def test_prenex_basic(self):
a,b,c = (Symbol(x) for x in "abc")
f = Not(And(a, Exists([b], And(a, b)), ForAll([c], Or(a, c))))
prenex = prenex_normal_form(f)
# Two prenex normal forms are possible
my_prenex_1 = Exists([c], ForAll([b], Not(And(a, And(a, b), Or(a, c)))))
my_prenex_2 = ForAll([b], Exists([c], Not(And(a, And(a, b), Or(a, c)))))
self.assertTrue(prenex == my_prenex_1 or prenex == my_prenex_2)
def test_prenex_examples(self):
for (f, _, _, logic) in get_example_formulae():
if get_env().factory.has_solvers(logic=logic):
prenex = prenex_normal_form(f)
try:
ok = is_valid(Iff(f, prenex), logic=logic)
except SolverReturnedUnknownResultError:
ok = not logic.quantifier_free
self.assertTrue(ok)
def test_prenex_examples(self):
for (f, _, _, logic) in get_example_formulae():
if get_env().factory.has_solvers(logic=logic):
prenex = prenex_normal_form(f)
try:
ok = is_valid(Iff(f, prenex), logic=logic)
except SolverReturnedUnknownResultError:
ok = not logic.quantifier_free
self.assertTrue(ok)
def test_prenex_basic(self):
a, b, c = (Symbol(x) for x in "abc")
f = Not(And(a, Exists([b], And(a, b)), ForAll([c], Or(a, c))))
prenex = prenex_normal_form(f)
# Two prenex normal forms are possible
my_prenex_1 = Exists([c], ForAll([b], Not(And(a, And(a, b), Or(a,
c)))))
my_prenex_2 = ForAll([b], Exists([c], Not(And(a, And(a, b), Or(a,
c)))))
self.assertTrue(prenex == my_prenex_1 or prenex == my_prenex_2)
def test_prenex_negated_forall(self):
a,b = (Symbol(x) for x in "ab")
f = Implies(ForAll([b], Implies(a, b)), b)
prenex = prenex_normal_form(f)
self.assertTrue(prenex.is_exists())
self.assertValid(Iff(f, prenex), logic=BOOL)
def test_prenex_simple_forall(self):
a,b = (Symbol(x) for x in "ab")
f = Or(b, ForAll([b], Implies(a, b)))
prenex = prenex_normal_form(f)
self.assertTrue(prenex.is_forall())
self.assertValid(Iff(f, prenex), logic=BOOL)
def test_prenex_simple_exists(self):
a,b = (Symbol(x) for x in "ab")
f = And(b, Exists([b], Implies(a, b)))
prenex = prenex_normal_form(f)
self.assertTrue(prenex.is_exists())
self.assertValid(Iff(f, prenex), logic=BOOL)
def test_prenex_negated_forall(self):
a, b = (Symbol(x) for x in "ab")
f = Implies(ForAll([b], Implies(a, b)), b)
prenex = prenex_normal_form(f)
self.assertTrue(prenex.is_exists())
self.assertValid(Iff(f, prenex), logic=BOOL)
def test_prenex_simple_forall(self):
a, b = (Symbol(x) for x in "ab")
f = Or(b, ForAll([b], Implies(a, b)))
prenex = prenex_normal_form(f)
self.assertTrue(prenex.is_forall())
self.assertValid(Iff(f, prenex), logic=BOOL)
def test_prenex_simple_exists(self):
a, b = (Symbol(x) for x in "ab")
f = And(b, Exists([b], Implies(a, b)))
prenex = prenex_normal_form(f)
self.assertTrue(prenex.is_exists())
self.assertValid(Iff(f, prenex), logic=BOOL)
