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import pytest
from logic import *
from utils import expr_handle_infix_ops, count, Symbol
def test_is_symbol():
assert is_symbol('x')
assert is_symbol('X')
assert is_symbol('N245')
assert not is_symbol('')
assert not is_symbol('1L')
assert not is_symbol([1, 2, 3])
def test_is_var_symbol():
assert is_var_symbol('xt')
assert not is_var_symbol('Txt')
assert not is_var_symbol('')
assert not is_var_symbol('52')
def test_is_prop_symbol():
assert not is_prop_symbol('xt')
assert is_prop_symbol('Txt')
assert not is_prop_symbol('')
assert not is_prop_symbol('52')
def test_variables():
assert variables(expr('F(x, x) & G(x, y) & H(y, z) & R(A, z, 2)')) == {x, y, z}
assert variables(expr('(x ==> y) & B(x, y) & A')) == {x, y}
def test_expr():
assert repr(expr('P <=> Q(1)')) == '(P <=> Q(1))'
assert repr(expr('P & Q | ~R(x, F(x))')) == '((P & Q) | ~R(x, F(x)))'
assert (expr_handle_infix_ops('P & Q ==> R & ~S')
== "P & Q |'==>'| R & ~S")
def test_extend():
assert extend({x: 1}, y, 2) == {x: 1, y: 2}
def test_subst():
assert subst({x: 42, y:0}, F(x) + y) == (F(42) + 0)
def test_PropKB():
kb = PropKB()
assert count(kb.ask(expr) for expr in [A, C, D, E, Q]) is 0
kb.tell(A & E)
assert kb.ask(A) == kb.ask(E) == {}
kb.tell(E |'==>'| C)
assert kb.ask(C) == {}
kb.retract(E)
assert kb.ask(E) is False
assert kb.ask(C) is False
def test_wumpus_kb():
# Statement: There is no pit in [1,1].
assert wumpus_kb.ask(~P11) == {}
# Statement: There is no pit in [1,2].
assert wumpus_kb.ask(~P12) == {}
# Statement: There is a pit in [2,2].
assert wumpus_kb.ask(P22) is False
# Statement: There is a pit in [3,1].
assert wumpus_kb.ask(P31) is False
# Statement: Neither [1,2] nor [2,1] contains a pit.
assert wumpus_kb.ask(~P12 & ~P21) == {}
# Statement: There is a pit in either [2,2] or [3,1].
assert wumpus_kb.ask(P22 | P31) == {}
def test_is_definite_clause():
assert is_definite_clause(expr('A & B & C & D ==> E'))
assert is_definite_clause(expr('Farmer(Mac)'))
assert not is_definite_clause(expr('~Farmer(Mac)'))
assert is_definite_clause(expr('(Farmer(f) & Rabbit(r)) ==> Hates(f, r)'))
assert not is_definite_clause(expr('(Farmer(f) & ~Rabbit(r)) ==> Hates(f, r)'))
assert not is_definite_clause(expr('(Farmer(f) | Rabbit(r)) ==> Hates(f, r)'))
def test_parse_definite_clause():
assert parse_definite_clause(expr('A & B & C & D ==> E')) == ([A, B, C, D], E)
assert parse_definite_clause(expr('Farmer(Mac)')) == ([], expr('Farmer(Mac)'))
assert parse_definite_clause(expr('(Farmer(f) & Rabbit(r)) ==> Hates(f, r)')) == ([expr('Farmer(f)'), expr('Rabbit(r)')], expr('Hates(f, r)'))
def test_pl_true():
assert pl_true(P, {}) is None
assert pl_true(P, {P: False}) is False
assert pl_true(P | Q, {P: True}) is True
assert pl_true((A | B) & (C | D), {A: False, B: True, D: True}) is True
assert pl_true((A & B) & (C | D), {A: False, B: True, D: True}) is False
assert pl_true((A & B) | (A & C), {A: False, B: True, C: True}) is False
assert pl_true((A | B) & (C | D), {A: True, D: False}) is None
assert pl_true(P | P, {}) is None
def test_tt_true():
assert tt_true(P | ~P)
assert tt_true('~~P <=> P')
assert not tt_true((P | ~Q) & (~P | Q))
assert not tt_true(P & ~P)
assert not tt_true(P & Q)
assert tt_true((P | ~Q) | (~P | Q))
assert tt_true('(A & B) ==> (A | B)')
assert tt_true('((A & B) & C) <=> (A & (B & C))')
assert tt_true('((A | B) | C) <=> (A | (B | C))')
assert tt_true('(A ==> B) <=> (~B ==> ~A)')
assert tt_true('(A ==> B) <=> (~A | B)')
