def test_localize_two_ass_one_gua(self):
"""
forall(i,j) a_i_j -> forall(i) b_i
replaced by
forall(i,j) (a_i_j -> b_i)
"""
a_i_j_is_true, b_j_is_true = _get_is_true('a', 'i',
'j'), _get_is_true('b', 'j')
b_i_is_true = _get_is_true('b', 'i')
prop = SpecProperty([ForallExpr(['i', 'j'], a_i_j_is_true)],
[ForallExpr(['j'], b_j_is_true)])
localized_prop = localize(prop)
expected_prop_i_j1 = SpecProperty(
[Bool(True)],
[ForallExpr(['i', 'j'], BinOp('->', a_i_j_is_true, b_j_is_true))])
expected_prop_i_j2 = SpecProperty(
[Bool(True)],
[ForallExpr(['i', 'j'], BinOp('->', a_i_j_is_true, b_i_is_true))])
assert str(localized_prop) == str(expected_prop_i_j1) or \
str(localized_prop) == str(expected_prop_i_j2), \
str(localized_prop)
def test_strengthen3(self):
"""
Forall(i,j) GFa_i * GFb_i_j * Gc_i_j -> Forall(k,m) GF(d_k_m) * G(e_k)
replaced by
'safety': Forall(i) Gc_i_j -> Forall(k) G(e_k)
'liveness': Forall(i,j) GFa_i * GFb_i_j * Gc_i -> Forall(k,m) GF(d_k_m)
"""
a_i, b_i_j, c_i_j = _get_is_true('a', 'i'), _get_is_true(
'b', 'i', 'j'), _get_is_true('c', 'i', 'j')
ass = ForallExpr(['i', 'j'],
BinOp(
'*', UnaryOp('G', UnaryOp('F', a_i)),
BinOp('*', UnaryOp('G', UnaryOp('F', b_i_j)),
UnaryOp('G', c_i_j))))
d_k_m = _get_is_true('d', 'k', 'm')
e_k = _get_is_true('e', 'k')
gua = ForallExpr(['k', 'm'],
BinOp('*', UnaryOp('G', UnaryOp('F', d_k_m)),
UnaryOp('G', e_k)))
property = SpecProperty([ass], [gua])
safety_properties, liveness_properties = strengthen(
property, self._get_converter())
#lazy..
print('safety_properties', safety_properties)
assert len(safety_properties) == 1, str(safety_properties)
assert len(list(chain(*[sp.assumptions
for sp in safety_properties]))) == 1
assert len(list(chain(*[sp.guarantees
for sp in safety_properties]))) == 1
print('liveness_properties', liveness_properties)
def visit_binary_op(self, binary_op:BinOp):
if binary_op.name == 'W':
bin_op_expr = BinOp('+',
BinOp('U', binary_op.arg1, binary_op.arg2),
UnaryOp('G', binary_op.arg1))
return self.dispatch(bin_op_expr)
else:
return super().visit_binary_op(binary_op)
def test_fix_indices_partially_fixed(self):
a_i_1 = _get_is_true('a', 'i', 1)
c_0 = _get_is_true('c', 0)
expr = ForallExpr(['i'], BinOp('*', a_i_1, c_0))
result = _fix_indices({'i': 2}, expr)
a_2_1 = _get_is_true('a', 2, 1)
expected_result = BinOp('*', a_2_1, c_0)
self.assertEqual(str(result), str(expected_result))
def guarantees(self):
""" Return G(tok_i -> Fsends_i)
"""
#TODO: introduce Globally/Finally class
expr = UnaryOp(
'G',
BinOp(
'->', BinOp('=', QuantifiedSignal(HAS_TOK_NAME, 'i'),
Number(1)),
UnaryOp(
'F',
BinOp('=', QuantifiedSignal(SENDS_NAME, 'i'), Number(1)))))
tok_released = ForallExpr(['i'], expr)
return [tok_released]
def and_properties(properties) -> SpecProperty:
property_expressions = [
