def _check_logic(self, formulas):
for f in formulas:
logic = get_logic(f, self.environment)
ok = any(logic <= l for l in self.LOGICS)
if not ok:
raise PysmtValueError("Logic not supported by Z3 interpolation."
"(detected logic is: %s)" % str(logic))
def eliminate_quantifiers(self, formula):
logic = get_logic(formula, self.environment)
if not logic <= LRA and not logic <= LIA:
raise PysmtValueError("Z3 quantifier elimination only "\
"supports LRA or LIA without combination."\
"(detected logic is: %s)" % str(logic))
simplifier = z3.Tactic('simplify')
eliminator = z3.Tactic('qe')
f = self.converter.convert(formula)
s = simplifier(f, elim_and=True,
pull_cheap_ite=True,
ite_extra_rules=True).as_expr()
res = eliminator(f).as_expr()
pysmt_res = None
try:
pysmt_res = self.converter.back(res)
except ConvertExpressionError:
if logic <= LRA:
raise
raise ConvertExpressionError(message=("Unable to represent" \
"expression %s in pySMT: the quantifier elimination for " \
"LIA is incomplete as it requires the modulus. You can " \
"find the Z3 expression representing the quantifier " \
"elimination as the attribute 'expression' of this " \
"exception object" % str(res)),
expression=res)
return pysmt_res
def smtlibscript_from_formula(formula):
script = SmtLibScript()
# Get the simplest SmtLib logic that contains the formula
f_logic = get_logic(formula)
smt_logic = None
try:
smt_logic = get_closer_smtlib_logic(f_logic)
except NoLogicAvailableError:
warnings.warn("The logic %s is not reducible to any SMTLib2 " \
"standard logic. Proceeding with non-standard " \
"logic '%s'" % (f_logic, f_logic))
smt_logic = f_logic
script.add(name=smtcmd.SET_LOGIC,
args=[smt_logic])
deps = formula.get_free_variables()
# Declare all variables
for symbol in deps:
assert symbol.is_symbol()
script.add(name=smtcmd.DECLARE_FUN, args=[symbol])
# Assert formula
script.add_command(SmtLibCommand(name=smtcmd.ASSERT,
args=[formula]))
# check-sat
script.add_command(SmtLibCommand(name=smtcmd.CHECK_SAT,
args=[]))
return script
def smtlibscript_from_formula(formula):
script = SmtLibScript()
# Get the simplest SmtLib logic that contains the formula
f_logic = get_logic(formula)
smt_logic = None
try:
smt_logic = get_closer_smtlib_logic(f_logic)
except NoLogicAvailableError:
warnings.warn("The logic %s is not reducible to any SMTLib2 " \
"standard logic. Proceeding with non-standard " \
"logic '%s'" % (f_logic, f_logic))
smt_logic = f_logic
script.add(name=smtcmd.SET_LOGIC, args=[smt_logic])
deps = formula.get_free_variables()
# Declare all variables
for symbol in deps:
assert symbol.is_symbol()
script.add(name=smtcmd.DECLARE_FUN, args=[symbol])
# Assert formula
script.add_command(SmtLibCommand(name=smtcmd.ASSERT, args=[formula]))
# check-sat
script.add_command(SmtLibCommand(name=smtcmd.CHECK_SAT, args=[]))
return script
def eliminate_quantifiers(self, formula):
logic = get_logic(formula, self.environment)
if not logic <= LRA and not logic <= LIA:
raise PysmtValueError("Z3 quantifier elimination only "\
"supports LRA or LIA without combination."\
"(detected logic is: %s)" % str(logic))
simplifier = z3.Tactic('simplify')
eliminator = z3.Tactic('qe')
f = self.converter.convert(formula)
s = simplifier(f,
elim_and=True,
pull_cheap_ite=True,
ite_extra_rules=True).as_expr()
res = eliminator(f).as_expr()
pysmt_res = None
try:
pysmt_res = self.converter.back(res)
except ConvertExpressionError:
if logic <= LRA:
raise
