def marking_predicate(self) -> mona.Formula:
m = mona.Variable("m")
unique_in_component = mona.UniversalFirstOrder(
[m],
mona.Conjunction([
mona.Disjunction([
mona.Conjunction(
[cast(mona.Formula, mona.ElementIn(m, pos))]
+ [cast(mona.Formula, mona.ElementNotIn(m, neg))
for neg in c.state_variables
if neg != pos])
for pos in c.state_variables])
for c in self.system.components]))
flow_invariant = mona.PredicateCall("flow_invariant",
self.system.state_variables)
trap_invariant = mona.PredicateCall("trap_invariant",
self.system.state_variables)
return mona.PredicateDefinition(
"marking",
self.system.state_variables,
[],
mona.Conjunction([
unique_in_component,
flow_invariant,
trap_invariant,
])).simplify()
def initially_marked_trap_predicate(self) -> mona.Formula:
inner = mona.Conjunction([
mona.PredicateCall("trap",
self.system.state_variables),
mona.PredicateCall("intersects_initial",
self.system.state_variables)])
return mona.PredicateDefinition(
"initially_marked_trap",
self.system.state_variables,
[],
inner).simplify()
def trap_invariant_predicate(self) -> mona.Formula:
trap_states = [mona.Variable(f"T{s}") for s in self.system.states]
precondition = mona.PredicateCall("initially_marked_trap", trap_states)
postcondition = mona.PredicateCall(
"intersection",
trap_states + self.system.state_variables)
return mona.PredicateDefinition(
"trap_invariant",
self.system.state_variables,
[],
mona.UniversalSecondOrder(trap_states,
mona.Implication(precondition,
postcondition))
).simplify()
def flow_invariant_predicate(self) -> mona.Formula:
flow_states = [mona.Variable(f"F{s}") for s in self.system.states]
precondition = mona.PredicateCall(
"initially_uniquely_marked_flow",
flow_states)
postcondition = mona.PredicateCall(
"unique_intersection",
flow_states + self.system.state_variables)
return mona.PredicateDefinition(
"flow_invariant",
self.system.state_variables,
[], mona.UniversalSecondOrder(
flow_states, mona.Implication(precondition, postcondition))
).simplify()
def deadlock_predicate(self) -> mona.Formula:
inner = mona.Conjunction(
[mona.PredicateCall(f"dead_transition_{number}",
self.system.state_variables)
for number in range(1, len(self.clauses) + 1)])
return mona.PredicateDefinition(
"deadlock",
self.system.state_variables,
[],
inner).simplify()
def as_mona(self):
left = self.left.as_mona()
right = self.right.as_mona()
return mona.PredicateCall("is_next", [left, right])
def as_mona(self):
argument = self.argument.as_mona()
return mona.PredicateCall("is_last", [argument])
def marking_predicate_call(self) -> mona.Formula:
return mona.PredicateCall("marking", self.system.state_variables)
def property_check(self, property_name: str) -> mona.Formula:
return mona.PredicateCall(property_name, self.system.state_variables)