def test_neg(self):
self.assertEqual(IntervalLattice().neg(), IntervalLattice())
self.assertEqual(IntervalLattice(0, 1).neg(), IntervalLattice(-1, 0))
self.assertEqual(IntervalLattice(upper=2).neg(), IntervalLattice(lower=-2))
self.assertEqual(IntervalLattice(lower=3).neg(), IntervalLattice(upper=-3))
self.assertEqual(IntervalLattice(1, 0).neg(), IntervalLattice(1, 0))
def add_variable(self, var: VariableIdentifier):
if var not in self.store.keys():
self.variables.add(var)
self.store[var] = IntervalLattice() # top
if isinstance(var.typ, SequenceLyraType):
length = LengthIdentifier(var)
self.variables.add(length)
self.store[length] = IntervalLattice(lower=0)
else:
raise ValueError(
f"Variable can not be added to a store if it is already present"
)
def test_init(self):
self.assertFalse(IntervalLattice().is_bottom())
self.assertTrue(IntervalLattice().is_top())
self.assertFalse(IntervalLattice(0, 1).is_bottom())
self.assertFalse(IntervalLattice(0, 1).is_top())
self.assertEqual(IntervalLattice(upper=2), IntervalLattice(-inf, 2))
self.assertEqual(IntervalLattice(lower=3), IntervalLattice(3, inf))
self.assertTrue(IntervalLattice(1, 0).is_bottom())
self.assertFalse(IntervalLattice(1, 0).is_top())
def add_variable(self, var: VariableIdentifier):
if var not in self.store.keys():
self.variables.add(var)
self.store[var] = IntervalLattice() # top
else:
raise ValueError(
f"Variable can not be added to a store if it is already present"
)
def forget_variable(self, var: VariableIdentifier):
if var in self.store.keys():
self.store[var].top()
if isinstance(var.typ, SequenceLyraType):
length = LengthIdentifier(var)
self.store[length] = IntervalLattice(lower=0)
else:
raise ValueError(
f"Variable can only be forgotten if it is abstracted in the store"
)
def __init__(self, type_element=None, range_element=None):
super().__init__()
if type_element is None:
type_element = TypeLattice().top()
if range_element is None:
range_element = IntervalLattice().top()
self._assumptions = {
AssumptionLattice.Assumption.type_assmp: type_element,
AssumptionLattice.Assumption.range_assmp: range_element
}
self.pp = None
def default(self, obj):
""" Turns the serialized objects back to assumptions
:param obj: current serialized object
:return: assumption representation of the serialized objects
"""
if not obj:
return None
if "0" in obj:
return obj["0"]
if "iterations" in obj:
num_iter = obj["iterations"]
assmps = obj["assmps"]
return InputAssumptionLattice(num_iter, assmps)
type_assumption = TypeLattice()
range_assumption = IntervalLattice()
if "type_assmp" in obj:
type_assmp = obj["type_assmp"]
if type_assmp == "Int":
type_assumption = TypeLattice().integer()
elif type_assmp == "Float":
type_assumption = TypeLattice().real()
if "range_assmp" in obj:
bounds = obj["range_assmp"]
if bounds == '⊥':
range_assumption = IntervalLattice().bottom()
elif bounds == 'T':
range_assumption = IntervalLattice()
else:
bounds = obj["range_assmp"][1:-1].split(',')
bounds[0] = -inf if bounds[0].strip() == "-inf" else int(bounds[0])
bounds[1] = inf if bounds[1].strip() == "inf" else int(bounds[1])
range_assumption = IntervalLattice(bounds[0], bounds[1])
return AssumptionLattice(type_assumption, range_assumption)
def decomp(self, exclude: 'IntervalKWrapper') \
-> Set['IntervalKWrapper']:
left = deepcopy(self) # left & right non-exclude
right = deepcopy(self)
k_state = self.store[self.k_var]
k_exclude = exclude.store[self.k_var]
if k_state.is_bottom():
left.store[self.k_var].bottom()
right.store[self.k_var].bottom()
elif k_exclude.is_bottom():
left.store[self.k_var] = IntervalLattice(k_state.lower,
k_state.upper)
right.store[self.k_var].bottom()
elif k_exclude.is_top(): # exclude everything
left.store[self.k_var].bottom()
right.store[self.k_var].bottom()
else:
left.store[self.k_var] = IntervalLattice(
k_state.lower, k_exclude.lower - 1) # bottom if empty
right.store[self.k_var] = IntervalLattice(
k_exclude.upper + 1, k_state.upper) # bottom if empty
return {left, right}
def test_add(self):
self.assertEqual(IntervalLattice().add(IntervalLattice(0, 1)), IntervalLattice())
self.assertEqual(IntervalLattice().add(IntervalLattice(1, 0)), IntervalLattice(1, 0))
self.assertEqual(IntervalLattice(0, 1).add(IntervalLattice()), IntervalLattice())
self.assertEqual(IntervalLattice(0, 1).add(IntervalLattice(1, 0)), IntervalLattice(1, 0))