raise ConvertExpressionError(message=("Unable to represent" \
"expression %s in pySMT: the quantifier elimination for " \
"LIA is incomplete as it requires the modulus. You can " \
"find the Z3 expression representing the quantifier " \
"elimination as the attribute 'expression' of this " \
"exception object" % str(res)),
expression=res)
return pysmt_res
def sequence_interpolant(self, formulas, solver_name=None, logic=None):
if logic is None or logic == AUTO_LOGIC:
_And = self.environment.formula_manager.And
logic = get_logic(_And(formulas))
with self.Interpolator(name=solver_name, logic=logic) as itp:
return itp.sequence_interpolant(formulas)
def get_implicant(self, formula, solver_name=None,
logic=None):
mgr = self.environment.formula_manager
if logic is None or logic == AUTO_LOGIC:
logic = get_logic(formula, self.environment)
with self.Solver(name=solver_name, logic=logic) \
as solver:
solver.add_assertion(formula)
check = solver.solve()
if not check:
return None
else:
model = solver.get_model()
atoms = formula.get_atoms()
res = []
for a in atoms:
fv = a.get_free_variables()
if any(v in model for v in fv):
if solver.get_value(a).is_true():
res.append(a)
else:
assert solver.get_value(a).is_false()
res.append(mgr.Not(a))
return mgr.And(res)
def establish_solver(self):
self.formulas = self.encode_constraints()
target_logic = get_logic(self.formulas)
print("Target Logic: %s" % target_logic)
self.solver = Solver(logic=target_logic)
self.solver.add_assertion(self.formulas)
self.num_sol = 0
def is_unsat(self, formula, solver_name=None, logic=None):
if logic is None or logic == AUTO_LOGIC:
logic = get_logic(formula, self.environment)
with self.Solver(name=solver_name, logic=logic,
generate_models=False,
incremental=False) as solver:
return solver.is_unsat(formula)
def is_sat(self, formula, solver_name=None, logic=None):
if logic is None or logic == AUTO_LOGIC:
logic = get_logic(formula, self.environment)
with self.Solver(name=solver_name, logic=logic,
generate_models=False, incremental=False) \
as solver:
return solver.is_sat(formula)
def get_implicant(self, formula, solver_name=None,
logic=None):
mgr = self.environment.formula_manager
if logic is None or logic == AUTO_LOGIC:
logic = get_logic(formula, self.environment)
with self.Solver(name=solver_name, logic=logic) \
as solver:
solver.add_assertion(formula)
check = solver.solve()
if not check:
return None
else:
model = solver.get_model()
atoms = formula.get_atoms()
res = []
for a in atoms:
fv = a.get_free_variables()
if any(v in model for v in fv):
if solver.get_value(a).is_true():
res.append(a)
else:
assert solver.get_value(a).is_false()
res.append(mgr.Not(a))
return mgr.And(res)
def sequence_interpolant(self, formulas, solver_name=None, logic=None):
if logic is None or logic == AUTO_LOGIC:
_And = self.environment.formula_manager.And
logic = get_logic(_And(formulas))
with self.Interpolator(name=solver_name, logic=logic) as itp:
return itp.sequence_interpolant(formulas)
def init_solver(self):
self.formula = self.encode_constraint()
target_logic = get_logic(self.formula)
print("Target Logic: %s" % target_logic)
self.solver = Solver(logic=target_logic)
self.solver.add_assertion(self.formula)
self.num_solution = 0
def _check_logic(self, formulas):
for f in formulas:
logic = get_logic(f, self.environment)
ok = any(logic <= l for l in self.LOGICS)
if not ok:
raise PysmtValueError(
"Logic not supported by Z3 interpolation."
