def dpll(clauses, symbols, model):
"""See if the clauses are true in a partial model.
http://en.wikipedia.org/wiki/DPLL_algorithm
"""
unknown_clauses = [] ## clauses with an unknown truth value
for c in clauses:
val = pl_true(c, model)
if val == False:
return False
if val != True:
unknown_clauses.append(c)
if not unknown_clauses:
return model
P, value = find_pure_symbol(symbols, unknown_clauses)
if P:
model_1 = model.copy()
model_1.update({P: value})
syms = [x for x in symbols if x != P]
return dpll(clauses, syms, model_1)
P, value = find_unit_clause(unknown_clauses, model)
if P:
model_1 = model.copy()
model_1.update({P: value})
syms = [x for x in symbols if x != P]
return dpll(clauses, syms, model_1)
P = symbols.pop()
model_1, model_2 = model.copy(), model.copy()
model_1.update({P: True})
model_2.update({P: False})
return dpll(clauses, symbols, model_1) or dpll(clauses, symbols, model_2)
def test_find_pure_symbol():
A, B, C = symbols('ABC')
assert find_pure_symbol([A], [A]) == (A, True)
assert find_pure_symbol([A, B], [~A | B, ~B | A]) == (None, None)
assert find_pure_symbol([A, B, C], [ A | ~B, ~B | ~C, C | A]) == (A, True)
assert find_pure_symbol([A, B, C], [~A | B, B | ~C, C | A]) == (B, True)
assert find_pure_symbol([A, B, C], [~A | ~B, ~B | ~C, C | A]) == (B, False)
assert find_pure_symbol([A, B, C], [~A | B, ~B | ~C, C | A]) == (None, None)