def is_top(self) -> bool:
"""The current store is top if `all` of its variables map to a top element."""
_store = all(element.is_top() for element in self.store.values())
_top = IntervalLattice(lower=0)
_lengths = all(
_top.less_equal(element) for element in self.lengths.values())
return _store and _lengths
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 visit_Literal(self, expr, state=None, evaluation=None):
if expr in evaluation:
return evaluation
evaluation[expr] = state.lattices[expr.typ].from_literal(expr)
if isinstance(expr.typ, StringLyraType):
evaluation[LengthIdentifier(expr)] = IntervalLattice(len(expr.val), len(expr.val))
return evaluation
def __init__(self,
variables: Set[VariableIdentifier],
lattices: Dict[LyraType, Type[Lattice]],
arguments: Dict[LyraType, Dict[str, Any]] = None):
"""Create a mapping Var -> L from each variable in Var to the corresponding element in L.
:param variables: set of program variables
:param lattices: dictionary from variable types to the corresponding lattice types
:param arguments: dictionary from variable types to arguments of the corresponding lattices
"""
super().__init__()
self._variables = variables
self._lattices = lattices
self._arguments = defaultdict(
lambda: dict()) if arguments is None else arguments
try:
self._store = {
v: lattices[v.typ](**self._arguments[v.typ])
for v in variables
}
self._lengths, self._keys, self._values = dict(), dict(), dict()
for v in variables:
if v.has_length:
self._lengths[v.length] = IntervalLattice(lower=0)
if v.is_dictionary:
_key = lattices[v.typ.key_typ](
**self._arguments[v.typ.key_typ])
self._keys[v.keys] = _key
_value = lattices[v.typ.val_typ](
**self._arguments[v.typ.val_typ])
self._values[v.values] = _value
except KeyError as key:
error = f"Missing lattice for variable type {repr(key.args[0])}!"
raise ValueError(error)
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 top(self) -> 'Store':
for var in self.store:
self.store[var].top()
for var in self.lengths:
self.lengths[var] = IntervalLattice(lower=0)
for var in self.keys:
self.keys[var].top()
for var in self.values:
self.values[var].top()
return self
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 add_variable(self, variable: VariableIdentifier):
self.variables.add(variable)
typ = variable.typ
self.store[variable] = self.lattices[typ](
**self.arguments[typ]).bottom()
if variable.has_length:
self.lengths[variable.length] = IntervalLattice(lower=0).bottom()
if variable.is_dictionary:
_key = self.lattices[typ.key_typ](
**self._arguments[typ.key_typ]).bottom()
self._keys[variable.keys] = _key
_value = self.lattices[typ.val_typ](
**self._arguments[typ.val_typ]).bottom()
self._values[variable.values] = _value
return self
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))
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))