"(detected logic is: %s)" % str(logic))
def binary_interpolant(self, formula_a, formula_b,
solver_name=None, logic=None):
if logic == AUTO_LOGIC:
logic = get_logic(
self.environment.formula_manager.And(formula_a, formula_b))
with self.Interpolator(name=solver_name, logic=logic) as itp:
return itp.binary_interpolant(formula_a, formula_b)
def binary_interpolant(self, formula_a, formula_b,
solver_name=None, logic=None):
if logic is None or logic == AUTO_LOGIC:
logic = get_logic(
self.environment.formula_manager.And(formula_a, formula_b))
with self.Interpolator(name=solver_name, logic=logic) as itp:
return itp.binary_interpolant(formula_a, formula_b)
def all_smt(formula, keys):
target_logic = get_logic(formula)
print("Target Logic: %s" % target_logic)
with Solver(logic=target_logic) as solver:
solver.add_assertion(formula)
while solver.solve():
partial_model = [EqualsOrIff(k, solver.get_value(k)) for k in keys]
print(partial_model)
solver.add_assertion(Not(And(partial_model)))
def all_smt(formula, keys):
target_logic = get_logic(formula)
print("Target Logic: %s" % target_logic)
with Solver(logic=target_logic) as solver:
solver.add_assertion(formula)
while solver.solve():
partial_model = [EqualsOrIff(k, solver.get_value(k)) for k in keys]
print(partial_model)
solver.add_assertion(Not(And(partial_model)))
def test_theory_oracle(self):
from pysmt.oracles import get_logic
s1 = Symbol("s1", STRING)
s2 = Symbol("s2", STRING)
f = Equals(StrConcat(s1, s1), s2)
theory = get_logic(f).theory
self.assertTrue(theory.strings, theory)
f = Not(
And(GE(StrLength(StrConcat(s1, s2)), StrLength(s1)),
GE(StrLength(StrConcat(s1, s2)), StrLength(s2))))
theory = get_logic(f).theory
self.assertTrue(theory.strings, theory)
f = And(GT(StrLength(s1), Int(2)), GT(StrLength(s2), StrLength(s1)),
And(StrSuffixOf(s2, s1), StrContains(s2, s1)))
theory = get_logic(f).theory
self.assertTrue(theory.strings, theory)
def eliminate_quantifiers(self, formula):
logic = get_logic(formula, self.environment)
if not logic <= pysmt.logics.BOOL:
raise NotImplementedError("BDD-based quantifier elimination only "\
"supports pure-boolean formulae."\
"(detected logic is: %s)" % str(logic))
bdd = self.converter.convert(formula)
pysmt_res = self.converter.back(bdd)
return pysmt_res
def get_model(self, formula, solver_name=None, logic=None):
if logic is None or logic == AUTO_LOGIC:
logic = get_logic(formula, self.environment)
with self.Solver(name=solver_name, logic=logic,
generate_models=True,
incremental=False) as solver:
solver.add_assertion(formula)
if solver.solve():
return solver.get_model()
return None
def eliminate_quantifiers(self, formula):
logic = get_logic(formula, self.environment)
if not logic <= pysmt.logics.BOOL:
raise NotImplementedError("BDD-based quantifier elimination only "\
"supports pure-boolean formulae."\
"(detected logic is: %s)" % str(logic))
bdd = self.converter.convert(formula)
pysmt_res = self.converter.back(bdd)
return pysmt_res
def get_model(self, formula, solver_name=None, logic=None):
if logic is None or logic == AUTO_LOGIC:
logic = get_logic(formula, self.environment)
with self.Solver(name=solver_name, logic=logic,
generate_models=True,
incremental=False) as solver:
solver.add_assertion(formula)
if solver.solve():
return solver.get_model()
return None
def get_model(self, formula, solver_name=None, logic=None):
if logic == AUTO_LOGIC:
logic = get_logic(formula, self.environment)
