def test_true_false():
x = symbols('x')
assert true is S.true
assert false is S.false
assert true is not True
assert false is not False
assert true
assert not false
assert true == True
assert false == False
assert not (true == False)
assert not (false == True)
assert not (true == false)
assert hash(true) == hash(True)
assert hash(false) == hash(False)
assert len(set([true, True])) == len(set([false, False])) == 1
assert isinstance(true, BooleanAtom)
assert isinstance(false, BooleanAtom)
# We don't want to subclass from bool, because bool subclasses from
# int. But operators like &, |, ^, <<, >>, and ~ act differently on 0 and
# 1 then we want them to on true and false. See the docstrings of the
# various And, Or, etc. functions for examples.
assert not isinstance(true, bool)
assert not isinstance(false, bool)
# Note: using 'is' comparison is important here. We want these to return
# true and false, not True and False
assert Not(true) is false
assert Not(True) is false
assert Not(false) is true
assert Not(False) is true
assert ~true is false
assert ~false is true
for T, F in cartes([True, true], [False, false]):
assert And(T, F) is false
assert And(F, T) is false
assert And(F, F) is false
assert And(T, T) is true
assert And(T, x) == x
assert And(F, x) is false
if not (T is True and F is False):
assert T & F is false
assert F & T is false
if not F is False:
assert F & F is false
if not T is True:
assert T & T is true
assert Or(T, F) is true
assert Or(F, T) is true
assert Or(F, F) is false
assert Or(T, T) is true
assert Or(T, x) is true
assert Or(F, x) == x
if not (T is True and F is False):
assert T | F is true
assert F | T is true
if not F is False:
assert F | F is false
if not T is True:
assert T | T is true
assert Xor(T, F) is true
assert Xor(F, T) is true
assert Xor(F, F) is false
assert Xor(T, T) is false
assert Xor(T, x) == ~x
assert Xor(F, x) == x
if not (T is True and F is False):
assert T ^ F is true
assert F ^ T is true
if not F is False:
assert F ^ F is false
if not T is True:
assert T ^ T is false
assert Nand(T, F) is true
assert Nand(F, T) is true
assert Nand(F, F) is true
assert Nand(T, T) is false
assert Nand(T, x) == ~x
assert Nand(F, x) is true
assert Nor(T, F) is false
assert Nor(F, T) is false
assert Nor(F, F) is true
assert Nor(T, T) is false
assert Nor(T, x) is false
assert Nor(F, x) == ~x
assert Implies(T, F) is false
assert Implies(F, T) is true
assert Implies(F, F) is true
assert Implies(T, T) is true
assert Implies(T, x) == x
assert Implies(F, x) is true
assert Implies(x, T) is true
assert Implies(x, F) == ~x
if not (T is True and F is False):
assert T >> F is false
assert F << T is false
assert F >> T is true
assert T << F is true
if not F is False:
assert F >> F is true
assert F << F is true
if not T is True:
assert T >> T is true
assert T << T is true
assert Equivalent(T, F) is false
assert Equivalent(F, T) is false
assert Equivalent(F, F) is true
assert Equivalent(T, T) is true
assert Equivalent(T, x) == x
assert Equivalent(F, x) == ~x
assert Equivalent(x, T) == x
assert Equivalent(x, F) == ~x
assert ITE(T, T, T) is true
assert ITE(T, T, F) is true
assert ITE(T, F, T) is false
assert ITE(T, F, F) is false
assert ITE(F, T, T) is true
assert ITE(F, T, F) is false
assert ITE(F, F, T) is true
assert ITE(F, F, F) is false
def test_true_false():
assert true is S.true
assert false is S.false
assert true is not True
assert false is not False
assert true
assert not false
assert true == True
assert false == False
assert not (true == False)
assert not (false == True)
assert not (true == false)
assert hash(true) == hash(True)
assert hash(false) == hash(False)
assert len({true, True}) == len({false, False}) == 1
assert isinstance(true, BooleanAtom)
assert isinstance(false, BooleanAtom)
# We don't want to subclass from bool, because bool subclasses from
# int. But operators like &, |, ^, <<, >>, and ~ act differently on 0 and
# 1 then we want them to on true and false. See the docstrings of the
# various And, Or, etc. functions for examples.
assert not isinstance(true, bool)
assert not isinstance(false, bool)
# Note: using 'is' comparison is important here. We want these to return
# true and false, not True and False
assert Not(true) is false
assert Not(True) is false
assert Not(false) is true
assert Not(False) is true
assert ~true is false
assert ~false is true
for T, F in cartes([True, true], [False, false]):
assert And(T, F) is false
assert And(F, T) is false
assert And(F, F) is false
assert And(T, T) is true
assert And(T, x) == x
assert And(F, x) is false
if not (T is True and F is False):
assert T & F is false
assert F & T is false
if not F is False:
assert F & F is false
if not T is True:
assert T & T is true
assert Or(T, F) is true
assert Or(F, T) is true
assert Or(F, F) is false
assert Or(T, T) is true
assert Or(T, x) is true
assert Or(F, x) == x
if not (T is True and F is False):
assert T | F is true
assert F | T is true
if not F is False:
assert F | F is false
if not T is True:
assert T | T is true
assert Xor(T, F) is true
assert Xor(F, T) is true
assert Xor(F, F) is false
assert Xor(T, T) is false
assert Xor(T, x) == ~x
assert Xor(F, x) == x
if not (T is True and F is False):
assert T ^ F is true
assert F ^ T is true
if not F is False:
assert F ^ F is false
if not T is True:
assert T ^ T is false
assert Nand(T, F) is true
assert Nand(F, T) is true
assert Nand(F, F) is true
assert Nand(T, T) is false
assert Nand(T, x) == ~x
assert Nand(F, x) is true
assert Nor(T, F) is false
assert Nor(F, T) is false
assert Nor(F, F) is true
assert Nor(T, T) is false
assert Nor(T, x) is false
assert Nor(F, x) == ~x
assert Implies(T, F) is false
assert Implies(F, T) is true
assert Implies(F, F) is true
assert Implies(T, T) is true
assert Implies(T, x) == x
assert Implies(F, x) is true
assert Implies(x, T) is true
assert Implies(x, F) == ~x
if not (T is True and F is False):
assert T >> F is false
assert F << T is false
assert F >> T is true
assert T << F is true
if not F is False:
assert F >> F is true
assert F << F is true
if not T is True:
assert T >> T is true
assert T << T is true
assert Equivalent(T, F) is false
assert Equivalent(F, T) is false
assert Equivalent(F, F) is true
assert Equivalent(T, T) is true
assert Equivalent(T, x) == x
assert Equivalent(F, x) == ~x
assert Equivalent(x, T) == x
assert Equivalent(x, F) == ~x
assert ITE(T, T, T) is true
assert ITE(T, T, F) is true
assert ITE(T, F, T) is false
assert ITE(T, F, F) is false
assert ITE(F, T, T) is true
assert ITE(F, T, F) is false
assert ITE(F, F, T) is true
assert ITE(F, F, F) is false
assert all(i.simplify(1, 2) is i for i in (S.true, S.false))
