def get_proof_term(self, t):
if not t.is_conj():
return refl(t)
d_pos = dict()
d_neg = dict()
qu = deque([ProofTerm.assume(t)])
# collect each conjunct's proof term in conjuntion
while qu:
pt = qu.popleft()
if pt.prop.is_conj():
conj1, conj2 = pt.prop.arg1, pt.prop.arg
pt_conj1, pt_conj2 = apply_theorem('conjD1',
pt), apply_theorem(
'conjD2', pt)
if conj1 == false:
th = ProofTerm.theorem("falseE")
inst = matcher.first_order_match(th.prop.arg, t)
pt_false_implies_conj = th.substitution(inst)
return ProofTerm.equal_intr(pt_conj1.implies_intr(t),
pt_false_implies_conj)
elif conj2 == false:
th = ProofTerm.theorem("falseE")
inst = matcher.first_order_match(th.prop.arg, t)
pt_false_implies_conj = th.substitution(inst)
return ProofTerm.equal_intr(pt_conj2.implies_intr(t),
pt_false_implies_conj)
if conj1.is_conj():
qu.appendleft(pt_conj1)
else:
if conj1.is_not():
d_neg[conj1] = pt_conj1
else:
d_pos[conj1] = pt_conj1
if conj2.is_conj():
qu.appendleft(pt_conj2)
else:
if conj2.is_not():
d_neg[conj2] = pt_conj2
else:
d_pos[conj2] = pt_conj2
else:
if pt.prop.is_not():
d_neg[pt.prop] = pt
else:
d_pos[pt.prop] = pt
# first check if there are opposite terms in conjunctions, if there exists, return a false proof term
for key in d_pos:
if Not(key) in d_neg:
pos_pt, neg_pt = d_pos[key], d_neg[Not(key)]
pt_conj_pos_neg = apply_theorem("conjI", pos_pt, neg_pt)
pt_conj_implies_false = pt_conj_pos_neg.on_prop(
rewr_conv("conj_pos_neg")).implies_intr(t)
th = ProofTerm.theorem("falseE")
inst = matcher.first_order_match(th.prop.arg, t)
pt_false_implies_conj = th.substitution(inst)
return ProofTerm.equal_intr(pt_conj_implies_false,
pt_false_implies_conj)
d_pos.update(d_neg)
d = d_pos
def right_assoc(ts):
l = len(ts)
if l == 1:
return d[ts[0]]
elif l == 2:
return apply_theorem('conjI', d[ts[0]], d[ts[1]])
else:
return apply_theorem('conjI', d[ts[0]], right_assoc(ts[1:]))
# pt_right = functools.reduce(lambda x, y: apply_theorem('conjI', x, d[y]), sorted(d.keys()), d[sorted(d.keys())[0]])
if true not in d:
sorted_keys = term_ord.sorted_terms(d.keys())
else:
d_keys_without_true = term_ord.sorted_terms(
[k for k in d if k != true])
sorted_keys = [true] + d_keys_without_true
sorted_keys_num = len(sorted_keys)
pt_right = functools.reduce(lambda x, y: apply_theorem('conjI', d[sorted_keys[sorted_keys_num - y - 2]], x), \
range(sorted_keys_num - 1), d[sorted_keys[-1]])
# pt_right = right_assoc(sorted_keys)
# order implies original
dd = dict()
norm_conj = And(*sorted_keys)
norm_conj_pt = ProofTerm.assume(norm_conj)
for k in sorted_keys:
if k != sorted_keys[-1]:
dd[k] = apply_theorem('conjD1', norm_conj_pt)
norm_conj_pt = apply_theorem('conjD2', norm_conj_pt)
else:
dd[k] = norm_conj_pt
def traverse(t):
if not t.is_conj():
return dd[t]
else:
return apply_theorem('conjI', traverse(t.arg1),
traverse(t.arg))
pt_left = traverse(t)
pt_final = ProofTerm.equal_intr(pt_right.implies_intr(t),
pt_left.implies_intr(norm_conj))
if true in d:
return pt_final.on_rhs(rewr_conv("conj_true_left"),
top_sweep_conv(sort_disj()))
else:
return pt_final.on_rhs(top_sweep_conv(sort_disj()))
def imp_disj_iff(goal):
"""Goal is of the form A_1 | ... | A_m <--> B_1 | ... | B_n, where
the sets {A_1, ..., A_m} and {B_1, ..., B_n} are equal."""
pt1 = ProofTerm('imp_disj', Implies(goal.lhs, goal.rhs))
pt2 = ProofTerm('imp_disj', Implies(goal.rhs, goal.lhs))
return ProofTerm.equal_intr(pt1, pt2)
