stream and returns them to the parser.  Bison does not create
this function automatically; you must write it so that @code{yyparse} can
call it.  The function is sometimes referred to as a lexical scanner.

In simple programs, @code{yylex} is often defined at the end of the Bison
grammar file.  If @code{yylex} is defined in a separate source file, you
need to arrange for the token-type macro definitions to be available there.
To do this, use the @samp{-d} option when you run Bison, so that it will
write these macro definitions into a separate header file
@file{@var{name}.tab.h} which you can include in the other source files
that need it.  @xref{Invocation, ,Invoking Bison}.

@menu
* Calling Convention::  How @code{yyparse} calls @code{yylex}.
* Token Values::      How @code{yylex} must return the semantic value
                        of the token it has read.
* Token Positions::   How @code{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 (@pxref{Pure Decl, ,A Pure (Reentrant) Parser}).
@end menu

@node Calling Convention
@subsection Calling Convention for @code{yylex}

The value that @code{yylex} returns must be the numeric code for the type
of token it has just found, or 0 for end-of-input.

When a token is referred to in the grammar rules by a name, that name
in the parser file becomes a C macro whose definition is the proper
numeric code for that token type.  So @code{yylex} can use the name
to indicate that type.  @xref{Symbols}.

When a token is referred to in the grammar rules by a character literal,
the numeric code for that character is also the code for the token type.
So @code{yylex} can simply return that character code.  The null character
must not be used this way, because its code is zero and that is what
signifies end-of-input.

Here is an example showing these things:

@example
int
yylex (void)
@{
  @dots{}
  if (c == EOF)     /* Detect end of file. */
    return 0;
  @dots{}
  if (c == '+' || c == '-')
    return c;      /* Assume token type for `+' is '+'. */
  @dots{}
  return INT;      /* Return the type of the token. */
  @dots{}
@}
@end example

@noindent
This interface has been designed so that the output from the @code{lex}
utility can be used without change as the definition of @code{yylex}.

If the grammar uses literal string tokens, there are two ways that
@code{yylex} can determine the token type codes for them:

@itemize @bullet
@item
If the grammar defines symbolic token names as aliases for the
literal string tokens, @code{yylex} can use these symbolic names like
all others.  In this case, the use of the literal string tokens in
the grammar file has no effect on @code{yylex}.

@item
@code{yylex} can find the multicharacter token in the @code{yytname}
table.  The index of the token in the table is the token type's code.
The name of a multicharacter token is recorded in @code{yytname} with a
double-quote, the token's characters, and another double-quote.  The
token's characters are not escaped in any way; they appear verbatim in
the contents of the string in the table.

Here's code for looking up a token in @code{yytname}, assuming that the
characters of the token are stored in @code{token_buffer}.

@smallexample
for (i = 0; i < YYNTOKENS; i++)
  @{
    if (yytname[i] != 0
        && yytname[i][0] == '"'
        && strncmp (yytname[i] + 1, token_buffer,
                    strlen (token_buffer))
        && yytname[i][strlen (token_buffer) + 1] == '"'
        && yytname[i][strlen (token_buffer) + 2] == 0)
      break;
  @}
@end smallexample

The @code{yytname} table is generated only if you use the
@code{%token-table} declaration.  @xref{Decl Summary}.
@end itemize

@node Token Values
@subsection Semantic Values of Tokens

@vindex yylval
In an ordinary (non-reentrant) parser, the semantic value of the token must
be stored into the global variable @code{yylval}.  When you are using
just one data type for semantic values, @code{yylval} has that type.
Thus, if the type is @code{int} (the default), you might write this in
@code{yylex}:

@example
@group
  @dots{}
  yylval = value;  /* Put value onto Bison stack. */
  return INT;      /* Return the type of the token. */
  @dots{}
@end group
@end example

When you are using multiple data types, @code{yylval}'s type is a union
made from the @code{%union} declaration (@pxref{Union Decl, ,The
Collection of Value Types}).  So when you store a token's value, you
must use the proper member of the union.  If the @code{%union}
declaration looks like this:

@example
@group
%union @{
  int intval;
  double val;
  symrec *tptr;
@}
@end group
@end example

@noindent
then the code in @code{yylex} might look like this:

@example
@group
  @dots{}
  yylval.intval = value; /* Put value onto Bison stack. */
  return INT;          /* Return the type of the token. */
  @dots{}
@end group
@end example

@node Token Positions
@subsection Textual Positions of Tokens

@vindex yylloc
If you are using the @samp{@@@var{n}}-feature (@pxref{Locations, ,
Tracking Locations}) in actions to keep track of the
textual locations of tokens and groupings, then you must provide this
information in @code{yylex}.  The function @code{yyparse} expects to
find the textual location of a token just parsed in the global variable
@code{yylloc}.  So @code{yylex} must store the proper data in that
variable.

By default, the value of @code{yylloc} is a structure and you need only
initialize the members that are going to be used by the actions.  The
four members are called @code{first_line}, @code{first_column},
@code{last_line} and @code{last_column}.  Note that the use of this
feature makes the parser noticeably slower.

@tindex YYLTYPE
The data type of @code{yylloc} has the name @code{YYLTYPE}.

@node Pure Calling
@subsection Calling Conventions for Pure Parsers

When you use the Bison declaration @code{%pure-parser} to request a
pure, reentrant parser, the global communication variables @code{yylval}
and @code{yylloc} cannot be used.  (@xref{Pure Decl, ,A Pure (Reentrant)
Parser}.)  In such parsers the two global variables are replaced by
pointers passed as arguments to @code{yylex}.  You must declare them as
shown here, and pass the information back by storing it through those
pointers.

@example
int
yylex (YYSTYPE *lvalp, YYLTYPE *llocp)
@{
  @dots{}
  *lvalp = value;  /* Put value onto Bison stack.  */
  return INT;      /* Return the type of the token.  */
  @dots{}
@}
@end example

If the grammar file does not use the @samp{@@} constructs to refer to
textual positions, then the type @code{YYLTYPE} will not be defined.  In
this case, omit the second argument; @code{yylex} will be called with
only one argument.

@vindex YYPARSE_PARAM
If you use a reentrant parser, you can optionally pass additional
parameter information to it in a reentrant way.  To do so, define the
macro @code{YYPARSE_PARAM} as a variable name.  This modifies the
@code{yyparse} function to accept one argument, of type @code{void *},
with that name.

When you call @code{yyparse}, pass the address of an object, casting the
address to @code{void *}.  The grammar actions can refer to the contents
of the object by casting the pointer value back to its proper type and
then dereferencing it.  Here's an example.  Write this in the parser:

@example
%@{
struct parser_control
@{
  int nastiness;
  int randomness;
@};

#define YYPARSE_PARAM parm
%@}
@end example

@noindent
Then call the parser like this:

@example
struct parser_control
@{
  int nastiness;
  int randomness;
@};

@dots{}

@{
  struct parser_control foo;
  @dots{}  /* @r{Store proper data in @code{foo}.}  */
  value = yyparse ((void *) &foo);
  @dots{}
@}
@end example

@noindent
In the grammar actions, use expressions like this to refer to the data:

@example
((struct parser_control *) parm)->randomness
@end example

@vindex YYLEX_PARAM
If you wish to pass the additional parameter data to @code{yylex},
define the macro @code{YYLEX_PARAM} just like @code{YYPARSE_PARAM}, as
shown here:

@example
%@{
struct parser_control
@{
  int nastiness;
  int randomness;
@};

#define YYPARSE_PARAM parm
#define YYLEX_PARAM parm
%@}
@end example

You should then define @code{yylex} to accept one additional
argument---the value of @code{parm}.  (This makes either two or three
arguments in total, depending on whether an argument of type
@code{YYLTYPE} is passed.)  You can declare the argument as a pointer to
the proper object type, or you can declare it as @code{void *} and
access the contents as shown above.

You can use @samp{%pure-parser} to request a reentrant parser without
also using @code{YYPARSE_PARAM}.  Then you should call @code{yyparse}
with no arguments, as usual.

@node Error Reporting
@section The Error Reporting Function @code{yyerror}
@cindex error reporting function
@findex yyerror
@cindex parse error
@cindex syntax error

The Bison parser detects a @dfn{parse error} or @dfn{syntax error}
whenever it reads a token which cannot satisfy any syntax rule.  An
action in the grammar can also explicitly proclaim an error, using the
macro @code{YYERROR} (@pxref{Action Features, ,Special Features for Use
in Actions}).

The Bison parser expects to report the error by calling an error
reporting function named @code{yyerror}, which you must supply.  It is
called by @code{yyparse} whenever a syntax error is found, and it
receives one argument.  For a parse error, the string is normally
@w{@code{"parse error"}}.

@findex YYERROR_VERBOSE
If you define the macro @code{YYERROR_VERBOSE} in the Bison declarations
section (@pxref{Bison Declarations, ,The Bison Declarations Section}),
then Bison provides a more verbose and specific error message string
instead of just plain @w{@code{"parse error"}}.  It doesn't matter what
definition you use for @code{YYERROR_VERBOSE}, just whether you define
it.

The parser can detect one other kind of error: stack overflow.  This
happens when the input contains constructions that are very deeply
nested.  It isn't likely you will encounter this, since the Bison
parser extends its stack automatically up to a very large limit.  But
if overflow happens, @code{yyparse} calls @code{yyerror} in the usual
fashion, except that the argument string is @w{@code{"parser stack
overflow"}}.

The following definition suffices in simple programs:

@example
@group
void
yyerror (char *s)
@{
@end group
@group
  fprintf (stderr, "%s\n", s);
@}
@end group
@end example

After @code{yyerror} returns to @code{yyparse}, the latter will attempt
error recovery if you have written suitable error recovery grammar rules
(@pxref{Error Recovery}).  If recovery is impossible, @code{yyparse} will
immediately return 1.

@vindex yynerrs
The variable @code{yynerrs} contains the number of syntax errors
encountered so far.  Normally this variable is global; but if you
request a pure parser (@pxref{Pure Decl, ,A Pure (Reentrant) Parser})
then it is a local variable which only the actions can access.

@node Action Features
@section Special Features for Use in Actions
@cindex summary, action features
@cindex action features summary

Here is a table of Bison constructs, variables and macros that
are useful in actions.

@table @samp
@item $$
Acts like a variable that contains the semantic value for the
grouping made by the current rule.  @xref{Actions}.

@item $@var{n}
Acts like a variable that contains the semantic value for the
@var{n}th component of the current rule.  @xref{Actions}.

@item $<@var{typealt}>$
Like @code{$$} but specifies alternative @var{typealt} in the union
specified by the @code{%union} declaration.  @xref{Action Types, ,Data
Types of Values in Actions}.

@item $<@var{typealt}>@var{n}
Like @code{$@var{n}} but specifies alternative @var{typealt} in the
union specified by the @code{%union} declaration.
@xref{Action Types, ,Data Types of Values in Actions}.

