def test_priority_union_is_associative():
for xWrapped, yWrapped, zWrapped in all3VecTriplesSet:
x, y, z = xWrapped.unwrap(), yWrapped.unwrap(), zWrapped.unwrap()
assert np.array_equal(
fv.priority_union(fv.priority_union(x, y), z),
fv.priority_union(x, fv.priority_union(y, z))
) #, f"({x}+{y})+{z} = {fv.priority_union(x,y)} + {z} = fv.priority_union()"
def test_priority_union_stack_right_as_expected():
counterexamples = set()
for xWrapped in all3VecsSet:
x = xWrapped.unwrap()
stackRightResult = fv.priority_union(x, all3Vecs)
nonVectorResult = np.array([fv.priority_union(x, v) for v in all3Vecs],
dtype=INT8)
stackRightResultSet = fv.stack_to_set(stackRightResult)
nonVectorResultSet = fv.stack_to_set(nonVectorResult)
if stackRightResultSet != nonVectorResultSet:
counterexamples.add((xWrapped))
assert len(counterexamples) == 0, f"Counterexamples:\n{counterexamples}"
def test_priority_union_left_does_NOT_preserve_partial_order():
prunion_pres_po_cxs_lefts = []
for xWrapped in all3VecsSet:
x = xWrapped.unwrap()
rightArg = lambda right: fv.priority_union(x, right)
current_prunion_pres_po_cxs_left = fv.preserves_partial_order(
all3Vecs, rightArg, returnCounterexamples=True)
prunion_pres_po_cxs_lefts.append(current_prunion_pres_po_cxs_left)
prunion_pres_po_cxs_left = grand_union(prunion_pres_po_cxs_lefts)
assert len(prunion_pres_po_cxs_left) > 0
def test_priority_union_right_preserves_partial_order():
prunion_pres_po_cxs_rights = []
for xWrapped in all3VecsSet:
x = xWrapped.unwrap()
leftArg = lambda left: fv.priority_union(left, x)
current_prunion_pres_po_cxs_right = fv.preserves_partial_order(
all3Vecs, leftArg, returnCounterexamples=True)
prunion_pres_po_cxs_rights.append(current_prunion_pres_po_cxs_right)
prunion_pres_po_cxs_right = grand_union(prunion_pres_po_cxs_rights)
assert len(prunion_pres_po_cxs_right) == 0, f"{prunion_pres_po_cxs_right}"
def test_priority_union_right_inverse_all_expected_to_be_possible_are():
Ms = fv.stack_to_set(all3Vecs)
allPairs = {(c, b) for c in Ms for b in Ms}
for (cWrapped, bWrapped) in allPairs:
c, b = cWrapped.unwrap(), bWrapped.unwrap()
ri = fv.right_inv_priority_union(c, b)
if ri is not None:
for a in ri:
assert np.array_equal(fv.priority_union(a, b),
c), f"{a}+{b}≠{c}"
def test_priority_union_left_inverse_all_expected_to_be_possible_are():
Ms = fv.stack_to_set(all3Vecs)
allPairs = {(a, c) for a in Ms for c in Ms}
for (aWrapped, cWrapped) in allPairs:
a, c = aWrapped.unwrap(), cWrapped.unwrap()
li = fv.left_inv_priority_union(a, c)
if li is not None:
for b in li:
assert np.array_equal(fv.priority_union(a, b),
c), f"{a}+{b}≠{c}"
def test_priority_union_left_is_a_lattice_HM_over_LCs():
prunion_lhm_LCs_cxs_lefts = []
for xWrapped in all3VecsSet:
x = xWrapped.unwrap()
xLC = fv.lower_closure(x)
rightArg = lambda right: fv.priority_union(x, right)
current_prunion_lhm_LCs_cxs_left = fv.is_lattice_homomorphism(
xLC, rightArg, returnCounterexamples=True)
prunion_lhm_LCs_cxs_lefts.append(current_prunion_lhm_LCs_cxs_left)
prunion_lhm_LCs_cxs_left = grand_union(prunion_lhm_LCs_cxs_lefts)
assert len(prunion_lhm_LCs_cxs_left) == 0, f"{prunion_lhm_LCs_cxs_left}"
def test_priority_union_right_does_NOT_preserve_joins():
prunion_pres_join_cxs_rights = []
for xWrapped in all3VecsSet:
x = xWrapped.unwrap()
leftArg = lambda left: fv.priority_union(left, x)
current_prunion_pres_join_cxs_right = fv.preserves_join(
all3Vecs, leftArg, returnCounterexamples=True)
prunion_pres_join_cxs_rights.append(
current_prunion_pres_join_cxs_right)
prunion_pres_join_cxs_right = grand_union(prunion_pres_join_cxs_rights)
assert len(
prunion_pres_join_cxs_right) > 0 #, f"{prunion_pres_join_cxs_right}"
def test_priority_union_right_is_a_meet_SL_HM_over_UCs():
prunion_mslhm_UCs_cxs_rights = []
for xWrapped in all3VecsSet:
x = xWrapped.unwrap()
xUC = fv.upper_closure(x)
leftArg = lambda left: fv.priority_union(left, x)
current_prunion_mslhm_UCs_cxs_right = fv.is_meet_semilattice_homomorphism(
xUC, leftArg, returnCounterexamples=True)
prunion_mslhm_UCs_cxs_rights.append(
current_prunion_mslhm_UCs_cxs_right)
prunion_mslhm_UCs_cxs_right = grand_union(prunion_mslhm_UCs_cxs_rights)
assert len(
prunion_mslhm_UCs_cxs_right) == 0, f"{prunion_mslhm_UCs_cxs_right}"
joinsA = {
fv.HashableArray(fv.join_specification(a.unwrap(), b.unwrap()))
for a, b in allJoinablePairs
}
joinsB = {
fv.HashableArray(
fv.join_specification_stack(
np.array([a.unwrap(), b.unwrap()], dtype=INT8)))
for a, b in allJoinablePairs
}
missingFromB = joinsA - joinsB
missingFromA = joinsB - joinsA
assert joinsA == joinsB, f"Missing from stack-based result:\n{missingFromB}\nMissing from pairwise result:\n{missingFromA}"
all3VecIO = [(a, b, fv.priority_union(a, b)) for a in all3Vecs
for b in all3Vecs]
#########################################
# priority union implementation testing #
#########################################
def test_priority_union_stack_left_as_expected():
counterexamples = set()
for xWrapped in all3VecsSet:
x = xWrapped.unwrap()
stackLeftResult = fv.priority_union(all3Vecs, x)
nonVectorResult = np.array([fv.priority_union(v, x) for v in all3Vecs],
dtype=INT8)
stackLeftResultSet = fv.stack_to_set(stackLeftResult)
