def test_NEXT_check_ltl_onepb(self):
with tests.Configure(self, __file__, "/example.smv"):
# false in the initial state
formula = parseLTL("() a")
# however the violation is not detected when no move is allowed
status, trace = check.check_ltl_onepb(formula, 0)
self.assertEqual("Ok", status)
self.assertIsNone(trace)
status, trace = check.check_ltl_onepb(formula, 1)
self.assertEqual("Violation", status)
self.assertIsNotNone(trace)
self.assertEqual(1, len(trace))
# true in the initial state
formula = parseLTL("()() a")
# not reachable
status, trace = check.check_ltl_onepb(formula, 0)
self.assertEqual("Ok", status)
self.assertIsNone(trace)
# not quite yet
status, trace = check.check_ltl_onepb(formula, 1)
self.assertEqual("Ok", status)
self.assertIsNone(trace)
# ok
status, trace = check.check_ltl_onepb(formula, 2)
self.assertEqual("Ok", status)
self.assertIsNone(trace)
# and even for longer traces
status, trace = check.check_ltl_onepb(formula, 3)
self.assertEqual("Ok", status)
self.assertIsNone(trace)
def test_EVENTUALLY_check_ltl_onepb(self):
with tests.Configure(self, __file__, "/example.smv"):
# proving a violation of this prop necessitates at least two
# steps: flip --> flop --> flip
formula = parseLTL("<>(a <=> b)")
status, trace = check.check_ltl_onepb(formula, 0)
self.assertEqual("Ok", status)
self.assertIsNone(trace)
status, trace = check.check_ltl_onepb(formula, 1)
self.assertEqual("Ok", status)
self.assertIsNone(trace)
# a loop is identified
status, trace = check.check_ltl_onepb(formula, 2)
self.assertEqual("Violation", status)
self.assertIsNotNone(trace)
self.assertEqual(2, len(trace))
# valid in the initial state (hence for any bound)
formula = parseLTL("<>(a | b)")
for k in range(10):
status, trace = check.check_ltl_onepb(formula, k)
self.assertEqual("Ok", status)
self.assertIsNone(trace)
def test_arithmetic_unary_minus(self):
# number can be negated
ast = parsing.parseLTL("-12")
self.assertEqual("Proposition(- (12))", str(ast))
# and so does a variable
ast = parsing.parseLTL("-a")
self.assertEqual("Proposition(- (a))", str(ast))
# or a nested expression
ast = parsing.parseLTL("-( 6 * 8)")
self.assertEqual("Proposition(- ((6) * (8)))", str(ast))
def test_parse_parenthesized(self):
# no impact on vars
ast = parsing.parseLTL("(a)")
self.assertEqual("Proposition(a)", str(ast))
# it permits to change the side-associativity
# can be chained (right associative)
ast = parsing.parseLTL("(phi | psi) | chi")
self.assertEqual("((Proposition(phi) Or Proposition(psi)) Or Proposition(chi))", str(ast))
ast = parsing.parseLTL("(phi & psi) & chi")
self.assertEqual("((Proposition(phi) And Proposition(psi)) And Proposition(chi))", str(ast))
ast = parsing.parseLTL("(phi => psi) => chi")
self.assertEqual("((Proposition(phi) Imply Proposition(psi)) Imply Proposition(chi))", str(ast))
ast = parsing.parseLTL("(phi <=> psi) <=> chi")
self.assertEqual("((Proposition(phi) Equiv Proposition(psi)) Equiv Proposition(chi))", str(ast))
ast = parsing.parseLTL("([]a) & b")
self.assertEqual("((Globally Proposition(a)) And Proposition(b))", str(ast))
ast = parsing.parseLTL("(<>a) & b")
self.assertEqual("((Eventually Proposition(a)) And Proposition(b))", str(ast))
ast = parsing.parseLTL("([]a) U (<>b)")
self.assertEqual("((Globally Proposition(a)) Until (Eventually Proposition(b)))", str(ast))
ast = parsing.parseLTL("([]a) W (<>b)")
self.assertEqual("((Globally Proposition(a)) WeakUntil (Eventually Proposition(b)))", str(ast))
def test_NEXT_check_ltl(self):