@item YYABORT;
Return immediately from @code{yyparse}, indicating failure.
@xref{Parser Function, ,The Parser Function @code{yyparse}}.

@item YYACCEPT;
Return immediately from @code{yyparse}, indicating success.
@xref{Parser Function, ,The Parser Function @code{yyparse}}.

@item YYBACKUP (@var{token}, @var{value});
@findex YYBACKUP
Unshift a token.  This macro is allowed only for rules that reduce
a single value, and only when there is no look-ahead token.
It is also disallowed in GLR parsers.
It installs a look-ahead token with token type @var{token} and
semantic value @var{value}; then it discards the value that was
going to be reduced by this rule.

If the macro is used when it is not valid, such as when there is
a look-ahead token already, then it reports a syntax error with
a message @samp{cannot back up} and performs ordinary error
recovery.

In either case, the rest of the action is not executed.

@item YYEMPTY
@vindex YYEMPTY
Value stored in @code{yychar} when there is no look-ahead token.

@item YYERROR;
@findex YYERROR
Cause an immediate syntax error.  This statement initiates error
recovery just as if the parser itself had detected an error; however, it
does not call @code{yyerror}, and does not print any message.  If you
want to print an error message, call @code{yyerror} explicitly before
the @samp{YYERROR;} statement.  @xref{Error Recovery}.

@item YYRECOVERING
This macro stands for an expression that has the value 1 when the parser
is recovering from a syntax error, and 0 the rest of the time.
@xref{Error Recovery}.

@item yychar
Variable containing the current look-ahead token.  (In a pure parser,
this is actually a local variable within @code{yyparse}.)  When there is
no look-ahead token, the value @code{YYEMPTY} is stored in the variable.
@xref{Look-Ahead, ,Look-Ahead Tokens}.

@item yyclearin;
Discard the current look-ahead token.  This is useful primarily in
error rules.  @xref{Error Recovery}.

@item yyerrok;
Resume generating error messages immediately for subsequent syntax
errors.  This is useful primarily in error rules.
@xref{Error Recovery}.

@item @@$
@findex @@$
Acts like a structure variable containing information on the textual position
of the grouping made by the current rule.  @xref{Locations, ,
Tracking Locations}.

@c Check if those paragraphs are still useful or not.

@c @example
@c struct @{
@c   int first_line, last_line;
@c   int first_column, last_column;
@c @};
@c @end example

@c Thus, to get the starting line number of the third component, you would
@c use @samp{@@3.first_line}.

@c In order for the members of this structure to contain valid information,
@c you must make @code{yylex} supply this information about each token.
@c If you need only certain members, then @code{yylex} need only fill in
@c those members.

@c The use of this feature makes the parser noticeably slower.

@item @@@var{n}
@findex @@@var{n}
Acts like a structure variable containing information on the textual position
of the @var{n}th component of the current rule.  @xref{Locations, ,
Tracking Locations}.

@end table

@node Algorithm
@chapter The Bison Parser Algorithm
@cindex Bison parser algorithm
@cindex algorithm of parser
@cindex shifting
@cindex reduction
@cindex parser stack
@cindex stack, parser

As Bison reads tokens, it pushes them onto a stack along with their
semantic values.  The stack is called the @dfn{parser stack}.  Pushing a
token is traditionally called @dfn{shifting}.

For example, suppose the infix calculator has read @samp{1 + 5 *}, with a
@samp{3} to come.  The stack will have four elements, one for each token
that was shifted.

But the stack does not always have an element for each token read.  When
the last @var{n} tokens and groupings shifted match the components of a
grammar rule, they can be combined according to that rule.  This is called
@dfn{reduction}.  Those tokens and groupings are replaced on the stack by a
single grouping whose symbol is the result (left hand side) of that rule.
Running the rule's action is part of the process of reduction, because this
is what computes the semantic value of the resulting grouping.

For example, if the infix calculator's parser stack contains this:

@example
1 + 5 * 3
@end example

@noindent
and the next input token is a newline character, then the last three
elements can be reduced to 15 via the rule:

@example
expr: expr '*' expr;
@end example

@noindent
Then the stack contains just these three elements:

@example
1 + 15
@end example

@noindent
At this point, another reduction can be made, resulting in the single value
16.  Then the newline token can be shifted.

The parser tries, by shifts and reductions, to reduce the entire input down
to a single grouping whose symbol is the grammar's start-symbol
(@pxref{Language and Grammar, ,Languages and Context-Free Grammars}).

This kind of parser is known in the literature as a bottom-up parser.

@menu
* 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.
@end menu

@node Look-Ahead
@section Look-Ahead Tokens
@cindex look-ahead token

The Bison parser does @emph{not} always reduce immediately as soon as the
last @var{n} tokens and groupings match a rule.  This is because such a
simple strategy is inadequate to handle most languages.  Instead, when a
reduction is possible, the parser sometimes ``looks ahead'' at the next
token in order to decide what to do.

When a token is read, it is not immediately shifted; first it becomes the
@dfn{look-ahead token}, which is not on the stack.  Now the parser can
perform one or more reductions of tokens and groupings on the stack, while
the look-ahead token remains off to the side.  When no more reductions
should take place, the look-ahead token is shifted onto the stack.  This
does not mean that all possible reductions have been done; depending on the
token type of the look-ahead token, some rules may choose to delay their
application.

Here is a simple case where look-ahead is needed.  These three rules define
expressions which contain binary addition operators and postfix unary
factorial operators (@samp{!}), and allow parentheses for grouping.

@example
@group
expr:     term '+' expr
        | term
        ;
@end group

@group
term:     '(' expr ')'
        | term '!'
        | NUMBER
        ;
@end group
@end example

Suppose that the tokens @w{@samp{1 + 2}} have been read and shifted; what
should be done?  If the following token is @samp{)}, then the first three
tokens must be reduced to form an @code{expr}.  This is the only valid
course, because shifting the @samp{)} would produce a sequence of symbols
@w{@code{term ')'}}, and no rule allows this.

If the following token is @samp{!}, then it must be shifted immediately so
that @w{@samp{2 !}} can be reduced to make a @code{term}.  If instead the
parser were to reduce before shifting, @w{@samp{1 + 2}} would become an
@code{expr}.  It would then be impossible to shift the @samp{!} because
doing so would produce on the stack the sequence of symbols @code{expr
'!'}.  No rule allows that sequence.

@vindex yychar
The current look-ahead token is stored in the variable @code{yychar}.
@xref{Action Features, ,Special Features for Use in Actions}.

@node Shift/Reduce
@section Shift/Reduce Conflicts
@cindex conflicts
@cindex shift/reduce conflicts
@cindex dangling @code{else}
@cindex @code{else}, dangling

Suppose we are parsing a language which has if-then and if-then-else
statements, with a pair of rules like this:

@example
@group
if_stmt:
          IF expr THEN stmt
        | IF expr THEN stmt ELSE stmt
        ;
@end group
@end example

@noindent
Here we assume that @code{IF}, @code{THEN} and @code{ELSE} are
terminal symbols for specific keyword tokens.

When the @code{ELSE} token is read and becomes the look-ahead token, the
contents of the stack (assuming the input is valid) are just right for
reduction by the first rule.  But it is also legitimate to shift the
@code{ELSE}, because that would lead to eventual reduction by the second
rule.

This situation, where either a shift or a reduction would be valid, is
called a @dfn{shift/reduce conflict}.  Bison is designed to resolve
these conflicts by choosing to shift, unless otherwise directed by
operator precedence declarations.  To see the reason for this, let's
contrast it with the other alternative.

Since the parser prefers to shift the @code{ELSE}, the result is to attach
the else-clause to the innermost if-statement, making these two inputs
equivalent:

@example
if x then if y then win (); else lose;

if x then do; if y then win (); else lose; end;
@end example

But if the parser chose to reduce when possible rather than shift, the
result would be to attach the else-clause to the outermost if-statement,
making these two inputs equivalent:

@example
if x then if y then win (); else lose;

if x then do; if y then win (); end; else lose;
@end example

The conflict exists because the grammar as written is ambiguous: either
parsing of the simple nested if-statement is legitimate.  The established
convention is that these ambiguities are resolved by attaching the
else-clause to the innermost if-statement; this is what Bison accomplishes
by choosing to shift rather than reduce.  (It would ideally be cleaner to
write an unambiguous grammar, but that is very hard to do in this case.)
This particular ambiguity was first encountered in the specifications of
Algol 60 and is called the ``dangling @code{else}'' ambiguity.

To avoid warnings from Bison about predictable, legitimate shift/reduce
conflicts, use the @code{%expect @var{n}} declaration.  There will be no
warning as long as the number of shift/reduce conflicts is exactly @var{n}.
@xref{Expect Decl, ,Suppressing Conflict Warnings}.

The definition of @code{if_stmt} above is solely to blame for the
conflict, but the conflict does not actually appear without additional
rules.  Here is a complete Bison input file that actually manifests the
conflict:

@example
@group
%token IF THEN ELSE variable
%%
@end group
@group
stmt:     expr
        | if_stmt
        ;
@end group

@group
if_stmt:
          IF expr THEN stmt
        | IF expr THEN stmt ELSE stmt
        ;
@end group

expr:     variable
        ;
@end example

@node Precedence
@section Operator Precedence
@cindex operator precedence
@cindex precedence of operators

Another situation where shift/reduce conflicts appear is in arithmetic
expressions.  Here shifting is not always the preferred resolution; the
Bison declarations for operator precedence allow you to specify when to
shift and when to reduce.

@menu
* 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.
@end menu

@node Why Precedence
@subsection When Precedence is Needed

Consider the following ambiguous grammar fragment (ambiguous because the
input @w{@samp{1 - 2 * 3}} can be parsed in two different ways):

@example
@group
expr:     expr '-' expr
        | expr '*' expr
        | expr '<' expr
        | '(' expr ')'
        @dots{}
        ;
@end group
@end example

@noindent
Suppose the parser has seen the tokens @samp{1}, @samp{-} and @samp{2};
should it reduce them via the rule for the subtraction operator?  It
depends on the next token.  Of course, if the next token is @samp{)}, we
must reduce; shifting is invalid because no single rule can reduce the
token sequence @w{@samp{- 2 )}} or anything starting with that.  But if
the next token is @samp{*} or @samp{<}, we have a choice: either
shifting or reduction would allow the parse to complete, but with
different results.

To decide which one Bison should do, we must consider the results.  If
the next operator token @var{op} is shifted, then it must be reduced
first in order to permit another opportunity to reduce the difference.
The result is (in effect) @w{@samp{1 - (2 @var{op} 3)}}.  On the other
hand, if the subtraction is reduced before shifting @var{op}, the result
is @w{@samp{(1 - 2) @var{op} 3}}.  Clearly, then, the choice of shift or
reduce should depend on the relative precedence of the operators
@samp{-} and @var{op}: @samp{*} should be shifted first, but not
@samp{<}.

