def _visit_prop(self, sig: Signal, number: Number) -> str:
# TODO: run it
# Encode into SMT proposition `DstFormulaProp`, i.e., smth. like
# (r&E(c), q_next)
# It should become
# \exists c: reach(q_next, tau(t, r, ?c)) &
# rank(q,t)<>rank(q_next, tau(t, r, ?c))
assert number == Number(
1), "program invariant: propositions are positive"
dstFormProp = self.encoder.dstPropMgr.get_dst_form_prop(
sig.name)
ext_label, q_next = dstFormProp.ext_label, dstFormProp.dst_state
# build s_m_next, s_q_next
tau_input_args_dict, free_input_args = build_inputs_values(
self.encoder.inputs, ext_label.fixed_inputs)
tau_input_args_dict[ARG_MODEL_STATE] = smt_name_m(self.m)
s_m_next = call_func(self.encoder.tau_desc,
tau_input_args_dict)
s_q_next = smt_name_q(q_next)
# build reach_next
reach_next_args = {
ARG_A_STATE: s_q_next,
ARG_MODEL_STATE: s_m_next
}
reach_next = call_func(self.encoder.reach_func_desc,
reach_next_args)
# build rank_cmp
rank_args = {
ARG_A_STATE: smt_name_q(self.q),
ARG_MODEL_STATE: smt_name_m(self.m)
}
rank_next_args = reach_next_args
rank = call_func(self.encoder.rank_func_desc, rank_args)
rank_next = call_func(self.encoder.rank_func_desc,
rank_next_args)
rank_cmp_op = self.encoder._get_greater_op(q_next)
rank_cmp = rank_cmp_op(rank,
rank_next) if rank_cmp_op else true()
# build `\exists[forall]: reach_next & rank_cmp`
reach_and_rank_cmp = op_and([reach_next, rank_cmp])
op = (forall_bool,
exists_bool)[ext_label.type_ == ExtLabel.EXISTS]
return op(free_input_args, reach_and_rank_cmp)
def encode_initialization(self) -> List[str]:
q_init = self.aht.init_node
m_init = self.model_init_state
reach_args = {
ARG_A_STATE: smt_name_q(q_init),
ARG_MODEL_STATE: smt_name_m(m_init)
}
return [assertion(call_func(self.reach_func_desc, reach_args))]
def encode_initialization(self) -> List[str]:
assertions = []
for q, m in product(self.automaton.init_nodes,
[self.model_init_state]):
vals_by_vars = {
ARG_MODEL_STATE: smt_name_m(m),
ARG_A_STATE: smt_name_q(q)
}
assertions.append(
assertion(call_func(self.reach_func_desc, vals_by_vars)))
return assertions
def encode_get_model_values(tau_desc: FuncDesc,
descr_by_output: Dict[Signal, FuncDesc],
last_allowed_states: Iterable[int]) -> List[str]:
func_descs = [tau_desc] + list(descr_by_output.values())
res = []
for func_desc in func_descs:
for input_dict in _get_all_possible_inputs(func_desc,
last_allowed_states):
res.append(get_value(call_func(func_desc, input_dict)))
return res
def _encode_prop_outputs(self) -> List[str]:
res = []
for pSig, func in self.desc_by_pSig.items():
body = call_func(
self.reach_func_desc, {
ARG_MODEL_STATE:
ARG_MODEL_STATE,
ARG_A_STATE:
smt_name_q(next(iter(self.atm_by_sig[pSig].init_nodes)))
})
res += [define_fun(func, body)]
return res
def visit_binary_op(me, binary_op: BinOp):
assert binary_op.name in '=*+', binary_op
if binary_op.name == '=':
assert binary_op.arg2 == Number(1), binary_op
return call_func(
self.desc_by_sig[binary_op.arg1],
{ARG_MODEL_STATE: smt_name_m(self.model_init_state)})
else:
op = (op_and, op_or)[binary_op.name == '+']
smt1 = me.dispatch(binary_op.arg1)
smt2 = me.dispatch(binary_op.arg2)
return op([smt1, smt2])
