class TestFormula(unittest.TestCase):
def setUp(self):
self.a1 = Formula("X")
self.a2 = Formula("Y")
self.l1 = Formula("!", Formula("X"))
self.fand1 = Formula("&", Formula("X"), Formula("Y"))
self.for1 = Formula("|", Formula("X"), Formula("Y"))
def test_init_atomic(self):
formula = Formula("X")
self.assertIsInstance(formula, Formula)
self.assertEqual(None, formula.connective)
self.assertEqual("X", formula.subformula1)
def test_init_atomic_wrong(self):
self.assertRaises(Exception, Formula, "!")
def test_init_unary(self):
formula = Formula("!", self.a1)
self.assertIsInstance(formula, Formula)
self.assertEqual("not", formula.connective)
self.assertEqual(self.a1, formula.subformula1)
def test_init_unary_wrong(self):
self.assertRaises(Exception, Formula, "&", Formula("X"))
self.assertRaises(Exception, Formula, "!", "X")
def test_init_binary(self):
formula = Formula("&", self.a1, self.a2)
self.assertIsInstance(formula, Formula)
self.assertEqual("and", formula.connective)
self.assertEqual(self.a1, formula.subformula1)
self.assertEqual(self.a2, formula.subformula2)
def test_init_binary_wrong(self):
self.assertRaises(Exception, Formula, "&", "X", "Y")
self.assertRaises(Exception, Formula, "?", Formula("X"), Formula("Y"))
self.assertRaises(Exception, Formula, "!", Formula("X"), Formula("Y"))
def test_str_atomic(self):
self.assertEqual("X", str(self.a1))
def test_str_unary(self):
self.assertEqual("!X", str(self.l1))
def test_str_binary(self):
self.assertEqual("(X & Y)", str(self.fand1))
def test_str_complex(self):
formula = Formula("&", self.for1, self.l1)
self.assertEqual("((X | Y) & !X)", str(formula))
def test_eq_ne_atomic(self):
formula1 = Formula("X")
formula2 = Formula("X")
formula3 = Formula("Y")
self.assertEqual(formula1, formula2)
self.assertNotEqual(formula1, formula3)
def test_eq_ne(self):
formula1 = Formula("&", Formula("X"), Formula("Y"))
formula2 = Formula("&", Formula("X"), Formula("Y"))
formula3 = Formula("|", Formula("X"), Formula("Y"))
formula4 = Formula("&", Formula("X"), Formula("X"))
self.assertEqual(formula1, formula2)
self.assertNotEqual(formula1, formula3)
self.assertNotEqual(formula1, formula4)
def test_is_alpha_none(self):
# atomic
self.assertIsNone(self.a1.is_alpha())
# literal
self.assertIsNone(self.l1.is_alpha())
# secondary connectives
s1 = Formula("<=>", self.a1, self.a2)
s2 = Formula("!=", self.a1, self.a2)
self.assertIsNone(s1.is_alpha())
self.assertIsNone(s2.is_alpha())
# not not
f1 = self.l1.negate().negate()
self.assertIsNone(f1.is_alpha())
f2 = self.fand1.negate().negate()
self.assertIsNone(f2.is_alpha())
f3 = self.for1.negate().negate()
self.assertIsNone(f3.is_alpha())
def test_is_alpha_primary(self):
self.assertTrue(self.fand1.is_alpha())
self.assertFalse(self.for1.is_alpha())
f1 = Formula("!", self.fand1)
self.assertFalse(f1.is_alpha())
f2 = Formula("!", self.for1)
self.assertTrue(f2.is_alpha())
def test_is_beta_none(self):
# atomic
self.assertIsNone(self.a1.is_beta())
# literal
self.assertIsNone(self.l1.is_beta())
# secondary connectives
s1 = Formula("<=>", self.a1, self.a2)
s2 = Formula("!=", self.a1, self.a2)
self.assertIsNone(s1.is_beta())
self.assertIsNone(s2.is_beta())
# not not
f1 = self.l1.negate().negate()
self.assertIsNone(f1.is_beta())
