def test_solve(sentence: nnf.NNF):
solution = sentence.solve()
if solution is None:
assert not sentence.satisfiable()
else:
assert sentence.satisfiable()
assert sentence.satisfied_by(solution)
def test_simplify_preserves_meaning(sentence: nnf.NNF, merge_nodes):
simple = sentence.simplify(merge_nodes)
assert sentence.equivalent(simple)
for model in sentence.models():
assert simple.satisfied_by(model)
for model in simple.models():
assert sentence.condition(model).simplify(merge_nodes) == nnf.true
def test_models_deterministic_sanity(sentence: nnf.NNF):
"""Running _models_deterministic() on a non-deterministic decomposable
sentence may return duplicate models but should not return unsatisfying
models and should return each satisfying model at least once.
"""
assert model_set(sentence._models_decomposable()) == model_set(
sentence._models_deterministic())
def test_simplify_solves_DNNF_satisfiability(sentence: nnf.NNF, merge_nodes):
if sentence.satisfiable():
event("Sentence is satisfiable")
assert sentence.simplify(merge_nodes) != nnf.false
else:
event("Sentence is not satisfiable")
assert sentence.simplify(merge_nodes) == nnf.false
def test_models(sentence: nnf.NNF):
real_models = [
model for model in all_models(sentence.vars())
if sentence.satisfied_by(model)
]
models = list(sentence.models())
assert len(real_models) == len(models)
assert model_set(real_models) == model_set(models)
def test_implies(a: nnf.NNF, b: nnf.NNF):
if a.implies(b):
event("Implication")
for model in a.models():
assert b.condition(model).valid()
else:
event("No implication")
assert any(not b.condition(model).valid() for model in a.models())
def test_to_MODS(sentence: nnf.NNF):
assume(len(sentence.vars()) <= 5)
mods = sentence.to_MODS()
assert mods.is_MODS()
assert mods.is_DNF()
assert mods.is_DNF(strict=True)
assert mods.smooth()
assert isinstance(mods, Or)
assert mods.model_count() == len(mods.children)
def test_validity(sentence: nnf.NNF):
if sentence.valid():
event("Valid sentence")
assert all(
sentence.satisfied_by(model)
for model in nnf.all_models(sentence.vars()))
else:
event("Invalid sentence")
assert any(not sentence.satisfied_by(model)
for model in nnf.all_models(sentence.vars()))
def test_simplify_merges_internal_nodes(sentence: nnf.NNF):
if any(
any(type(node) == type(child) for child in node.children)
for node in sentence.walk() if isinstance(node, nnf.Internal)):
event("Sentence contained immediately mergeable nodes")
# Nodes may also be merged after intermediate nodes are removed
for node in sentence.simplify().walk():
if isinstance(node, nnf.Internal):
for child in node.children:
assert type(node) != type(child)
def test_simplify_eliminates_bools(sentence: nnf.NNF, merge_nodes):
assume(sentence != nnf.true and sentence != nnf.false)
if any(node == nnf.true or node == nnf.false for node in sentence.walk()):
event("Sentence contained booleans originally")
sentence = sentence.simplify(merge_nodes)
if sentence == nnf.true or sentence == nnf.false:
event("Sentence simplified to boolean")
else:
for node in sentence.walk():
assert node != nnf.true and node != nnf.false
def test_DNNF_sat_strategies(sentence: nnf.NNF, merge_nodes):
sat = sentence.satisfiable()
if sat:
assert sentence.simplify(merge_nodes) != nnf.false
assert amc.SAT(sentence)
event("Sentence satisfiable")
else:
assert sentence.simplify(merge_nodes) == nnf.false
assert not amc.SAT(sentence)
event("Sentence not satisfiable")
def test_smoothing(sentence: nnf.NNF):
if not sentence.smooth():
event("Sentence not smooth yet")
smoothed = sentence.make_smooth()
assert type(sentence) is type(smoothed)
assert smoothed.smooth()
assert sentence.equivalent(smoothed)
assert smoothed.make_smooth() == smoothed
else:
event("Sentence already smooth")
assert sentence.make_smooth() == sentence
def test_implicates_implicants_negation_rule(sentence: nnf.NNF):
"""Any implicate is also a negated implicant of the negated sentence.
