Section LogCorrect.
Context {orig_base_params : BaseParams}.
Context {orig_multi_params : MultiParams orig_base_params}.
Context {orig_failure_params : FailureParams orig_multi_params}.
Context {data_serializer : Serializer data}.
Context {name_serializer : Serializer name}.
Context {msg_serializer : Serializer msg}.
Context {input_serializer : Serializer input}.
Variable snapshot_interval : nat.
Instance log_base_params : BaseParams := @log_base_params orig_base_params.
Instance log_multi_params : DiskOpMultiParams log_base_params := log_multi_params snapshot_interval.
Instance log_failure_params : DiskOpFailureParams log_multi_params := log_failure_params snapshot_interval.
Proof using.
intros.
unfold apply_log.
rewrite fold_left_app.
reflexivity.
Qed.
Definition disk_correct dsk h st  :=
exists s (entries : list entry) (snap : data),
dsk Count = Some (serialize (length entries)) /\
dsk Log = Some s /\
IOStreamWriter.unwrap s = IOStreamWriter.unwrap (list_serialize_rec entry _ entries) /\
dsk Snapshot = Some (serialize snap) /\
log_num_entries st = length entries /\
(apply_log h snap entries = log_data st).
Proof using.
intros.
unfold disk_correct in *.
unfold log_net_handlers, log_handler_result in *;
break_if; do 2 break_let.
- find_inversion.
simpl.
exists IOStreamWriter.empty, [], d.
intuition.
- find_inversion.
simpl.
break_exists.
intuition.
match goal with
| _ : dsk Log = Some ?s, _ : apply_log _ ?d ?entries = _ |- _ =>
exists (s +$+ (serialize (inr (src, m) : entry))), (entries ++ [inr (src, m)]), d
end.
intuition.
+ match goal with
| H : context [log_num_entries] |- _ => rewrite H
end.
rewrite app_length.
simpl.
rewrite NPeano.Nat.add_1_r.
reflexivity.
+ break_match.
* find_inversion.
reflexivity.
* congruence.
+ cheerios_crush.
rewrite serialize_snoc.
match goal with
| H : IOStreamWriter.unwrap _ = IOStreamWriter.unwrap _ |- _ => rewrite H
end.
reflexivity.
+ match goal with
| H : context [log_num_entries] |- _ => rewrite H
end.
rewrite app_length.
simpl.
rewrite NPeano.Nat.add_1_r.
reflexivity.
+ rewrite apply_log_app.
match goal with
| H : context [apply_log] |- _ => rewrite H
end.
simpl.
match goal with
| H : context [net_handlers] |- _ => rewrite H
end.
reflexivity.
Qed.
Proof using.
intros.
unfold disk_correct in *.
unfold log_input_handlers, log_handler_result in *;
break_if; do 2 break_let.
- find_inversion.
simpl.
exists IOStreamWriter.empty, [], d.
intuition.
- find_inversion.
simpl.
break_exists.
intuition.
match goal with
| _ : dsk Log = Some ?s, _ : apply_log _ ?d ?entries = _ |- _ =>
exists (s +$+ (serialize (inl m : entry))), (entries ++ [inl m]), d
end.
intuition.
+ match goal with
| H : context [log_num_entries] |- _ => rewrite H
end.
rewrite app_length.
simpl.
rewrite NPeano.Nat.add_1_r.
reflexivity.
+ break_match.
* find_inversion.
reflexivity.
* congruence.
+ cheerios_crush.
rewrite serialize_snoc.
match goal with
| H : IOStreamWriter.unwrap _ = IOStreamWriter.unwrap _ |- _ => rewrite H
end.
reflexivity.
+ match goal with
| H : context [log_num_entries] |- _ => rewrite H
end.
rewrite app_length.
simpl.
rewrite NPeano.Nat.add_1_r.
reflexivity.
+ rewrite apply_log_app.
match goal with
| H : context [apply_log] |- _ => rewrite H
end.
simpl.
match goal with
| H : context [input_handlers] |- _ => rewrite H
end.
reflexivity.
Qed.
Proof using.
intros net h d dsk H_correct H_reboot.
unfold do_log_reboot, disk_to_channel, channel_to_log, from_channel in *.
unfold disk_correct in *. break_exists. intuition.
repeat find_rewrite.
repeat rewrite IOStreamWriter.channel_wrap_unwrap in *.
repeat rewrite serialize_deserialize_id_nil in H_reboot.
rewrite <- (app_nil_r (IOStreamWriter.unwrap _)) in H_reboot.
repeat find_rewrite.
rewrite list_serialize_deserialize_id_rec in H_reboot.
find_inversion.
exists (IOStreamWriter.empty).
exists [].
exists (reboot (apply_log h x1 x0)).
intuition.
Qed.
Proof using.
intros net failed tr H_st h.
remember step_failure_disk_ops_init as x.
change net with (snd (failed, net)).
induction H_st using refl_trans_1n_trace_n1_ind.
- subst.
intros.
simpl in *.
unfold disk_correct.
simpl.
exists IOStreamWriter.empty, [], (init_handlers h).
intuition.
- concludes.
match goal with H : step_failure_disk_ops _ _ _ |- _ => invcs H end.
+ break_if.
* rewrite e in *.
intuition.
match goal with
| [G : disk_correct _ _ _, H : log_net_handlers _ _ _ _ _ = _ |- _] =>
apply (log_net_handlers_spec _ _ _ _ _ _ _ _ _ _  G H)
end.
reflexivity.
* assumption.
+ break_if.
* rewrite e in *.
match goal with
| [G : disk_correct _ _ _, H : log_input_handlers _ _ _ _ = _ |- _] =>
apply (log_input_handlers_spec  _ _ _ _ _ _ _ _ _ G H)
end.
reflexivity.
* assumption.
+ assumption.
+ assumption.
+ assumption.
+ break_if.
* repeat find_rewrite.
find_apply_lem_hyp disk_correct_reboot;
assumption.
* assumption.
Qed.

Lemma reboot_invariant : forall net failed tr,
@step_failure_disk_ops_star _ _ log_failure_params step_failure_disk_ops_init (failed, net) tr ->
forall h d dsk, do_reboot h (disk_to_channel (nwdoDisk net h)) = (d, dsk) ->
log_data d = reboot (log_data (nwdoState net h)).