Question

Say I have a grammar like this:

expr : expr '+' expr   { $$ = operation('+', $1, $3); }
     | expr '-' expr   { $$ = operation('-', $1, $3); }
     | expr '*' expr   { $$ = operation('*', $1, $3); }
     | expr '/' expr   { $$ = operation('/', $1, $3); }
     | num
     ;

Where each of those operators has a precedence attached and is marked as left associative.

Then I want to refactor my grammar such that:

op   : '+' | '-' | '*' | '/' ;

expr : expr op expr { $$ = operation($2, $1, $3); }
     | num
     ;

How does yacc (if even at all) determine the associativity and precedence of op in this case? Will it trace its way through all the possible precedences/associativities of +, -, * and / when evaluating op, or does defining an associativity for nonterminal symbols make no sense?

AFAIK, with precedence order for nonterminals, it uses the precedence of the rightmost terminal symbol, but I can’t find any documentation on the associativity rules themselves for nonterminals.

Answer 1

The “normal” way to do this (as far as I’m aware) is to define a different expr type for each operator, that way you get very explicit control over what’s happening.

Python’s grammar is a good example of this: http://docs.python.org/reference/grammar.html.