def test_dnf_form() -> None:
assert venn_from_str('1 & 2', int).to_dnf_set().is_equivalent_to(
venn_from_str('1 & 2', int))
assert venn_from_str('1 | 2', int).to_dnf_set().is_equivalent_to(
venn_from_str('1 | 2', int))
assert UniversalSet().to_dnf_set().is_equivalent_to(UniversalSet())
assert EmptySet().to_dnf_set().is_equivalent_to(EmptySet())
def test_superset_subset_for_unary_sets() -> None:
# UniversalSet == UniversalSet
assert UniversalSet().is_superset_of(UniversalSet())
assert UniversalSet().is_subset_of(UniversalSet())
# UniversalSet contains all other sets
assert UniversalSet().is_superset_of(EmptySet())
assert UniversalSet().is_superset_of(ValueSet(1))
# EmptySet is contained in all sets
assert EmptySet().is_subset_of(EmptySet())
assert EmptySet().is_superset_of(EmptySet())
assert EmptySet().is_subset_of(ValueSet(2))
# PropertySets <-> PropertySets
assert ValueSet(2).is_superset_of(ValueSet(2))
assert ValueSet(2).is_subset_of(ValueSet(2))
assert not ValueSet(2).is_subset_of(ValueSet(3))
assert not ValueSet(2).is_superset_of(ValueSet(3))
# PropertySet <-> UniversalSet
assert ValueSet(1).is_subset_of(UniversalSet())
assert not UniversalSet().is_subset_of(ValueSet(1))
assert UniversalSet().is_superset_of(ValueSet(1))
assert not ValueSet(1).is_superset_of(UniversalSet())
# PropertySet <-> EmptySet
assert ValueSet(2).is_superset_of(EmptySet())
assert not EmptySet().is_superset_of(ValueSet(2))
assert EmptySet().is_subset_of(ValueSet(1))
assert not ValueSet(1).is_subset_of(EmptySet())
def test_nary_sets_constructor() -> None:
assert Union() == EmptySet()
assert Intersection() == UniversalSet()
assert DisjunctiveUnion() == EmptySet()
assert Union(venn_from_str('1', int)).is_equivalent_to(venn_from_str('1', int))
assert Intersection(venn_from_str('1', int)).is_equivalent_to(venn_from_str('1', int))
assert DisjunctiveUnion(venn_from_str('1', int)).is_equivalent_to(venn_from_str('1', int))
def test_is_equivalent_to() -> None:
assert UniversalSet().is_equivalent_to(UniversalSet())
assert EmptySet().is_equivalent_to(EmptySet())
assert not UniversalSet().is_equivalent_to(ValueSet(1))
assert not ValueSet(1).is_equivalent_to(UniversalSet())
assert UniversalSet().is_equivalent_to(Union(ValueSet(1), Complement(ValueSet(1))))
def test_nested_list_form() -> None:
assert venn_from_str('1', int).to_dnf_nested_list() == [[venn_from_str('1', int)]]
x = venn_from_str('1 & ( 2 | 3 )', int)
assert [ValueSet(1), ValueSet(2)] in x.to_dnf_nested_list()
assert [ValueSet(1), ValueSet(3)] in x.to_dnf_nested_list()
assert venn_from_str('1 & 2', int).to_dnf_nested_list() == [[ValueSet(1), ValueSet(2)]]
assert venn_from_str('1 | 2', int).to_dnf_nested_list() == [[ValueSet(1)], [ValueSet(2)]]
assert UniversalSet().to_dnf_nested_list() == [[UniversalSet()]]
assert EmptySet().to_dnf_nested_list() == [[EmptySet()]]
def test_list_form() -> None:
assert venn_from_str('1', int).to_dnf_list() == [venn_from_str('1', int)]
assert venn_from_str('1 & 2', int).to_dnf_list() == [venn_from_str('1 & 2', int)]
assert set(venn_from_str('1 | 2', int).to_dnf_list()) == {ValueSet(1), ValueSet(2)}
