def get_contrapositives(seq):
"""Given multiple antecedents and succedents, return a set of sequents with
various antecedents or succedents negated such that each result sequent
corresponds has a succedent set corresponding to exactly one of the
original antecedents or succedents. For example.
A, B |- C, D
yields the set
B, ~C, ~D |- ~A
A, ~C, ~D |- ~B
A, B, ~D |- C
A, B, ~C |- D
"""
ante_succ_pairs = []
for succedent in map(weaken_sequent, seq.succedents):
try:
antecedents = try_get_negated(succedent)
except NotNegatable:
antecedents = set()
ante_succ_pairs.append((antecedents, set([succedent])))
for antecedent in map(weaken_sequent, seq.antecedents):
try:
succedents = try_get_negated(antecedent)
except NotNegatable:
succedents = set()
ante_succ_pairs.append((set([antecedent]), succedents))
result = set()
for _, succedents in ante_succ_pairs:
if succedents:
succedent = iter(succedents).next()
antecedents_product = []
for other_antecedents, other_succedents in ante_succ_pairs:
if other_succedents != succedents:
antecedents_product.append(other_antecedents)
for antecedents in itertools.product(*antecedents_product):
if succedent in antecedents:
continue
try:
antecedents = try_simplify_antecedents(set(antecedents))
except Inconsistent:
continue
result.add(Sequent(antecedents, succedents))
return result
def get_pointed(seq):
"""Return a set of sequents each with a single succedent."""
result = set()
if len(seq.succedents) == 1:
for succedent in seq.succedents:
if succedent.name != 'OPTIONALLY':
result.add(seq)
elif len(seq.succedents) > 1:
for succedent in seq.succedents:
remaining = set_without(seq.succedents, succedent)
try:
neg_remaining = map(try_get_negated, remaining)
except NotNegatable:
continue
for negated in itertools.product(*neg_remaining):
try:
antecedents = try_simplify_antecedents(
set(negated) | seq.antecedents)
except Inconsistent:
continue
result.add(Sequent(antecedents, set([succedent])))
else:
raise ValueError('get_contrapositives never returns empty succedents')
return result
