Mathematical Expressions Generator

The following python code generates mathematical expressions using simple (slightly modified) generative grammar.

def gen(grammar, N, N_max, S):
 if N > N_max:
  return []
 result = []
 terminal = True
 for rule in grammar:
  for i in range(0, len(S)):
   ch = S[i]
   if ch == rule[0]:
    Snew = S[0:i] + rule[1] + S[(i + 1):len(S)]
    result = result + gen(grammar, N + 1, N_max, Snew)
    terminal = False
 if terminal:
  return [S]
 return list(set(result))

grammar = [
 ["S", "(S + S)"],
 ["S", "(S * S)"],
 ["S", "(S - S)"],
 ["S", "(-S)"],
 ["S", "x"],
 ["S", "y"],
 ["S", "z"],
 ["S", "0"],
 ["S", "1"],
 ["S", "2"],
 ["S", "3"],
]

for f in gen(grammar, 0, 4, "S"):
 print f

Output:

(y * (-0))
(3 + 1)
((-z) - 2)
((-y) * z)
(-(3 - x))
((-3) - z)
(3 * 1)
...
(-(2 * 2))