@cindex associativity
What about input such as @w{@samp{1 - 2 - 5}}; should this be
@w{@samp{(1 - 2) - 5}} or should it be @w{@samp{1 - (2 - 5)}}?  For most
operators we prefer the former, which is called @dfn{left association}.
The latter alternative, @dfn{right association}, is desirable for
assignment operators.  The choice of left or right association is a
matter of whether the parser chooses to shift or reduce when the stack
contains @w{@samp{1 - 2}} and the look-ahead token is @samp{-}: shifting
makes right-associativity.

@node Using Precedence
@subsection Specifying Operator Precedence
@findex %left
@findex %right
@findex %nonassoc

Bison allows you to specify these choices with the operator precedence
declarations @code{%left} and @code{%right}.  Each such declaration
contains a list of tokens, which are operators whose precedence and
associativity is being declared.  The @code{%left} declaration makes all
those operators left-associative and the @code{%right} declaration makes
them right-associative.  A third alternative is @code{%nonassoc}, which
declares that it is a syntax error to find the same operator twice ``in a
row''.

The relative precedence of different operators is controlled by the
order in which they are declared.  The first @code{%left} or
@code{%right} declaration in the file declares the operators whose
precedence is lowest, the next such declaration declares the operators
whose precedence is a little higher, and so on.

@node Precedence Examples
@subsection Precedence Examples

In our example, we would want the following declarations:

@example
%left '<'
%left '-'
%left '*'
@end example

In a more complete example, which supports other operators as well, we
would declare them in groups of equal precedence.  For example, @code{'+'} is
declared with @code{'-'}:

@example
%left '<' '>' '=' NE LE GE
%left '+' '-'
%left '*' '/'
@end example

@noindent
(Here @code{NE} and so on stand for the operators for ``not equal''
and so on.  We assume that these tokens are more than one character long
and therefore are represented by names, not character literals.)

@node How Precedence
@subsection How Precedence Works

The first effect of the precedence declarations is to assign precedence
levels to the terminal symbols declared.  The second effect is to assign
precedence levels to certain rules: each rule gets its precedence from
the last terminal symbol mentioned in the components.  (You can also
specify explicitly the precedence of a rule.  @xref{Contextual
Precedence, ,Context-Dependent Precedence}.)

Finally, the resolution of conflicts works by comparing the precedence
of the rule being considered with that of the look-ahead token.  If the
token's precedence is higher, the choice is to shift.  If the rule's
precedence is higher, the choice is to reduce.  If they have equal
precedence, the choice is made based on the associativity of that
precedence level.  The verbose output file made by @samp{-v}
(@pxref{Invocation, ,Invoking Bison}) says how each conflict was
resolved.

Not all rules and not all tokens have precedence.  If either the rule or
the look-ahead token has no precedence, then the default is to shift.

@node Contextual Precedence
@section Context-Dependent Precedence
@cindex context-dependent precedence
@cindex unary operator precedence
@cindex precedence, context-dependent
@cindex precedence, unary operator
@findex %prec

Often the precedence of an operator depends on the context.  This sounds
outlandish at first, but it is really very common.  For example, a minus
sign typically has a very high precedence as a unary operator, and a
somewhat lower precedence (lower than multiplication) as a binary operator.

The Bison precedence declarations, @code{%left}, @code{%right} and
@code{%nonassoc}, can only be used once for a given token; so a token has
only one precedence declared in this way.  For context-dependent
precedence, you need to use an additional mechanism: the @code{%prec}
modifier for rules.

The @code{%prec} modifier declares the precedence of a particular rule by
specifying a terminal symbol whose precedence should be used for that rule.
It's not necessary for that symbol to appear otherwise in the rule.  The
modifier's syntax is:

@example
%prec @var{terminal-symbol}
@end example

@noindent
and it is written after the components of the rule.  Its effect is to
assign the rule the precedence of @var{terminal-symbol}, overriding
the precedence that would be deduced for it in the ordinary way.  The
altered rule precedence then affects how conflicts involving that rule
are resolved (@pxref{Precedence, ,Operator Precedence}).

Here is how @code{%prec} solves the problem of unary minus.  First, declare
a precedence for a fictitious terminal symbol named @code{UMINUS}.  There
are no tokens of this type, but the symbol serves to stand for its
precedence:

@example
@dots{}
%left '+' '-'
%left '*'
%left UMINUS
@end example

Now the precedence of @code{UMINUS} can be used in specific rules:

@example
@group
exp:    @dots{}
        | exp '-' exp
        @dots{}
        | '-' exp %prec UMINUS
@end group
@end example

@node Parser States
@section Parser States
@cindex finite-state machine
@cindex parser state
@cindex state (of parser)

The function @code{yyparse} is implemented using a finite-state machine.
The values pushed on the parser stack are not simply token type codes; they
represent the entire sequence of terminal and nonterminal symbols at or
near the top of the stack.  The current state collects all the information
about previous input which is relevant to deciding what to do next.

Each time a look-ahead token is read, the current parser state together
with the type of look-ahead token are looked up in a table.  This table
entry can say, ``Shift the look-ahead token.''  In this case, it also
specifies the new parser state, which is pushed onto the top of the
parser stack.  Or it can say, ``Reduce using rule number @var{n}.''
This means that a certain number of tokens or groupings are taken off
the top of the stack, and replaced by one grouping.  In other words,
that number of states are popped from the stack, and one new state is
pushed.

There is one other alternative: the table can say that the look-ahead token
is erroneous in the current state.  This causes error processing to begin
(@pxref{Error Recovery}).

@node Reduce/Reduce
@section Reduce/Reduce Conflicts
@cindex reduce/reduce conflict
@cindex conflicts, reduce/reduce

A reduce/reduce conflict occurs if there are two or more rules that apply
to the same sequence of input.  This usually indicates a serious error
in the grammar.

For example, here is an erroneous attempt to define a sequence
of zero or more @code{word} groupings.

@example
sequence: /* empty */
                @{ printf ("empty sequence\n"); @}
        | maybeword
        | sequence word
                @{ printf ("added word %s\n", $2); @}
        ;

maybeword: /* empty */
                @{ printf ("empty maybeword\n"); @}
        | word
                @{ printf ("single word %s\n", $1); @}
        ;
@end example

@noindent
The error is an ambiguity: there is more than one way to parse a single
@code{word} into a @code{sequence}.  It could be reduced to a
@code{maybeword} and then into a @code{sequence} via the second rule.
Alternatively, nothing-at-all could be reduced into a @code{sequence}
via the first rule, and this could be combined with the @code{word}
using the third rule for @code{sequence}.

There is also more than one way to reduce nothing-at-all into a
@code{sequence}.  This can be done directly via the first rule,
or indirectly via @code{maybeword} and then the second rule.

You might think that this is a distinction without a difference, because it
does not change whether any particular input is valid or not.  But it does
affect which actions are run.  One parsing order runs the second rule's
action; the other runs the first rule's action and the third rule's action.
In this example, the output of the program changes.

Bison resolves a reduce/reduce conflict by choosing to use the rule that
appears first in the grammar, but it is very risky to rely on this.  Every
reduce/reduce conflict must be studied and usually eliminated.  Here is the
proper way to define @code{sequence}:

@example
sequence: /* empty */
                @{ printf ("empty sequence\n"); @}
        | sequence word
                @{ printf ("added word %s\n", $2); @}
        ;
@end example

Here is another common error that yields a reduce/reduce conflict:

@example
sequence: /* empty */
        | sequence words
        | sequence redirects
        ;

words:    /* empty */
        | words word
        ;

redirects:/* empty */
        | redirects redirect
        ;
@end example

@noindent
The intention here is to define a sequence which can contain either
@code{word} or @code{redirect} groupings.  The individual definitions of
@code{sequence}, @code{words} and @code{redirects} are error-free, but the
three together make a subtle ambiguity: even an empty input can be parsed
in infinitely many ways!

Consider: nothing-at-all could be a @code{words}.  Or it could be two
@code{words} in a row, or three, or any number.  It could equally well be a
@code{redirects}, or two, or any number.  Or it could be a @code{words}
followed by three @code{redirects} and another @code{words}.  And so on.

Here are two ways to correct these rules.  First, to make it a single level
of sequence:

@example
sequence: /* empty */
        | sequence word
        | sequence redirect
        ;
@end example

Second, to prevent either a @code{words} or a @code{redirects}
from being empty:

@example
sequence: /* empty */
        | sequence words
        | sequence redirects
        ;

words:    word
        | words word
        ;

redirects:redirect
        | redirects redirect
        ;
@end example

@node Mystery Conflicts
@section Mysterious Reduce/Reduce Conflicts

Sometimes reduce/reduce conflicts can occur that don't look warranted.
Here is an example:

@example
@group
%token ID

%%
def:    param_spec return_spec ','
        ;
param_spec:
             type
        |    name_list ':' type
        ;
@end group
@group
return_spec:
             type
        |    name ':' type
        ;
@end group
@group
type:        ID
        ;
@end group
@group
name:        ID
        ;
name_list:
             name
        |    name ',' name_list
        ;
@end group
@end example

It would seem that this grammar can be parsed with only a single token
of look-ahead: when a @code{param_spec} is being read, an @code{ID} is
a @code{name} if a comma or colon follows, or a @code{type} if another
@code{ID} follows.  In other words, this grammar is LR(1).

@cindex LR(1)
@cindex LALR(1)
However, Bison, like most parser generators, cannot actually handle all
LR(1) grammars.  In this grammar, two contexts, that after an @code{ID}
at the beginning of a @code{param_spec} and likewise at the beginning of
a @code{return_spec}, are similar enough that Bison assumes they are the
same.  They appear similar because the same set of rules would be
active---the rule for reducing to a @code{name} and that for reducing to
a @code{type}.  Bison is unable to determine at that stage of processing
that the rules would require different look-ahead tokens in the two
contexts, so it makes a single parser state for them both.  Combining
the two contexts causes a conflict later.  In parser terminology, this
occurrence means that the grammar is not LALR(1).

In general, it is better to fix deficiencies than to document them.  But
this particular deficiency is intrinsically hard to fix; parser
generators that can handle LR(1) grammars are hard to write and tend to
produce parsers that are very large.  In practice, Bison is more useful
as it is now.

When the problem arises, you can often fix it by identifying the two
parser states that are being confused, and adding something to make them
look distinct.  In the above example, adding one rule to
@code{return_spec} as follows makes the problem go away:

@example
@group
%token BOGUS
@dots{}
%%
@dots{}
return_spec:
             type
        |    name ':' type
        /* This rule is never used.  */
        |    ID BOGUS
        ;
@end group
@end example

This corrects the problem because it introduces the possibility of an
additional active rule in the context after the @code{ID} at the beginning of
@code{return_spec}.  This rule is not active in the corresponding context
in a @code{param_spec}, so the two contexts receive distinct parser states.
As long as the token @code{BOGUS} is never generated by @code{yylex},
the added rule cannot alter the way actual input is parsed.