with self.Solver(name=solver_name, logic=logic) \
as solver:
solver.add_assertion(formula)
check = solver.solve()
retval = None
if check:
retval = solver.get_model()
return retval
def get_model(self, formula, solver_name=None, logic=None):
if logic == AUTO_LOGIC:
logic = get_logic(formula, self.environment)
with self.Solver(name=solver_name, logic=logic) \
as solver:
solver.add_assertion(formula)
check = solver.solve()
retval = None
if check:
retval = solver.get_model()
return retval
def test_theory_oracle(self):
from pysmt.oracles import get_logic
s1 = Symbol("s1", STRING)
s2 = Symbol("s2", STRING)
f = Equals(StrConcat(s1, s1), s2)
theory = get_logic(f).theory
self.assertTrue(theory.strings, theory)
f = Not(And(GE(StrLength(StrConcat(s1, s2)),
StrLength(s1)),
GE(StrLength(StrConcat(s1, s2)),
StrLength(s2))))
theory = get_logic(f).theory
self.assertTrue(theory.strings, theory)
f = And(GT(StrLength(s1), Int(2)),
GT(StrLength(s2), StrLength(s1)),
And(StrSuffixOf(s2, s1), StrContains(s2, s1)))
theory = get_logic(f).theory
self.assertTrue(theory.strings, theory)
def _check_sat(cls, zsolver, using_nla=False, myseed=None):
zlogic = 'QF_NIA' if using_nla else 'QF_LIA'
solver_opts = {"random_seed": myseed} if myseed else {}
zf = z3.And(zsolver.assertions())
# @timeit
def _convert(zf):
zvs = z3.z3util.get_vars(zf)
vs = [
Symbol(v.decl().name(), INT if v.is_int() else REAL)
for v in zvs
]
z3s = Solver(name='z3', logic=zlogic)
f = z3s.converter.back(zf)
return vs, f
vs, f = _convert(zf)
f_logic = get_logic(f)
# @timeit
def _solve(f):
with Portfolio(
[
("cvc4", solver_opts),
# ("z3", solver_opts),
("yices", solver_opts)
],
logic=f_logic,
incremental=True,
generate_models=True) as solver:
# with z3s as solver:
solver.add_assertion(f)
model = []
try:
# mlog.debug("PySMT: solving {}".format(f))
r = solver.solve()
# mlog.debug("r: {}".format(r))
if r:
# for v in vs:
# # mv = solver.get_value(v).constant_value()
# mv = solver.get_py_value(v)
# model.append((v.symbol_name(), int(mv)))
py_model = solver.get_model()
model = [(v.symbol_name(),
int(py_model.get_py_value(v))) for v in vs]
# mlog.debug("model: {}".format(model))
return (z3.sat if r else z3.unsat), model
except Exception as e:
mlog.debug("check_sat: {}".format(e))
return z3.unknown, []
return _solve(f)
def is_unsat(self, formula, solver_name=None, logic=None, portfolio=None):
if logic is None or logic == AUTO_LOGIC:
logic = get_logic(formula, self.environment)
if portfolio is not None:
solver = Portfolio(solvers_set=portfolio,
environment=self.environment,
logic=logic,
generate_models=False, incremental=False)
else:
solver = self.Solver(name=solver_name, logic=logic,
generate_models=False, incremental=False)
with solver:
return solver.is_unsat(formula)
def simplify(self, formula):
from pysmt.oracles import get_logic
from pysmt.logics import BOOL, QF_BOOL
if self.bool_abstraction:
logic = get_logic(formula)
if logic > QF_BOOL and logic != BOOL:
res = self.abstract_and_simplify(formula)
else:
res = self.back(self.convert(formula))
else:
res = self.back(self.convert(formula))
self._validate(formula, res)
return res
def simplify(self, formula):
from pysmt.oracles import get_logic
from pysmt.logics import BOOL, QF_BOOL
if self.bool_abstraction:
logic = get_logic(formula)
if logic > QF_BOOL and logic != BOOL:
res = self.abstract_and_simplify(formula)
else:
res = self.back(self.convert(formula))
else:
res = self.back(self.convert(formula))
self._validate(formula, res)
