Section RaftMsgRefinement.
Context {orig_base_params : BaseParams}.
Context {one_node_params : OneNodeParams orig_base_params}.
Context {raft_params : RaftParams orig_base_params}.
Proof using.
intros.
unfold handleMessage, update_elections_data_net in *.
break_match; repeat break_let; repeat find_inversion;
[eapply_prop msg_refined_raft_net_invariant_request_vote|
eapply_prop msg_refined_raft_net_invariant_request_vote_reply|
eapply_prop msg_refined_raft_net_invariant_append_entries|
eapply_prop msg_refined_raft_net_invariant_append_entries_reply]; eauto;
unfold send_packets in *; simpl in *; intros; subst; auto; find_apply_hyp_hyp; intuition.
Qed.
Proof using.
intros.
unfold handleInput, update_elections_data_input in *.
break_match; repeat break_let; repeat find_inversion;
[eapply_prop msg_refined_raft_net_invariant_timeout|
eapply_prop msg_refined_raft_net_invariant_client_request]; eauto; subst; auto.
Qed.
Proof using.
intros.
induction H10.
- intuition.
-  match goal with [H : step_failure _ _ _ |- _ ] => invcs H end.
+ unfold mgv_refined_net_handlers in *. simpl in *.
unfold refined_net_handlers in *. simpl in *.
unfold RaftNetHandler in *.
repeat break_let.
repeat find_inversion.
remember (update_elections_data_net (pDst p) (pSrc p) (snd (pBody p))
(nwState net (pDst p))) as post_ghost_state.
assert
(msg_refined_raft_intermediate_reachable
{|
nwPackets := (xs ++ ys) ++ send_packets (pDst p)
(@add_ghost_msg _ _ ghost_log_params (pDst p)
(post_ghost_state, r0) l4);
nwState := update name_eq_dec (nwState net) (pDst p)
(post_ghost_state, r0) |})
by (subst; eapply MRRIR_handleMessage; eauto; in_crush).
assert
(msg_refined_raft_intermediate_reachable
{|
nwPackets := (xs ++ ys) ++
send_packets (pDst p)
(@add_ghost_msg _ _ ghost_log_params (pDst p)
(post_ghost_state, r0) l4)
++
send_packets (pDst p)
(@add_ghost_msg _ _ ghost_log_params (pDst p)
(post_ghost_state, r1) l5);
nwState := update name_eq_dec (nwState net) (pDst p)
(post_ghost_state, r1) |}) by
(eapply MRRIR_doLeader; eauto;
try solve [in_crush];
simpl in *; intros; repeat break_if; try congruence; auto).
subst.
eapply_prop msg_refined_raft_net_invariant_do_generic_server. eauto.
eapply_prop msg_refined_raft_net_invariant_do_leader. eauto.
eapply msg_refined_raft_invariant_handle_message with (P := P); eauto using in_app_or.
auto.
simpl. break_if; intuition eauto.
eauto.
simpl. eapply in_app_or.
simpl.
{ clear H11.
match goal with
| H : msg_refined_raft_intermediate_reachable ?net |-
msg_refined_raft_intermediate_reachable ?net' =>
assert (net = net')
end.
simpl.
f_equal; auto.
- repeat rewrite app_ass. auto.
- apply functional_extensionality.
intros. repeat break_if; simpl; auto.
- repeat find_rewrite; auto.
}
simpl in *. break_if; eauto; congruence.
simpl in *.
intros. repeat break_if; auto.
intros. simpl in *.
in_crush.
unfold add_ghost_msg in *. do_in_map.
subst. do_in_app. intuition; try do_in_app; intuition.
* left. apply in_app_iff. left. apply in_app_iff. right.
simpl in *.
rewrite map_map.
apply in_map_iff.
eexists; intuition; eauto.
simpl in *. f_equal. f_equal.
unfold write_ghost_log. simpl.
find_apply_lem_hyp doGenericServer_log.
find_apply_lem_hyp doLeader_log.
repeat find_rewrite. auto.
* left. apply in_app_iff. right.
simpl in *.
rewrite map_map.
apply in_map_iff.
eexists; intuition; eauto.
simpl in *. f_equal. f_equal.
unfold write_ghost_log. simpl.
find_apply_lem_hyp doGenericServer_log.
find_apply_lem_hyp doLeader_log.
repeat find_rewrite. auto.