with tests.Configure(self, __file__, "/example.smv"):
status, l, trace = check.check_ltl(parseLTL("()() a"), 5)
self.assertEqual('Ok', status)
self.assertEqual(5, l)
self.assertIsNone(trace)
status, l, trace = check.check_ltl(parseLTL("() a"), 5)
self.assertEqual('Violation', status)
self.assertEqual(1, l)
self.assertIsNotNone(trace)
def test_EVENTUALLY_check_ltl(self):
with tests.Configure(self, __file__, "/example.smv"):
status, l, trace = check.check_ltl(parseLTL("<>(a <=> !b)"), 5)
self.assertEqual('Ok', status)
self.assertEqual(5, l)
self.assertIsNone(trace)
status, l, trace = check.check_ltl(parseLTL("<>(a & b)"), 5)
self.assertEqual('Violation', status)
self.assertEqual(2, l)
self.assertIsNotNone(trace)
def test_parse_variable_containing_FALSE(self):
ast = parsing.parseLTL("@FALSE")
# everything from the unknown punctuation on is discarded
self.assertEqual("Proposition(@FALSE)", str(ast))
ast = parsing.parseLTL("FALSE@")
# everything from the unknown punctuation on is discarded
self.assertEqual("Proposition(FALSE@)", str(ast))
ast = parsing.parseLTL("FALSE.")
# everything from the unknown punctuation on is discarded
self.assertEqual("Proposition(FALSE.)", str(ast))
def test_generate_problem_with_fairness(self):
'''
This test clearly shows the difference in validating a property with
or without fairness constraint
'''
with tests.Configure(self, __file__, "/philo.smv"):
# length 0
# nusmv has fairness always on.
fml_node = Node.from_ptr(
parse_ltl_spec("G (p1.waiting -> F !p1.waiting)"))
smv = ltlspec.generate_ltl_problem(self.befsm, fml_node, 0)
self.assertEqual(SatSolverResult.UNSATISFIABLE,
self.satisfiability(smv))
formula = parseLTL("[](p1.waiting => <>!p1.waiting)")
unfair = gen.generate_problem(formula,
self.befsm,
0,
no_fairness=True)
self.assertEqual(SatSolverResult.UNSATISFIABLE,
self.satisfiability(unfair))
fair = gen.generate_problem(formula,
self.befsm,
0,
no_fairness=False)
self.assertEqual(SatSolverResult.UNSATISFIABLE,
self.satisfiability(fair))
# length 1
fml_node = Node.from_ptr(
parse_ltl_spec("G (p1.waiting -> F !p1.waiting)"))
smv = ltlspec.generate_ltl_problem(self.befsm, fml_node, 1)
self.assertEqual(SatSolverResult.UNSATISFIABLE,
self.satisfiability(smv))
formula = parseLTL("[](p1.waiting => <>!p1.waiting)")
unfair = gen.generate_problem(formula,
self.befsm,
1,
no_fairness=True)
self.assertEqual(SatSolverResult.SATISFIABLE,
self.satisfiability(unfair))
fair = gen.generate_problem(formula,
self.befsm,
1,
no_fairness=False)
self.assertEqual(SatSolverResult.UNSATISFIABLE,
self.satisfiability(fair))
def test_GLOBALLY_check_ltl_onepb(self):
with tests.Configure(self, __file__, "/example.smv"):
formula = parseLTL("[](a <=> !b)")
for k in range(10):
status, trace = check.check_ltl_onepb(formula, k)
self.assertEqual("Ok", status)
self.assertIsNone(trace)
# already violated in the initial state
formula = parseLTL("[](a <=> b)")
status, trace = check.check_ltl_onepb(formula, 0)
self.assertEqual("Violation", status)
self.assertIsNotNone(trace)
self.assertEqual(0, len(trace))
def test_arithmetic_modulus(self):
# numbers
ast = parsing.parseLTL("6 mod 8")
self.assertEqual("Proposition((6) mod (8))", str(ast))
# vars
ast = parsing.parseLTL("a mod b")
self.assertEqual("Proposition((a) mod (b))", str(ast))
# chainable
ast = parsing.parseLTL("a mod b mod c")
self.assertEqual("Proposition((a) mod (b) mod (c))", str(ast))
# priority over +/-
ast = parsing.parseLTL("a + b mod c")
self.assertEqual("Proposition((a) + ((b) mod (c)))", str(ast))
ast = parsing.parseLTL("a mod b - c")
