Where are the shift/reduce conflicts in this Bison code coming from?

Question

I'm trying to parse this syntax:

34 + 1 − 8, 32 * 87 + 6 / 4, 34 / 8

I'm expecting to ground it like this:

(, (- (+ 34 1) 8) (/ (+ (* 32 87) 6) 4) (/ 34 8))

This is the code for BISON:

%token NUMBER
%token COMMA
%token OPERATOR
%left OPERATOR
%left COMMA
%%

term: NUMBER | term op term ;
op: OPERATOR | COMMA;
%%

There is a problem:

test.y: conflicts: 2 shift/reduce

How can I solve it?

Answer 1

The problem is with your definition of term:

term: NUMBER | term op term ;

When parsing this, at each number, the question is: should I read another token to know if I have the first, or the second form.

A solution could be to define:

term: NUMBER reminder;
reminder: /* empty */ | op term;

The grammar, once adapted, looks like the following:

%token NUMBER
%token COMMA
%token OPERATOR
%left OPERATOR
%left COMMA
%%

term: NUMBER reminder;
reminder: /* empty */ | op term;
op: OPERATOR | COMMA;
%%

compiles without warnings with bison (GNU Bison) 2.4.1.

Answer 2

To find where the conflicts are, use the --verbose option and look at the file example.output where your input file is example.y. Here is the file I got from your input:

State 7 conflicts: 2 shift/reduce

(omitted)

state 7

    2 term: term . op term
    2     | term op term .

    COMMA     shift, and go to state 4
    OPERATOR  shift, and go to state 5

    COMMA     [reduce using rule 2 (term)]
    OPERATOR  [reduce using rule 2 (term)]
    $default  reduce using rule 2 (term)

    op  go to state 6