.implicates() gives some implicates, and .implicants() gives all
implicants.
So sentence.negate().implicants().negate() gives all implicates,
and sentence.negate().implicates().negate() gives some implicants.
"""
assume(sentence.size() <= 30)
assert (sentence.negate().implicants().negate().children >=
sentence.implicates().children)
assert (sentence.negate().implicates().negate().children <=
sentence.implicants().children)
def test_pairwise(sentence: nnf.NNF):
new = sentence.make_pairwise()
assert new.equivalent(sentence)
if new not in {nnf.true, nnf.false}:
assert all(
len(node.children) == 2 for node in new.walk()
if isinstance(node, nnf.Internal))
def process_theory(node: NNF):
if node.is_CNF():
return node
res = []
if isinstance(node, Var):
res.append(node)
assert isinstance(node, Internal)
if len(node.children) == 1:
[child] = node.children
res.append(process_node(child))
else:
left, right = node.children
if isinstance(node, And):
left_to_cnf = distribute(left)
right_to_cnf = distribute(right)
return And({left_to_cnf, right_to_cnf})
elif isinstance(node, Or):
left_to_cnf = distribute(left)
right_to_cnf = distribute(right)
return merge_cnf(left_to_cnf, right_to_cnf)
return res
def test_tseitin(sentence: nnf.NNF):
# Assumption to reduce the time in testing
assume(sentence.size() <= 10)
T = tseitin.to_CNF(sentence)
assert T.is_CNF()
assert T.is_CNF(strict=True)
assert tseitin.to_CNF(T) == T
assert T.forget_aux().equivalent(sentence)
models = list(complete_models(T.models(), sentence.vars() | T.vars()))
for mt in models:
assert sentence.satisfied_by(mt)
assert len(models) == sentence.model_count()
def test_dimacs_cnf_serialize_accepts_only_cnf(sentence: nnf.NNF):
if sentence.is_CNF():
event("CNF sentence")
dimacs.dumps(sentence, mode='cnf')
else:
event("Not CNF sentence")
with pytest.raises(dimacs.EncodeError):
dimacs.dumps(sentence, mode='cnf')
def test_equivalent(sentence: nnf.NNF):
assert sentence.equivalent(sentence)
assert sentence.equivalent(sentence | nnf.false)
assert sentence.equivalent(sentence & (nnf.Var('A') | ~nnf.Var('A')))
if sentence.satisfiable():
assert not sentence.equivalent(sentence & nnf.false)
assert not sentence.equivalent(sentence & nnf.Var('A'))
else:
assert sentence.equivalent(sentence & nnf.false)
assert sentence.equivalent(sentence & nnf.Var('A'))
def dump(obj: NNF,
fp: t.TextIO,
*,
num_variables: t.Optional[int] = None,
var_labels: t.Optional[t.Dict[Name, int]] = None,
comment_header: t.Optional[str] = None,
mode: str = 'sat') -> None:
"""Dump a sentence into an open file in a DIMACS format.
Variable names have to be integers. If the variables in the sentence you
want to dump are not integers, you can pass a ``var_labels`` dictionary
to map names to integers.
:param obj: The sentence to dump.
:param fp: The open file.
:param num_variables: Override the number of variables, in case there
are variables that don't appear in the sentence.
:param var_labels: A dictionary mapping variable names to integers,
to rename non-integer variables.
:param comment_header: A comment to include at the top of the file. May
include newlines.
:param mode: Either ``'sat'`` to dump in the general SAT format,
or ``'cnf'`` to dump in the specialized CNF format.