return res
def is_unsat(self, formula, solver_name=None, logic=None, portfolio=None):
if logic is None or logic == AUTO_LOGIC:
logic = get_logic(formula, self.environment)
if portfolio is not None:
solver = Portfolio(solvers_set=portfolio,
environment=self.environment,
logic=logic,
generate_models=False, incremental=False)
else:
solver = self.Solver(name=solver_name, logic=logic,
generate_models=False, incremental=False)
with solver:
return solver.is_unsat(formula)
def get_unsat_core(self, clauses, solver_name=None, logic=None):
if logic is None or logic == AUTO_LOGIC:
logic = get_logic(self.environment.formula_manager.And(clauses),
self.environment)
with self.UnsatCoreSolver(name=solver_name, logic=logic) \
as solver:
for c in clauses:
solver.add_assertion(c)
check = solver.solve()
if check:
return None
return solver.get_unsat_core()
def get_unsat_core(self, clauses, solver_name=None, logic=None):
if logic is None or logic == AUTO_LOGIC:
logic = get_logic(self.environment.formula_manager.And(clauses),
self.environment)
with self.UnsatCoreSolver(name=solver_name, logic=logic) \
as solver:
for c in clauses:
solver.add_assertion(c)
check = solver.solve()
if check:
return None
return solver.get_unsat_core()
def smtlibscript_from_formula(formula, logic=None):
script = SmtLibScript()
if logic is None:
# Get the simplest SmtLib logic that contains the formula
f_logic = get_logic(formula)
smt_logic = None
try:
smt_logic = get_closer_smtlib_logic(f_logic)
except NoLogicAvailableError:
warnings.warn("The logic %s is not reducible to any SMTLib2 " \
"standard logic. Proceeding with non-standard " \
"logic '%s'" % (f_logic, f_logic),
stacklevel=3)
smt_logic = f_logic
elif not (isinstance(logic, Logic) or isinstance(logic, str)):
raise UndefinedLogicError(str(logic))
else:
if logic not in SMTLIB2_LOGICS:
warnings.warn("The logic %s is not reducible to any SMTLib2 " \
"standard logic. Proceeding with non-standard " \
"logic '%s'" % (logic, logic),
stacklevel=3)
smt_logic = logic
script.add(name=smtcmd.SET_LOGIC,
args=[smt_logic])
# Declare all types
types = get_env().typeso.get_types(formula, custom_only=True)
for type_ in types:
script.add(name=smtcmd.DECLARE_SORT, args=[type_.decl])
deps = formula.get_free_variables()
# Declare all variables
for symbol in deps:
assert symbol.is_symbol()
script.add(name=smtcmd.DECLARE_FUN, args=[symbol])
# Assert formula
script.add_command(SmtLibCommand(name=smtcmd.ASSERT,
args=[formula]))
# check-sat
script.add_command(SmtLibCommand(name=smtcmd.CHECK_SAT,
args=[]))
return script
def exist_elim(self, variables, formula):
logic = get_logic(formula, self.env)
if not logic <= LRA:
raise NotImplementedError("MathSAT quantifier elimination only"\
" supports LRA (detected logic " \
"is: %s)" % str(logic))
fterm = self.converter.convert(formula)
tvars = [self.converter.convert(x) for x in variables]
algo = mathsat.MSAT_EXIST_ELIM_ALLSMT_FM
if self.algorithm == 'lw':
algo = mathsat.MSAT_EXIST_ELIM_VTS
res = mathsat.msat_exist_elim(self.msat_env, fterm, tvars, algo)
return self.converter.back(res)
def exist_elim(self, variables, formula):
logic = get_logic(formula, self.env)
if not logic <= LRA:
raise NotImplementedError("MathSAT quantifier elimination only"\
" supports LRA (detected logic " \
"is: %s)" % str(logic))
fterm = self.converter.convert(formula)
tvars = [self.converter.convert(x) for x in variables]
algo = mathsat.MSAT_EXIST_ELIM_ALLSMT_FM