BinOp('->', and_expressions(p.assumptions),
and_expressions(p.guarantees)) for p in properties
]
return SpecProperty([Bool(True)], [and_expressions(property_expressions)])
def normalize_conjuncts(conjuncts:list) -> Expr:
""" sound, complete
forall(i,j) a_i_j and forall(i) b_i ----> forall(i,j) (a_i_j and b_i)
forall(i) a_i and forall(j) b_j ----> forall(i) (a_i and b_i)
"""
if len(conjuncts) == 0:
return Bool(True)
if len(conjuncts) == 1 and isinstance(conjuncts[0], Bool):
return conjuncts[0]
for e in conjuncts:
assert isinstance(e, ForallExpr), 'global non-parameterized properties are not supported'
max_indices = max(conjuncts, key=lambda e: len(e.arg1))
new_indices = max_indices.arg1
normalized_underlying_expr = None
for e in conjuncts:
old_indices = e.arg1
new_by_old = dict((o, new_indices[i]) for i, o in enumerate(old_indices))
new_underlying_e = _replace_indices(new_by_old, e.arg2)
if normalized_underlying_expr is None:
normalized_underlying_expr = new_underlying_e
else:
normalized_underlying_expr = BinOp('*', normalized_underlying_expr, new_underlying_e)
normalized_expr = ForallExpr(new_indices, normalized_underlying_expr)
return normalized_expr
def test_get_conjuncts_and_op(self):
a, b = Signal('a'), Signal('b')
conjunction_expr = BinOp('*', a, b)
conjuncts = _get_conjuncts(conjunction_expr)
assert len(conjuncts) == 2
assert a in conjuncts
assert b in conjuncts
def test_denormalize(self):
a_i, b_i = _get_is_true('a', 'i'), _get_is_true('b', 'i')
expr = ForallExpr(['i'], BinOp('*', a_i, b_i))
denormalized_expressions = _denormalize(expr)
assert len(denormalized_expressions) == 2, str(
denormalized_expressions)
def implications(self) -> list:
expr = UnaryOp(
'G',
UnaryOp('F',
BinOp('=', QuantifiedSignal(HAS_TOK_NAME, 'i'),
Number(1))))
fair_tok_sched = ForallExpr(['i'], expr)
return [fair_tok_sched]
def test_fix_indices_main(self):
expr = parse_expr('Forall(i,j,k,m) (a_i_j_k=1 * b_i_m=1)')
result = _fix_indices({'i': 1, 'j': 2, 'k': 3}, expr)
expected_result = ForallExpr(['m'],
BinOp('*', _get_is_true('a', 1, 2, 3),
_get_is_true('b', 1, 'm')))
self.assertEqual(str(expected_result), str(result))
def to_boolean_nusmv(lts: LTS, specification: SpecProperty) -> str:
nof_state_bits = int(max(1, math.ceil(math.log(len(lts.states), 2))))
bits_by_state = dict((state, bin_fixed_list(i, nof_state_bits))
for (i, state) in enumerate(sorted(lts.states)))
state_bits = lmap(_ith_state_bit, range(nof_state_bits))
_assert_no_intersection(state_bits,
list(lts.input_signals) + lts.output_signals)
dot_lines = StrAwareList()
dot_lines += 'MODULE main'
dot_lines += 'IVAR'
dot_lines += [
' {signal} : boolean;'.format(signal=s.name)
for s in lts.input_signals
]
dot_lines += 'VAR'
dot_lines += [' {si} : boolean;'.format(si=si) for si in state_bits]
