* 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
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
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
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
@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
@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
;
@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
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}.
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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