if self.algorithm == 'lw':
algo = mathsat.MSAT_EXIST_ELIM_VTS
res = mathsat.msat_exist_elim(self.msat_env(), fterm, tvars, algo)
return self.converter.back(res)
def smtlibscript_from_formula(formula, logic=None):
script = SmtLibScript()
if logic is None:
# Get the simplest SmtLib logic that contains the formula
f_logic = get_logic(formula)
smt_logic = None
try:
smt_logic = get_closer_smtlib_logic(f_logic)
except NoLogicAvailableError:
warnings.warn("The logic %s is not reducible to any SMTLib2 " \
"standard logic. Proceeding with non-standard " \
"logic '%s'" % (f_logic, f_logic),
stacklevel=3)
smt_logic = f_logic
elif not (isinstance(logic, Logic) or isinstance(logic, str)):
raise UndefinedLogicError(str(logic))
else:
if logic not in SMTLIB2_LOGICS:
warnings.warn("The logic %s is not reducible to any SMTLib2 " \
"standard logic. Proceeding with non-standard " \
"logic '%s'" % (logic, logic),
stacklevel=3)
smt_logic = logic
script.add(name=smtcmd.SET_LOGIC, args=[smt_logic])
# Declare all types
types = get_env().typeso.get_types(formula, custom_only=True)
for type_ in types:
script.add(name=smtcmd.DECLARE_SORT, args=[type_.decl])
deps = formula.get_free_variables()
# Declare all variables
for symbol in deps:
assert symbol.is_symbol()
script.add(name=smtcmd.DECLARE_FUN, args=[symbol])
# Assert formula
script.add_command(SmtLibCommand(name=smtcmd.ASSERT, args=[formula]))
# check-sat
script.add_command(SmtLibCommand(name=smtcmd.CHECK_SAT, args=[]))
return script
def get_models(self, fml, blocking, count):
t_logic = get_logic(fml)
models = []
m_index = 0
with Solver(logic=t_logic) as solver:
solver.add_assertion(fml)
while (solver.solve()):
partial_model = [
EqualsOrIff(b, solver.get_value(b)) for b in blocking
]
m = solver.get_model()
models.append(m)
solver.add_assertion(Not(And(partial_model)))
m_index += 1
if m_index > count:
break
return models
def smtlibscript_from_formula(formula):
script = SmtLibScript()
# Get the simplest SmtLib logic that contains the formula
f_logic = get_logic(formula)
smt_logic = get_closer_smtlib_logic(f_logic)
script.add(name=smtcmd.SET_LOGIC,
args=[smt_logic])
deps = formula.get_free_variables()
# Declare all variables
for symbol in deps:
assert symbol.is_symbol()
script.add(name=smtcmd.DECLARE_FUN, args=[symbol])
# Assert formula
script.add_command(SmtLibCommand(name=smtcmd.ASSERT,
args=[formula]))
# check-sat
script.add_command(SmtLibCommand(name=smtcmd.CHECK_SAT,
args=[]))
return script
def solve_safety_inc_int(self, hts, prop, k):
init = hts.single_init()
trans = hts.single_trans()
invar = hts.single_invar()
solver_proof = self.solver.copy("inc_int_proof")
solver = self.solver.copy("inc_int")
has_next = TS.has_next(prop)
map_10 = dict([(TS.get_timed_name(v.symbol_name(), 1), TS.get_timed_name(v.symbol_name(), 0)) for v in hts.vars])
itp = Interpolator(logic=get_logic(trans))
init = And(init, invar)
nprop = Not(prop)
def check_overappr(Ri, R):
self._reset_assertions(solver_proof)
self._add_assertion(solver_proof, And(Ri, Not(R)))
if not self._solve(solver_proof):
Logger.log("Proof found with k=%s"%(t), 1)
return TRUE()
Logger.log("Extending initial states (%s)"%int_c, 1)
return Or(R, Ri)
t = 1 if has_next else 0
trans_t = self.unroll(trans, invar, k+1, gen_list=True)
pivot = 2
trans_tA = And(trans_t[:pivot])
init_0 = self.at_time(init, 0)
is_sat = True
Ri = None
self._reset_assertions(solver)
while (t < k+1):
Logger.log("\nSolving for k=%s"%t, 1)