In this particular example, there is another way to solve the problem:
rewrite the rule for @code{return_spec} to use @code{ID} directly
instead of via @code{name}.  This also causes the two confusing
contexts to have different sets of active rules, because the one for
@code{return_spec} activates the altered rule for @code{return_spec}
rather than the one for @code{name}.

@example
param_spec:
             type
        |    name_list ':' type
        ;
return_spec:
             type
        |    ID ':' type
        ;
@end example

@node Generalized LR Parsing
@section Generalized LR (GLR) Parsing
@cindex GLR parsing
@cindex generalized LR (GLR) parsing
@cindex ambiguous grammars
@cindex non-deterministic parsing

Bison produces @emph{deterministic} parsers that choose uniquely
when to reduce and which reduction to apply
based on a summary of the preceding input and on one extra token of lookahead.
As a result, normal Bison handles a proper subset of the family of
context-free languages.
Ambiguous grammars, since they have strings with more than one possible
sequence of reductions cannot have deterministic parsers in this sense.
The same is true of languages that require more than one symbol of
lookahead, since the parser lacks the information necessary to make a
decision at the point it must be made in a shift-reduce parser.
Finally, as previously mentioned (@pxref{Mystery Conflicts}),
there are languages where Bison's particular choice of how to
summarize the input seen so far loses necessary information.

When you use the @samp{%glr-parser} declaration in your grammar file,
Bison generates a parser that uses a different algorithm, called
Generalized LR (or GLR).  A Bison GLR parser uses the same basic
algorithm for parsing as an ordinary Bison parser, but behaves
differently in cases where there is a shift-reduce conflict that has not
been resolved by precedence rules (@pxref{Precedence}) or a
reduce-reduce conflict.  When a GLR parser encounters such a situation, it
effectively @emph{splits} into a several parsers, one for each possible
shift or reduction.  These parsers then proceed as usual, consuming
tokens in lock-step.  Some of the stacks may encounter other conflicts
and split further, with the result that instead of a sequence of states,
a Bison GLR parsing stack is what is in effect a tree of states.

In effect, each stack represents a guess as to what the proper parse
is.  Additional input may indicate that a guess was wrong, in which case
the appropriate stack silently disappears.  Otherwise, the semantics
actions generated in each stack are saved, rather than being executed
immediately.  When a stack disappears, its saved semantic actions never
get executed.  When a reduction causes two stacks to become equivalent,
their sets of semantic actions are both saved with the state that
results from the reduction.  We say that two stacks are equivalent
when they both represent the same sequence of states,
and each pair of corresponding states represents a
grammar symbol that produces the same segment of the input token
stream.

Whenever the parser makes a transition from having multiple
states to having one, it reverts to the normal LALR(1) parsing
algorithm, after resolving and executing the saved-up actions.
At this transition, some of the states on the stack will have semantic
values that are sets (actually multisets) of possible actions.  The
parser tries to pick one of the actions by first finding one whose rule
has the highest dynamic precedence, as set by the @samp{%dprec}
declaration.  Otherwise, if the alternative actions are not ordered by
precedence, but there the same merging function is declared for both
rules by the @samp{%merge} declaration,
Bison resolves and evaluates both and then calls the merge function on
the result.  Otherwise, it reports an ambiguity.

It is possible to use a data structure for the GLR parsing tree that
permits the processing of any LALR(1) grammar in linear time (in the
size of the input), any unambiguous (not necessarily LALR(1)) grammar in
quadratic worst-case time, and any general (possibly ambiguous)
context-free grammar in cubic worst-case time.  However, Bison currently
uses a simpler data structure that requires time proportional to the
length of the input times the maximum number of stacks required for any
prefix of the input.  Thus, really ambiguous or non-deterministic
grammars can require exponential time and space to process.  Such badly
behaving examples, however, are not generally of practical interest.
Usually, non-determinism in a grammar is local---the parser is ``in
doubt'' only for a few tokens at a time.  Therefore, the current data
structure should generally be adequate.  On LALR(1) portions of a
grammar, in particular, it is only slightly slower than with the default
Bison parser.

@node Stack Overflow
@section Stack Overflow, and How to Avoid It
@cindex stack overflow
@cindex parser stack overflow
@cindex overflow of parser stack

The Bison parser stack can overflow if too many tokens are shifted and
not reduced.  When this happens, the parser function @code{yyparse}
returns a nonzero value, pausing only to call @code{yyerror} to report
the overflow.

@vindex YYMAXDEPTH
By defining the macro @code{YYMAXDEPTH}, you can control how deep the
parser stack can become before a stack overflow occurs.  Define the
macro with a value that is an integer.  This value is the maximum number
of tokens that can be shifted (and not reduced) before overflow.
It must be a constant expression whose value is known at compile time.

The stack space allowed is not necessarily allocated.  If you specify a
large value for @code{YYMAXDEPTH}, the parser actually allocates a small
stack at first, and then makes it bigger by stages as needed.  This
increasing allocation happens automatically and silently.  Therefore,
you do not need to make @code{YYMAXDEPTH} painfully small merely to save
space for ordinary inputs that do not need much stack.

@cindex default stack limit
The default value of @code{YYMAXDEPTH}, if you do not define it, is
10000.

@vindex YYINITDEPTH
You can control how much stack is allocated initially by defining the
macro @code{YYINITDEPTH}.  This value too must be a compile-time
constant integer.  The default is 200.

@node Error Recovery
@chapter Error Recovery
@cindex error recovery
@cindex recovery from errors

It is not usually acceptable to have a program terminate on a parse
error.  For example, a compiler should recover sufficiently to parse the
rest of the input file and check it for errors; a calculator should accept
another expression.

In a simple interactive command parser where each input is one line, it may
be sufficient to allow @code{yyparse} to return 1 on error and have the
caller ignore the rest of the input line when that happens (and then call
@code{yyparse} again).  But this is inadequate for a compiler, because it
forgets all the syntactic context leading up to the error.  A syntax error
deep within a function in the compiler input should not cause the compiler
to treat the following line like the beginning of a source file.

@findex error
You can define how to recover from a syntax error by writing rules to
recognize the special token @code{error}.  This is a terminal symbol that
is always defined (you need not declare it) and reserved for error
handling.  The Bison parser generates an @code{error} token whenever a
syntax error happens; if you have provided a rule to recognize this token
in the current context, the parse can continue.

For example:

@example
stmnts:  /* empty string */
        | stmnts '\n'
        | stmnts exp '\n'
        | stmnts error '\n'
@end example

The fourth rule in this example says that an error followed by a newline
makes a valid addition to any @code{stmnts}.

What happens if a syntax error occurs in the middle of an @code{exp}?  The
error recovery rule, interpreted strictly, applies to the precise sequence
of a @code{stmnts}, an @code{error} and a newline.  If an error occurs in
the middle of an @code{exp}, there will probably be some additional tokens
and subexpressions on the stack after the last @code{stmnts}, and there
will be tokens to read before the next newline.  So the rule is not
applicable in the ordinary way.

But Bison can force the situation to fit the rule, by discarding part of
the semantic context and part of the input.  First it discards states and
objects from the stack until it gets back to a state in which the
@code{error} token is acceptable.  (This means that the subexpressions
already parsed are discarded, back to the last complete @code{stmnts}.)  At
this point the @code{error} token can be shifted.  Then, if the old
look-ahead token is not acceptable to be shifted next, the parser reads
tokens and discards them until it finds a token which is acceptable.  In
this example, Bison reads and discards input until the next newline
so that the fourth rule can apply.

The choice of error rules in the grammar is a choice of strategies for
error recovery.  A simple and useful strategy is simply to skip the rest of
the current input line or current statement if an error is detected:

@example
stmnt: error ';'  /* on error, skip until ';' is read */
@end example

It is also useful to recover to the matching close-delimiter of an
opening-delimiter that has already been parsed.  Otherwise the
close-delimiter will probably appear to be unmatched, and generate another,
spurious error message:

@example
primary:  '(' expr ')'
        | '(' error ')'
        @dots{}
        ;
@end example

Error recovery strategies are necessarily guesses.  When they guess wrong,
one syntax error often leads to another.  In the above example, the error
recovery rule guesses that an error is due to bad input within one
@code{stmnt}.  Suppose that instead a spurious semicolon is inserted in the
middle of a valid @code{stmnt}.  After the error recovery rule recovers
from the first error, another syntax error will be found straightaway,
since the text following the spurious semicolon is also an invalid
@code{stmnt}.

To prevent an outpouring of error messages, the parser will output no error
message for another syntax error that happens shortly after the first; only
after three consecutive input tokens have been successfully shifted will
error messages resume.

Note that rules which accept the @code{error} token may have actions, just
as any other rules can.

@findex yyerrok
You can make error messages resume immediately by using the macro
@code{yyerrok} in an action.  If you do this in the error rule's action, no
error messages will be suppressed.  This macro requires no arguments;
@samp{yyerrok;} is a valid C statement.

@findex yyclearin
The previous look-ahead token is reanalyzed immediately after an error.  If
this is unacceptable, then the macro @code{yyclearin} may be used to clear
this token.  Write the statement @samp{yyclearin;} in the error rule's
action.

For example, suppose that on a parse error, an error handling routine is
called that advances the input stream to some point where parsing should
once again commence.  The next symbol returned by the lexical scanner is
probably correct.  The previous look-ahead token ought to be discarded
with @samp{yyclearin;}.

@vindex YYRECOVERING
The macro @code{YYRECOVERING} stands for an expression that has the
value 1 when the parser is recovering from a syntax error, and 0 the
rest of the time.  A value of 1 indicates that error messages are
currently suppressed for new syntax errors.

@node Context Dependency
@chapter Handling Context Dependencies

The Bison paradigm is to parse tokens first, then group them into larger
syntactic units.  In many languages, the meaning of a token is affected by
its context.  Although this violates the Bison paradigm, certain techniques
(known as @dfn{kludges}) may enable you to write Bison parsers for such
languages.

@menu
* 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.
@end menu

(Actually, ``kludge'' means any technique that gets its job done but is
neither clean nor robust.)

@node Semantic Tokens
@section Semantic Info in Token Types

The C language has a context dependency: the way an identifier is used
depends on what its current meaning is.  For example, consider this:

@example
foo (x);
@end example

This looks like a function call statement, but if @code{foo} is a typedef
name, then this is actually a declaration of @code{x}.  How can a Bison
parser for C decide how to parse this input?

The method used in GNU C is to have two different token types,
@code{IDENTIFIER} and @code{TYPENAME}.  When @code{yylex} finds an
identifier, it looks up the current declaration of the identifier in order
to decide which token type to return: @code{TYPENAME} if the identifier is
declared as a typedef, @code{IDENTIFIER} otherwise.

The grammar rules can then express the context dependency by the choice of
token type to recognize.  @code{IDENTIFIER} is accepted as an expression,
but @code{TYPENAME} is not.  @code{TYPENAME} can start a declaration, but
@code{IDENTIFIER} cannot.  In contexts where the meaning of the identifier
is @emph{not} significant, such as in declarations that can shadow a
typedef name, either @code{TYPENAME} or @code{IDENTIFIER} is
accepted---there is one rule for each of the two token types.

