def testEvalSem2(self):
com = Seq(incr_one, incr_one)
st = mk_const_fun(natT, zero)
st2 = fun_upd_of_seq(0, 2)
goal = Sem(com, st, st2)
prf = hoare.eval_Sem_macro().get_proof_term(thy, goal, []).export()
self.assertEqual(thy.check_proof(prf), Thm([], goal))
def testEvalSem(self):
com = Seq(Assign(zero, abs(s, one)),
Assign(one, abs(s, nat.to_binary(2))))
st = mk_const_fun(natT, zero)
st2 = fun_upd_of_seq(0, 1, 1, 2)
goal = Sem(com, st, st2)
prf = hoare.eval_Sem_macro().get_proof_term(thy, goal, []).export()
self.assertEqual(thy.check_proof(prf), Thm([], goal))
def testEvalSem5(self):
com = While(abs(s, logic.neg(eq(s(zero), nat.to_binary(3)))),
assn_true, incr_one)
st = mk_const_fun(natT, zero)
st2 = fun_upd_of_seq(0, 3)
goal = Sem(com, st, st2)
prf = hoare.eval_Sem_macro().get_proof_term(thy, goal, []).export()
rpt = ProofReport()
self.assertEqual(thy.check_proof(prf, rpt), Thm([], goal))
def process_file(input, output):
thy = basic.load_theory('hoare')
dn = os.path.dirname(os.path.realpath(__file__))
with open(os.path.join(dn, 'examples/' + input + '.json'), encoding='utf-8') as a:
data = json.load(a)
output = json_output.JSONTheory(output, ["hoare"], "Generated from " + input)
content = data['content']
eval_count = 0
vcg_count = 0
for run in content:
if run['ty'] == 'eval':
com = parse_hoare(run['com'])
st1 = mk_const_fun(nat.natT, nat.zero)
for k, v in sorted(run['init'].items()):
st1 = mk_fun_upd(st1, nat.to_binary(str_to_nat(k)), nat.to_binary(v))
st2 = mk_const_fun(nat.natT, nat.zero)
for k, v in sorted(run['final'].items()):
st2 = mk_fun_upd(st2, nat.to_binary(str_to_nat(k)), nat.to_binary(v))
Sem = hoare.Sem(natFunT)
goal = Sem(com, st1, st2)
prf = ProofTermDeriv("eval_Sem", thy, goal, []).export()
rpt = ProofReport()
th = thy.check_proof(prf, rpt)
output.add_theorem("eval" + str(eval_count), th, prf)
eval_count += 1
elif run['ty'] == 'vcg':
com = parse_hoare(run['com'])
pre = Term.mk_abs(st, parse_cond(run['pre']))
post = Term.mk_abs(st, parse_cond(run['post']))
Valid = hoare.Valid(natFunT)
goal = Valid(pre, com, post)
prf = hoare.vcg_solve(thy, goal).export()
rpt = ProofReport()
th = thy.check_proof(prf, rpt)
output.add_theorem("vcg" + str(vcg_count), th, prf)
vcg_count += 1
else:
raise TypeError()
output.export_json()
def testEvalSem4(self):
com = Cond(abs(s, logic.neg(eq(s(zero), one))), incr_one, Skip)
st = mk_const_fun(natT, zero)
st2 = fun_upd_of_seq(0, 1)
goal = Sem(com, st, st2)
prf = hoare.eval_Sem_macro().get_proof_term(thy, goal, []).export()
self.assertEqual(thy.check_proof(prf), Thm([], goal))
goal = Sem(com, st2, st2)
prf = hoare.eval_Sem_macro().get_proof_term(thy, goal, []).export()
self.assertEqual(thy.check_proof(prf), Thm([], goal))
def testProveEvalI(self):
s = function.mk_fun_upd(function.mk_const_fun(natT, zero), one,
nat.to_binary(7))
test_data = [
(expr.Plus(expr.V(one),
expr.N(nat.to_binary(5))), nat.to_binary(12)),
(expr.Plus(expr.V(zero),
expr.N(nat.to_binary(5))), nat.to_binary(5)),
(expr.Times(expr.V(one),
expr.N(nat.to_binary(5))), nat.to_binary(35)),
]
for t, n in test_data:
goal = expr.avalI(s, t, n)
prf = expr.prove_avalI_macro().get_proof_term(thy, goal,
[]).export()
self.assertEqual(thy.check_proof(prf), Thm([], goal))
def fun_upd_of_seq(*ns):
return mk_fun_upd(mk_const_fun(natT, zero),
*[nat.to_binary(n) for n in ns])