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_transitions_ucw(reach_func_desc: FuncDesc,
rank_func_desc: FuncDesc,
tau_desc: FuncDesc,
desc_by_output: Dict[Signal, FuncDesc],
inputs: List[Signal],
q: Node,
m: int,
i_o: Label,
state_to_final_scc: dict = None) -> List[str]:
# syntax sugar
def smt_r(smt_m: str, smt_q: str):
return call_func(rank_func_desc, {
ARG_MODEL_STATE: smt_m,
ARG_A_STATE: smt_q
})
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
})
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)
#
smt_m, smt_q = smt_name_m(m), smt_name_q(q)
smt_m_next = smt_tau(smt_m, i_o)
smt_pre = op_and(
[smt_reach(smt_m, smt_q),
smt_out(smt_m, i_o, inputs, desc_by_output)])
smt_post_conjuncts = []
for q_next, is_fin in q.transitions[i_o]:
if is_final_sink(q_next):
smt_post_conjuncts = [false()]
break
smt_q_next = smt_name_q(q_next)
smt_post_conjuncts.append(smt_reach(smt_m_next, smt_q_next))
greater_op = _get_greater_op_ucw(q, is_fin, q_next, state_to_final_scc)
if greater_op is not None:
smt_post_conjuncts.append(
greater_op(smt_r(smt_m, smt_q), smt_r(smt_m_next, smt_q_next)))
smt_post = op_and(smt_post_conjuncts)
pre_implies_post = op_implies(smt_pre, smt_post)
free_input_args = get_free_input_args(i_o, inputs)
return [assertion(forall_bool(free_input_args, pre_implies_post))]
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_transitions_nbw(m: int, q: Node, reach_func_desc: FuncDesc,
rank_func_desc: FuncDesc, tau_desc: FuncDesc,
desc_by_output: Dict[Signal, FuncDesc],
inputs: List[Signal]) -> List[str]:
# syntax sugar
def smt_r(smt_m: str, smt_q: str):
return call_func(rank_func_desc, {
ARG_MODEL_STATE: smt_m,
ARG_A_STATE: smt_q
})
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
})
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)
# reach(q,t) ->
# OR{(q,io,q') \in \delta(q)}:
# sys_out=o & reach(q',t') & rank(q,t,q',t')
s_m = smt_name_m(m)
s_q = smt_name_q(q)
s_pre = smt_reach(s_m, s_q)
s_disjuncts = list() # type: List[str]
for lbl, qn_flag_pairs in q.transitions.items(
): # type: (Label, Set[Tuple[Node, bool]])
s_m_next = smt_tau(s_m, lbl)
s_out = smt_out(s_m, lbl, inputs, desc_by_output)
free_inputs = get_free_input_args(lbl, inputs)
for (q_next, is_acc) in qn_flag_pairs:
if is_final_sink(q_next):
s_disj = exists_bool(free_inputs, s_out)
s_disjuncts.append(s_disj)
break
s_q_next = smt_name_q(q_next)
s_reach = smt_reach(s_m_next, s_q_next)
if is_acc:
s_rank = true() # TODO: SCCs
else:
s_rank = op_gt(smt_r(s_m, s_q), smt_r(s_m_next, s_q_next))
s_disj = exists_bool(free_inputs, op_and([s_out, s_reach, s_rank]))
s_disjuncts.append(s_disj)
s_assertion = op_implies(s_pre, op_or(s_disjuncts))
return [assertion(s_assertion)]
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 _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 _get_all_possible_inputs(func_desc: FuncDesc, last_allowed_states):
arg_type_pairs = func_desc.ordered_argname_type_pairs
get_values = lambda t: {
bool_type(): (true(), false()),
TYPE_MODEL_STATE: [smt_name_m(m) for m in last_allowed_states],
}[t]
records = product(*[get_values(t) for (_, t) in arg_type_pairs])
args = lmap(lambda a_t: a_t[0], arg_type_pairs)
dicts = []
for record in records:
assert len(args) == len(record)
arg_value_pairs = zip(args, record)
dicts.append(dict(arg_value_pairs))
return dicts
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