def formulaDistributeDisjunctions(f):
"""
Convert a Skolemized formula in prefix-NNF form into Conjunctive
Normal Form.
"""
arg1 = None
arg2 = None
if f.isQuantified():
arg1 = f.child1
arg2 = formulaDistributeDisjunctions(f.child2)
f = Formula(f.op, arg1, arg2)
elif f.isLiteral():
pass
else:
if f.hasSubform1():
arg1 = formulaDistributeDisjunctions(f.child1)
if f.hasSubform2():
arg2 = formulaDistributeDisjunctions(f.child2)
f = Formula(f.op, arg1, arg2)
if f.op == "|":
if f.child1.op == "&":
# (P&Q)|R -> (P|R) & (Q|R)
arg1 = Formula("|", f.child1.child1, f.child2)
arg2 = Formula("|", f.child1.child2, f.child2)
f = Formula("&", arg1, arg2)
f = formulaDistributeDisjunctions(f)
elif f.child2.op == "&":
# (R|(P&Q) -> (R|P) & (R|Q)
arg1 = Formula("|", f.child1, f.child2.child1)
arg2 = Formula("|", f.child1, f.child2.child2)
f = Formula("&", arg1, arg2)
f = formulaDistributeDisjunctions(f)
return f
def formulaNNF(f, polarity):
"""
Convert f into a NNF. Equivalences (<=>) are eliminated
polarity-dependend, top to bottom. Returns (f', m), where f' is a
NNF of f, and m indicates if f!=f'
"""
normalform = False
modified = False
while not normalform:
normalform = True
f, m = rootFormulaNNF(f, polarity)
modified |= m
if f.op == "~":
handle, m = formulaNNF(f.child1, -polarity)
if m:
normalform = False
f = Formula("~", handle)
elif f.op in ["!", "?"]:
handle, m = formulaNNF(f.child2, polarity)
if m:
normalform = False
f = Formula(f.op, f.child1, handle)
elif f.op in ["|", "&"]:
handle1, m1 = formulaNNF(f.child1, polarity)
handle2, m2 = formulaNNF(f.child2, polarity)
m = m1 or m2
if m:
normalform = False
f = Formula(f.op, handle1, handle2)
else:
assert f.isLiteral()
modified |= m
return f, modified