def smt_out(smt_m: str, i_o: Label, inputs: Iterable[Signal],
descr_by_output: Dict[Signal, FuncDesc]) -> str:
args_dict = build_tau_args_dict(inputs, smt_m, i_o)
conjuncts = []
for sig, val in i_o.items():
out_desc = descr_by_output.get(sig)
if out_desc is None:
continue
condition_on_out = call_func(out_desc, args_dict)
if val is False:
condition_on_out = op_not(condition_on_out)
conjuncts.append(condition_on_out)
return op_and(conjuncts)
def _encode_meaning_of_forbidding_atoms(self) -> List[str]:
res = list()
for k, a in enumerate(self.forbidding_atoms):
states_to_forbid = set(
filter(lambda n: n.k <= k, self.automaton.nodes))
forbid_k_meaning = op_implies(
a,
op_and(
map(
lambda q_m: op_not(
call_func(
self.reach_func_desc, {
ARG_A_STATE: smt_name_q(q_m[0]),
ARG_MODEL_STATE: smt_name_m(q_m[1])
})),
product(states_to_forbid, self.max_model_states))))
res.append(assertion(forbid_k_meaning))
return res
def _encode_state(self, q: Node, m: int) -> List[str]:
q_transitions = lfilter(lambda t: t.src == q, self.aht_transitions)
# Encoding:
# - if q is existential, then one of the transitions must fire:
#
# reach(q,t) ->
# OR{state_label \in q_transitions}: sys_out=state_label & reach(q',t')
#
# - if q is universal, then all transitions of that system output should fire
#
# reach(q,t) ->
# AND{state_label \in q_transitions}: sys_out=state_label -> reach(q',t')
#
# build s_premise `reach(q,t)`
s_m = smt_name_m(m)
s_q = smt_name_q(q)
s_premise = call_func(self.reach_func_desc, {
ARG_MODEL_STATE: s_m,
ARG_A_STATE: s_q
})
# build s_conclusion `exists`
s_conclusion_out_sExpr_pairs = set() # type: Set[Tuple[str, str]]
for t in q_transitions: # type: Transition
s_t_state_label = smt_out(s_m, t.state_label, self.inputs,
self.descr_by_output)
s_dst_expr = self._translate_dst_expr_into_smt(t.dst_expr, q, m)
s_conclusion_out_sExpr_pairs.add((s_t_state_label, s_dst_expr))
if q.is_existential:
s_conclusion_elements = lmap(lambda sce: op_and(sce),
s_conclusion_out_sExpr_pairs)
else:
s_conclusion_elements = lmap(
lambda sce: op_implies(sce[0], sce[1]),
s_conclusion_out_sExpr_pairs)
s_conclusion = (op_and, op_or)[q.is_existential](s_conclusion_elements)
s_assertion = op_implies(s_premise, s_conclusion)
return [assertion(s_assertion)]
def encode_model_bound(allowed_model_states: Iterable[int],
tau_desc: FuncDesc) -> List[str]:
res = [comment('encoding model bound: ' + str(allowed_model_states))]
# all args of tau function are quantified
args_dict = dict((a, smt_name_free_arg(a))
for (a, ty) in tau_desc.ordered_argname_type_pairs)
free_vars = [(args_dict[a], ty)
for (a, ty) in tau_desc.ordered_argname_type_pairs]
smt_m_next = call_func(tau_desc, args_dict)
disjuncts = []
for allowed_m in iter(allowed_model_states):
disjuncts.append(op_eq(smt_m_next, smt_name_m(allowed_m)))
condition = forall(free_vars, op_or(disjuncts))
res.append(assertion(condition))
return res
def smt_tau(smt_m: str, i_o: Label):
tau_args = build_tau_args_dict(inputs, smt_m, i_o)
return call_func(tau_desc, tau_args)
def smt_reach(smt_m: str, smt_q: str):
return call_func(reach_func_desc, {
ARG_MODEL_STATE: smt_m,
ARG_A_STATE: smt_q
})