This technique is simple to use if the decision of which kinds of
identifiers to allow is made at a place close to where the identifier is
parsed.  But in C this is not always so: C allows a declaration to
redeclare a typedef name provided an explicit type has been specified
earlier:

@example
typedef int foo, bar, lose;
static foo (bar);        /* @r{redeclare @code{bar} as static variable} */
static int foo (lose);   /* @r{redeclare @code{foo} as function} */
@end example

Unfortunately, the name being declared is separated from the declaration
construct itself by a complicated syntactic structure---the ``declarator''.

As a result, part of the Bison parser for C needs to be duplicated, with
all the nonterminal names changed: once for parsing a declaration in
which a typedef name can be redefined, and once for parsing a
declaration in which that can't be done.  Here is a part of the
duplication, with actions omitted for brevity:

@example
initdcl:
          declarator maybeasm '='
          init
        | declarator maybeasm
        ;

notype_initdcl:
          notype_declarator maybeasm '='
          init
        | notype_declarator maybeasm
        ;
@end example

@noindent
Here @code{initdcl} can redeclare a typedef name, but @code{notype_initdcl}
cannot.  The distinction between @code{declarator} and
@code{notype_declarator} is the same sort of thing.

There is some similarity between this technique and a lexical tie-in
(described next), in that information which alters the lexical analysis is
changed during parsing by other parts of the program.  The difference is
here the information is global, and is used for other purposes in the
program.  A true lexical tie-in has a special-purpose flag controlled by
the syntactic context.

@node Lexical Tie-ins
@section Lexical Tie-ins
@cindex lexical tie-in

One way to handle context-dependency is the @dfn{lexical tie-in}: a flag
which is set by Bison actions, whose purpose is to alter the way tokens are
parsed.

For example, suppose we have a language vaguely like C, but with a special
construct @samp{hex (@var{hex-expr})}.  After the keyword @code{hex} comes
an expression in parentheses in which all integers are hexadecimal.  In
particular, the token @samp{a1b} must be treated as an integer rather than
as an identifier if it appears in that context.  Here is how you can do it:

@example
@group
%@{
int hexflag;
%@}
%%
@dots{}
@end group
@group
expr:   IDENTIFIER
        | constant
        | HEX '('
                @{ hexflag = 1; @}
          expr ')'
                @{ hexflag = 0;
                   $$ = $4; @}
        | expr '+' expr
                @{ $$ = make_sum ($1, $3); @}
        @dots{}
        ;
@end group

@group
constant:
          INTEGER
        | STRING
        ;
@end group
@end example

@noindent
Here we assume that @code{yylex} looks at the value of @code{hexflag}; when
it is nonzero, all integers are parsed in hexadecimal, and tokens starting
with letters are parsed as integers if possible.

The declaration of @code{hexflag} shown in the prologue of the parser file
is needed to make it accessible to the actions (@pxref{Prologue, ,The Prologue}).
You must also write the code in @code{yylex} to obey the flag.

@node Tie-in Recovery
@section Lexical Tie-ins and Error Recovery

Lexical tie-ins make strict demands on any error recovery rules you have.
@xref{Error Recovery}.

The reason for this is that the purpose of an error recovery rule is to
abort the parsing of one construct and resume in some larger construct.
For example, in C-like languages, a typical error recovery rule is to skip
tokens until the next semicolon, and then start a new statement, like this:

@example
stmt:   expr ';'
        | IF '(' expr ')' stmt @{ @dots{} @}
        @dots{}
        error ';'
                @{ hexflag = 0; @}
        ;
@end example

If there is a syntax error in the middle of a @samp{hex (@var{expr})}
construct, this error rule will apply, and then the action for the
completed @samp{hex (@var{expr})} will never run.  So @code{hexflag} would
remain set for the entire rest of the input, or until the next @code{hex}
keyword, causing identifiers to be misinterpreted as integers.

To avoid this problem the error recovery rule itself clears @code{hexflag}.

There may also be an error recovery rule that works within expressions.
For example, there could be a rule which applies within parentheses
and skips to the close-parenthesis:

@example
@group
expr:   @dots{}
        | '(' expr ')'
                @{ $$ = $2; @}
        | '(' error ')'
        @dots{}
@end group
@end example

If this rule acts within the @code{hex} construct, it is not going to abort
that construct (since it applies to an inner level of parentheses within
the construct).  Therefore, it should not clear the flag: the rest of
the @code{hex} construct should be parsed with the flag still in effect.

What if there is an error recovery rule which might abort out of the
@code{hex} construct or might not, depending on circumstances?  There is no
way you can write the action to determine whether a @code{hex} construct is
being aborted or not.  So if you are using a lexical tie-in, you had better
make sure your error recovery rules are not of this kind.  Each rule must
be such that you can be sure that it always will, or always won't, have to
clear the flag.

@c ================================================== Debugging Your Parser

@node Debugging
@chapter Debugging Your Parser

Developing a parser can be a challenge, especially if you don't
understand the algorithm (@pxref{Algorithm, ,The Bison Parser
Algorithm}).  Even so, sometimes a detailed description of the automaton
can help (@pxref{Understanding, , Understanding Your Parser}), or
tracing the execution of the parser can give some insight on why it
behaves improperly (@pxref{Tracing, , Tracing Your Parser}).

@menu
* Understanding::     Understanding the structure of your parser.
* Tracing::           Tracing the execution of your parser.
@end menu

@node Understanding
@section Understanding Your Parser

As documented elsewhere (@pxref{Algorithm, ,The Bison Parser Algorithm})
Bison parsers are @dfn{shift/reduce automata}.  In some cases (much more
frequent than one would hope), looking at this automaton is required to
tune or simply fix a parser.  Bison provides two different
representation of it, either textually or graphically (as a @sc{vcg}
file).

The textual file is generated when the options @option{--report} or
@option{--verbose} are specified, see @xref{Invocation, , Invoking
Bison}.  Its name is made by removing @samp{.tab.c} or @samp{.c} from
the parser output file name, and adding @samp{.output} instead.
Therefore, if the input file is @file{foo.y}, then the parser file is
called @file{foo.tab.c} by default.  As a consequence, the verbose
output file is called @file{foo.output}.

The following grammar file, @file{calc.y}, will be used in the sequel:

@example
%token NUM STR
%left '+' '-'
%left '*'
%%
exp: exp '+' exp
   | exp '-' exp
   | exp '*' exp
   | exp '/' exp
   | NUM
   ;
useless: STR;
%%
@end example

@command{bison} reports that @samp{calc.y contains 1 useless nonterminal
and 1 useless rule} and that @samp{calc.y contains 7 shift/reduce
conflicts}.  When given @option{--report=state}, in addition to
@file{calc.tab.c}, it creates a file @file{calc.output} with contents
detailed below.  The order of the output and the exact presentation
might vary, but the interpretation is the same.

The first section includes details on conflicts that were solved thanks
to precedence and/or associativity:

@example
Conflict in state 8 between rule 2 and token '+' resolved as reduce.
Conflict in state 8 between rule 2 and token '-' resolved as reduce.
Conflict in state 8 between rule 2 and token '*' resolved as shift.
@exdent @dots{}
@end example

@noindent
The next section lists states that still have conflicts.

@example
State 8 contains 1 shift/reduce conflict.
State 9 contains 1 shift/reduce conflict.
State 10 contains 1 shift/reduce conflict.
State 11 contains 4 shift/reduce conflicts.
@end example

@noindent
@cindex token, useless
@cindex useless token
@cindex nonterminal, useless
@cindex useless nonterminal
@cindex rule, useless
@cindex useless rule
The next section reports useless tokens, nonterminal and rules.  Useless
nonterminals and rules are removed in order to produce a smaller parser,
but useless tokens are preserved, since they might be used by the
scanner (note the difference between ``useless'' and ``not used''
below):

@example
Useless nonterminals:
   useless

Terminals which are not used:
   STR

Useless rules:
#6     useless: STR;
@end example

@noindent
The next section reproduces the exact grammar that Bison used:

@example
Grammar

  Number, Line, Rule
    0   5 $axiom -> exp $
    1   5 exp -> exp '+' exp
    2   6 exp -> exp '-' exp
    3   7 exp -> exp '*' exp
    4   8 exp -> exp '/' exp
    5   9 exp -> NUM
@end example

@noindent
and reports the uses of the symbols:

@example
Terminals, with rules where they appear

$ (0) 0
'*' (42) 3
'+' (43) 1
'-' (45) 2
'/' (47) 4
error (256)
NUM (258) 5

Nonterminals, with rules where they appear

$axiom (8)
    on left: 0
exp (9)
    on left: 1 2 3 4 5, on right: 0 1 2 3 4
@end example

@noindent
@cindex item
@cindex pointed rule
@cindex rule, pointed
Bison then proceeds onto the automaton itself, describing each state
with it set of @dfn{items}, also known as @dfn{pointed rules}.  Each
item is a production rule together with a point (marked by @samp{.})
that the input cursor.

@example
state 0

    $axiom  ->  . exp $   (rule 0)

    NUM 	shift, and go to state 1

    exp 	go to state 2
@end example

This reads as follows: ``state 0 corresponds to being at the very
beginning of the parsing, in the initial rule, right before the start
symbol (here, @code{exp}).  When the parser returns to this state right
after having reduced a rule that produced an @code{exp}, the control
flow jumps to state 2.  If there is no such transition on a nonterminal
symbol, and the lookahead is a @code{NUM}, then this token is shifted on
the parse stack, and the control flow jumps to state 1.  Any other
lookahead triggers a parse error.''

@cindex core, item set
@cindex item set core
@cindex kernel, item set
@cindex item set core
Even though the only active rule in state 0 seems to be rule 0, the
report lists @code{NUM} as a lookahead symbol because @code{NUM} can be
at the beginning of any rule deriving an @code{exp}.  By default Bison
reports the so-called @dfn{core} or @dfn{kernel} of the item set, but if
you want to see more detail you can invoke @command{bison} with
@option{--report=itemset} to list all the items, include those that can
be derived:

@example
state 0

    $axiom  ->  . exp $   (rule 0)
    exp  ->  . exp '+' exp   (rule 1)
    exp  ->  . exp '-' exp   (rule 2)
    exp  ->  . exp '*' exp   (rule 3)
    exp  ->  . exp '/' exp   (rule 4)
    exp  ->  . NUM   (rule 5)

    NUM         shift, and go to state 1

    exp         go to state 2
@end example

@noindent
In the state 1...

@example
state 1

    exp  ->  NUM .   (rule 5)

    $default	reduce using rule 5 (exp)
@end example

@noindent
the rule 5, @samp{exp: NUM;}, is completed.  Whatever the lookahead
(@samp{$default}), the parser will reduce it.  If it was coming from
state 0, then, after this reduction it will return to state 0, and will
jump to state 2 (@samp{exp: go to state 2}).