self.assertEqual("Proposition(((a) mod (b)) - (c))", str(ast))
def test_arithmetic_subtraction(self):
# numbers
ast = parsing.parseLTL("6 - 8")
self.assertEqual("Proposition((6) - (8))", str(ast))
# vars
ast = parsing.parseLTL("a - b")
self.assertEqual("Proposition((a) - (b))", str(ast))
# chainable
ast = parsing.parseLTL("a - b - c")
self.assertEqual("Proposition((a) - (b) - (c))", str(ast))
# priority over <</>>
ast = parsing.parseLTL("a - b << c")
self.assertEqual("Proposition(((a) - (b)) << (c))", str(ast))
ast = parsing.parseLTL("a - b >> c")
self.assertEqual("Proposition(((a) - (b)) >> (c))", str(ast))
def test_arithmetic_multiplication(self):
# numbers
ast = parsing.parseLTL("6 * 8")
self.assertEqual("Proposition((6) * (8))", str(ast))
# vars
ast = parsing.parseLTL("a * b")
self.assertEqual("Proposition((a) * (b))", str(ast))
# chainable
ast = parsing.parseLTL("a * b * c")
self.assertEqual("Proposition((a) * (b) * (c))", str(ast))
# priority over +/-
ast = parsing.parseLTL("a + b * c")
self.assertEqual("Proposition((a) + ((b) * (c)))", str(ast))
ast = parsing.parseLTL("a * b - c")
self.assertEqual("Proposition(((a) * (b)) - (c))", str(ast))
def test_arithmetic_division(self):
# numbers
ast = parsing.parseLTL("6 / 8")
self.assertEqual("Proposition((6) / (8))", str(ast))
# vars
ast = parsing.parseLTL("a / b")
self.assertEqual("Proposition((a) / (b))", str(ast))
# chainable
ast = parsing.parseLTL("a / b / c")
self.assertEqual("Proposition((a) / (b) / (c))", str(ast))
# priority over +/-
ast = parsing.parseLTL("a + b / c")
self.assertEqual("Proposition((a) + ((b) / (c)))", str(ast))
ast = parsing.parseLTL("a / b - c")
self.assertEqual("Proposition(((a) / (b)) - (c))", str(ast))
def test_arithmetic_lshift(self):
# numbers
ast = parsing.parseLTL("6 << 8")
self.assertEqual("Proposition((6) << (8))", str(ast))
# vars
ast = parsing.parseLTL("a << b")
self.assertEqual("Proposition((a) << (b))", str(ast))
# chainable
ast = parsing.parseLTL("a << b << c")
self.assertEqual("Proposition((a) << (b) << (c))", str(ast))
# priority over comparison
ast = parsing.parseLTL("a << b <= c")
self.assertEqual("Proposition(((a) << (b)) <= (c))", str(ast))
ast = parsing.parseLTL("a << b = c")
self.assertEqual("Proposition(((a) << (b)) = (c))", str(ast))
def test_UNTIL_check_ltl(self):
with tests.Configure(self, __file__, "/never_b.smv"):
status, l, trace = check.check_ltl(parseLTL("b U a"), 5)
self.assertEqual('Ok', status)
self.assertEqual(5, l)
self.assertIsNone(trace)
status, l, trace = check.check_ltl(parseLTL("a U b"), 5)
self.assertEqual('Violation', status)
self.assertEqual(1, l)
self.assertIsNotNone(trace)
status, l, trace = check.check_ltl(parseLTL("b W !a"), 5)
self.assertEqual('Violation', status)
self.assertEqual(0, l)
self.assertIsNotNone(trace)
def test_nnf_eventually(self):
with tests.Configure(self, __file__, "/example.smv"):
formula = parseLTL("<> a")
not_neg = "(Eventually Proposition(a))"
self.assertEqual(not_neg, str(formula.nnf(False)))
negated = "(Globally (Not Proposition(a)))"
self.assertEqual(negated, str(formula.nnf(True)))
# when members need nnfing too
formula = parseLTL("<> (!a)")
not_neg = "(Eventually (Not Proposition(a)))"
self.assertEqual(not_neg, str(formula.nnf(False)))
negated = "(Globally Proposition(a))"
self.assertEqual(negated, str(formula.nnf(True)))
def validate_generate_problem(self, bound, custom_text, nusmv_text):
fsm = self.befsm
# formulae
formula = parseLTL(custom_text)
fml_node = Node.from_ptr(parse_ltl_spec(nusmv_text))