* right.
simpl in *.
rewrite map_map.
apply in_map_iff.
eexists; intuition; eauto.
+ unfold mgv_refined_input_handlers in *. simpl in *.
unfold refined_input_handlers in *. simpl in *.
unfold RaftInputHandler in *.
repeat break_let.
repeat find_inversion.
remember (update_elections_data_input h inp
(nwState net h))
as post_ghost_state.
assert
(msg_refined_raft_intermediate_reachable
{|
nwPackets := (nwPackets net) ++ send_packets h
(@add_ghost_msg _ _ ghost_log_params h
(post_ghost_state, r0) l4);
nwState := update name_eq_dec (nwState net) h
(post_ghost_state, r0) |})
by (subst; eapply MRRIR_handleInput; eauto; in_crush).
assert
(msg_refined_raft_intermediate_reachable
{|
nwPackets := (nwPackets net) ++
send_packets h
(@add_ghost_msg _ _ ghost_log_params h
(post_ghost_state, r0) l4)
++
send_packets h
(@add_ghost_msg _ _ ghost_log_params h
(post_ghost_state, r1) l6);
nwState := update name_eq_dec (nwState net) h
(post_ghost_state, r1) |}) by
(eapply MRRIR_doLeader; eauto;
try solve [in_crush];
simpl in *; intros; repeat break_if; try congruence; auto).
subst.
eapply_prop msg_refined_raft_net_invariant_do_generic_server. eauto.
eapply_prop msg_refined_raft_net_invariant_do_leader. eauto.
eapply msg_refined_raft_invariant_handle_input with (P := P); eauto using in_app_or.
auto.
simpl. break_if; intuition eauto.
eauto.
simpl. eapply in_app_or.
simpl.
{ clear H11.
match goal with
| H : msg_refined_raft_intermediate_reachable ?net |-
msg_refined_raft_intermediate_reachable ?net' =>
assert (net = net')
end.
simpl.
f_equal; auto.
- repeat rewrite app_ass. auto.
- apply functional_extensionality.
intros. repeat break_if; simpl; auto.
- repeat find_rewrite; auto.
}
simpl in *. break_if; eauto; congruence.
simpl in *.
intros. repeat break_if; auto.
intros. simpl in *.
in_crush.
unfold add_ghost_msg in *. do_in_map.
subst. do_in_app. intuition; try do_in_app; intuition.
* left. apply in_app_iff. left. apply in_app_iff. right.
simpl in *.
rewrite map_map.
apply in_map_iff.
eexists; intuition; eauto.
simpl in *. f_equal. f_equal.
unfold write_ghost_log. simpl.
find_apply_lem_hyp doGenericServer_log.
find_apply_lem_hyp doLeader_log.
repeat find_rewrite. auto.
* left. apply in_app_iff. right.
simpl in *.
rewrite map_map.
apply in_map_iff.
eexists; intuition; eauto.
simpl in *. f_equal. f_equal.
unfold write_ghost_log. simpl.
find_apply_lem_hyp doGenericServer_log.
find_apply_lem_hyp doLeader_log.
repeat find_rewrite. auto.
* right.
simpl in *.
rewrite map_map.
apply in_map_iff.
eexists; intuition; eauto.
+ match goal with
| [ H : nwPackets ?net = _ |- _ {| nwPackets := ?ps ; nwState := ?st |} ] =>
assert (forall p, In p (nwPackets {| nwPackets := ps ; nwState := st |}) ->
In p (nwPackets net)) by (intros; simpl in *; find_rewrite; in_crush)
end.
eapply_prop msg_refined_raft_net_invariant_state_same_packet_subset; [|eauto|idtac|];
eauto.
+ match goal with
| [ H : nwPackets ?net = _ |- _ {| nwPackets := ?ps ; nwState := ?st |} ] =>
assert (forall p, In p (nwPackets {| nwPackets := ps ; nwState := st |}) ->
In p (nwPackets net)) by (intros; simpl in *; find_rewrite; in_crush)
end.
eapply_prop msg_refined_raft_net_invariant_state_same_packet_subset; [|eauto|idtac|];
eauto.
+ auto.
+ eapply_prop msg_refined_raft_net_invariant_reboot; eauto;
intros; simpl in *; repeat break_if; intuition; subst; intuition eauto.
destruct (nwState net h); auto.