assert tt_true('(A <=> B) <=> ((A ==> B) & (B ==> A))')
assert tt_true('~(A & B) <=> (~A | ~B)')
assert tt_true('~(A | B) <=> (~A & ~B)')
assert tt_true('(A & (B | C)) <=> ((A & B) | (A & C))')
assert tt_true('(A | (B & C)) <=> ((A | B) & (A | C))')
def test_dpll():
assert (dpll_satisfiable(A & ~B & C & (A | ~D) & (~E | ~D) & (C | ~D) & (~A | ~F) & (E | ~F)
& (~D | ~F) & (B | ~C | D) & (A | ~E | F) & (~A | E | D))
== {B: False, C: True, A: True, F: False, D: True, E: False})
assert dpll_satisfiable(A & ~B) == {A: True, B: False}
assert dpll_satisfiable(P & ~P) is False
def test_find_pure_symbol():
assert find_pure_symbol([A, B, C], [A|~B,~B|~C,C|A]) == (A, True)
assert find_pure_symbol([A, B, C], [~A|~B,~B|~C,C|A]) == (B, False)
assert find_pure_symbol([A, B, C], [~A|B,~B|~C,C|A]) == (None, None)
def test_unit_clause_assign():
assert unit_clause_assign(A|B|C, {A:True}) == (None, None)
assert unit_clause_assign(B|C, {A:True}) == (None, None)
assert unit_clause_assign(B|~A, {A:True}) == (B, True)
def test_find_unit_clause():
assert find_unit_clause([A|B|C, B|~C, ~A|~B], {A:True}) == (B, False)
def test_unify():
assert unify(x, x, {}) == {}
assert unify(x, 3, {}) == {x: 3}
def test_pl_fc_entails():
assert pl_fc_entails(horn_clauses_KB, expr('Q'))
assert not pl_fc_entails(horn_clauses_KB, expr('SomethingSilly'))
def test_tt_entails():
assert tt_entails(P & Q, Q)
assert not tt_entails(P | Q, Q)
assert tt_entails(A & (B | C) & E & F & ~(P | Q), A & E & F & ~P & ~Q)
def test_prop_symbols():
assert prop_symbols(expr('x & y & z | A')) == {A}
assert prop_symbols(expr('(x & B(z)) ==> Farmer(y) | A')) == {A, expr('Farmer(y)'), expr('B(z)')}
def test_constant_symbols():
assert constant_symbols(expr('x & y & z | A')) == {A}
assert constant_symbols(expr('(x & B(z)) & Father(John) ==> Farmer(y) | A')) == {A, expr('John')}
def test_predicate_symbols():
assert predicate_symbols(expr('x & y & z | A')) == set()
assert predicate_symbols(expr('(x & B(z)) & Father(John) ==> Farmer(y) | A')) == {
('B', 1),
('Father', 1),
('Farmer', 1)}
assert predicate_symbols(expr('(x & B(x, y, z)) & F(G(x, y), x) ==> P(Q(R(x, y)), x, y, z)')) == {
('B', 3),
('F', 2),
('G', 2),
('P', 4),
('Q', 1),
('R', 2)}
def test_eliminate_implications():
assert repr(eliminate_implications('A ==> (~B <== C)')) == '((~B | ~C) | ~A)'
assert repr(eliminate_implications(A ^ B)) == '((A & ~B) | (~A & B))'
assert repr(eliminate_implications(A & B | C & ~D)) == '((A & B) | (C & ~D))'
def test_dissociate():
assert dissociate('&', [A & B]) == [A, B]
assert dissociate('|', [A, B, C & D, P | Q]) == [A, B, C & D, P, Q]
assert dissociate('&', [A, B, C & D, P | Q]) == [A, B, C, D, P | Q]
def test_associate():
assert (repr(associate('&', [(A & B), (B | C), (B & C)]))
== '(A & B & (B | C) & B & C)')
assert (repr(associate('|', [A | (B | (C | (A & B)))]))
== '(A | B | C | (A & B))')
def test_move_not_inwards():
assert repr(move_not_inwards(~(A | B))) == '(~A & ~B)'
assert repr(move_not_inwards(~(A & B))) == '(~A | ~B)'
assert repr(move_not_inwards(~(~(A | ~B) | ~~C))) == '((A | ~B) & ~C)'
def test_distribute_and_over_or():
def test_enatilment(s, has_and = False):
result = distribute_and_over_or(s)
if has_and:
assert result.op == '&'
assert tt_entails(s, result)
assert tt_entails(result, s)
test_enatilment((A & B) | C, True)
test_enatilment((A | B) & C, True)
test_enatilment((A | B) | C, False)
test_enatilment((A & B) | (C | D), True)
def test_to_cnf():
