Operator Precedence
* Why Precedence:: An example showing why precedence is needed.
-* Using Precedence:: How to specify precedence in Bison grammars.
+* Using Precedence:: How to specify precedence and associativity.
+* Precedence Only:: How to specify precedence only.
* Precedence Examples:: How these features are used in the previous example.
* How Precedence:: How they work.
%token NUM
%left '-' '+'
%left '*' '/'
-%left NEG /* negation--unary minus */
-%right '^' /* exponentiation */
+%precedence NEG /* negation--unary minus */
+%right '^' /* exponentiation */
%% /* The grammar follows. */
input: /* empty */
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
+associativity/precedence. (These tokens are single-character literals, which
ordinarily don't need to be declared. We declare them here to specify
-the associativity.)
+the associativity/precedence.)
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
+by @samp{*} and @samp{/}, and so on. Unary minus is not associative,
+only precedence matters (@code{%precedence}. @xref{Precedence, ,Operator
Precedence}.
The other important new feature is the @code{%prec} in the grammar
%left '-' '+'
%left '*' '/'
-%left NEG
+%precedence NEG
%right '^'
%% /* The grammar follows. */
%right '='
%left '-' '+'
%left '*' '/'
-%left NEG /* negation--unary minus */
-%right '^' /* exponentiation */
+%precedence NEG /* negation--unary minus */
+%right '^' /* exponentiation */
@end group
%% /* The grammar follows. */
@end smallexample
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
+Alternatively, you can use @code{%left}, @code{%right},
+@code{%precedence}, or
@code{%nonassoc} instead of @code{%token}, if you wish to specify
associativity and precedence. @xref{Precedence Decl, ,Operator
Precedence}.
@cindex declaring operator precedence
@cindex operator precedence, declaring
-Use the @code{%left}, @code{%right} or @code{%nonassoc} declaration to
+Use the @code{%left}, @code{%right}, @code{%nonassoc}, or
+@code{%precedence} 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
means that @samp{@var{x} @var{op} @var{y} @var{op} @var{z}} is
considered a syntax error.
+@code{%precedence} gives only precedence to the @var{symbols}, and
+defines no associativity at all. Use this to define precedence only,
+and leave any potential conflict due to associativity enabled.
+
@item
The precedence of an operator determines how it nests with other operators.
All the tokens declared in a single precedence declaration have equal
@menu
* Why Precedence:: An example showing why precedence is needed.
-* Using Precedence:: How to specify precedence in Bison grammars.
+* Using Precedence:: How to specify precedence and associativity.
+* Precedence Only:: How to specify precedence only.
* Precedence Examples:: How these features are used in the previous example.
* How Precedence:: How they work.
@end menu
@node Using Precedence
@subsection Specifying Operator Precedence
@findex %left
-@findex %right
@findex %nonassoc
+@findex %precedence
+@findex %right
Bison allows you to specify these choices with the operator precedence
declarations @code{%left} and @code{%right}. Each such declaration
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 last alternative, @code{%precedence}, allows to define only
+precedence and no associativity at all. As a result, any
+associativity-related conflict that remains will be reported as an
+compile-time error. The directive @code{%nonassoc} creates run-time
+error: using the operator in a associative way is a syntax error. The
+directive @code{%precedence} creates compile-time errors: an operator
+@emph{can} be involved in an associativity-related conflict, contrary to
+what expected the grammar author.
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
+order in which they are declared. The first precedence/associativity
+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 Only
+@subsection Specifying Precedence Only
+@findex %precedence
+
+Since @acronym{POSIX} Yacc defines only @code{%left}, @code{%right}, and
+@code{%nonassoc}, which all defines precedence and associativity, little
+attention is paid to the fact that precedence cannot be defined without
+defining associativity. Yet, sometimes, when trying to solve a
+conflict, precedence suffices. In such a case, using @code{%left},
+@code{%right}, or @code{%nonassoc} might hide future (associativity
+related) conflicts that would remain hidden.
+
+The dangling @code{else} ambiguity (@pxref{Shift/Reduce, , Shift/Reduce
+Conflicts}) can be solved explictly. This shift/reduce conflicts occurs
+in the following situation, where the period denotes the current parsing
+state:
+
+@example
+if @var{e1} then if @var{e2} then @var{s1} . else @var{s2}
+@end example
+
+The conflict involves the reduction of the rule @samp{IF expr THEN
+stmt}, which precedence is by default that of its last token
+(@code{THEN}), and the shifting of the token @code{ELSE}. The usual
+disambiguation (attach the @code{else} to the closest @code{if}),
+shifting must be preferred, i.e., the precedence of @code{ELSE} must be
+higher than that of @code{THEN}. But neither is expected to be involved
+in an associativity related conflict, which can be specified as follows.
+
+@example
+%precedence THEN
+%precedence ELSE
+@end example
+
+The unary-minus is another typical example where associativity is
+usually over-specified, see @ref{Infix Calc, , Infix Notation
+Calculator: @code{calc}}. The @code{%left} directive is traditionaly
+used to declare the precedence of @code{NEG}, which is more than needed
+since it also defines its associativity. While this is harmless in the
+traditional example, who knows how @code{NEG} might be used in future
+evolutions of the grammar@dots{}
+
@node Precedence Examples
@subsection Precedence Examples
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
+The Bison precedence declarations
+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.
@end deffn
@deffn {Directive} %left
-Bison declaration to assign left associativity to token(s).
+Bison declaration to assign precedence and left associativity to token(s).
@xref{Precedence Decl, ,Operator Precedence}.
@end deffn
@end deffn
@deffn {Directive} %nonassoc
-Bison declaration to assign nonassociativity to token(s).
+Bison declaration to assign precedence and nonassociativity to token(s).
@xref{Precedence Decl, ,Operator Precedence}.
@end deffn
@xref{Contextual Precedence, ,Context-Dependent Precedence}.
@end deffn
+@deffn {Directive} %precedence
+Bison declaration to assign precedence to token(s), but no associativity
+@xref{Precedence Decl, ,Operator Precedence}.
+@end deffn
+
@deffn {Directive} %pure-parser
Deprecated version of @code{%define api.pure} (@pxref{Decl Summary, ,%define}),
for which Bison is more careful to warn about unreasonable usage.
@end deffn
@deffn {Directive} %right
-Bison declaration to assign right associativity to token(s).
+Bison declaration to assign precedence and right associativity to token(s).
@xref{Precedence Decl, ,Operator Precedence}.
@end deffn
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