@example
state 2

    $axiom  ->  exp . $   (rule 0)
    exp  ->  exp . '+' exp   (rule 1)
    exp  ->  exp . '-' exp   (rule 2)
    exp  ->  exp . '*' exp   (rule 3)
    exp  ->  exp . '/' exp   (rule 4)

    $   	shift, and go to state 3
    '+' 	shift, and go to state 4
    '-' 	shift, and go to state 5
    '*' 	shift, and go to state 6
    '/' 	shift, and go to state 7
@end example

@noindent
In state 2, the automaton can only shift a symbol.  For instance,
because of the item @samp{exp -> exp . '+' exp}, if the lookahead if
@samp{+}, it will be shifted on the parse stack, and the automaton
control will jump to state 4, corresponding to the item @samp{exp -> exp
'+' . exp}.  Since there is no default action, any other token than
those listed above will trigger a parse error.

The state 3 is named the @dfn{final state}, or the @dfn{accepting
state}:

@example
state 3

    $axiom  ->  exp $ .   (rule 0)

    $default	accept
@end example

@noindent
the initial rule is completed (the start symbol and the end
of input were read), the parsing exits successfully.

The interpretation of states 4 to 7 is straightforward, and is left to
the reader.

@example
state 4

    exp  ->  exp '+' . exp   (rule 1)

    NUM 	shift, and go to state 1

    exp 	go to state 8

state 5

    exp  ->  exp '-' . exp   (rule 2)

    NUM 	shift, and go to state 1

    exp 	go to state 9

state 6

    exp  ->  exp '*' . exp   (rule 3)

    NUM 	shift, and go to state 1

    exp 	go to state 10

state 7

    exp  ->  exp '/' . exp   (rule 4)

    NUM 	shift, and go to state 1

    exp 	go to state 11
@end example

As was announced in beginning of the report, @samp{State 8 contains 1
shift/reduce conflict}:

@example
state 8

    exp  ->  exp . '+' exp   (rule 1)
    exp  ->  exp '+' exp .   (rule 1)
    exp  ->  exp . '-' exp   (rule 2)
    exp  ->  exp . '*' exp   (rule 3)
    exp  ->  exp . '/' exp   (rule 4)

    '*' 	shift, and go to state 6
    '/' 	shift, and go to state 7

    '/' 	[reduce using rule 1 (exp)]
    $default	reduce using rule 1 (exp)
@end example

Indeed, there are two actions associated to the lookahead @samp{/}:
either shifting (and going to state 7), or reducing rule 1.  The
conflict means that either the grammar is ambiguous, or the parser lacks
information to make the right decision.  Indeed the grammar is
ambiguous, as, since we did not specify the precedence of @samp{/}, the
sentence @samp{NUM + NUM / NUM} can be parsed as @samp{NUM + (NUM /
NUM)}, which corresponds to shifting @samp{/}, or as @samp{(NUM + NUM) /
NUM}, which corresponds to reducing rule 1.

Because in LALR(1) parsing a single decision can be made, Bison
arbitrarily chose to disable the reduction, see @ref{Shift/Reduce, ,
Shift/Reduce Conflicts}.  Discarded actions are reported in between
square brackets.

Note that all the previous states had a single possible action: either
shifting the next token and going to the corresponding state, or
reducing a single rule.  In the other cases, i.e., when shifting
@emph{and} reducing is possible or when @emph{several} reductions are
possible, the lookahead is required to select the action.  State 8 is
one such state: if the lookahead is @samp{*} or @samp{/} then the action
is shifting, otherwise the action is reducing rule 1.  In other words,
the first two items, corresponding to rule 1, are not eligible when the
lookahead is @samp{*}, since we specified that @samp{*} has higher
precedence that @samp{+}.  More generally, some items are eligible only
with some set of possible lookaheads.  When run with
@option{--report=lookahead}, Bison specifies these lookaheads:

@example
state 8

    exp  ->  exp . '+' exp  [$, '+', '-', '/']   (rule 1)
    exp  ->  exp '+' exp .  [$, '+', '-', '/']   (rule 1)
    exp  ->  exp . '-' exp   (rule 2)
    exp  ->  exp . '*' exp   (rule 3)
    exp  ->  exp . '/' exp   (rule 4)

    '*'         shift, and go to state 6
    '/'         shift, and go to state 7

    '/'         [reduce using rule 1 (exp)]
    $default    reduce using rule 1 (exp)
@end example

The remaining states are similar:

@example
state 9

    exp  ->  exp . '+' exp   (rule 1)
    exp  ->  exp . '-' exp   (rule 2)
    exp  ->  exp '-' exp .   (rule 2)
    exp  ->  exp . '*' exp   (rule 3)
    exp  ->  exp . '/' exp   (rule 4)

    '*' 	shift, and go to state 6
    '/' 	shift, and go to state 7

    '/' 	[reduce using rule 2 (exp)]
    $default	reduce using rule 2 (exp)

state 10

    exp  ->  exp . '+' exp   (rule 1)
    exp  ->  exp . '-' exp   (rule 2)
    exp  ->  exp . '*' exp   (rule 3)
    exp  ->  exp '*' exp .   (rule 3)
    exp  ->  exp . '/' exp   (rule 4)

    '/' 	shift, and go to state 7

    '/' 	[reduce using rule 3 (exp)]
    $default	reduce using rule 3 (exp)

state 11

    exp  ->  exp . '+' exp   (rule 1)
    exp  ->  exp . '-' exp   (rule 2)
    exp  ->  exp . '*' exp   (rule 3)
    exp  ->  exp . '/' exp   (rule 4)
    exp  ->  exp '/' exp .   (rule 4)

    '+' 	shift, and go to state 4
    '-' 	shift, and go to state 5
    '*' 	shift, and go to state 6
    '/' 	shift, and go to state 7

    '+' 	[reduce using rule 4 (exp)]
    '-' 	[reduce using rule 4 (exp)]
    '*' 	[reduce using rule 4 (exp)]
    '/' 	[reduce using rule 4 (exp)]
    $default	reduce using rule 4 (exp)
@end example

@noindent
Observe that state 11 contains conflicts due to the lack of precedence
of @samp{/} wrt @samp{+}, @samp{-}, and @samp{*}, but also because the
associativity of @samp{/} is not specified.


@node Tracing
@section Tracing Your Parser
@findex yydebug
@cindex debugging
@cindex tracing the parser

If a Bison grammar compiles properly but doesn't do what you want when it
runs, the @code{yydebug} parser-trace feature can help you figure out why.

There are several means to enable compilation of trace facilities:

@table @asis
@item the macro @code{YYDEBUG}
@findex YYDEBUG
Define the macro @code{YYDEBUG} to a nonzero value when you compile the
parser.  This is compliant with POSIX Yacc.  You could use
@samp{-DYYDEBUG=1} as a compiler option or you could put @samp{#define
YYDEBUG 1} in the prologue of the grammar file (@pxref{Prologue, , The
Prologue}).

@item the option @option{-t}, @option{--debug}
Use the @samp{-t} option when you run Bison (@pxref{Invocation,
,Invoking Bison}).  This is POSIX compliant too.

@item the directive @samp{%debug}
@findex %debug
Add the @code{%debug} directive (@pxref{Decl Summary, ,Bison
Declaration Summary}).  This is a Bison extension, which will prove
useful when Bison will output parsers for languages that don't use a
preprocessor.  Useless POSIX and Yacc portability matter to you, this is
the preferred solution.
@end table

We suggest that you always enable the debug option so that debugging is
always possible.

The trace facility outputs messages with macro calls of the form
@code{YYFPRINTF (stderr, @var{format}, @var{args})} where
@var{format} and @var{args} are the usual @code{printf} format and
arguments.  If you define @code{YYDEBUG} to a nonzero value but do not
define @code{YYFPRINTF}, @code{<stdio.h>} is automatically included
and @code{YYPRINTF} is defined to @code{fprintf}.

Once you have compiled the program with trace facilities, the way to
request a trace is to store a nonzero value in the variable @code{yydebug}.
You can do this by making the C code do it (in @code{main}, perhaps), or
you can alter the value with a C debugger.

Each step taken by the parser when @code{yydebug} is nonzero produces a
line or two of trace information, written on @code{stderr}.  The trace
messages tell you these things:

@itemize @bullet
@item
Each time the parser calls @code{yylex}, what kind of token was read.

@item
Each time a token is shifted, the depth and complete contents of the
state stack (@pxref{Parser States}).

@item
Each time a rule is reduced, which rule it is, and the complete contents
of the state stack afterward.
@end itemize

To make sense of this information, it helps to refer to the listing file
produced by the Bison @samp{-v} option (@pxref{Invocation, ,Invoking
Bison}).  This file shows the meaning of each state in terms of
positions in various rules, and also what each state will do with each
possible input token.  As you read the successive trace messages, you
can see that the parser is functioning according to its specification in
the listing file.  Eventually you will arrive at the place where
something undesirable happens, and you will see which parts of the
grammar are to blame.

The parser file is a C program and you can use C debuggers on it, but it's
not easy to interpret what it is doing.  The parser function is a
finite-state machine interpreter, and aside from the actions it executes
the same code over and over.  Only the values of variables show where in
the grammar it is working.

@findex YYPRINT
The debugging information normally gives the token type of each token
read, but not its semantic value.  You can optionally define a macro
named @code{YYPRINT} to provide a way to print the value.  If you define
@code{YYPRINT}, it should take three arguments.  The parser will pass a
standard I/O stream, the numeric code for the token type, and the token
value (from @code{yylval}).

Here is an example of @code{YYPRINT} suitable for the multi-function
calculator (@pxref{Mfcalc Decl, ,Declarations for @code{mfcalc}}):

@smallexample
#define YYPRINT(file, type, value)   yyprint (file, type, value)

static void
yyprint (FILE *file, int type, YYSTYPE value)
@{
  if (type == VAR)
    fprintf (file, " %s", value.tptr->name);
  else if (type == NUM)
    fprintf (file, " %d", value.val);
@}
@end smallexample

@c ================================================= Invoking Bison

@node Invocation
@chapter Invoking Bison
@cindex invoking Bison
@cindex Bison invocation
@cindex options for invoking Bison

The usual way to invoke Bison is as follows:

@example
bison @var{infile}
@end example

Here @var{infile} is the grammar file name, which usually ends in
@samp{.y}.  The parser file's name is made by replacing the @samp{.y}
with @samp{.tab.c}.  Thus, the @samp{bison foo.y} filename yields
@file{foo.tab.c}, and the @samp{bison hack/foo.y} filename yields
@file{hack/foo.tab.c}. It's is also possible, in case you are writing
C++ code instead of C in your grammar file, to name it @file{foo.ypp}
or @file{foo.y++}. Then, the output files will take an extention like
the given one as input (repectively @file{foo.tab.cpp} and @file{foo.tab.c++}).
This feature takes effect with all options that manipulate filenames like
@samp{-o} or @samp{-d}.

