Set Implicit Arguments.
Class GhostMultiParams `(P : MultiParams) :=
{
ghost_data : Type;
ghost_init : ghost_data ;
ghost_net_handlers :
name -> name -> msg -> (ghost_data * data) -> ghost_data;
ghost_input_handlers :
name -> input -> (ghost_data * data) -> ghost_data
}.
Section GhostVars.
Context {base_params : BaseParams}.
Context {multi_params : MultiParams base_params}.
Context {failure_params : FailureParams multi_params}.
Context {ghost_params : GhostMultiParams multi_params}.
Definition refined_net_handlers me src m st :=
let '(out, st', ps) :=
net_handlers me src m (snd st) in
(out, (ghost_net_handlers me src m st, st'), ps).
Definition refined_input_handlers me inp st :=
let '(out, st', ps) := input_handlers me inp (snd st) in
(out, (ghost_input_handlers me inp st, st'), ps).
Definition refined_init_handlers (n : name) : ghost_data * data :=
(ghost_init, init_handlers n).
Definition refined_reboot (st : ghost_data * data) :=
(fst st , reboot (snd st)).
Instance refined_base_params : BaseParams :=
{
data := (ghost_data * data)%type ;
input := input ;
output := output
}.
Instance refined_multi_params : MultiParams _ :=
{
name := name ;
msg := msg ;
msg_eq_dec := msg_eq_dec ;
name_eq_dec := name_eq_dec ;
nodes := nodes ;
all_names_nodes := all_names_nodes ;
no_dup_nodes := no_dup_nodes ;
init_handlers := refined_init_handlers;
net_handlers := refined_net_handlers ;
input_handlers := refined_input_handlers
}.
Instance refined_failure_params : FailureParams _ :=
{
reboot := refined_reboot
}.
Definition deghost_packet p :=
@mkPacket _ multi_params
(@pSrc _ refined_multi_params p)
(pDst p)
(pBody p).
Definition deghost (net : @network _ refined_multi_params) : (@network _ multi_params).
refine (@mkNetwork _ multi_params
(map deghost_packet
(nwPackets net))
_
).
intros.
destruct net.
concludes.
destruct nwState. auto.
Defined.
Arguments deghost_packet /_.
Definition deghost_prop I (failed_net : list name * network) : Prop :=
I ((fst failed_net), deghost (snd failed_net)).
Instance refined_base_params_tot_map :
BaseParamsTotalMap refined_base_params base_params :=
{
tot_map_data := snd ;
tot_map_input := id ;
tot_map_output := id
}.
Instance refined_multi_params_name_tot_map :
MultiParamsNameTotalMap refined_multi_params multi_params :=
{
tot_map_name := id ;
tot_map_name_inv := id
}.
Instance refined_multi_params_name_tot_map_bijective :
MultiParamsNameTotalMapBijective refined_multi_params_name_tot_map :=
{
tot_map_name_inv_inverse := fun _ => eq_refl ;
tot_map_name_inverse_inv := fun _ => eq_refl
}.
Instance refined_multi_params_tot_msg_map :
MultiParamsMsgTotalMap refined_multi_params multi_params :=
{
tot_map_msg := id
}.
Program Instance refined_multi_params_map_congruency :
MultiParamsTotalMapCongruency refined_base_params_tot_map
refined_multi_params_name_tot_map refined_multi_params_tot_msg_map :=
{
tot_init_handlers_eq := fun _ => eq_refl ;
tot_net_handlers_eq := _ ;
tot_input_handlers_eq := _
}.
Next Obligation.
rewrite /tot_mapped_net_handlers /= /refined_net_handlers /= /tot_map_name_msgs /= /id /=.
repeat break_let.
find_inversion.
by rewrite /= -/id map_id map_fst_snd_id.
Qed.
Next Obligation.
rewrite /tot_mapped_input_handlers /=.
repeat break_let.
unfold refined_input_handlers in *.
repeat break_let.
find_inversion.
by rewrite /id /= map_id /tot_map_name_msgs /= /id /= map_fst_snd_id.
Qed.
Instance refined_failure_params_map_congruency :
FailureParamsTotalMapCongruency refined_failure_params
failure_params refined_base_params_tot_map :=
{
tot_reboot_eq := fun _ => eq_refl
}.

Lemma map_id_tr :
forall out,
map (fun e : name * (input + list output) =>
let (n, s) := e in
match s with
| inl io => (n, inl io)
| inr lo => (n, inr (map id lo))
end) out = out.