GCC does this match.pd. Here's the add_zero example, I think:

    /* Simplifications of operations with one constant operand and
       simplifications to constants or single values.  */
    
    (for op (plus pointer_plus minus bit_ior bit_xor)
      (simplify
        (op @0 integer_zerop)
        (non_lvalue @0)))

https://gcc.gnu.org/git/?p=gcc.git;a=blob;f=gcc/match.pd

The floating point case can be more complicated because of signed zeros and signaling NaNs, see fold_real_zero_addition_p.