f2 = self.fand1.negate().negate()
self.assertIsNone(f2.is_beta())
f3 = self.for1.negate().negate()
self.assertIsNone(f3.is_beta())
def test_is_beta_primary(self):
self.assertFalse(self.fand1.is_beta())
self.assertTrue(self.for1.is_beta())
f1 = Formula("!", self.fand1)
self.assertTrue(f1.is_beta())
f2 = Formula("!", self.for1)
self.assertFalse(f2.is_beta())
def test_is_literal_atomic(self):
self.assertTrue(self.a1.is_literal())
def test_is_literal_unary(self):
self.assertTrue(self.l1.is_literal())
formula2 = Formula("!", self.fand1)
self.assertFalse(formula2.is_literal())
def test_is_literal_binary(self):
self.assertFalse(self.fand1.is_literal())
self.assertFalse(self.for1.is_literal())
def test_is_literal_top_bottom(self):
self.assertTrue(Formula("T").is_literal())
self.assertTrue(Formula("F").is_literal())
self.assertFalse(Formula("!", Formula("T")).is_literal())
self.assertFalse(Formula("!", Formula("F")).is_literal())
def test_negate(self):
self.assertIsInstance(self.fand1.negate(), Formula)
self.assertEqual(Formula("!", self.fand1), self.fand1.negate())
def test_complement(self):
# binary
self.assertIsInstance(self.fand1.complement(), Formula)
self.assertEqual(self.fand1.negate(), self.fand1.complement())
# literal
self.assertIsInstance(self.l1.complement(), Formula)
self.assertEqual(self.a1, self.l1.complement())
# atomic
self.assertIsInstance(self.a1.complement(), Formula)
self.assertEqual(self.l1, self.a1.complement())
def test_components_atomic(self):
(comp1, comp2) = self.a1.components()
self.assertIsNot(comp1, self.a1)
self.assertEqual(comp1, self.a1)
self.assertEqual(None, comp2)
def test_components_unary(self):
(comp1, comp2) = self.l1.components()
self.assertIsNot(comp1, self.l1)
self.assertEqual(comp1, self.l1)
self.assertEqual(None, comp2)
def test_components_binary(self):
formula = Formula("&", self.a1, self.a2)
(comp1, comp2) = formula.components()
self.assertIsNot(comp1, self.a1)
self.assertIsNot(comp2, self.a2)
self.assertEqual(comp1, self.a1)
self.assertEqual(comp2, self.a2)
def test_nnf_atomic(self):
self.assertIsNot(self.a1, self.a1.nnf())
self.assertEqual(self.a1, self.a1.nnf())
def test_nnf_unary_literal(self):
self.assertIsNot(self.l1, self.l1.nnf())
self.assertEqual(self.l1, self.l1.nnf())
def test_nnf_unary(self):
sub = Formula("&", self.a1, self.a2)
formula = Formula("!", sub)
exp = Formula("|",
Formula("!", Formula("X")),
Formula("!", Formula("Y")))
self.assertEqual(exp, formula.nnf())
self.assertIsNot(self.a1, formula.nnf().subformula1.subformula1)
self.assertIsNot(self.a2, formula.nnf().subformula2.subformula1)
def test_nnf_not_not(self):
formula = Formula("!", Formula("!", self.a1))
self.assertIsNot(self.a1, formula.nnf())
self.assertEqual(self.a1, formula.nnf())
def test_nnf_binary(self):
sub1 = Formula("!", Formula("!", self.a1))
sub2 = Formula("!", Formula("!", self.a2))
formula = Formula("&", sub1, sub2)
exp = Formula("&", self.a1, self.a2)
self.assertEqual(exp, formula.nnf())
self.assertIsNot(self.a1, formula.nnf().subformula1)
self.assertIsNot(self.a2, formula.nnf().subformula2)
def test_cnf_atomic(self):
exp = Generalization("and", [Generalization("or", [self.a1])])
self.assertEqual(exp, self.a1.cnf())
def test_cnf_literal(self):