assert (repr(to_cnf(wumpus_world_inference & ~expr('~P12'))) ==
"((~P12 | B11) & (~P21 | B11) & (P12 | P21 | ~B11) & ~B11 & P12)")
assert repr(to_cnf((P & Q) | (~P & ~Q))) == '((~P | P) & (~Q | P) & (~P | Q) & (~Q | Q))'
assert repr(to_cnf("B <=> (P1 | P2)")) == '((~P1 | B) & (~P2 | B) & (P1 | P2 | ~B))'
assert repr(to_cnf("a | (b & c) | d")) == '((b | a | d) & (c | a | d))'
assert repr(to_cnf("A & (B | (D & E))")) == '(A & (D | B) & (E | B))'
assert repr(to_cnf("A | (B | (C | (D & E)))")) == '((D | A | B | C) & (E | A | B | C))'
def test_pl_resolution():
# TODO: Add fast test cases
assert pl_resolution(wumpus_kb, ~P11)
def test_standardize_variables():
e = expr('F(a, b, c) & G(c, A, 23)')
assert len(variables(standardize_variables(e))) == 3
# assert variables(e).intersection(variables(standardize_variables(e))) == {}
assert is_variable(standardize_variables(expr('x')))
def test_fol_bc_ask():
def test_ask(query, kb=None):
q = expr(query)
test_variables = variables(q)
answers = fol_bc_ask(kb or test_kb, q)
return sorted(
[dict((x, v) for x, v in list(a.items()) if x in test_variables)
for a in answers], key=repr)
assert repr(test_ask('Farmer(x)')) == '[{x: Mac}]'
assert repr(test_ask('Human(x)')) == '[{x: Mac}, {x: MrsMac}]'
assert repr(test_ask('Rabbit(x)')) == '[{x: MrsRabbit}, {x: Pete}]'
assert repr(test_ask('Criminal(x)', crime_kb)) == '[{x: West}]'
def test_fol_fc_ask():
def test_ask(query, kb=None):
q = expr(query)
test_variables = variables(q)
answers = fol_fc_ask(kb or test_kb, q)
return sorted(
[dict((x, v) for x, v in list(a.items()) if x in test_variables)
for a in answers], key=repr)
assert repr(test_ask('Criminal(x)', crime_kb)) == '[{x: West}]'
assert repr(test_ask('Enemy(x, America)', crime_kb)) == '[{x: Nono}]'
assert repr(test_ask('Farmer(x)')) == '[{x: Mac}]'
assert repr(test_ask('Human(x)')) == '[{x: Mac}, {x: MrsMac}]'
assert repr(test_ask('Rabbit(x)')) == '[{x: MrsRabbit}, {x: Pete}]'
def test_d():
assert d(x * x - x, x) == 2 * x - 1
def test_WalkSAT():
def check_SAT(clauses, single_solution={}):
# Make sure the solution is correct if it is returned by WalkSat
# Sometimes WalkSat may run out of flips before finding a solution
soln = WalkSAT(clauses)
if soln:
assert all(pl_true(x, soln) for x in clauses)
if single_solution: # Cross check the solution if only one exists
assert all(pl_true(x, single_solution) for x in clauses)
assert soln == single_solution
# Test WalkSat for problems with solution
check_SAT([A & B, A & C])
check_SAT([A | B, P & Q, P & B])
check_SAT([A & B, C | D, ~(D | P)], {A: True, B: True, C: True, D: False, P: False})
# Test WalkSat for problems without solution
assert WalkSAT([A & ~A], 0.5, 100) is None
assert WalkSAT([A | B, ~A, ~(B | C), C | D, P | Q], 0.5, 100) is None
assert WalkSAT([A | B, B & C, C | D, D & A, P, ~P], 0.5, 100) is None
def test_SAT_plan():
transition = {'A': {'Left': 'A', 'Right': 'B'},
'B': {'Left': 'A', 'Right': 'C'},
'C': {'Left': 'B', 'Right': 'C'}}
assert SAT_plan('A', transition, 'C', 2) is None
assert SAT_plan('A', transition, 'B', 3) == ['Right']
assert SAT_plan('C', transition, 'A', 3) == ['Left', 'Left']
transition = {(0, 0): {'Right': (0, 1), 'Down': (1, 0)},
(0, 1): {'Left': (1, 0), 'Down': (1, 1)},
(1, 0): {'Right': (1, 0), 'Up': (1, 0), 'Left': (1, 0), 'Down': (1, 0)},
(1, 1): {'Left': (1, 0), 'Up': (0, 1)}}
assert SAT_plan((0, 0), transition, (1, 1), 4) == ['Right', 'Down']
if __name__ == '__main__':
pytest.main()
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