def testExport3(self):
"""Case with atoms."""
pt1 = ProofTerm.atom(0, Thm.mk_equals(x, y))
pt2 = ProofTerm.atom(1, Thm.mk_equals(y, z))
pt3 = ProofTerm.transitive(pt1, pt2)
prf = Proof()
prf.add_item(0, rule="sorry", th=Thm.mk_equals(x, y))
prf.add_item(1, rule="sorry", th=Thm.mk_equals(y, z))
pt3.export(prf=prf)
self.assertEqual(thy.check_proof(prf), Thm.mk_equals(x, z))
def testTopSweepConv(self):
f = Const("f", TFun(natT, natT))
x = Var("x", natT)
th0 = eq(x, f(x))
cv = top_sweep_conv(rewr_conv(ProofTerm.atom(0, th0),
match_vars=False))
prf = Proof()
prf.add_item(0, "sorry", th=th0)
cv.get_proof_term(thy, f(x)).export(prf=prf)
self.assertEqual(thy.check_proof(prf), eq(f(x), f(f(x))))
def testLargeSum(self):
f = Const("f", TFun(natT, natT))
g = Const("g", TFun(natT, natT))
x = Var("x", natT)
th0, th1 = eq(one, zero), eq(f(x), g(x))
cv = top_conv(
else_conv(rewr_conv(ProofTerm.atom(0, th0)),
rewr_conv(ProofTerm.atom(1, th1))))
f1 = f(one)
g0 = g(zero)
t = plus(*([f1] * 50))
res = plus(*([g0] * 50))
self.assertEqual(cv.eval(thy, t), eq(t, res))
prf = Proof()
prf.add_item(0, "sorry", th=th0)
prf.add_item(1, "sorry", th=th1)
cv.get_proof_term(thy, t).export(prf=prf)
self.assertEqual(thy.check_proof(prf, check_level=1), eq(t, res))
def testRewrConvWithAssum(self):
x = Const("x", natT)
y = Const("y", natT)
x_eq_y = Term.mk_equals(x, y)
th = Thm([], Term.mk_implies(x_eq_y, x_eq_y))
cv = arg_conv(rewr_conv(ProofTerm.atom(0, th)))
f = Const("f", TFun(natT, natT))
res = Thm([x_eq_y], Term.mk_equals(f(x), f(y)))
self.assertEqual(cv.eval(thy, f(x)), res)
prf = Proof()
prf.add_item(0, "sorry", th=th)
cv.get_proof_term(thy, f(x)).export(prf=prf)
self.assertEqual(thy.check_proof(prf), res)
def testRewrConv(self):
f = Const("f", TFun(natT, natT))
g = Const("g", TFun(natT, natT))
x = Var("x", natT)
assum0 = eq(one, zero)
assum1 = eq(f(x), g(x))
# Test conversion using 1 = 0
cv1 = rewr_conv(ProofTerm.atom(0, assum0))
prf = Proof()
prf.add_item(0, "sorry", th=assum0)
eq_th = eq(one, zero)
cv1.get_proof_term(thy, one).export(prf=prf)
self.assertEqual(cv1.eval(thy, one), eq_th)
self.assertEqual(thy.check_proof(prf), eq_th)
self.assertRaises(ConvException, cv1.eval, thy, zero)
self.assertRaises(ConvException, cv1.get_proof_term, thy, zero)
# Test conversion using f x = g x
cv2 = rewr_conv(ProofTerm.atom(0, assum1))
eq0 = eq(f(zero), g(zero))
eq1 = eq(f(one), g(one))
self.assertEqual(cv2.eval(thy, f(zero)), eq0)
self.assertEqual(cv2.eval(thy, f(one)), eq1)
prf0 = Proof()
prf0.add_item(0, "sorry", th=assum1)
cv2.get_proof_term(thy, f(zero)).export(prf=prf0)
self.assertEqual(thy.check_proof(prf0), eq0)
self.assertRaises(ConvException, cv1.eval, thy, zero)
prf1 = Proof()
prf1.add_item(0, "sorry", th=assum1)
cv2.get_proof_term(thy, f(one)).export(prf=prf1)
self.assertEqual(thy.check_proof(prf1), eq1)
self.assertRaises(ConvException, cv1.get_proof_term, thy, zero)