+.\" @(#)ss6 4.1 (Berkeley) %G%
+.\"
+.SH
+6: Precedence
+.PP
+There is one common situation
+where the rules given above for resolving conflicts are not sufficient;
+this is in the parsing of arithmetic expressions.
+Most of the commonly used constructions for arithmetic expressions can be naturally
+described by the notion of
+.I precedence
+levels for operators, together with information about left
+or right associativity.
+It turns out that ambiguous grammars with appropriate disambiguating rules
+can be used to create parsers that are faster and easier to
+write than parsers constructed from unambiguous grammars.
+The basic notion is to write grammar rules
+of the form
+.DS
+expr : expr OP expr
+.DE
+and
+.DS
+expr : UNARY expr
+.DE
+for all binary and unary operators desired.
+This creates a very ambiguous grammar, with many parsing conflicts.
+As disambiguating rules, the user specifies the precedence, or binding
+strength, of all the operators, and the associativity
+of the binary operators.
+This information is sufficient to allow Yacc to resolve the parsing conflicts
+in accordance with these rules, and construct a parser that realizes the desired
+precedences and associativities.
+.PP
+The precedences and associativities are attached to tokens in the declarations section.
+This is done by a series of lines beginning with a Yacc keyword: %left, %right,
+or %nonassoc, followed by a list of tokens.
+All of the tokens on the same line are assumed to have the same precedence level
+and associativity; the lines are listed in
+order of increasing precedence or binding strength.
+Thus,
+.DS
+%left \'+\' \'\-\'
+%left \'*\' \'/\'
+.DE
+describes the precedence and associativity of the four arithmetic operators.
+Plus and minus are left associative, and have lower precedence than
+star and slash, which are also left associative.
+The keyword %right is used to describe right associative operators,
+and the keyword %nonassoc is used to describe operators, like
+the operator .LT. in Fortran, that may not associate with themselves; thus,
+.DS
+A .LT. B .LT. C
+.DE
+is illegal in Fortran, and such an operator would be described with the keyword
+%nonassoc in Yacc.
+As an example of the behavior of these declarations, the description
+.DS
+%right \'=\'
+%left \'+\' \'\-\'
+%left \'*\' \'/\'
+
+%%
+
+expr : expr \'=\' expr
+ | expr \'+\' expr
+ | expr \'\-\' expr
+ | expr \'*\' expr
+ | expr \'/\' expr
+ | NAME
+ ;
+.DE
+might be used to structure the input
+.DS
+a = b = c*d \- e \- f*g
+.DE
+as follows:
+.DS
+a = ( b = ( ((c*d)\-e) \- (f*g) ) )
+.DE
+When this mechanism is used,
+unary operators must, in general, be given a precedence.
+Sometimes a unary operator and a binary operator
+have the same symbolic representation, but different precedences.
+An example is unary and binary \'\-\'; unary minus may be given the same
+strength as multiplication, or even higher, while binary minus has a lower strength than
+multiplication.
+The keyword, %prec, changes the precedence level associated with a particular grammar rule.
+%prec appears immediately after the body of the grammar rule, before the action or closing semicolon,
+and is followed by a token name or literal.
+It
+causes the precedence of the grammar rule to become that of the following token name or literal.
+For example, to make unary minus have the same precedence as multiplication the rules might resemble:
+.DS
+%left \'+\' \'\-\'
+%left \'*\' \'/\'
+
+%%
+
+expr : expr \'+\' expr
+ | expr \'\-\' expr
+ | expr \'*\' expr
+ | expr \'/\' expr
+ | \'\-\' expr %prec \'*\'
+ | NAME
+ ;
+.DE
+.PP
+A token declared
+by %left, %right, and %nonassoc need not be, but may be, declared by %token as well.
+.PP
+The precedences and associativities are used by Yacc to
+resolve parsing conflicts; they give rise to disambiguating rules.
+Formally, the rules work as follows:
+.IP 1.
+The precedences and associativities are recorded for those tokens and literals
+that have them.
+.IP 2.
+A precedence and associativity is associated with each grammar rule; it is the precedence
+and associativity of the last token or literal in the body of the rule.
+If the %prec construction is used, it overrides this default.
+Some grammar rules may have no precedence and associativity associated with them.
+.IP 3.
+When there is a reduce/reduce conflict, or there is a shift/reduce conflict
+and either the input symbol or the grammar rule has no precedence and associativity,
+then the two disambiguating rules given at the beginning of the section are used,
+and the conflicts are reported.
+.IP 4.
+If there is a shift/reduce conflict, and both the grammar rule and the input character
+have precedence and associativity associated with them, then the conflict is resolved
+in favor of the action (shift or reduce) associated with the higher precedence.
+If the precedences are the same, then the associativity is used; left
+associative implies reduce, right associative implies shift, and nonassociating
+implies error.
+.PP
+Conflicts resolved by precedence are not counted in the number of shift/reduce and reduce/reduce
+conflicts reported by Yacc.
+This means that mistakes in the specification of precedences may
+disguise errors in the input grammar; it is a good idea to be sparing
+with precedences, and use them in an essentially ``cookbook'' fashion,
+until some experience has been gained.
+The
+.I y.output
+file
+is very useful in deciding whether the parser is actually doing
+what was intended.
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