self.assertEqual(IntervalLattice(1, 0).add(IntervalLattice()), IntervalLattice(1, 0))
self.assertEqual(IntervalLattice(1, 0).add(IntervalLattice(0, 1)), IntervalLattice(1, 0))
self.assertEqual(IntervalLattice(upper=3).add(IntervalLattice(lower=2)), IntervalLattice())
self.assertEqual(IntervalLattice(2, 4).add(IntervalLattice(1, 3)), IntervalLattice(3, 7))
self.assertEqual(IntervalLattice(1, 2).add(IntervalLattice(3, 4)), IntervalLattice(4, 6))
def test_widening(self):
self.assertEqual(IntervalLattice().widening(IntervalLattice(0, 1)), IntervalLattice())
self.assertEqual(IntervalLattice().widening(IntervalLattice(1, 0)), IntervalLattice())
self.assertEqual(IntervalLattice(0, 1).widening(IntervalLattice()), IntervalLattice())
widening1 = IntervalLattice(0, 1).widening(IntervalLattice(1, 0))
self.assertEqual(widening1, IntervalLattice(0, 1))
self.assertEqual(IntervalLattice(1, 0).widening(IntervalLattice()), IntervalLattice())
widening2 = IntervalLattice(1, 0).widening(IntervalLattice(0, 1))
self.assertEqual(widening2, IntervalLattice(0, 1))
widening3 = IntervalLattice(upper=3).widening(IntervalLattice(lower=2))
self.assertEqual(widening3, IntervalLattice())
widening4 = IntervalLattice(2, 4).widening(IntervalLattice(1, 3))
self.assertEqual(widening4, IntervalLattice(upper=4))
widening5 = IntervalLattice(1, 2).widening(IntervalLattice(3, 4))
self.assertEqual(widening5, IntervalLattice(lower=1))
def test_meet(self):
self.assertEqual(IntervalLattice().meet(IntervalLattice(0, 1)), IntervalLattice(0, 1))
self.assertEqual(IntervalLattice().meet(IntervalLattice(1, 0)), IntervalLattice(1, 0))
self.assertEqual(IntervalLattice(0, 1).meet(IntervalLattice()), IntervalLattice(0, 1))
self.assertEqual(IntervalLattice(0, 1).meet(IntervalLattice(1, 0)), IntervalLattice(1, 0))
self.assertEqual(IntervalLattice(1, 0).meet(IntervalLattice()), IntervalLattice(1, 0))
self.assertEqual(IntervalLattice(1, 0).meet(IntervalLattice(0, 1)), IntervalLattice(1, 0))
meet = IntervalLattice(upper=3).meet(IntervalLattice(lower=2))
self.assertEqual(meet, IntervalLattice(2, 3))
self.assertEqual(IntervalLattice(2, 4).meet(IntervalLattice(1, 3)), IntervalLattice(2, 3))
self.assertEqual(IntervalLattice(1, 2).meet(IntervalLattice(3, 4)), IntervalLattice(1, 0))
def test_join(self):
self.assertEqual(IntervalLattice().join(IntervalLattice(0, 1)), IntervalLattice())
self.assertEqual(IntervalLattice().join(IntervalLattice(1, 0)), IntervalLattice())
self.assertEqual(IntervalLattice(0, 1).join(IntervalLattice()), IntervalLattice())
self.assertEqual(IntervalLattice(0, 1).join(IntervalLattice(1, 0)), IntervalLattice(0, 1))
self.assertEqual(IntervalLattice(1, 0).join(IntervalLattice()), IntervalLattice())
self.assertEqual(IntervalLattice(1, 0).join(IntervalLattice(0, 1)), IntervalLattice(0, 1))
join = IntervalLattice(upper=3).join(IntervalLattice(lower=2))
self.assertEqual(join, IntervalLattice())
self.assertEqual(IntervalLattice(2, 4).join(IntervalLattice(1, 3)), IntervalLattice(1, 4))
self.assertEqual(IntervalLattice(1, 2).join(IntervalLattice(3, 4)), IntervalLattice(1, 4))
def test_leq(self):
self.assertFalse(IntervalLattice().less_equal(IntervalLattice(0, 1)))
self.assertFalse(IntervalLattice().less_equal(IntervalLattice(1, 0)))
self.assertTrue(IntervalLattice(0, 1).less_equal(IntervalLattice()))
self.assertFalse(IntervalLattice(0, 1).less_equal(IntervalLattice(1, 0)))
self.assertTrue(IntervalLattice(1, 0).less_equal(IntervalLattice()))
self.assertTrue(IntervalLattice(1, 0).less_equal(IntervalLattice(0, 1)))
def test_sub(self):
self.assertEqual(IntervalLattice().sub(IntervalLattice(0, 1)), IntervalLattice())
self.assertEqual(IntervalLattice().sub(IntervalLattice(1, 0)), IntervalLattice(1, 0))
self.assertEqual(IntervalLattice(0, 1).sub(IntervalLattice()), IntervalLattice())
self.assertEqual(IntervalLattice(0, 1).sub(IntervalLattice(1, 0)), IntervalLattice(1, 0))
self.assertEqual(IntervalLattice(1, 0).sub(IntervalLattice()), IntervalLattice(1, 0))
self.assertEqual(IntervalLattice(1, 0).sub(IntervalLattice(0, 1)), IntervalLattice(1, 0))
sub = IntervalLattice(upper=3).sub(IntervalLattice(lower=2))
self.assertEqual(sub, IntervalLattice(upper=1))
self.assertEqual(IntervalLattice(2, 4).sub(IntervalLattice(1, 3)), IntervalLattice(-1, 3))
self.assertEqual(IntervalLattice(1, 2).sub(IntervalLattice(3, 4)), IntervalLattice(-3, -1))