def test_minimum(self):
self.assertTrue(
pcabuilder.InitProp('A or false').minimum() == pcaprop.Variable(
'A'))
self.assertTrue(
pcabuilder.InitProp('false or (A iff B)').minimum() == pcaprop.
EquivalenceOp(pcaprop.Variable('A'), pcaprop.Variable('B')))
self.assertTrue(
pcabuilder.InitProp('A and false').minimum() ==
pcaprop.FalseProp())
self.assertTrue(
pcabuilder.InitProp('false and (A iff B)').minimum() ==
pcaprop.FalseProp())
self.assertTrue(
pcabuilder.InitProp(
'B iff (A and (false and (A iff B)))').minimum() ==
pcaprop.EquivalenceOp(pcaprop.Variable('B'), pcaprop.FalseProp()))
self.assertTrue(
pcabuilder.InitProp('Z iff (A and (B and bot))').minimum() ==
pcaprop.EquivalenceOp(pcaprop.Variable('Z'), pcaprop.FalseProp()))
self.assertTrue(
pcabuilder.InitProp('Z iff (not A or not(B or bot))').minimum() ==
pcaprop.EquivalenceOp(
pcaprop.Variable('Z'),
pcaprop.DisjunctionOp(
pcaprop.NegationOp(pcaprop.Variable('A')),
pcaprop.NegationOp(pcaprop.Variable('B')))))
def test_commutativity(self):
self.assertTrue(
pcabuilder.InitProp('A and B').commutativity() == pcaprop.
ConjunctionOp(pcaprop.Variable('B'), pcaprop.Variable('A')))
self.assertTrue(
pcabuilder.InitProp('A and (C and B)').commutativity() ==
pcaprop.ConjunctionOp(
pcaprop.ConjunctionOp(pcaprop.Variable(
'B'), pcaprop.Variable('C')), pcaprop.Variable('A')))
self.assertTrue(
pcabuilder.InitProp('A or (C and ( D or B))').commutativity() ==
pcaprop.DisjunctionOp(
pcaprop.ConjunctionOp(
pcaprop.DisjunctionOp(pcaprop.Variable('B'),
pcaprop.Variable('D')),
pcaprop.Variable('C')), pcaprop.Variable('A')))
self.assertTrue(
pcabuilder.InitProp('B implies (A and B)').commutativity() ==
pcaprop.ImplicationOp(
pcaprop.Variable('B'),
pcaprop.ConjunctionOp(pcaprop.Variable('B'),
pcaprop.Variable('A'))))
self.assertTrue(
pcabuilder.InitProp('not not (A and B)').commutativity() ==
pcaprop.NegationOp(
pcaprop.NegationOp(
pcaprop.ConjunctionOp(pcaprop.Variable('B'),
pcaprop.Variable('A')))))
def test_prop(self):
a = pcaparser.PARSER.parse('P or B iff C and A implies (P and C)')
to_assert = pcaprop.EquivalenceOp(pcaprop.DisjunctionOp(pcaprop.Variable('P'), pcaprop.Variable('B')),
pcaprop.ImplicationOp(
pcaprop.ConjunctionOp(pcaprop.Variable('C'), pcaprop.Variable('A')),
pcaprop.ConjunctionOp(pcaprop.Variable('P'), pcaprop.Variable('C'))))
self.assertEqual(a, to_assert)
a = pcaparser.PARSER.parse('true or not A implies false and not not not B or A')
to_assert = pcaprop.ImplicationOp(
pcaprop.DisjunctionOp(pcaprop.TrueProp(), pcaprop.NegationOp(pcaprop.Variable('A'))),
pcaprop.DisjunctionOp(
pcaprop.ConjunctionOp(pcaprop.FalseProp(), pcaprop.NegationOp(
pcaprop.NegationOp(pcaprop.NegationOp(pcaprop.Variable('B'))))),
pcaprop.Variable('A')))
self.assertEqual(a, to_assert)
def test_prop(self):
a = pcaprop.TrueProp()
b = pcaprop.NegationOp(a)
self.assertTrue(a)
self.assertFalse(b.eval())
self.assertTrue(pcaprop.DisjunctionOp(a, b.eval()).eval())
self.assertFalse(pcaprop.ConjunctionOp(b.eval(), a).eval())
def test_implication(self):
self.assertTrue(
pcabuilder.InitProp('A implies (B implies C) ').implication() ==
pcaprop.DisjunctionOp(
pcaprop.NegationOp(pcaprop.Variable('A')),
pcaprop.DisjunctionOp(
pcaprop.NegationOp(pcaprop.Variable('B')),
pcaprop.Variable('C'))))
self.assertTrue(
pcabuilder.InitProp('A or not (A implies B)').implication() ==
pcaprop.DisjunctionOp(
pcaprop.Variable('A'),
pcaprop.NegationOp(
pcaprop.DisjunctionOp(
pcaprop.NegationOp(pcaprop.Variable('A')),