exp = Generalization("and", [Generalization("or", [self.l1])])
self.assertEqual(exp, self.l1.cnf())
def test_cnf_alpha(self):
exp = Generalization("and", [
Generalization("or", [self.a1]),
Generalization("or", [self.a2])])
self.assertEqual(exp, self.fand1.cnf())
def test_cnf_beta(self):
exp = Generalization("and", [Generalization("or", [self.a1, self.a2])])
self.assertEqual(exp, self.for1.cnf())
def test_cnf_not_not(self):
exp = Generalization("and", [Generalization("or", [self.a1])])
self.assertEqual(exp, Formula("!", self.l1).cnf())
def test_cnf_not_top(self):
formula = Formula("!", Formula("T"))
exp = Generalization("and", [Generalization("or", [Formula("F")])])
self.assertEqual(exp, formula.cnf())
def test_cnf_not_bottom(self):
formula = Formula("!", Formula("F"))
exp = Generalization("and", [Generalization("or", [Formula("T")])])
self.assertEqual(exp, formula.cnf())
def test_cnf_particular(self):
# components
p = Formula("P")
np = Formula("!", p)
q = Formula("Q")
nq = Formula("!", q)
r = Formula("R")
# formulas
f1s = "-(P-> (Q-> R)) -> ((P->Q) -> (P -> R))"
f1 = parser.parse(f1s)
f2s = "-(P&Q) -> R"
f2 = parser.parse(f2s)
# expected
exp1 = Generalization("and", [
Generalization("or", [np, nq, r, p, np, r]),
Generalization("or", [np, nq, r, nq, np, r])])
exp2 = Generalization("and", [
Generalization("or", [p, r]),
Generalization("or", [q, r])])
# assertions
self.assertEqual(exp1, f1.cnf())
self.assertEqual(exp2, f2.cnf())
class TestFormula(unittest.TestCase):
def setUp(self):
self.a1 = Formula("X")
self.a2 = Formula("Y")
self.l1 = Formula("!", Formula("X"))
self.fand1 = Formula("&", Formula("X"), Formula("Y"))
self.for1 = Formula("|", Formula("X"), Formula("Y"))
def test_init_atomic(self):
formula = Formula("X")
self.assertIsInstance(formula, Formula)
self.assertEqual(None, formula.connective)
self.assertEqual("X", formula.subformula1)
def test_init_atomic_wrong(self):
self.assertRaises(Exception, Formula, "!")
def test_init_unary(self):
formula = Formula("!", self.a1)
self.assertIsInstance(formula, Formula)
self.assertEqual("not", formula.connective)
self.assertEqual(self.a1, formula.subformula1)
def test_init_unary_wrong(self):
self.assertRaises(Exception, Formula, "&", Formula("X"))
self.assertRaises(Exception, Formula, "!", "X")
def test_init_binary(self):
formula = Formula("&", self.a1, self.a2)
self.assertIsInstance(formula, Formula)
self.assertEqual("and", formula.connective)
self.assertEqual(self.a1, formula.subformula1)
self.assertEqual(self.a2, formula.subformula2)
def test_init_binary_wrong(self):
self.assertRaises(Exception, Formula, "&", "X", "Y")
self.assertRaises(Exception, Formula, "?", Formula("X"), Formula("Y"))
self.assertRaises(Exception, Formula, "!", Formula("X"), Formula("Y"))
def test_str_atomic(self):
self.assertEqual("X", str(self.a1))
def test_str_unary(self):
self.assertEqual("!X", str(self.l1))
def test_str_binary(self):
self.assertEqual("(X & Y)", str(self.fand1))
def test_str_complex(self):
formula = Formula("&", self.for1, self.l1)
self.assertEqual("((X | Y) & !X)", str(formula))
def test_eq_ne_atomic(self):
formula1 = Formula("X")
formula2 = Formula("X")
formula3 = Formula("Y")
self.assertEqual(formula1, formula2)
self.assertNotEqual(formula1, formula3)