int_c = 0
R = init_0
# trans_t is composed as trans_i, invar_i, trans_i+1, invar_i+1, ...
self._add_assertion(solver, trans_t[2*t])
self._add_assertion(solver, trans_t[(2*t)+1])
while True:
Logger.log("Add init and invar", 2)
self._push(solver)
self._add_assertion(solver, R)
npropt = self.at_time(nprop, t-1 if has_next else t)
Logger.log("Add property time %d"%t, 2)
self._add_assertion(solver, npropt)
Logger.log("Interpolation at k=%s"%(t), 2)
if t > 0:
trans_tB = And(trans_t[pivot:(t*2)])
Ri = And(itp.binary_interpolant(And(R, trans_tA), And(trans_tB, npropt)))
is_sat = Ri == None
if is_sat and self._solve(solver):
if R == init_0:
Logger.log("Counterexample found with k=%s"%(t), 1)
model = self._get_model(solver)
return (t, model)
else:
Logger.log("No counterexample or proof found with k=%s"%(t), 1)
Logger.msg(".", 0, not(Logger.level(1)))
self._pop(solver)
break
else:
self._pop(solver)
if Ri is None:
break
Ri = substitute(Ri, map_10)
res = check_overappr(Ri, R)
if res == TRUE():
Logger.log("Proof found with k=%s"%(t), 1)
return (t, True)
R = res
int_c += 1
t += 1
return (t-1, None)
def test_get_logic(self):
for example in get_example_formulae():
target_logic = example.logic
res = get_logic(example.expr)
self.assertEqual(res, target_logic, "%s - %s != %s" % \
(example.expr, target_logic, res))
# represents the grid distance (aka Manhattan distance) of (x,y) from
# the origin.
z = Symbol("z", REAL)
distance= z.Equals(x + y)
# We want to characterize the set of points in the rectangle, in terms
# of their grid distance from the origin. In other words, we want to
# constraint z to be able to assume values that are possible within
# the rectangle. We want a formula in z that is satisfiable iff there
# is a value for z s.t. exists a value for x,y within the rectangle.
# An example of the type of information that we expect to see is the
# maximum and minimum value of z.
f3 = Exists([x,y], rect & distance)
qe_f3 = qelim(f3)
print(qe_f3.serialize())
# Depending on the solver in use you might get a different
# result. Try: qelim(f3, solver_name="msat_fm")
#
# MathSAT Fourier Motzkin (FM) returns a compact result: (0.0
# <= z) & (z <= 15.0) , meaning that the further point in grid
# distance is at most 15.0 units away from the origin.
#
# By definition, the expression obtained after performing quantifier
# elimination is in the quantifier free fragment of the logic. It is
# therefore possible to remove the quantifiers using qelim, and use a
# solver that does not support quantifiers natively to solve the new
# formula.
from pysmt.oracles import get_logic
print(get_logic(f3), get_logic(qe_f3))
def is_unsat(self, formula, solver_name=None, logic=None):
if logic == AUTO_LOGIC:
logic = get_logic(formula, self.environment)
with self.Solver(name=solver_name, logic=logic) \
as solver:
return solver.is_unsat(formula)
def test_oracle(self):
x = FreshSymbol(REAL)
f = Equals(Times(x, x), Real(2))
logic = get_logic(f)
self.assertFalse(logic.theory.linear)
def test_get_logic(self):
for example in EXAMPLE_FORMULAS:
target_logic = example.logic
res = get_logic(example.expr)
self.assertEqual(res, target_logic, "%s - %s != %s" % \
(example.expr, target_logic, res))
def test_oracle(self):
x = FreshSymbol(REAL)
f = Equals(Times(x, x), Real(2))
logic = get_logic(f)
self.assertFalse(logic.theory.linear)
def qelim(self, formula, solver_name=None, logic=None):
if logic is None or logic == AUTO_LOGIC:
logic = get_logic(formula, self.environment)
with self.QuantifierEliminator(name=solver_name, logic=logic) as qe:
return qe.eliminate_quantifiers(formula)
def is_unsat(self, formula, solver_name=None, logic=None):
if logic == AUTO_LOGIC:
logic = get_logic(formula, self.environment)
with self.Solver(name=solver_name, logic=logic) \
as solver:
