def test_logic_not():
assert Not(False) is True
assert Not('a') != '~a'
assert Not('~a') != 'a'
# NOTE: we may want to change default Not behaviour and put this
# functionality into some method.
assert Not(And('a', 'b')) == Or(Not('a'), Not('b'))
assert Not(Or('a', 'b')) == And(Not('a'), Not('b'))
pytest.raises(ValueError, lambda: Not(ValueError))
def test_logic_onearg():
assert And() is True
assert Or() is False
assert And(T) == T
assert And(F) == F
assert Or(T) == T
assert Or(F) == F
assert And('a') == 'a'
assert Or('a') == 'a'
def test_FactRules_parse():
f = FactRules('a -> b')
assert f.prereq == {'b': {'a'}, 'a': {'b'}}
f = FactRules('a -> ~b')
assert f.prereq == {'b': {'a'}, 'a': {'b'}}
f = FactRules('~a -> b')
assert f.prereq == {'b': {'a'}, 'a': {'b'}}
f = FactRules('~a -> ~b')
assert f.prereq == {'b': {'a'}, 'a': {'b'}}
f = FactRules('~z == nz')
assert f.prereq == {'z': {'nz'}, 'nz': {'z'}}
pytest.raises(ValueError, lambda: FactRules('a ? b'))
f = FactRules('a -> b & ~b') # trivial test
assert not f.prereq
# tautologies
assert not FactRules('a -> a | b').prereq
# XXX: We don't support non-atomic left operands, so use Prover directly
p = Prover()
p.process_rule(And('a', 'b'), 'a')
p.process_rule(Or('a', 'b'), 'a')
assert not p.proved_rules
def test_logic_cmp():
l1 = And('a', Not('b'))
l2 = And('a', Not('b'))
assert hash(l1) == hash(l2)
assert (l1 == l2) == T
assert (l1 != l2) == F
assert And('a', 'b', 'c') == And('b', 'a', 'c')
assert And('a', 'b', 'c') == And('c', 'b', 'a')
assert And('a', 'b', 'c') == And('c', 'a', 'b')
def test_logic_fromstring():
s = Logic.fromstring
assert s('a') == 'a'
assert s('~a') == Not('a')
assert s('a & b') == And('a', 'b')
assert s('a | b') == Or('a', 'b')
assert s('a | b & c') == And(Or('a', 'b'), 'c')
assert s('a & b | c') == Or(And('a', 'b'), 'c')
assert s('a & b & c') == And('a', 'b', 'c')
assert s('a | b | c') == Or('a', 'b', 'c')
pytest.raises(ValueError, lambda: s('| a'))
pytest.raises(ValueError, lambda: s('& a'))
pytest.raises(ValueError, lambda: s('a | | b'))
pytest.raises(ValueError, lambda: s('a | & b'))
pytest.raises(ValueError, lambda: s('a & & b'))
pytest.raises(ValueError, lambda: s('a |'))
pytest.raises(ValueError, lambda: s('a|b'))
pytest.raises(ValueError, lambda: s('~'))
pytest.raises(ValueError, lambda: s('~ a'))
pytest.raises(ValueError, lambda: s('a b'))
pytest.raises(ValueError, lambda: s(''))
def test_logic_expand():
t = And(Or('a', 'b'), 'c')
assert t.expand() == Or(And('a', 'c'), And('b', 'c'))
t = And(Or('a', Not('b')), 'b')
assert t.expand() == And('a', 'b')
t = And(Or('a', 'b'), Or('c', 'd'))
assert t.expand() == \
Or(And('a', 'c'), And('a', 'd'), And('b', 'c'), And('b', 'd'))
def test_logic_eval_TF():
assert And(F, F) == F
assert And(F, T) == F
assert And(T, F) == F
assert And(T, T) == T
assert Or(F, F) == F
assert Or(F, T) == T
assert Or(T, F) == T
assert Or(T, T) == T
assert And('a', T) == 'a'
assert And('a', F) == F
assert Or('a', T) == T
assert Or('a', F) == 'a'
def test_apply_beta_to_alpha_route():
APPLY = apply_beta_to_alpha_route
pytest.raises(TypeError, lambda: APPLY({}, [(Not('a'), 'b')]))
# indicates empty alpha-chain with attached beta-rule #bidx
def Q(bidx):