pcaprop.Variable('B')))))
def _implication(op):
if isinstance(op, (pcaprop.Variable, pcaprop.TrueProp, pcaprop.FalseProp)):
return op
if isinstance(op, pcaprop.UnaryOp):
return op.__class__(_implication(op.prop))
if isinstance(op, pcaprop.BinaryOp):
prop_l = _implication(op.prop_l)
prop_r = _implication(op.prop_r)
if isinstance(op, pcaprop.ImplicationOp):
return pcaprop.DisjunctionOp(pcaprop.NegationOp(prop_l), prop_r)
return op.__class__(prop_l, prop_r)
def _de_morgan(op):
if isinstance(op, (pcaprop.Variable, pcaprop.TrueProp, pcaprop.FalseProp)):
return op
if isinstance(op, pcaprop.UnaryOp):
return op.__class__(_de_morgan(op.prop))
if isinstance(op, pcaprop.BinaryOp):
prop_l = _de_morgan(op.prop_l)
prop_r = _de_morgan(op.prop_r)
if isinstance(op, pcaprop.DisjunctionOp):
return pcaprop.NegationOp(pcaprop.ConjunctionOp(pcaprop.NegationOp(prop_l),
pcaprop.NegationOp(prop_r)))
if isinstance(op, pcaprop.ConjunctionOp):
return pcaprop.NegationOp(pcaprop.DisjunctionOp(pcaprop.NegationOp(prop_l),
pcaprop.NegationOp(prop_r)))
return op.__class__(prop_l, prop_r)
def test_idempotence(self):
self.assertTrue(
pcabuilder.InitProp('A and A').idempotence() == pcaprop.Variable(
'A'))
self.assertTrue(
pcabuilder.InitProp('not not (A and A)').idempotence() ==
pcaprop.NegationOp(pcaprop.NegationOp(pcaprop.Variable('A'))))
self.assertTrue(
pcabuilder.InitProp('B or not (A and A)').idempotence() ==
pcaprop.DisjunctionOp(pcaprop.Variable('B'),
pcaprop.NegationOp(pcaprop.Variable('A'))))
self.assertTrue(
pcabuilder.InitProp('B or not (A and ( A or A))').idempotence() ==
pcaprop.DisjunctionOp(pcaprop.Variable('B'),
pcaprop.NegationOp(pcaprop.Variable('A'))))
self.assertFalse(
pcabuilder.InitProp('not not (A and B)').idempotence() ==
pcaprop.NegationOp(pcaprop.NegationOp(pcaprop.Variable('A'))))
def exp_not(self, value):
return pcaprop.NegationOp(value[1])
def test_precedence(self):
a = pcaprop.Variable("A")
b = pcaprop.Variable("B")
self.assertEqual((a + b >> ~a * b), pcaprop.ImplicationOp(
pcaprop.DisjunctionOp(a, b), pcaprop.ConjunctionOp(pcaprop.NegationOp(a), b)))
def test_creation(self):
a = pcaprop.Variable("A")
b = pcaprop.Variable("B")
c = pcaprop.Variable("C")
self.assertEqual(a >> (~(a * b) + c), pcaprop.ImplicationOp(
a, pcaprop.DisjunctionOp(pcaprop.NegationOp(pcaprop.ConjunctionOp(a, b)), c)))
def test_de_morgan(self):
self.assertEqual(
list(pcabuilder.InitProp('not(A or B)').interpretations()),
list(pcabuilder.InitProp('(not A) and (not B)').interpretations()))
self.assertTrue(
pcabuilder.InitProp(
'(not(A and B)) ⇔ ((not A) or (not B))').tautology())
self.assertTrue(
pcabuilder.InitProp(
'(not(A or B)) ⇔ ((not A) and (not B))').tautology())
self.assertEqual(
pcabuilder.InitProp('¬(A or B)').de_morgan(),
pcaprop.NegationOp(
pcaprop.NegationOp(
pcaprop.ConjunctionOp(
pcaprop.NegationOp(pcaprop.Variable('A')),
pcaprop.NegationOp(pcaprop.Variable('B'))))))
self.assertEqual(
pcabuilder.InitProp('¬(A and B)').de_morgan(),
pcaprop.NegationOp(
pcaprop.NegationOp(
pcaprop.DisjunctionOp(
pcaprop.NegationOp(pcaprop.Variable('A')),
pcaprop.NegationOp(pcaprop.Variable('B'))))))
to_test = pcaprop.NegationOp(
pcaprop.ConjunctionOp(
pcaprop.NegationOp(pcaprop.Variable('A')),
pcaprop.NegationOp(
pcaprop.NegationOp(
pcaprop.NegationOp(
pcaprop.DisjunctionOp(
pcaprop.NegationOp(pcaprop.Variable('A')),
pcaprop.NegationOp(pcaprop.Variable('B'))))))))
self.assertEqual(
pcabuilder.InitProp('A or ¬(A and B)').de_morgan(), to_test)