def testComputeWP(self):
Q = Var("Q", TFun(natFunT, BoolType))
test_data = [
(Assign(zero, Lambda(s, one)),
Lambda(s, Q(mk_fun_upd(s, zero, one)))),
(Seq(Assign(zero, Lambda(s, one)), Assign(one, Lambda(s, Nat(2)))),
Lambda(s, Q(mk_fun_upd(s, zero, one, one, Nat(2))))),
]
for c, P in test_data:
prf = imp.compute_wp(natFunT, c, Q).export()
self.assertEqual(theory.check_proof(prf), Thm([], Valid(P, c, Q)))
def testMkAssign(self):
a, b = Var("a", TFun(NatType, NatType)), Var("b", BoolType)
var_map = {a: 0, b: 1}
s = Var("s", gcl.stateT)
test_data = [
({
a(one): zero
}, function.mk_fun_upd(s, Para(Ident(zero), one), NatV(zero))),
({
b: one
}, function.mk_fun_upd(s, Ident(one), NatV(one))),
]
for assign, res in test_data:
self.assertEqual(gcl.mk_assign(var_map, s, assign), res)
def testPrintFunction(self):
f = Var("f", TFun(Ta, Ta))
Tb = TVar('b')
Tc = TVar('c')
g = Var('g', TFun(Tb, Tc))
h = Var('h', TFun(Ta, Tb))
test_data = [
(function.mk_fun_upd(f, a, b), "(f)(a := b)"),
(function.mk_fun_upd(f, a, b, b, a), "(f)(a := b, b := a)"),
(function.mk_comp(g, h), "g O h"),
(function.mk_comp(g, h)(a), "(g O h) a"),
(function.mk_const_fun(NatType, nat.zero), "%x::nat. (0::nat)"),
]
basic.load_theory('function')
with global_setting(unicode=False):
for t, s in test_data:
self.assertEqual(printer.print_term(t), s)
def process_file(input, output):
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[:5]:
if run['ty'] == 'eval':
com = parse_com(run['com'])
st1 = mk_const_fun(NatType, nat.zero)
for k, v in sorted(run['init'].items()):
st1 = mk_fun_upd(st1, Nat(str_to_nat(k)), Nat(v))
st2 = mk_const_fun(NatType, nat.zero)
for k, v in sorted(run['final'].items()):
st2 = mk_fun_upd(st2, Nat(str_to_nat(k)), Nat(v))
Sem = imp.Sem(natFunT)
goal = Sem(com, st1, st2)
prf = ProofTerm("eval_Sem", goal, []).export()
rpt = ProofReport()
th = theory.check_proof(prf, rpt)
output.add_theorem("eval" + str(eval_count), th, prf)
eval_count += 1
elif run['ty'] == 'vcg':
com = parse_com(run['com'])
pre = Lambda(st, parse_cond(run['pre']))
post = Lambda(st, parse_cond(run['post']))
Valid = imp.Valid(natFunT)
goal = Valid(pre, com, post)
prf = imp.vcg_solve(goal).export()
rpt = ProofReport()
th = theory.check_proof(prf, rpt)
output.add_theorem("vcg" + str(vcg_count), th, prf)
vcg_count += 1
else:
raise TypeError
output.export_json()
def testProveAvalIFail(self):
s = fun_upd_of_seq(1, 7)
s2 = Var("s2", TFun(NatType, NatType))
s3 = function.mk_fun_upd(s2, zero, one)
macro = expr.prove_avalI_macro()
# Value does not match
self.assertFalse(macro.can_eval(expr.avalI(s, V(one), Nat(5))))
# State cannot be evaluated
self.assertFalse(macro.can_eval(expr.avalI(s2, V(one), Nat(5))))
self.assertFalse(macro.can_eval(expr.avalI(s3, V(one), Nat(5))))
# Goal is not avalI
self.assertFalse(macro.can_eval(Eq(V(one), N(zero))))
def mk_assign(var_map, s, assigns):
"""Given a dictionary of assignments, form the corresponding term.
Example: given var_map {a: 0, b: 1}, where a is a function
and b is a scalar.
mk_assign(var_map, s, {a(i): 2}) = (s)(Para (Ident 0) i := 2)
mk_assign(var_map, s, {b: 1}) = (s)(Ident 1 := 1)
"""
assign_args = []
for k, v in assigns.items():
k2 = convert_term(var_map, s, k)
assert k2.fun == s, "mk_assign: key is not an identifer."
assign_args.append(k2.arg)
assign_args.append(convert_term(var_map, s, v))
return function.mk_fun_upd(s, *assign_args)
def compute_wp(T, c, Q):
"""Compute the weakest precondition for the given command
and postcondition. Here c is the program and Q is the postcondition.
The computation is by case analysis on the form of c. The function
returns a proof term showing [...] |- Valid P c Q, where P is the
computed precondition, and [...] contains the additional subgoals.
"""
if c.is_const("Skip"): # Skip
return apply_theorem("skip_rule", concl=Valid(T)(Q, c, Q))
elif c.is_comb("Assign", 2): # Assign a b
a, b = c.args
s = Var("s", T)
P2 = Lambda(s, Q(function.mk_fun_upd(s, a, b(s).beta_conv())))
return apply_theorem("assign_rule",
inst=Inst(b=b),
concl=Valid(T)(P2, c, Q))
elif c.is_comb("Seq", 2): # Seq c1 c2
c1, c2 = c.args
wp1 = compute_wp(T, c2, Q) # Valid Q' c2 Q
wp2 = compute_wp(T, c1, wp1.prop.args[0]) # Valid Q'' c1 Q'
return apply_theorem("seq_rule", wp2, wp1)
elif c.is_comb("Cond", 3): # Cond b c1 c2
b, c1, c2 = c.args
wp1 = compute_wp(T, c1, Q)
wp2 = compute_wp(T, c2, Q)
res = apply_theorem("if_rule", wp1, wp2, inst=Inst(b=b))
return res
elif c.is_comb("While", 3): # While b I c
_, I, _ = c.args
pt = apply_theorem("while_rule", concl=Valid(T)(I, c, Q))
pt0 = ProofTerm.assume(pt.assums[0])
pt1 = vcg(T, pt.assums[1])
return pt.implies_elim(pt0, pt1)
else:
raise NotImplementedError
def testStripFunUpd(self):
self.assertEqual(strip_fun_upd(f), (f, []))
self.assertEqual(strip_fun_upd(mk_fun_upd(f, a1, b1)), (f, [(a1, b1)]))
self.assertEqual(strip_fun_upd(mk_fun_upd(f, a1, b1, a2, b2)),
(f, [(a1, b1), (a2, b2)]))
def testMkFunUpd(self):
self.assertEqual(mk_fun_upd(f, a1, b1, a2, b2),
mk_fun_upd(mk_fun_upd(f, a1, b1), a2, b2))
def fun_upd_of_seq(*ns):
return mk_fun_upd(function.mk_const_fun(NatType, zero),
*[Nat(n) for n in ns])