dot_lines += 'DEFINE'
dot_lines += [
' {out_name} := {formula} ;'.format(out_name=out_name,
formula=_get_formula(
out_name, out_model,
bits_by_state))
for (out_name, out_model) in lts.model_by_name.items()
]
dot_lines += 'ASSIGN'
for i, sb in enumerate(state_bits):
sb_init = str(bits_by_state[list(lts.init_states)[0]][i]).upper()
dot_lines += ' init({sb}) := {init_sb};'.format(sb=sb,
init_sb=sb_init)
dot_lines += ' next({sb}) := '.format(sb=sb)
dot_lines += ' case'
for (label, next_state) in lts.tau_model.items():
sb_next = str(bits_by_state[next_state][i]).upper()
dot_lines += ' {formula} : {next_state};'.format(
formula=_clause_to_formula(label, bits_by_state),
next_state=sb_next)
dot_lines += ' TRUE : FALSE;' # default: unreachable states, don't care
dot_lines += ' esac;'
expr = BinOp('->', and_expressions(specification.assumptions),
and_expressions(specification.guarantees))
expr = WeakToUntilConverterVisitor().dispatch(
expr) # SMV does not have Weak until
dot_lines += 'LTLSPEC ' + AstToSmvProperty().dispatch(expr)
return '\n'.join(dot_lines)
def test_strengthen2(self):
"""
Forall(i) GFa_i and G(b_i) -> Forall(j) GF(c_j) and G(d_j)
replaced by
'liveness': Forall(i) GFa_i and G(b_i) -> Forall(j) GF(c_j)
and
'safety': Forall(i) G(b_i) -> Forall(j) G(d_j)
"""
a_i, b_i = QuantifiedSignal('a', 'i'), QuantifiedSignal('b', 'i')
c_j, d_j = QuantifiedSignal('c', 'j'), QuantifiedSignal('d', 'j')
ass = ForallExpr(['i'],
BinOp('*', UnaryOp('G', UnaryOp('F', a_i)),
UnaryOp('G', b_i)))
gua = ForallExpr(['j'],
BinOp('*', UnaryOp('G', UnaryOp('F', c_j)),
UnaryOp('G', d_j)))
property = SpecProperty([ass], [gua])
safety_properties, liveness_properties = strengthen(
property, self._get_converter())
assert len(liveness_properties) == 1, str(liveness_properties)
assert len(safety_properties) == 1, str(safety_properties)
expected_liveness_gua = ForallExpr(['j'],
UnaryOp('G', UnaryOp('F', c_j)))
#: :type: SpecProperty
liveness_prop = liveness_properties[0]
assert str(liveness_prop.assumptions) == str([ass]), str(liveness_prop)
assert str(liveness_prop.guarantees) == str([expected_liveness_gua])
safety_prop = safety_properties[0]
expected_safety_ass = ForallExpr(['i'], UnaryOp('G', b_i))
expected_safety_gua = ForallExpr(['j'], UnaryOp('G', d_j))
expected_safety_prop = SpecProperty([expected_safety_ass],
[expected_safety_gua])
assert str(expected_safety_prop) == str(safety_prop), str(safety_prop)
def _get_log_encoded_expr(signal:QuantifiedSignal, new_sched_signal_name:str, cutoff:int) -> Expr:
assert len(signal.binding_indices) == 1
proc_index = signal.binding_indices[0]
nof_sched_bits = int(max(1, math.ceil(math.log(cutoff, 2))))
bits = bin_fixed_list(proc_index, nof_sched_bits)
#TODO: use quantified signal or signal?