"""
if num_variables is None:
if var_labels is None:
names = t.cast("t.FrozenSet[int]", obj.vars())
for name in names:
if not isinstance(name, int) or name <= 0:
raise EncodeError(
"{!r} is not an integer > 0. Try supplying a "
"var_labels dictionary.".format(name))
num_vars = max(names, default=0) # type: int
else:
num_vars = max(var_labels.values(), default=0)
else:
num_vars = num_variables
if mode == 'sat':
_dump_sat(obj,
fp,
num_variables=num_vars,
var_labels=var_labels,
comment_header=comment_header)
elif mode == 'cnf':
_dump_cnf(obj,
fp,
num_variables=num_vars,
var_labels=var_labels,
comment_header=comment_header)
def test_forget(sentence: nnf.NNF):
# Assumption to reduce the time in testing
assume(sentence.size() <= 15)
# Test that forgetting a backbone variable doesn't change the theory
T = sentence & Var('added_var')
assert sentence.equivalent(T.forget({'added_var'}))
# Test the tseitin projection
assert sentence.equivalent(sentence.to_CNF().forget_aux())
# Test that models of a projected theory are consistent with the original
names = list(sentence.vars())[:2]
T = sentence.forget(names)
assert not any([v in T.vars() for v in names])
for m in T.models():
assert sentence.condition(m).satisfiable()
def print_stats(sentence: NNF) -> None:
if sentence.is_CNF():
print("Sentence is in CNF.")
if sentence.decomposable():
print("Sentence is decomposable.")
if sentence.smooth():
print("Sentence is smooth.")
print("Variables: {}".format(len(sentence.vars())))
print("Size: {}".format(sentence.size()))
if sentence.is_CNF():
print("Clauses: {}".format(len(sentence))) # type: ignore
sizes = {len(clause) for clause in sentence} # type: ignore
low, high = min(sizes), max(sizes)
if low == high:
print("Clause size: {}".format(low))
else:
print("Clause size: {}-{}".format(low, high))
def test_implicates(sentence: nnf.NNF):
implicates = sentence.implicates()
assert implicates.equivalent(sentence)
assert implicates.is_CNF(strict=True)
assert not any(a.children < b.children for a in implicates.children
for b in implicates.children)
def test_is_MODS(sentence: nnf.NNF):
assert sentence.is_MODS()
def test_implicants(sentence: nnf.NNF):
implicants = sentence.implicants()
assert implicants.equivalent(sentence)
assert implicants.is_DNF()
assert not any(a.children < b.children for a in implicants.children
for b in implicants.children)
def test_pickling(sentence: nnf.NNF):
new = pickle.loads(pickle.dumps(sentence))
assert sentence == new
assert sentence is not new
assert sentence.object_count() == new.object_count()
def test_project(sentence: nnf.NNF):
# Test that we get the same as projecting and forgetting
assume(len(sentence.vars()) > 3)
vars1 = list(sentence.vars())[:2]
vars2 = list(sentence.vars())[2:]
assert sentence.forget(vars1).equivalent(sentence.project(vars2))
def test_iff(a: nnf.NNF, b: nnf.NNF):
c = operators.iff(a, b)
for model in nnf.all_models(c.vars()):
assert ((a.satisfied_by(model) == b.satisfied_by(model)
) == c.satisfied_by(model))
def test_implied_by(a: nnf.NNF, b: nnf.NNF):
c = operators.implied_by(a, b)
for model in nnf.all_models(c.vars()):
assert ((b.satisfied_by(model) and not a.satisfied_by(model)) !=
c.satisfied_by(model))
def test_nor(a: nnf.NNF, b: nnf.NNF):
c = operators.nor(a, b)
for model in nnf.all_models(c.vars()):
assert ((a.satisfied_by(model) or b.satisfied_by(model)) !=
c.satisfied_by(model))
def test_implicants_idempotent(sentence: nnf.NNF):
assume(len(sentence.vars()) <= 6)
implicants = sentence.implicants()
implicates = sentence.implicates()
assert implicants.implicants() == implicants
assert implicates.implicants() == implicants