return set(), [bidx]
# x -> a &(a,b) -> x -- x -> a
A = {'x': {'a'}}
B = [(And('a', 'b'), 'x')]
assert APPLY(A, B) == {'x': ({'a'}, []), 'a': Q(0), 'b': Q(0)}
# x -> a &(a,~x) -> b -- x -> a
A = {'x': {'a'}}
B = [(And('a', Not('x')), 'b')]
assert APPLY(A, B) == {'x': ({'a'}, []), Not('x'): Q(0), 'a': Q(0)}
# x -> a b &(a,b) -> c -- x -> a b c
A = {'x': {'a', 'b'}}
B = [(And('a', 'b'), 'c')]
assert APPLY(A, B) == \
{'x': ({'a', 'b', 'c'}, []), 'a': Q(0), 'b': Q(0)}
# x -> a &(a,b) -> y -- x -> a [#0]
A = {'x': {'a'}}
B = [(And('a', 'b'), 'y')]
assert APPLY(A, B) == {'x': ({'a'}, [0]), 'a': Q(0), 'b': Q(0)}
# x -> a b c &(a,b) -> c -- x -> a b c
A = {'x': {'a', 'b', 'c'}}
B = [(And('a', 'b'), 'c')]
assert APPLY(A, B) == \
{'x': ({'a', 'b', 'c'}, []), 'a': Q(0), 'b': Q(0)}
# x -> a b &(a,b,c) -> y -- x -> a b [#0]
A = {'x': {'a', 'b'}}
B = [(And('a', 'b', 'c'), 'y')]
assert APPLY(A, B) == \
{'x': ({'a', 'b'}, [0]), 'a': Q(0), 'b': Q(0), 'c': Q(0)}
# x -> a b &(a,b) -> c -- x -> a b c d
# c -> d c -> d
A = {'x': {'a', 'b'}, 'c': {'d'}}
B = [(And('a', 'b'), 'c')]
assert APPLY(A, B) == {
'x': ({'a', 'b', 'c', 'd'}, []),
'c': ({'d'}, []),
'a': Q(0),
'b': Q(0)
}
# x -> a b &(a,b) -> c -- x -> a b c d e
# c -> d &(c,d) -> e c -> d e
A = {'x': {'a', 'b'}, 'c': {'d'}}
B = [(And('a', 'b'), 'c'), (And('c', 'd'), 'e')]
assert APPLY(A, B) == {
'x': ({'a', 'b', 'c', 'd', 'e'}, []),
'c': ({'d', 'e'}, []),
'a': Q(0),
'b': Q(0),
'd': Q(1)
}
# x -> a b &(a,y) -> z -- x -> a b y z
# &(a,b) -> y
A = {'x': {'a', 'b'}}
B = [(And('a', 'y'), 'z'), (And('a', 'b'), 'y')]
assert APPLY(A, B) == {
'x': ({'a', 'b', 'y', 'z'}, []),
'a': (set(), [0, 1]),
'y': Q(0),
'b': Q(1)
}
# x -> a b &(a,~b) -> c -- x -> a b
A = {'x': {'a', 'b'}}
B = [(And('a', Not('b')), 'c')]
assert APPLY(A, B) == \
{'x': ({'a', 'b'}, []), 'a': Q(0), Not('b'): Q(0)}
# ~x -> ~a ~b &(~a,b) -> c -- ~x -> ~a ~b
A = {Not('x'): {Not('a'), Not('b')}}
B = [(And(Not('a'), 'b'), 'c')]
assert APPLY(A, B) == \
{Not('x'): ({Not('a'), Not('b')}, []), Not('a'): Q(0), 'b': Q(0)}
# x -> a b &(b,c) -> ~a -- x -> a b
A = {'x': {'a', 'b'}}
B = [(And('b', 'c'), Not('a'))]
assert APPLY(A, B) == {'x': ({'a', 'b'}, []), 'b': Q(0), 'c': Q(0)}
# x -> a b &(a, b) -> c -- x -> a b c p
# c -> p a
A = {'x': {'a', 'b'}, 'c': {'p', 'a'}}
B = [(And('a', 'b'), 'c')]
assert APPLY(A, B) == {
'x': ({'a', 'b', 'c', 'p'}, []),
'c': ({'p', 'a'}, []),
'a': Q(0),
'b': Q(0)
}
def test_logic_xnotx():
assert And('a', Not('a')) == F
assert Or('a', Not('a')) == T
def test_logic_expand():
t = And(Or('a', 'b'), 'c')
assert t.expand() == Or(And('a', 'c'), And('b', 'c'))
t = And(Or('a', Not('b')), 'b')
assert t.expand() == And('a', 'b')
t = And(Or('a', 'b'), Or('c', 'd'))
assert t.expand() == \
Or(And('a', 'c'), And('a', 'd'), And('b', 'c'), And('b', 'd'))
def test_logic_combine_args():
assert And('a', 'b', 'a') == And('a', 'b')
assert Or('a', 'b', 'a') == Or('a', 'b')
assert And(And('a', 'b'), And('c', 'd')) == And('a', 'b', 'c', 'd')
assert Or(Or('a', 'b'), Or('c', 'd')) == Or('a', 'b', 'c', 'd')
assert Or('t', And('n', 'p', 'r'), And('n', 'r'), And('n', 'p', 'r'), 't', And('n', 'r')) == \
Or('t', And('n', 'p', 'r'), And('n', 'r'))