# IMPORTANT NOTE: each instantiation of the problem creates new CNF
# literal which appears in the clauses list (even in canonical form)
# hence, the canonical forms of the different instantiations cannot
# simply be compared as there is no a priori way to know what CNF
# literal reconcile with what other.
# However, the different expressions should all have the exact same
# satisfiability. So, that's how this test proceeds.
smv = ltlspec.generate_ltl_problem(fsm, fml_node, bound)
tool = gen.generate_problem(formula, fsm, bound)
manual = gen.model_problem(fsm, bound) &\
formula.nnf(True).bounded_semantics(fsm, bound)
sat_smv = self.satisfiability(smv)
sat_tool = self.satisfiability(tool)
sat_man = self.satisfiability(manual)
self.assertEqual(sat_tool, sat_man)
self.assertEqual(sat_tool, sat_smv)
def test_arithmetic_rshift(self):
# numbers
ast = parsing.parseLTL("6 >> 8")
self.assertEqual("Proposition((6) >> (8))", str(ast))
# vars
ast = parsing.parseLTL("a >> b")
self.assertEqual("Proposition((a) >> (b))", str(ast))
# chainable
ast = parsing.parseLTL("a >> b >> c")
self.assertEqual("Proposition((a) >> (b) >> (c))", str(ast))
# priority over comparison
ast = parsing.parseLTL("a >> b <= c")
self.assertEqual("Proposition(((a) >> (b)) <= (c))", str(ast))
ast = parsing.parseLTL("a >> b = c")
self.assertEqual("Proposition(((a) >> (b)) = (c))", str(ast))
def test_nnf_next(self):
with tests.Configure(self, __file__, "/example.smv"):
formula = parseLTL("() a")
# w/o member nnf-ing
not_neg = "(Next Proposition(a))"
self.assertEqual(not_neg, str(formula.nnf(False)))
negated = "(Next (Not Proposition(a)))"
self.assertEqual(negated, str(formula.nnf(True)))
# w/ member nnf-ing
formula = parseLTL("() !a")
not_neg = "(Next (Not Proposition(a)))"
self.assertEqual(not_neg, str(formula.nnf(False)))
negated = "(Next Proposition(a))"
self.assertEqual(negated, str(formula.nnf(True)))
def test_parse_next(self):
ast = parsing.parseLTL("() phi")
self.assertEqual("(Next Proposition(phi))", str(ast))
# spacing is irrelevant
ast = parsing.parseLTL("()phi")
self.assertEqual("(Next Proposition(phi))", str(ast))
# can be chained
ast = parsing.parseLTL("() () () phi")
self.assertEqual("(Next (Next (Next Proposition(phi))))", str(ast))
# space is irrelevant (even when chained)
ast = parsing.parseLTL("()()()phi")
self.assertEqual("(Next (Next (Next Proposition(phi))))", str(ast))
# it may accept a constant
ast = parsing.parseLTL("()TRUE")
self.assertEqual("(Next Constant(TRUE))", str(ast))
# it may accept a parenthesized expression
ast = parsing.parseLTL("()(a | b)")
self.assertEqual("(Next (Proposition(a) Or Proposition(b)))", str(ast))
# it may accept a timed expression
ast = parsing.parseLTL("()[]a")
self.assertEqual("(Next (Globally Proposition(a)))", str(ast))
def test_parse_globally(self):
ast = parsing.parseLTL("[] phi")
self.assertEqual("(Globally Proposition(phi))", str(ast))
# spacing is irrelevant
ast = parsing.parseLTL("[]phi")
self.assertEqual("(Globally Proposition(phi))", str(ast))
# can be chained
ast = parsing.parseLTL("[] [] [] phi")
self.assertEqual("(Globally (Globally (Globally Proposition(phi))))", str(ast))
# space is irrelevant (even when chained)
ast = parsing.parseLTL("[][][]phi")
self.assertEqual("(Globally (Globally (Globally Proposition(phi))))", str(ast))