- eapply msg_refined_raft_invariant_handle_input; eauto.
- eapply msg_refined_raft_invariant_handle_message; eauto.
- eapply_prop msg_refined_raft_net_invariant_do_leader; eauto.
- eapply_prop msg_refined_raft_net_invariant_do_generic_server; eauto.
Qed.
Proof using.
intros.
unfold handleMessage, update_elections_data_net in *.
break_match; repeat break_let; repeat find_inversion;
[eapply_prop msg_refined_raft_net_invariant_request_vote'|
eapply_prop msg_refined_raft_net_invariant_request_vote_reply'|
eapply_prop msg_refined_raft_net_invariant_append_entries'|
eapply_prop msg_refined_raft_net_invariant_append_entries_reply']; eauto;
unfold send_packets in *; simpl in *; intros; subst; auto; find_apply_hyp_hyp; intuition.
Qed.
Proof using.
intros.
unfold handleInput, update_elections_data_input in *.
break_match; repeat break_let; repeat find_inversion;
[eapply_prop msg_refined_raft_net_invariant_timeout'|
eapply_prop msg_refined_raft_net_invariant_client_request']; eauto; subst; auto.
Qed.
Proof using.
intros.
induction H10.
- intuition.
-  match goal with [H : step_failure _ _ _ |- _ ] => invcs H end.
+ match goal with
| [ H : msg_refined_raft_intermediate_reachable _ |- _ ?x ] =>
assert (msg_refined_raft_intermediate_reachable x) as Hpost
by (eapply MRRIR_step_failure; eauto; eapply StepFailure_deliver; eauto)
end.
unfold mgv_refined_net_handlers in *. simpl in *.
unfold refined_net_handlers in *. simpl in *.
unfold RaftNetHandler, update_elections_data_net in *.
repeat break_let.
repeat find_inversion.
match goal with
| [ H : msg_refined_raft_intermediate_reachable ?net, H' : context [net]  |- _ ] =>
match type of H' with
| msg_refined_raft_intermediate_reachable _ => move H after H'
end
end.
remember (update_elections_data_net (pDst p) (pSrc p) (snd (pBody p))
(nwState net (pDst p))) as post_ghost_state.
assert
(msg_refined_raft_intermediate_reachable
{|
nwPackets := (xs ++ ys) ++ send_packets (pDst p)
(@add_ghost_msg _ _ ghost_log_params (pDst p)
(post_ghost_state, r0) l4);
nwState := update name_eq_dec (nwState net) (pDst p)
(post_ghost_state, r0) |}) as Hr0
by (subst; eapply MRRIR_handleMessage; eauto; in_crush).
assert
(msg_refined_raft_intermediate_reachable
{|
nwPackets := (xs ++ ys) ++
send_packets (pDst p)
(@add_ghost_msg _ _ ghost_log_params (pDst p)
(post_ghost_state, r0) l4)
++
send_packets (pDst p)
(@add_ghost_msg _ _ ghost_log_params (pDst p)
(post_ghost_state, r1) l5);
nwState := update name_eq_dec (nwState net) (pDst p)
(post_ghost_state, r1) |}) as Hr1 by
(eapply MRRIR_doLeader; eauto;
try solve [in_crush];
simpl in *; intros; repeat break_if; try congruence; auto).
subst.
eapply_prop msg_refined_raft_net_invariant_do_generic_server'. eauto.
eapply_prop msg_refined_raft_net_invariant_do_leader'. eauto.
eapply msg_refined_raft_invariant_handle_message' with (P := P); auto.
eauto. eauto.   auto. eauto.  eauto. eauto using in_app_or. auto.
exact Hr1.
simpl. break_if; intuition eauto.
simpl. intros. break_if; intuition eauto.
simpl. in_crush. auto. auto.
simpl. break_if; eauto; congruence.
simpl. intros.
break_if; subst;
repeat rewrite update_same by auto;
repeat rewrite update_neq by auto; auto.
simpl. in_crush.
(* here *)
unfold add_ghost_msg in *. do_in_map.
subst. do_in_app. intuition; try do_in_app; intuition.
* left. apply in_app_iff. right. apply in_app_iff. left.
simpl in *.
rewrite map_map.
apply in_map_iff.
eexists; intuition; eauto.
simpl in *. f_equal. f_equal.
unfold write_ghost_log. simpl.
find_apply_lem_hyp doGenericServer_log.
find_apply_lem_hyp doLeader_log.
repeat find_rewrite. auto.
