commutative operations in bison for parallel operation

The mfcalc in the bison manual shows a simple example for a calculator.


This decribes the associatvity of the operators as we have learned at
school year 3, so that we can slit up nested operations in single operations


%left '+' '-'
%left '*' '/'
%right NEG
%right '^'
...


This describes what to do with a single operation as we learned at
school year 1 (ok, except pow)


expr:
expr '+' expr {$<expr>$ = $<expr>1 + $<expr>3; }
| expr '-' expr {$$ = $1 - $3; }
| expr '*' expr {$$ = $1 * $3; }
| expr '/' expr {$$ = $1 / $3; }
| '-' expr %prec NEG {$$ = -$2; }
| expr '^' expr {$$ = pow($1,$3); }
| '(' expr ')' {$$ = $2;}




If I feed the parser with 1+2+3+4+5
the parser stack shows me (rpn-like)


1 2 + 3 + 4 + 5 +


so each operation waits for the completion of the previous operation.
We cannot parallelize this. I can remember from priamry scholl, that
addition is commutative. How can I tell the bison parser generator
about it, that he arranges the stack like this.


1 2 + 3 4 + +


I could calc


1 2 +


and


3 4 +


in parallel then. Actually I don't do the actions as described above,
I put the tokens and values on my own stck and than I calculate each
single triple. Do I really have to re-arrange the stack myself? The
way bison feeds the stack basing on the parser definition, is not
appropriate for parallel operation.
[Yes, you have to arrange the stack yourself. Bison doesn't have any
idea of the semantics of what it's parsing. -John]

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