x = venn_from_str('1 & ( 2 | 3 )', int)
assert any(elem.is_equivalent_to(venn_from_str('1 & 2', int)) for elem in x.to_dnf_list())
assert any(elem.is_equivalent_to(venn_from_str('1 & 3', int)) for elem in x.to_dnf_list())
assert UniversalSet().to_dnf_list() == [UniversalSet()]
assert EmptySet().to_dnf_list() == [EmptySet()]
def test_union_properties(sets: List[Set]) -> None:
for x in sets:
assert UniversalSet().is_equivalent_to(Union(x, Complement(x)))
assert UniversalSet().is_equivalent_to(Union(Complement(x), x))
assert Union(x, Complement(x)).is_equivalent_to(UniversalSet())
assert Union(Complement(x), x).is_equivalent_to(UniversalSet())
assert x.is_equivalent_to(Union(EmptySet(), x))
assert x.is_equivalent_to(Union(x, EmptySet()))
assert UniversalSet().is_equivalent_to(Union(UniversalSet(), x))
assert UniversalSet().is_equivalent_to(Union(x, UniversalSet()))
assert x.is_equivalent_to(Union(x, x))
def synthesis_factor(state_target: StateTarget) -> VennSet[Target]:
fac = EmptySet() # type: VennSet[Target]
for rxn in (x for x in reaction_targets
if x.synthesises(state_target)):
fac = Union(fac, ValueSet(rxn))
for prod_rxn in (x for x in reaction_targets
if x.produces(state_target)):
sources = []
for source in prod_rxn.consumed_targets:
sources.append(
[source] +
[x for x in reaction_targets if x.synthesises(source)])
for source_combi in product(*sources):
# At least one source should be synthesised.
if all(isinstance(x, StateTarget) for x in source_combi):
continue
assert any(
isinstance(x, ReactionTarget) and x.synthesised_targets
for x in source_combi)
fac = Union(
fac,
Intersection(ValueSet(prod_rxn),
*(ValueSet(x) for x in source_combi)))
return fac
def kappa(state_target: StateTarget, level: int) -> VennSet[Target]:
res = EmptySet() # type: VennSet[Target]
for r in (x for x in reaction_targets if x.consumes(state_target)):
rxn_term = ValueSet(r) # type: VennSet[Target]
for s in (x for x in state_targets if r.consumes(x)):
rxn_term = Intersection(rxn_term, ValueSet(s),
degradation_factor(s))
res = Union(res, rxn_term)
return res
def sets() -> List[Set]:
return [
EmptySet(),
ValueSet(1),
UniversalSet(),
Union(ValueSet(1), ValueSet(2)),
Intersection(ValueSet(1), ValueSet(2)),
Intersection(ValueSet(1), Complement(ValueSet(2))),
Union(Intersection(ValueSet(1), ValueSet(2)), ValueSet(3)),
Union(Intersection(ValueSet(1), ValueSet(2)), Intersection(ValueSet(3), ValueSet(4))),
Union(Complement(Union(ValueSet(1), Complement(ValueSet(2)))), Intersection(ValueSet(3), ValueSet(4)))
]
def pi(state_target: StateTarget, level: int) -> VennSet[Target]:
res = EmptySet() # type: VennSet[Target]
for r in (x for x in reaction_targets if x.produces(state_target)):
rxn_term = ValueSet(r) # type: VennSet[Target]
for s in (x for x in state_targets if r.consumes(x)):
if r.degraded_targets:
state_term = ValueSet(s) # type: VennSet[Target]
else:
state_term = Intersection(ValueSet(s),
degradation_factor(s))
for l in range(level):
state_term = Union(state_term, sigma(s, level - 1))
rxn_term = Intersection(rxn_term, state_term)
res = Union(res, rxn_term)
return res