def test_eq_ne(self):
formula1 = Formula("&", Formula("X"), Formula("Y"))
formula2 = Formula("&", Formula("X"), Formula("Y"))
formula3 = Formula("|", Formula("X"), Formula("Y"))
formula4 = Formula("&", Formula("X"), Formula("X"))
self.assertEqual(formula1, formula2)
self.assertNotEqual(formula1, formula3)
self.assertNotEqual(formula1, formula4)
def test_is_alpha_none(self):
# atomic
self.assertIsNone(self.a1.is_alpha())
# literal
self.assertIsNone(self.l1.is_alpha())
# secondary connectives
s1 = Formula("<=>", self.a1, self.a2)
s2 = Formula("!=", self.a1, self.a2)
self.assertIsNone(s1.is_alpha())
self.assertIsNone(s2.is_alpha())
# not not
f1 = self.l1.negate().negate()
self.assertIsNone(f1.is_alpha())
f2 = self.fand1.negate().negate()
self.assertIsNone(f2.is_alpha())
f3 = self.for1.negate().negate()
self.assertIsNone(f3.is_alpha())
def test_is_alpha_primary(self):
self.assertTrue(self.fand1.is_alpha())
self.assertFalse(self.for1.is_alpha())
f1 = Formula("!", self.fand1)
self.assertFalse(f1.is_alpha())
f2 = Formula("!", self.for1)
self.assertTrue(f2.is_alpha())
def test_is_beta_none(self):
# atomic
self.assertIsNone(self.a1.is_beta())
# literal
self.assertIsNone(self.l1.is_beta())
# secondary connectives
s1 = Formula("<=>", self.a1, self.a2)
s2 = Formula("!=", self.a1, self.a2)
self.assertIsNone(s1.is_beta())
self.assertIsNone(s2.is_beta())
# not not
f1 = self.l1.negate().negate()
self.assertIsNone(f1.is_beta())
f2 = self.fand1.negate().negate()
self.assertIsNone(f2.is_beta())
f3 = self.for1.negate().negate()
self.assertIsNone(f3.is_beta())
def test_is_beta_primary(self):
self.assertFalse(self.fand1.is_beta())
self.assertTrue(self.for1.is_beta())
f1 = Formula("!", self.fand1)
self.assertTrue(f1.is_beta())
f2 = Formula("!", self.for1)
self.assertFalse(f2.is_beta())
def test_is_literal_atomic(self):
self.assertTrue(self.a1.is_literal())
def test_is_literal_unary(self):
self.assertTrue(self.l1.is_literal())
formula2 = Formula("!", self.fand1)
self.assertFalse(formula2.is_literal())
def test_is_literal_binary(self):
self.assertFalse(self.fand1.is_literal())
self.assertFalse(self.for1.is_literal())
def test_is_literal_top_bottom(self):
self.assertTrue(Formula("T").is_literal())
self.assertTrue(Formula("F").is_literal())
self.assertFalse(Formula("!", Formula("T")).is_literal())
self.assertFalse(Formula("!", Formula("F")).is_literal())
def test_negate(self):
self.assertIsInstance(self.fand1.negate(), Formula)
self.assertEqual(Formula("!", self.fand1), self.fand1.negate())
def test_complement(self):
# binary
self.assertIsInstance(self.fand1.complement(), Formula)
self.assertEqual(self.fand1.negate(), self.fand1.complement())
# literal
self.assertIsInstance(self.l1.complement(), Formula)
self.assertEqual(self.a1, self.l1.complement())
# atomic
self.assertIsInstance(self.a1.complement(), Formula)
self.assertEqual(self.l1, self.a1.complement())
def test_components_atomic(self):
(comp1, comp2) = self.a1.components()
self.assertIsNot(comp1, self.a1)
self.assertEqual(comp1, self.a1)
self.assertEqual(None, comp2)
def test_components_unary(self):
(comp1, comp2) = self.l1.components()
self.assertIsNot(comp1, self.l1)
self.assertEqual(comp1, self.l1)
self.assertEqual(None, comp2)
