Shift / reduce conflicts in grammar of arithmetic expression with n-ary sums / products

Question

Parsing binary sums / products are easy, but I'm having troubles defining a grammar that parses

a + b * c + d + e

as

sum(a, prod(b, c), d, e)

My initial (naive) attempt generated 61 shift / reduce conflicts.

I'm using java cup (but I suppose a solution for any other parser generator would be easily translated).

Answer 1

The following ANTLR grammar:

parse
  :  exp EOF
  ;

exp
  :  add_exp
  ;

add_exp
  :  mul_exp ('+' mul_exp)* 
  ;

mul_exp
  :  atom ('*' atom)* 
  ;

atom
  :  Number
  |  '(' exp ')'
  ;

Number
  :  'a'..'z'
  ;

parses the input a + b * c + d + e as:

As you can see, the mul_exp is the furthest away in the tree and (using an appropriate "walk" through your tree) will be evaluated first.

and the input a + b * (c + d) + e is parsed as:

The images were generated with ANTLRWorks.

EDIT:

A tool like ANTLRWorks makes debugging a grammar a breeze! For example, if I click on the atom rule in the grammar above, the following is automatically generated and displayed at the bottom of the screen:

Of course, that rule isn't complex at all, but when you do get to work with more complex rules, it's pretty darn easy to visualize them like that.

HTH.