For example :

@example
bison -d @var{infile.yxx}
@end example
@noindent
will produce @file{infile.tab.cxx} and @file{infile.tab.hxx}. and

@example
bison -d @var{infile.y} -o @var{output.c++}
@end example
@noindent
will produce @file{output.c++} and @file{outfile.h++}.


@menu
* 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.
@end menu

@node Bison Options
@section Bison Options

Bison supports both traditional single-letter options and mnemonic long
option names.  Long option names are indicated with @samp{--} instead of
@samp{-}.  Abbreviations for option names are allowed as long as they
are unique.  When a long option takes an argument, like
@samp{--file-prefix}, connect the option name and the argument with
@samp{=}.

Here is a list of options that can be used with Bison, alphabetized by
short option.  It is followed by a cross key alphabetized by long
option.

@c Please, keep this ordered as in `bison --help'.
@noindent
Operations modes:
@table @option
@item -h
@itemx --help
Print a summary of the command-line options to Bison and exit.

@item -V
@itemx --version
Print the version number of Bison and exit.

@need 1750
@item -y
@itemx --yacc
Equivalent to @samp{-o y.tab.c}; the parser output file is called
@file{y.tab.c}, and the other outputs are called @file{y.output} and
@file{y.tab.h}.  The purpose of this option is to imitate Yacc's output
file name conventions.  Thus, the following shell script can substitute
for Yacc:

@example
bison -y $*
@end example
@end table

@noindent
Tuning the parser:

@table @option
@item -S @var{file}
@itemx --skeleton=@var{file}
Specify the skeleton to use.  You probably don't need this option unless
you are developing Bison.

@item -t
@itemx --debug
In the parser file, define the macro @code{YYDEBUG} to 1 if it is not
already defined, so that the debugging facilities are compiled.
@xref{Tracing, ,Tracing Your Parser}.

@item --locations
Pretend that @code{%locations} was specified.  @xref{Decl Summary}.

@item -p @var{prefix}
@itemx --name-prefix=@var{prefix}
Pretend that @code{%name-prefix="@var{prefix}"} was specified.
@xref{Decl Summary}.

@item -l
@itemx --no-lines
Don't put any @code{#line} preprocessor commands in the parser file.
Ordinarily Bison puts them in the parser file so that the C compiler
and debuggers will associate errors with your source file, the
grammar file.  This option causes them to associate errors with the
parser file, treating it as an independent source file in its own right.

@item -n
@itemx --no-parser
Pretend that @code{%no-parser} was specified.  @xref{Decl Summary}.

@item -k
@itemx --token-table
Pretend that @code{%token-table} was specified.  @xref{Decl Summary}.
@end table

@noindent
Adjust the output:

@table @option
@item -d
@itemx --defines
Pretend that @code{%defines} was specified, i.e., write an extra output
file containing macro definitions for the token type names defined in
the grammar and the semantic value type @code{YYSTYPE}, as well as a few
@code{extern} variable declarations.  @xref{Decl Summary}.

@item --defines=@var{defines-file}
Same as above, but save in the file @var{defines-file}.

@item -b @var{file-prefix}
@itemx --file-prefix=@var{prefix}
Pretend that @code{%verbose} was specified, i.e, specify prefix to use
for all Bison output file names. @xref{Decl Summary}.

@item -r @var{things}
@itemx --report=@var{things}
Write an extra output file containing verbose description of the comma
separated list of @var{things} among:

@table @code
@item state
Description of the grammar, conflicts (resolved and unresolved), and
LALR automaton.

@item lookahead
Implies @code{state} and augments the description of the automaton with
each rule's lookahead set.

@item itemset
Implies @code{state} and augments the description of the automaton with
the full set of items for each state, instead of its core only.
@end table

For instance, on the following grammar

@item -v
@itemx --verbose
Pretend that @code{%verbose} was specified, i.e, write an extra output
file containing verbose descriptions of the grammar and
parser. @xref{Decl Summary}.

@item -o @var{filename}
@itemx --output=@var{filename}
Specify the @var{filename} for the parser file.

The other output files' names are constructed from @var{filename} as
described under the @samp{-v} and @samp{-d} options.

@item -g
Output a VCG definition of the LALR(1) grammar automaton computed by
Bison. If the grammar file is @file{foo.y}, the VCG output file will
be @file{foo.vcg}.

@item --graph=@var{graph-file}
The behaviour of @var{--graph} is the same than @samp{-g}. The only
difference is that it has an optionnal argument which is the name of
the output graph filename.
@end table

@node Option Cross Key
@section Option Cross Key

Here is a list of options, alphabetized by long option, to help you find
the corresponding short option.

@tex
\def\leaderfill{\leaders\hbox to 1em{\hss.\hss}\hfill}

{\tt
\line{ --debug \leaderfill -t}
\line{ --defines \leaderfill -d}
\line{ --file-prefix \leaderfill -b}
\line{ --graph \leaderfill -g}
\line{ --help \leaderfill -h}
\line{ --name-prefix \leaderfill -p}
\line{ --no-lines \leaderfill -l}
\line{ --no-parser \leaderfill -n}
\line{ --output \leaderfill -o}
\line{ --token-table \leaderfill -k}
\line{ --verbose \leaderfill -v}
\line{ --version \leaderfill -V}
\line{ --yacc \leaderfill -y}
}
@end tex

@ifinfo
@example
--debug                               -t
--defines=@var{defines-file}          -d
--file-prefix=@var{prefix}                  -b @var{file-prefix}
--graph=@var{graph-file}              -d
--help                                -h
--name-prefix=@var{prefix}                  -p @var{name-prefix}
--no-lines                            -l
--no-parser                           -n
--output=@var{outfile}                      -o @var{outfile}
--token-table                         -k
--verbose                             -v
--version                             -V
--yacc                                -y
@end example
@end ifinfo

@node VMS Invocation
@section Invoking Bison under VMS
@cindex invoking Bison under VMS
@cindex VMS

The command line syntax for Bison on VMS is a variant of the usual
Bison command syntax---adapted to fit VMS conventions.

To find the VMS equivalent for any Bison option, start with the long
option, and substitute a @samp{/} for the leading @samp{--}, and
substitute a @samp{_} for each @samp{-} in the name of the long option.
For example, the following invocation under VMS:

@example
bison /debug/name_prefix=bar foo.y
@end example

@noindent
is equivalent to the following command under POSIX.

@example
bison --debug --name-prefix=bar foo.y
@end example

The VMS file system does not permit filenames such as
@file{foo.tab.c}.  In the above example, the output file
would instead be named @file{foo_tab.c}.

@node Table of Symbols
@appendix Bison Symbols
@cindex Bison symbols, table of
@cindex symbols in Bison, table of

@table @code
@item @@$
In an action, the location of the left-hand side of the rule.
  @xref{Locations, , Locations Overview}.

@item @@@var{n}
In an action, the location of the @var{n}-th symbol of the right-hand
side of the rule.  @xref{Locations, , Locations Overview}.

@item $$
In an action, the semantic value of the left-hand side of the rule.
@xref{Actions}.

@item $@var{n}
In an action, the semantic value of the @var{n}-th symbol of the
right-hand side of the rule.  @xref{Actions}.

@item error
A token name reserved for error recovery.  This token may be used in
grammar rules so as to allow the Bison parser to recognize an error in
the grammar without halting the process.  In effect, a sentence
containing an error may be recognized as valid.  On a parse error, the
token @code{error} becomes the current look-ahead token.  Actions
corresponding to @code{error} are then executed, and the look-ahead
token is reset to the token that originally caused the violation.
@xref{Error Recovery}.

@item YYABORT
Macro to pretend that an unrecoverable syntax error has occurred, by
making @code{yyparse} return 1 immediately.  The error reporting
function @code{yyerror} is not called.  @xref{Parser Function, ,The
Parser Function @code{yyparse}}.

@item YYACCEPT
Macro to pretend that a complete utterance of the language has been
read, by making @code{yyparse} return 0 immediately.
@xref{Parser Function, ,The Parser Function @code{yyparse}}.

@item YYBACKUP
Macro to discard a value from the parser stack and fake a look-ahead
token.  @xref{Action Features, ,Special Features for Use in Actions}.

@item YYDEBUG
Macro to define to equip the parser with tracing code. @xref{Tracing,
,Tracing Your Parser}.

@item YYERROR
Macro to pretend that a syntax error has just been detected: call
@code{yyerror} and then perform normal error recovery if possible
(@pxref{Error Recovery}), or (if recovery is impossible) make
@code{yyparse} return 1.  @xref{Error Recovery}.

@item YYERROR_VERBOSE
Macro that you define with @code{#define} in the Bison declarations
section to request verbose, specific error message strings when
@code{yyerror} is called.

@item YYINITDEPTH
Macro for specifying the initial size of the parser stack.
@xref{Stack Overflow}.

@item YYLEX_PARAM
Macro for specifying an extra argument (or list of extra arguments) for
@code{yyparse} to pass to @code{yylex}.  @xref{Pure Calling,, Calling
Conventions for Pure Parsers}.

@item YYLTYPE
Macro for the data type of @code{yylloc}; a structure with four
members.  @xref{Location Type, , Data Types of Locations}.

@item yyltype
Default value for YYLTYPE.

@item YYMAXDEPTH
Macro for specifying the maximum size of the parser stack.
@xref{Stack Overflow}.

@item YYPARSE_PARAM
Macro for specifying the name of a parameter that @code{yyparse} should
accept.  @xref{Pure Calling,, Calling Conventions for Pure Parsers}.

@item YYRECOVERING
Macro whose value indicates whether the parser is recovering from a
syntax error.  @xref{Action Features, ,Special Features for Use in Actions}.

@item YYSTACK_USE_ALLOCA
Macro used to control the use of @code{alloca}. If defined to @samp{0},
the parser will not use @code{alloca} but @code{malloc} when trying to
grow its internal stacks. Do @emph{not} define @code{YYSTACK_USE_ALLOCA}
to anything else.

@item YYSTYPE
Macro for the data type of semantic values; @code{int} by default.
@xref{Value Type, ,Data Types of Semantic Values}.

@item yychar
External integer variable that contains the integer value of the current
look-ahead token.  (In a pure parser, it is a local variable within
@code{yyparse}.)  Error-recovery rule actions may examine this variable.
@xref{Action Features, ,Special Features for Use in Actions}.

@item yyclearin
Macro used in error-recovery rule actions.  It clears the previous
look-ahead token.  @xref{Error Recovery}.

@item yydebug
External integer variable set to zero by default.  If @code{yydebug}
is given a nonzero value, the parser will output information on input
symbols and parser action.  @xref{Tracing, ,Tracing Your Parser}.

@item yyerrok
Macro to cause parser to recover immediately to its normal mode
after a parse error.  @xref{Error Recovery}.