# it may accept a constant
ast = parsing.parseLTL("[]TRUE")
self.assertEqual("(Globally Constant(TRUE))", str(ast))
# it may accept a parenthesized expression
ast = parsing.parseLTL("[](a | b)")
self.assertEqual("(Globally (Proposition(a) Or Proposition(b)))", str(ast))
# it may accept a timed expression
ast = parsing.parseLTL("[]<>a")
self.assertEqual("(Globally (Eventually Proposition(a)))", str(ast))
def test_nnf_imply(self):
with tests.Configure(self, __file__, "/example.smv"):
# when the operands dont need to be nnf-ed
formula = parseLTL("a => b")
not_neg = "((Not Proposition(a)) Or Proposition(b))"
self.assertEqual(not_neg, str(formula.nnf(False)))
negated = "(Proposition(a) And (Not Proposition(b)))"
self.assertEqual(negated, str(formula.nnf(True)))
# when the operands need to be nnf-ed
formula = parseLTL("a => !b")
not_neg = "((Not Proposition(a)) Or (Not Proposition(b)))"
self.assertEqual(not_neg, str(formula.nnf(False)))
negated = "(Proposition(a) And Proposition(b))"
self.assertEqual(negated, str(formula.nnf(True)))
def check(formula, args):
try:
parsed_fml = parseLTL(formula.strip())
status,length,trace = check_ltl(parsed_fml, args.bound, args.no_fairness, args.no_invariants, args.dry_run)
if status != 'Ok':
print("-- {} for length {}".format(status, length))
print(trace)
except Exception as e:
print("The specification contains a syntax error")
print(e)
def test_check_ltl_arithmetics(self):
"""
This tests the use of the invariants flag when performing the check.
"""
with tests.Configure(self, __file__, "/numbers.smv"):
formula = parseLTL("[] a < 7")
status, _, trace = check.check_ltl(formula, 10, no_invar=False)
self.assertEqual("Ok", status)
self.assertIsNone(trace)
def test_UNTIL_check_ltl_onepb(self):
with tests.Configure(self, __file__, "/never_b.smv"):
# entailed by the automaton
formula = parseLTL("a U b")
# not reachable
status, trace = check.check_ltl_onepb(formula, 0)
self.assertEqual("Ok", status)
self.assertIsNone(trace)
# this is where U differs from W: at infinity, b must hold
status, trace = check.check_ltl_onepb(formula, 1)
self.assertEqual("Violation", status)
self.assertIsNotNone(trace)
self.assertEqual(1, len(trace))
# true in the initial state
formula = parseLTL("b U a")
status, trace = check.check_ltl_onepb(formula, 0)
self.assertEqual("Ok", status)
self.assertIsNone(trace)
status, trace = check.check_ltl_onepb(formula, 1)
self.assertEqual("Ok", status)
self.assertIsNone(trace)
status, trace = check.check_ltl_onepb(formula, 2)
self.assertEqual("Ok", status)
self.assertIsNone(trace)
status, trace = check.check_ltl_onepb(formula, 3)
self.assertEqual("Ok", status)
self.assertIsNone(trace)
# violated right away
formula = parseLTL("b U !a")
status, trace = check.check_ltl_onepb(formula, 0)
self.assertEqual("Violation", status)
self.assertIsNotNone(trace)
self.assertEqual(0, len(trace))
def test_nnf_weakuntil(self):
with tests.Configure(self, __file__, "/example.smv"):
# rules of pseudo duality:
# (p U q) <-> (!q W (!p & !q))
# (p W q) <-> (!q U (!p & !q))
# without operands nnfing
formula = parseLTL("(p W q)")
not_neg = "(Proposition(p) WeakUntil Proposition(q))"
self.assertEqual(not_neg, str(formula.nnf(False)))
negated = "((Not Proposition(q)) Until ((Not Proposition(p)) And (Not Proposition(q))))"
