def testSolve(self):
if not z3wrapper.z3_loaded:
return
context.set_context('nat',
vars={
"s": 'nat => nat',
"A": 'nat',
"B": 'nat'
})
test_data = [
("s 0 = 0 & s 1 = 0 --> s 1 = s 0 * B", True),
("s 1 = s 0 * B & ~~s 0 = A --> s 1 = A * B", True),
("s 1 = s 0 * B & ~s 0 = A --> s 1 + B = (s 0 + 1) * B", True),
("A * B + 1 = 1 + B * A", True),
("s 0 = s 1", False),
("s 0 + s 1 = A --> A + s 2 = B --> s 0 + s 2 + s 1 = B", True),
("s 0 + s 1 = A --> A + s 2 = B --> s 0 + s 2 = B", False),
("(!n. s n = 0) --> s 2 = 0", True),
("(!n. s n = 0) --> s 0 = 1", False),
]
for s, res in test_data:
t = parser.parse_term(s)
self.assertEqual(z3wrapper.solve(t), res)
def testSolveNat(self):
if not z3wrapper.z3_loaded:
return
context.set_context('set', vars={'x': 'nat', 'y': 'nat', 'z': 'nat'})
test_data = [('x - y + z = x + z - y', False),
('x >= y --> x - y + z = x + z - y', True)]
for s, res in test_data:
t = parser.parse_term(s)
self.assertEqual(z3wrapper.solve(t), res)
def verify_subgoal(self, inv_id, rule_id, case_id, hint):
"""Verify the subgoal from the given hints.
In addition to the assumptions given in get_subgoal, we need
some additional assumptions, including distinctness of states.
"""
goal = self.get_subgoal(inv_id, rule_id, case_id, hint)
goal = self.replace_states(goal)
if z3wrapper.z3_loaded:
ans = z3wrapper.solve(goal)
else:
ans = True
return goal, ans
def testSolve(self):
if not z3wrapper.z3_loaded:
return
ctxt = {"s": TFun(natT, natT), "A": natT, "B": natT}
test_data = [
("s 0 = 0 & s 1 = 0 --> s 1 = s 0 * B", True),
("s 1 = s 0 * B & ~~s 0 = A --> s 1 = A * B", True),
("s 1 = s 0 * B & ~s 0 = A --> s 1 + B = (s 0 + 1) * B", True),
("A * B + 1 = 1 + B * A", True),
("s 0 = s 1", False),
("s 0 + s 1 = A --> A + s 2 = B --> s 0 + s 2 + s 1 = B", True),
("s 0 + s 1 = A --> A + s 2 = B --> s 0 + s 2 = B", False),
("(!n. s n = 0) --> s 2 = 0", True),
("(!n. s n = 0) --> s 0 = 1", False),
]
for s, res in test_data:
t = parser.parse_term(thy, ctxt, s)
self.assertEqual(z3wrapper.solve(t), res)
def testSolveReal(self):
if not z3wrapper.z3_loaded:
return
context.set_context('real',
vars={
'a': 'real',
'b': 'real',
'x': 'real',
'f': 'real => real',
'S': 'real set',
'T': 'real set',
'n': 'nat'
})
test_data = [
('max a b = (1/2) * (a + b + abs(a - b))', True),
('(x Mem T --> 0 <= f x) --> S Sub T --> (if x Mem S then f x else 0) <= (if x Mem T then f x else 0)',
True),
('{x. (a <= x & x <= b) & ~(a < x & x < b)} Sub {a, b}', True),
('max (if x Mem S then (1::real) else 0) (if x Mem T then 1 else 0) = (if x Mem (S Un T) then 1 else 0)',
True),
('min (if x Mem S then (1::real) else 0) (if x Mem T then 1 else 0) = (if x Mem (S Int T) then 1 else 0)',
True),
('S Int T = empty_set --> (if x Mem S then (1::real) else 0) + (if x Mem T then 1 else 0) = (if x Mem (S Un T) then 1 else 0)',
True),
('S ∪ T = S ∩ T ∪ {x. x ∈ S ∧ ¬x ∈ T} ∪ {x. x ∈ T ∧ ¬x ∈ S}',
True),
('(0::real) <= (if x Mem s & 1 / (of_nat n + 1) <= abs (f x) then 1 else 0)',
True),
('(0::real) <= of_nat n + 1', True),
('1 / (of_nat n + 1) < b --> 1 < (of_nat n + 1) * b', True),
('1 / (a + 1) < b --> 1 < (a + 1) * b', False),
('a <= of_nat n --> a < of_nat (n + 1)', True),
('~(n = 0) --> of_nat (n - 1) + (1::real) = of_nat n', True),
('(1::real) = 0 --> real_inverse a = b', True),
]
for s, res in test_data:
t = parser.parse_term(s)
self.assertEqual(z3wrapper.solve(t), res)
def verify():
"""Verify a program by generating verification conditions,
and attempt to solve the conditions using SMT.
"""
data = json.loads(request.get_data().decode("utf-8"))
basic.load_theory('hoare')
pre = parser2.cond_parser.parse(data['pre'])
post = parser2.cond_parser.parse(data['post'])
com = parser2.com_parser.parse(data['com'])
com.pre = [pre]
com.compute_wp(post)
lines = com.get_lines(data['vars'])
for line in lines:
if line['ty'] == 'vc':
vc_hol = line['prop']
line['prop'] = printer.print_term(line['prop'])
line['smt'] = z3wrapper.solve(vc_hol)
return jsonify({
'lines': lines,
})
def testSolveSet(self):
if not z3wrapper.z3_loaded:
return
context.set_context('set',
vars={
'm': 'nat',
'S': 'nat set',
'T': 'nat set',
'x': 'nat',
'a': "'a",
'A': "'a set"
})
test_data = [('x Mem S --> S Sub T --> x Mem T', True),
('m Mem univ', True),
('(?x1. x = x1 & x1 Mem S) --> x Mem S', True),
('(?a1. a = a1 & a1 Mem A) --> a Mem A', True),
('x Mem (diff S T) --> x Mem S', True),
('x Mem S --> x Mem (diff S T)', False)]
for s, res in test_data:
t = parser.parse_term(s)
self.assertEqual(z3wrapper.solve(t), res)