@item yyerror
User-supplied function to be called by @code{yyparse} on error.  The
function receives one argument, a pointer to a character string
containing an error message.  @xref{Error Reporting, ,The Error
Reporting Function @code{yyerror}}.

@item yylex
User-supplied lexical analyzer function, called with no arguments to get
the next token.  @xref{Lexical, ,The Lexical Analyzer Function
@code{yylex}}.

@item yylval
External variable in which @code{yylex} should place the semantic
value associated with a token.  (In a pure parser, it is a local
variable within @code{yyparse}, and its address is passed to
@code{yylex}.)  @xref{Token Values, ,Semantic Values of Tokens}.

@item yylloc
External variable in which @code{yylex} should place the line and column
numbers associated with a token.  (In a pure parser, it is a local
variable within @code{yyparse}, and its address is passed to
@code{yylex}.)  You can ignore this variable if you don't use the
@samp{@@} feature in the grammar actions.  @xref{Token Positions,
,Textual Positions of Tokens}.

@item yynerrs
Global variable which Bison increments each time there is a parse error.
(In a pure parser, it is a local variable within @code{yyparse}.)
@xref{Error Reporting, ,The Error Reporting Function @code{yyerror}}.

@item yyparse
The parser function produced by Bison; call this function to start
parsing.  @xref{Parser Function, ,The Parser Function @code{yyparse}}.

@item %debug
Equip the parser for debugging.  @xref{Decl Summary}.

@item %defines
Bison declaration to create a header file meant for the scanner.
@xref{Decl Summary}.

@item %dprec
Bison declaration to assign a precedence to a rule that is used at parse
time to resolve reduce/reduce conflicts.  @xref{GLR Parsers}.

@item %file-prefix="@var{prefix}"
Bison declaration to set the prefix of the output files. @xref{Decl
Summary}.

@item %glr-parser
Bison declaration to produce a GLR parser.  @xref{GLR Parsers}.

@c @item %source-extension
@c Bison declaration to specify the generated parser output file extension.
@c @xref{Decl Summary}.
@c
@c @item %header-extension
@c Bison declaration to specify the generated parser header file extension
@c if required. @xref{Decl Summary}.

@item %left
Bison declaration to assign left associativity to token(s).
@xref{Precedence Decl, ,Operator Precedence}.

@item %merge
Bison declaration to assign a merging function to a rule.  If there is a
reduce/reduce conflict with a rule having the same merging function, the
function is applied to the two semantic values to get a single result.
@xref{GLR Parsers}.

@item %name-prefix="@var{prefix}"
Bison declaration to rename the external symbols. @xref{Decl Summary}.

@item %no-lines
Bison declaration to avoid generating @code{#line} directives in the
parser file.  @xref{Decl Summary}.

@item %nonassoc
Bison declaration to assign non-associativity to token(s).
@xref{Precedence Decl, ,Operator Precedence}.

@item %output="@var{filename}"
Bison declaration to set the name of the parser file. @xref{Decl
Summary}.

@item %prec
Bison declaration to assign a precedence to a specific rule.
@xref{Contextual Precedence, ,Context-Dependent Precedence}.

@item %pure-parser
Bison declaration to request a pure (reentrant) parser.
@xref{Pure Decl, ,A Pure (Reentrant) Parser}.

@item %right
Bison declaration to assign right associativity to token(s).
@xref{Precedence Decl, ,Operator Precedence}.

@item %start
Bison declaration to specify the start symbol.  @xref{Start Decl, ,The
Start-Symbol}.

@item %token
Bison declaration to declare token(s) without specifying precedence.
@xref{Token Decl, ,Token Type Names}.

@item %token-table
Bison declaration to include a token name table in the parser file.
@xref{Decl Summary}.

@item %type
Bison declaration to declare nonterminals.  @xref{Type Decl,
,Nonterminal Symbols}.

@item %union
Bison declaration to specify several possible data types for semantic
values.  @xref{Union Decl, ,The Collection of Value Types}.
@end table

@sp 1

These are the punctuation and delimiters used in Bison input:

@table @samp
@item %%
Delimiter used to separate the grammar rule section from the
Bison declarations section or the epilogue.
@xref{Grammar Layout, ,The Overall Layout of a Bison Grammar}.

@item %@{ %@}
All code listed between @samp{%@{} and @samp{%@}} is copied directly to
the output file uninterpreted.  Such code forms the prologue of the input
file.  @xref{Grammar Outline, ,Outline of a Bison
Grammar}.

@item /*@dots{}*/
Comment delimiters, as in C.

@item :
Separates a rule's result from its components.  @xref{Rules, ,Syntax of
Grammar Rules}.

@item ;
Terminates a rule.  @xref{Rules, ,Syntax of Grammar Rules}.

@item |
Separates alternate rules for the same result nonterminal.
@xref{Rules, ,Syntax of Grammar Rules}.
@end table

@node Glossary
@appendix Glossary
@cindex glossary

@table @asis
@item Backus-Naur Form (BNF)
Formal method of specifying context-free grammars.  BNF was first used
in the @cite{ALGOL-60} report, 1963.  @xref{Language and Grammar,
,Languages and Context-Free Grammars}.

@item Context-free grammars
Grammars specified as rules that can be applied regardless of context.
Thus, if there is a rule which says that an integer can be used as an
expression, integers are allowed @emph{anywhere} an expression is
permitted.  @xref{Language and Grammar, ,Languages and Context-Free
Grammars}.

@item Dynamic allocation
Allocation of memory that occurs during execution, rather than at
compile time or on entry to a function.

@item Empty string
Analogous to the empty set in set theory, the empty string is a
character string of length zero.

@item Finite-state stack machine
A ``machine'' that has discrete states in which it is said to exist at
each instant in time.  As input to the machine is processed, the
machine moves from state to state as specified by the logic of the
machine.  In the case of the parser, the input is the language being
parsed, and the states correspond to various stages in the grammar
rules.  @xref{Algorithm, ,The Bison Parser Algorithm }.

@item Generalized LR (GLR)
A parsing algorithm that can handle all context-free grammars, including those
that are not LALR(1).  It resolves situations that Bison's usual LALR(1)
algorithm cannot by effectively splitting off multiple parsers, trying all
possible parsers, and discarding those that fail in the light of additional
right context.  @xref{Generalized LR Parsing, ,Generalized LR Parsing}.

@item Grouping
A language construct that is (in general) grammatically divisible;
for example, `expression' or `declaration' in C.
@xref{Language and Grammar, ,Languages and Context-Free Grammars}.

@item Infix operator
An arithmetic operator that is placed between the operands on which it
performs some operation.

@item Input stream
A continuous flow of data between devices or programs.

@item Language construct
One of the typical usage schemas of the language.  For example, one of
the constructs of the C language is the @code{if} statement.
@xref{Language and Grammar, ,Languages and Context-Free Grammars}.

@item Left associativity
Operators having left associativity are analyzed from left to right:
@samp{a+b+c} first computes @samp{a+b} and then combines with
@samp{c}.  @xref{Precedence, ,Operator Precedence}.

@item Left recursion
A rule whose result symbol is also its first component symbol; for
example, @samp{expseq1 : expseq1 ',' exp;}.  @xref{Recursion, ,Recursive
Rules}.

@item Left-to-right parsing
Parsing a sentence of a language by analyzing it token by token from
left to right.  @xref{Algorithm, ,The Bison Parser Algorithm }.

@item Lexical analyzer (scanner)
A function that reads an input stream and returns tokens one by one.
@xref{Lexical, ,The Lexical Analyzer Function @code{yylex}}.

@item Lexical tie-in
A flag, set by actions in the grammar rules, which alters the way
tokens are parsed.  @xref{Lexical Tie-ins}.

@item Literal string token
A token which consists of two or more fixed characters.  @xref{Symbols}.

@item Look-ahead token
A token already read but not yet shifted.  @xref{Look-Ahead, ,Look-Ahead
Tokens}.

@item LALR(1)
The class of context-free grammars that Bison (like most other parser
generators) can handle; a subset of LR(1).  @xref{Mystery Conflicts, ,
Mysterious Reduce/Reduce Conflicts}.

@item LR(1)
The class of context-free grammars in which at most one token of
look-ahead is needed to disambiguate the parsing of any piece of input.

@item Nonterminal symbol
A grammar symbol standing for a grammatical construct that can
be expressed through rules in terms of smaller constructs; in other
words, a construct that is not a token.  @xref{Symbols}.

@item Parse error
An error encountered during parsing of an input stream due to invalid
syntax.  @xref{Error Recovery}.

@item Parser
A function that recognizes valid sentences of a language by analyzing
the syntax structure of a set of tokens passed to it from a lexical
analyzer.

@item Postfix operator
An arithmetic operator that is placed after the operands upon which it
performs some operation.

@item Reduction
Replacing a string of nonterminals and/or terminals with a single
nonterminal, according to a grammar rule.  @xref{Algorithm, ,The Bison
Parser Algorithm }.

@item Reentrant
A reentrant subprogram is a subprogram which can be in invoked any
number of times in parallel, without interference between the various
invocations.  @xref{Pure Decl, ,A Pure (Reentrant) Parser}.

@item Reverse polish notation
A language in which all operators are postfix operators.

@item Right recursion
A rule whose result symbol is also its last component symbol; for
example, @samp{expseq1: exp ',' expseq1;}.  @xref{Recursion, ,Recursive
Rules}.

@item Semantics
In computer languages, the semantics are specified by the actions
taken for each instance of the language, i.e., the meaning of
each statement.  @xref{Semantics, ,Defining Language Semantics}.

@item Shift
A parser is said to shift when it makes the choice of analyzing
further input from the stream rather than reducing immediately some
already-recognized rule.  @xref{Algorithm, ,The Bison Parser Algorithm }.

@item Single-character literal
A single character that is recognized and interpreted as is.
@xref{Grammar in Bison, ,From Formal Rules to Bison Input}.

@item Start symbol
The nonterminal symbol that stands for a complete valid utterance in
the language being parsed.  The start symbol is usually listed as the
first nonterminal symbol in a language specification.
@xref{Start Decl, ,The Start-Symbol}.

@item Symbol table
A data structure where symbol names and associated data are stored
during parsing to allow for recognition and use of existing
information in repeated uses of a symbol.  @xref{Multi-function Calc}.

@item Token
A basic, grammatically indivisible unit of a language.  The symbol
that describes a token in the grammar is a terminal symbol.
The input of the Bison parser is a stream of tokens which comes from
the lexical analyzer.  @xref{Symbols}.

@item Terminal symbol
A grammar symbol that has no rules in the grammar and therefore is
grammatically indivisible.  The piece of text it represents is a token.
@xref{Language and Grammar, ,Languages and Context-Free Grammars}.
@end table

@node Copying This Manual
@appendix Copying This Manual

@menu
* GNU Free Documentation License::  License for copying this manual.
@end menu

@include fdl.texi

@node Index
@unnumbered Index

@printindex cp

@bye