conjuncts = [BinOp('=',
QuantifiedSignal(new_sched_signal_name, bit_index),
Number(1 if bit_value else 0))
for bit_index, bit_value in enumerate(bits)]
conjunction = and_expressions(conjuncts)
return conjunction
def test_localize_zero_ass(self):
"""
true -> forall(i) b_i
replaced by
forall(i) (true -> b_i)
"""
b_i_is_true = _get_is_true('b', 'i')
prop = SpecProperty([Bool(True)], [ForallExpr(['i'], b_i_is_true)])
localized_prop = localize(prop)
expected_prop = SpecProperty(
[Bool(True)],
[ForallExpr(['i'], BinOp('->', Bool(True), b_i_is_true))])
assert str(localized_prop) == str(expected_prop), str(localized_prop)
def test_sched_optimization(self):
scheduler = InterleavingScheduler()
forall_expr = scheduler.assumptions[0] # Forall(i) GFsched_i=1
instantiated_expr = _instantiate_expr(
forall_expr, 2, False) # GFsched_0=1 * GFsched_1=1
result_expr = _apply_log_bit_optimization('sch', instantiated_expr, 2,
scheduler)
expected_expr = BinOp(
'*', UnaryOp('G', UnaryOp('F', _get_is_true('sch', 0))),
UnaryOp('G', UnaryOp('F', _get_is_false('sch', 0))))
result_str = _get_sorted_conjuncts_str(result_expr)
expected_str = _get_sorted_conjuncts_str(expected_expr)
self.assertEqual(expected_str, result_str)
def localize(property:SpecProperty):
""" sound, but incomplete
forall(i) a_i -> forall(j) g_j
=>
forall(i) (a_i -> g_i)
forall(i,j) a_i_j -> forall(k) g_k
=>
forall(i,j) (a_i_j -> g_i)
"""
if not is_quantified_property(property):
return property
normalized_ass = normalize_conjuncts(property.assumptions)
normalized_gua = normalize_conjuncts(property.guarantees)
binding_indices_ass = _get_indices(normalized_ass)
binding_indices_gua = _get_indices(normalized_gua)
if len(binding_indices_ass) > len(binding_indices_gua):
max_expr, other_expr = normalized_ass, normalized_gua
else:
max_expr, other_expr = normalized_gua, normalized_ass
assert isinstance(max_expr, ForallExpr)
max_binding_indices = max_expr.arg1
ass_newindex_by_old = dict((o, max_binding_indices[i]) for i, o in enumerate(binding_indices_ass))
gua_newindex_by_old = dict((o, max_binding_indices[i]) for i, o in enumerate(binding_indices_gua))
replaced_ass = _replace_indices(ass_newindex_by_old, normalized_ass)
replaced_gua = _replace_indices(gua_newindex_by_old, normalized_gua)
replaced_underlying_ass = replaced_ass.arg2 if is_quantified_expr(replaced_ass) else replaced_ass
replaced_underlying_gua = replaced_gua.arg2 if is_quantified_expr(replaced_gua) else replaced_gua
new_gua = ForallExpr(max_binding_indices,
BinOp('->', replaced_underlying_ass, replaced_underlying_gua))
new_property = SpecProperty([Bool(True)], [new_gua])
return new_property
def visit_binary_op(self, binary_op:BinOp):
return BinOp(binary_op.name, self.dispatch(binary_op.arg1), self.dispatch(binary_op.arg2))
def test_get_conjuncts_no_conjuncts(self):
a, b = Signal('a'), Signal('b')
conjunction_expr = BinOp('+', a, b)
conjuncts = _get_conjuncts(conjunction_expr)
assert conjuncts == [conjunction_expr], str(conjunction_expr)
def test_get_conjuncts_recursion(self):
a, b, c = Signal('a'), Signal('b'), Signal('c')
conjunction_expr = BinOp('*', a, BinOp('*', b, c))
conjuncts = _get_conjuncts(conjunction_expr)
assert len(conjuncts) == 3
def expr_from_property(property: SpecProperty) -> Expr:
return BinOp('->', and_expressions(property.assumptions),
and_expressions(property.guarantees))
def to_expr(spec_property: SpecProperty) -> Expr:
return BinOp('->', and_expressions(spec_property.assumptions),
and_expressions(spec_property.guarantees))
def assumptions(self):
return [ForallExpr(['i'],
UnaryOp('G', UnaryOp('F',
BinOp('=',
QuantifiedSignal(self._FAIR_SCHED_NAME, 'i'),
Number(1)))))]
def _get_is_value(signal_name: str, value: Number, *binding_indices):
if len(binding_indices) == 0:
signal = Signal(signal_name)
else:
signal = QuantifiedSignal(signal_name, *binding_indices)
return BinOp('=', signal, value)