self.assertEqual(negated, str(formula.nnf(True)))
# wit operands nnfing
formula = parseLTL("((!p) W (!q))")
not_neg = "((Not Proposition(p)) WeakUntil (Not Proposition(q)))"
self.assertEqual(not_neg, str(formula.nnf(False)))
negated = "(Proposition(q) Until (Proposition(p) And Proposition(q)))"
self.assertEqual(negated, str(formula.nnf(True)))
def test_WEAKUNTIL_check_ltl_onepb(self):
with tests.Configure(self, __file__, "/never_b.smv"):
# entailed by the automaton
formula = parseLTL("a W b")
# not reachable
status, trace = check.check_ltl_onepb(formula, 0)
self.assertEqual("Ok", status)
self.assertIsNone(trace)
# already looping but no counter example
status, trace = check.check_ltl_onepb(formula, 1)
self.assertEqual("Ok", status)
self.assertIsNone(trace)
# true in the initial state
formula = parseLTL("b W a")
status, trace = check.check_ltl_onepb(formula, 0)
self.assertEqual("Ok", status)
self.assertIsNone(trace)
status, trace = check.check_ltl_onepb(formula, 1)
self.assertEqual("Ok", status)
self.assertIsNone(trace)
status, trace = check.check_ltl_onepb(formula, 2)
self.assertEqual("Ok", status)
self.assertIsNone(trace)
status, trace = check.check_ltl_onepb(formula, 3)
self.assertEqual("Ok", status)
self.assertIsNone(trace)
# violated right away
formula = parseLTL("b W !a")
status, trace = check.check_ltl_onepb(formula, 0)
self.assertEqual("Violation", status)
self.assertIsNotNone(trace)
self.assertEqual(0, len(trace))
def validate_bounded_semantics(self, bound, custom_text, nusmv_text):
fsm = self.befsm
# formulae
formula = parseLTL(custom_text)
fml_node = Node.from_ptr(parse_ltl_spec(nusmv_text))
tool = formula.bounded_semantics(fsm, bound)
smv = ltlspec.bounded_semantics(fsm, fml_node, bound)
# canonical forms
s_tool = tests.canonical_cnf(tool)
s_smv = tests.canonical_cnf(smv)
self.assertEqual(s_tool, s_smv)
def test_nnf_equiv(self):
with tests.Configure(self, __file__, "/example.smv"):
# when the operands dont need to be nnf-ed
formula = parseLTL("a <=> b")
# (!a | b) & (!b | a)
not_neg = "(((Not Proposition(a)) Or Proposition(b)) And ((Not Proposition(b)) Or Proposition(a)))"
self.assertEqual(not_neg, str(formula.nnf(False)))
# (a & !b) | (b & !a)
negated = "((Proposition(a) And (Not Proposition(b))) Or (Proposition(b) And (Not Proposition(a))))"
self.assertEqual(negated, str(formula.nnf(True)))
# when the operands need to be nnf-ed
formula = parseLTL("a <=> !b")
# (!a | !b) & (b | a)
not_neg = "(((Not Proposition(a)) Or (Not Proposition(b))) And (Proposition(b) Or Proposition(a)))"
self.assertEqual(not_neg, str(formula.nnf(False)))
# (a & b) | (!b & !a)
negated = "((Proposition(a) And Proposition(b)) Or ((Not Proposition(b)) And (Not Proposition(a))))"
self.assertEqual(negated, str(formula.nnf(True)))
def test_check_ltl_invariants(self):
"""
This tests the use of the invariants flag when performing the check.
"""
with tests.Configure(self, __file__, "/dummy_with_invar.smv"):
formula = parseLTL("[] v")
# invariants enforced
status, _, trace = check.check_ltl(formula, 10, no_invar=True)
self.assertEqual("Violation", status)
self.assertEqual(0, len(trace))
# invariants enforced
status, _, trace = check.check_ltl(formula, 10, no_invar=False)
self.assertEqual("Ok", status)
self.assertIsNone(trace)