def k_induction_attempt_inductive():
# Create an smt_switch.SmtSolver with Boolector as the backend
# and no logging
s = ss.create_btor_solver(False)
s.set_opt('produce-models', 'true')
s.set_opt('incremental', 'true')
prop, fts = build_simple_alu_fts(s)
# store sets of states in a dictionary for accessing below
states = {str(sv): sv for sv in fts.statevars}
# make the property inductive manually
prop = pono.Property(
s,
s.make_term(
And,
s.make_term(Equal, states['cfg'],
s.make_term(0, s.make_sort(BV, 1))), prop.prop))
print(
'\n============== Running k-induction on inductively strengthened property =============='
)
print('INIT\n\t{}'.format(fts.init))
print('TRANS\n\t{}'.format(fts.trans))
print('PROP\n\t{}'.format(prop.prop))
# Create KInduction engine -- using same solver (in future can change the solver)
kind = pono.KInduction(prop, fts, s)
res = kind.check_until(20)
print(res)
assert res is True, "Expecting k-induction to prove the inductively strengthened property"
print("KInduction returned true")
def test_history_modifier(create_solver):
solver = create_solver(False)
solver.set_opt("incremental", "true")
solver.set_opt("produce-models", "true")
bvsort8 = solver.make_sort(ss.sortkinds.BV, 8)
ts = pono.FunctionalTransitionSystem(solver)
counter = ts.make_statevar("counter", bvsort8)
ts.constrain_init(
ts.make_term(ss.primops.Equal, counter, ts.make_term(0, bvsort8)))
ts.assign_next(
counter,
ts.make_term(ss.primops.BVAdd, counter, ts.make_term(1, bvsort8)))
hm = pono.HistoryModifier(ts)
counter_delay_2 = hm.get_hist(counter, 2)
p = pono.Property(
solver,
ts.make_term(ss.primops.BVUlt, counter, ts.make_term(5, bvsort8)))
bmc = pono.Bmc(p, ts, solver)
res = bmc.check_until(10)
assert not res, "should be false"
witness = bmc.witness()
checked_at_least_one = False
for i, m in enumerate(witness):
if i > 1:
checked_at_least_one = True
# checking semantics of history modifier delay
assert witness[i][counter_delay_2] == witness[i - 2][counter]
assert checked_at_least_one
def test_vcd_trace(create_solver):
solver = create_solver(False)
solver.set_opt("incremental", "true")
solver.set_opt("produce-models", "true")
bvsort8 = solver.make_sort(ss.sortkinds.BV, 8)
ts = pono.FunctionalTransitionSystem(solver)
x = ts.make_statevar('x', bvsort8)
ts.constrain_init(
solver.make_term(ss.primops.Equal, x,
solver.make_term(0, x.get_sort())))
ts.assign_next(
x, ts.make_term(ss.primops.BVAdd, x, solver.make_term(1,
x.get_sort())))
prop_term = solver.make_term(ss.primops.BVUle, x,
solver.make_term(9, x.get_sort()))
prop = pono.Property(solver, prop_term)
bmc = pono.Bmc(prop, ts, solver)
res = bmc.check_until(10)
assert res == False, "res should be false, not just unknown (i.e. None)"
witness = bmc.witness()
with tempfile.NamedTemporaryFile() as temp:
assert os.stat(temp.name).st_size == 0, "Expect file to start empty"
vcd_printer = pono.VCDWitnessPrinter(ts, witness)
vcd_printer.dump_trace_to_file(temp.name)
assert os.stat(temp.name).st_size, "Expect file to be non-empty"
def process_guarantees(self, solver, rts, at_end_state_flag, ports):
for i, guarantee in enumerate(self.guarantees):
prop = pono.Property(
rts,
solver.make_term(
Implies,
at_end_state_flag,
guarantee.value(solver, ports)
)
)
interp = pono.KInduction(prop, solver)
assert interp.check_until(10), interp.witness()
def build_simple_alu_fts(
s: ss.SmtSolver
) -> Tuple[pono.Property, pono.FunctionalTransitionSystem]:
'''
Creates a simple alu transition system
@param s - an SmtSolver from smt_switch
@return a property
'''
# Instantiate a functional transition system
fts = pono.FunctionalTransitionSystem(s)
# Create a bit-vector sorts
bvsort1 = s.make_sort(BV, 1)
bvsort8 = s.make_sort(BV, 8)
# Create the states
cfg = fts.make_statevar('cfg', bvsort1)
spec_res = fts.make_statevar('spec_res', bvsort8)
imp_res = fts.make_statevar('imp_res', bvsort8)
# Create the inputs
a = fts.make_inputvar('a', bvsort8)
b = fts.make_inputvar('b', bvsort8)
# Add logic for cfg
## Start at 0
fts.constrain_init(s.make_term(Equal, cfg, s.make_term(0, bvsort1)))
## Keeps the same value
fts.assign_next(cfg, cfg)
# Set logic for results
## they start equal
fts.constrain_init(s.make_term(Equal, spec_res, imp_res))
## spec_res is the sum: spec_res' = a + b
fts.assign_next(spec_res, s.make_term(BVAdd, a, b))
## depends on the configuration: imp_res' == (cfg == 0) ? a + b : a - b
fts.assign_next(
imp_res,
s.make_term(Ite, s.make_term(Equal, cfg, s.make_term(0, bvsort1)),
s.make_term(BVAdd, a, b), s.make_term(BVSub, a, b)))
# Create a property: (spec_cnt == imp_cnt - 1)
prop = pono.Property(s, s.make_term(Equal, spec_res, imp_res))
return prop, fts
def test_kind_inductive_prop(create_solver):
s = create_solver(False)
s.set_opt('produce-models', 'true')
s.set_opt('incremental', 'true')
prop = build_simple_alu_fts(s)
states = {str(sv): sv for sv in prop.transition_system.statevars}
prop = c.Property(
prop.transition_system,
s.make_term(
And,
s.make_term(Equal, states['cfg'],
s.make_term(0, s.make_sort(BV, 1))), prop.prop))
kind = c.KInduction(prop, s)
res = kind.check_until(10)
assert res is True, "KInduction should be able to solve this manually strengthened property"