return solver.is_unsat(formula)
def qelim(self, formula, solver_name=None, logic=None):
if logic is None or logic == AUTO_LOGIC:
logic = get_logic(formula, self.environment)
with self.QuantifierEliminator(name=solver_name, logic=logic) as qe:
return qe.eliminate_quantifiers(formula)
def solve_safety_int(self, hts, prop, k):
init = hts.single_init()
trans = hts.single_trans()
invar = hts.single_invar()
has_next = TS.has_next(prop)
map_10 = dict([(TS.get_timed_name(v.symbol_name(), 1), TS.get_timed_name(v.symbol_name(), 0)) for v in hts.vars])
itp = Interpolator(logic=get_logic(trans))
init = And(init, invar)
nprop = Not(prop)
pivot = 2
t = 1 if has_next else 0
while (t < k+1):
Logger.log("\nSolving for k=%s"%t, 1)
int_c = 0
init_0 = self.at_time(init, 0)
R = init_0
trans_t = self.unroll(trans, invar, t, gen_list=True)
trans_tA = And(trans_t[:pivot]) if t > 0 else TRUE()
trans_tB = And(trans_t[pivot:]) if t > 0 else TRUE()
while True:
self._reset_assertions(self.solver)
Logger.log("Add init and invar", 2)
self._add_assertion(self.solver, R)
self._add_assertion(self.solver, And(trans_tA, trans_tB))
npropt = self.at_time(nprop, t-1 if has_next else t)
Logger.log("Add property time %d"%t, 2)
self._add_assertion(self.solver, npropt)
if self._solve(self.solver):
if R == init_0:
Logger.log("Counterexample found with k=%s"%(t), 1)
model = self._get_model(self.solver)
return (t, model)
else:
Logger.log("No counterexample or proof found with k=%s"%(t), 1)
Logger.msg(".", 0, not(Logger.level(1)))
break
else:
if len(trans_t) < 2:
Logger.log("No counterexample found with k=%s"%(t), 1)
Logger.msg(".", 0, not(Logger.level(1)))
break
Ri = And(itp.binary_interpolant(And(R, trans_tA), And(trans_tB, npropt)))
Ri = substitute(Ri, map_10)
self._reset_assertions(self.solver)
self._add_assertion(self.solver, And(Ri, Not(R)))
if not self._solve(self.solver):
Logger.log("Proof found with k=%s"%(t), 1)
return (t, True)
else:
R = Or(R, Ri)
int_c += 1
Logger.log("Extending initial states (%s)"%int_c, 1)
t += 1
return (t-1, None)
def test_get_logic(self):
for example in get_example_formulae():
target_logic = example.logic
res = get_logic(example.expr)
self.assertEqual(res, target_logic, "%s - %s != %s" % \
(example.expr, target_logic, res))
def test_get_logic(self):
for example in EXAMPLE_FORMULAS:
target_logic = example.logic
res = get_logic(example.expr)
self.assertEqual(res, target_logic, "%s - %s != %s" % (example.expr, target_logic, res))
# represents the grid distance (aka Manhattan distance) of (x,y) from
# the origin.
z = Symbol("z", REAL)
distance = z.Equals(x + y)
# We want to characterize the set of points in the rectangle, in terms
# of their grid distance from the origin. In other words, we want to
# constraint z to be able to assume values that are possible within
# the rectangle. We want a formula in z that is satisfiable iff there
# is a value for z s.t. exists a value for x,y within the rectangle.
# An example of the type of information that we expect to see is the
# maximum and minimum value of z.
f3 = Exists([x, y], rect & distance)
qe_f3 = qelim(f3)
print(qe_f3.serialize())
# Depending on the solver in use you might get a different
# result. Try: qelim(f3, solver_name="msat_fm")
#
# MathSAT Fourier Motzkin (FM) returns a compact result: (0.0
# <= z) & (z <= 15.0) , meaning that the further point in grid
# distance is at most 15.0 units away from the origin.
#
# By definition, the expression obtained after performing quantifier
# elimination is in the quantifier free fragment of the logic. It is
# therefore possible to remove the quantifiers using qelim, and use a
# solver that does not support quantifiers natively to solve the new
# formula.
from pysmt.oracles import get_logic
print(get_logic(f3), get_logic(qe_f3))