@settitle Bison @value{VERSION}
@setchapternewpage odd
-@iftex
@finalout
-@end iftex
@c SMALL BOOK version
@c This edition has been formatted so that you can format and print it in
@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
@syncodeindex vr cp
This file documents the Bison parser generator.
Copyright (C) 1988, 1989, 1990, 1991, 1992, 1993, 1995, 1998, 1999,
-2000, 2001
+2000, 2001, 2002
Free Software Foundation, Inc.
Permission is granted to make and distribute verbatim copies of
@page
@vskip 0pt plus 1filll
Copyright @copyright{} 1988, 1989, 1990, 1991, 1992, 1993, 1995, 1998,
-1999, 2000, 2001
+1999, 2000, 2001, 2002
Free Software Foundation, Inc.
@sp 2
* Error Recovery:: Writing rules for error recovery.
* Context Dependency:: What to do if your language syntax is too
messy for Bison to handle straightforwardly.
-* Debugging:: Debugging Bison parsers that parse wrong.
+* 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.
* 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
* 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,
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?
context-free grammar. The input to Bison is essentially machine-readable
BNF.
-Not all context-free languages can be handled by Bison, only those
-that are LALR(1). In brief, this means that it must be possible to
+@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
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
@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}.@refill
+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
@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.@refill
+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
@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.@refill
+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
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
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. In the same situation,
-C++ parsers may include @code{<cstddef>} and @code{<cstdlib>} instead.
-Other system headers may be included if you define @code{YYDEBUG} to a
-nonzero value (@pxref{Debugging, ,Debugging Your Parser}).
+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
@example
%@{
-@var{Prologue (declarations)}
+@var{Prologue}
%@}
@var{Bison declarations}
%%
@var{Grammar rules}
%%
-@var{Epilogue (additional code)}
+@var{Epilogue}
@end example
@noindent
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 the ASCII code for that character; you can use the same
+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,
@example
@group
/* Lexical analyzer returns a double floating point
- number on the stack and the token NUM, or the ASCII
- character read if not a number. Skips all blanks
+ 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>
@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.@refill
+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
(@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}.@refill
+returned to @code{yyparse}.
No change is needed in the handling of numeric values and arithmetic
operators in @code{yylex}.
@cindex Prologue
@cindex declarations
-The @var{prologue} section contains macro definitions and
+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
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 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
+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.
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 ASCII code, zero, is the code @code{yylex}
+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}}).
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 ASCII code for
+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.
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.
+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
@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.
+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
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}.@refill
+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:
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,@refill
+in the rule. In this example,
@example
@group
@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.@refill
+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
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:
+By default, it is defined this way for simple LALR(1) parsers:
@example
@group
-#define YYLLOC_DEFAULT(Current, Rhs, N) \
- Current.last_line = Rhs[N].last_line; \
- Current.last_column = Rhs[N].last_column;
+#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
result) should be modified by @code{YYLLOC_DEFAULT}.
@item
-Before @code{YYLLOC_DEFAULT} is executed, the output parser sets @code{@@$}
-to @code{@@1}.
-
-@item
-For consistency with semantic actions, valid indexes for the location array
-range from 1 to @var{n}.
+For consistency with semantic actions, valid indexes for the location
+array range from 1 to @var{n}.
@end itemize
@node Declarations
@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 ASCII characters.
+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
@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{Debugging, ,Debugging Your Parser}.
+@xref{Tracing, ,Tracing Your Parser}.
@item %defines
Write an extra output file containing macro definitions for the token
@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}.@refill
+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}.@refill
+@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
@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.
+that state. @xref{Understanding, , Understanding Your Parser}, for more
+information.
-This file also describes all the conflicts, both those resolved by
-operator precedence and the unresolved ones.
-The file's name is made by removing @samp{.tab.c} or @samp{.c} from
-the parser output file name, and adding @samp{.output} instead.@refill
-
-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}.@refill
@item %yacc
Pretend the option @option{--yacc} was given, i.e., imitate Yacc,
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}.@refill
+that need it. @xref{Invocation, ,Invoking Bison}.
@menu
* Calling Convention:: How @code{yyparse} calls @code{yylex}.
@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}.@refill
+@xref{Action Types, ,Data Types of Values in Actions}.
@item YYABORT;
Return immediately from @code{yyparse}, indicating failure.
@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.
* 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
@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.@refill
+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.
;
@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
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
-@findex YYDEBUG
+
+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.
-To enable compilation of trace facilities, you must define the macro
-@code{YYDEBUG} to a nonzero value when you compile the parser. 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}). Alternatively, use the @samp{-t}
-option when you run Bison (@pxref{Invocation, ,Invoking Bison}) or the
-@code{%debug} declaration (@pxref{Decl Summary, ,Bison Declaration
-Summary}). We suggest that you always define @code{YYDEBUG} so that
-debugging is always possible.
+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 (YYSTDERR, @var{format}, @var{args})} where
+@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 the macros are defined to @code{fprintf} and @code{stderr}. In
-the same situation, C++ parsers include @code{<cstdio.h>} instead, and
-use @code{std::fprintf} and @code{std::stderr}.
+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}.
@}
@end smallexample
+@c ================================================= Invoking Bison
+
@node Invocation
@chapter Invoking Bison
@cindex invoking Bison
@menu
* Bison Options:: All the options described in detail,
in alphabetical order by short options.
-* Environment Variables:: Variables which affect Bison execution.
* Option Cross Key:: Alphabetical list of long options.
* VMS Invocation:: Bison command syntax on VMS.
@end menu
@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:@refill
+for Yacc:
@example
bison -y $*
@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{Debugging, ,Debugging Your Parser}.
+@xref{Tracing, ,Tracing Your Parser}.
@item --locations
Pretend that @code{%locations} was specified. @xref{Decl Summary}.
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
the output graph filename.
@end table
-@node Environment Variables
-@section Environment Variables
-@cindex environment variables
-@cindex BISON_HAIRY
-@cindex BISON_SIMPLE
-
-Here is a list of environment variables which affect the way Bison
-runs.
-
-@table @samp
-@item BISON_SIMPLE
-@itemx BISON_HAIRY
-Much of the parser generated by Bison is copied verbatim from a file
-called @file{bison.simple}. If Bison cannot find that file, or if you
-would like to direct Bison to use a different copy, setting the
-environment variable @code{BISON_SIMPLE} to the path of the file will
-cause Bison to use that copy instead.
-
-When the @samp{%semantic-parser} declaration is used, Bison copies from
-a file called @file{bison.hairy} instead. The location of this file can
-also be specified or overridden in a similar fashion, with the
-@code{BISON_HAIRY} environment variable.
-
-@end table
-
@node Option Cross Key
@section Option Cross Key
@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
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
@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{Debugging, ,Debugging Your Parser}.
+symbols and parser action. @xref{Tracing, ,Tracing Your Parser}.
@item yyerrok
Macro to cause parser to recover immediately to its normal mode
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 tge prefix of the output files. @xref{Decl
+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}.
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}.
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
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.
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