def test_components_binary(self):
formula = Formula("&", self.a1, self.a2)
(comp1, comp2) = formula.components()
self.assertIsNot(comp1, self.a1)
self.assertIsNot(comp2, self.a2)
self.assertEqual(comp1, self.a1)
self.assertEqual(comp2, self.a2)
def test_nnf_atomic(self):
self.assertIsNot(self.a1, self.a1.nnf())
self.assertEqual(self.a1, self.a1.nnf())
def test_nnf_unary_literal(self):
self.assertIsNot(self.l1, self.l1.nnf())
self.assertEqual(self.l1, self.l1.nnf())
def test_nnf_unary(self):
sub = Formula("&", self.a1, self.a2)
formula = Formula("!", sub)
exp = Formula("|", Formula("!", Formula("X")),
Formula("!", Formula("Y")))
self.assertEqual(exp, formula.nnf())
self.assertIsNot(self.a1, formula.nnf().subformula1.subformula1)
self.assertIsNot(self.a2, formula.nnf().subformula2.subformula1)
def test_nnf_not_not(self):
formula = Formula("!", Formula("!", self.a1))
self.assertIsNot(self.a1, formula.nnf())
self.assertEqual(self.a1, formula.nnf())
def test_nnf_binary(self):
sub1 = Formula("!", Formula("!", self.a1))
sub2 = Formula("!", Formula("!", self.a2))
formula = Formula("&", sub1, sub2)
exp = Formula("&", self.a1, self.a2)
self.assertEqual(exp, formula.nnf())
self.assertIsNot(self.a1, formula.nnf().subformula1)
self.assertIsNot(self.a2, formula.nnf().subformula2)
def test_cnf_atomic(self):
exp = Generalization("and", [Generalization("or", [self.a1])])
self.assertEqual(exp, self.a1.cnf())
def test_cnf_literal(self):
exp = Generalization("and", [Generalization("or", [self.l1])])
self.assertEqual(exp, self.l1.cnf())
def test_cnf_alpha(self):
exp = Generalization(
"and",
[Generalization("or", [self.a1]),
Generalization("or", [self.a2])])
self.assertEqual(exp, self.fand1.cnf())
def test_cnf_beta(self):
exp = Generalization("and", [Generalization("or", [self.a1, self.a2])])
self.assertEqual(exp, self.for1.cnf())
def test_cnf_not_not(self):
exp = Generalization("and", [Generalization("or", [self.a1])])
self.assertEqual(exp, Formula("!", self.l1).cnf())
def test_cnf_not_top(self):
formula = Formula("!", Formula("T"))
exp = Generalization("and", [Generalization("or", [Formula("F")])])
self.assertEqual(exp, formula.cnf())
def test_cnf_not_bottom(self):
formula = Formula("!", Formula("F"))
exp = Generalization("and", [Generalization("or", [Formula("T")])])
self.assertEqual(exp, formula.cnf())
def test_cnf_particular(self):
# components
p = Formula("P")
np = Formula("!", p)
q = Formula("Q")
nq = Formula("!", q)
r = Formula("R")
# formulas
f1s = "-(P-> (Q-> R)) -> ((P->Q) -> (P -> R))"
f1 = parser.parse(f1s)
f2s = "-(P&Q) -> R"
f2 = parser.parse(f2s)
# expected
exp1 = Generalization("and", [
Generalization("or", [np, nq, r, p, np, r]),
Generalization("or", [np, nq, r, nq, np, r])
])
exp2 = Generalization(
"and",
[Generalization("or", [p, r]),
Generalization("or", [q, r])])
# assertions
self.assertEqual(exp1, f1.cnf())
self.assertEqual(exp2, f2.cnf())
def test_cnf_not_bottom(self):
formula = Formula("!", Formula("F"))
exp = Generalization("and", [Generalization("or", [Formula("T")])])
self.assertEqual(exp, formula.cnf())
def test_cnf_not_bottom(self):
formula = Formula("!", Formula("F"))
exp = Generalization("and", [Generalization("or", [Formula("T")])])
self.assertEqual(exp, formula.cnf())