* left. apply in_app_iff. right.
apply in_app_iff. right.
simpl in *.
rewrite map_map.
apply in_map_iff.
eexists; intuition; eauto.
simpl in *. f_equal. f_equal.
unfold write_ghost_log. simpl.
find_apply_lem_hyp doGenericServer_log.
find_apply_lem_hyp doLeader_log.
repeat find_rewrite. auto.
* right.
simpl in *.
rewrite map_map.
apply in_map_iff.
eexists; intuition; eauto.
+ match goal with
| [ H : msg_refined_raft_intermediate_reachable _ |- _ ?x ] =>
assert (msg_refined_raft_intermediate_reachable x) as Hpost
by (eapply MRRIR_step_failure; eauto; eapply StepFailure_input; eauto)
end.
unfold mgv_refined_input_handlers in *. simpl in *.
unfold refined_input_handlers in *. simpl in *.
unfold RaftInputHandler, update_elections_data_input in *.
repeat break_let.
repeat find_inversion.
match goal with
| [ H : msg_refined_raft_intermediate_reachable ?net, H' : context [net]  |- _ ] =>
match type of H' with
| msg_refined_raft_intermediate_reachable _ => move H after H'
end
end.
remember (update_elections_data_input h inp
(nwState net h))
as post_ghost_state.
assert
(msg_refined_raft_intermediate_reachable
{|
nwPackets := (nwPackets net) ++ send_packets h
(@add_ghost_msg _ _ ghost_log_params h
(post_ghost_state, r0) l4);
nwState := update name_eq_dec (nwState net) h
(post_ghost_state, r0) |}) as Hr0
by (subst; eapply MRRIR_handleInput; eauto; in_crush).
assert
(msg_refined_raft_intermediate_reachable
{|
nwPackets := (nwPackets net) ++
send_packets h
(@add_ghost_msg _ _ ghost_log_params h
(post_ghost_state, r0) l4)
++
send_packets h
(@add_ghost_msg _ _ ghost_log_params h
(post_ghost_state, r1) l6);
nwState := update name_eq_dec (nwState net) h
(post_ghost_state, r1) |}) as Hr1 by
(eapply MRRIR_doLeader; eauto;
try solve [in_crush];
simpl in *; intros; repeat break_if; try congruence; auto).
subst.
eapply_prop msg_refined_raft_net_invariant_do_generic_server'. eauto.
eapply_prop msg_refined_raft_net_invariant_do_leader'. eauto.
eapply msg_refined_raft_invariant_handle_input' with (P := P); auto.
eauto. eauto.   auto. eauto.  eauto. eauto using in_app_or. auto.
exact Hr1.
simpl. break_if; intuition eauto.
simpl. intros. break_if; intuition eauto.
simpl. in_crush. auto. auto.
simpl. break_if; eauto; congruence.
simpl. intros.
break_if; subst;
repeat rewrite update_same by auto;
repeat rewrite update_neq by auto; auto.
simpl. in_crush.
unfold add_ghost_msg in *. do_in_map.
subst. do_in_app. intuition; try do_in_app; intuition.
* left. apply in_app_iff. right. apply in_app_iff. left.
simpl in *.
rewrite map_map.
apply in_map_iff.
eexists; intuition; eauto.
simpl in *. f_equal. f_equal.
unfold write_ghost_log. simpl.
find_apply_lem_hyp doGenericServer_log.
find_apply_lem_hyp doLeader_log.
repeat find_rewrite. auto.
* left. apply in_app_iff. right.
apply in_app_iff. right.
simpl in *.
rewrite map_map.
apply in_map_iff.
eexists; intuition; eauto.
simpl in *. f_equal. f_equal.
unfold write_ghost_log. simpl.
find_apply_lem_hyp doGenericServer_log.
find_apply_lem_hyp doLeader_log.
repeat find_rewrite. auto.
* right.
simpl in *.
rewrite map_map.
apply in_map_iff.
eexists; intuition; eauto.
+ match goal with
| [ H : nwPackets ?net = _ |- _ {| nwPackets := ?ps ; nwState := ?st |} ] =>
assert (forall p, In p (nwPackets {| nwPackets := ps ; nwState := st |}) ->
In p (nwPackets net)) by (intros; simpl in *; find_rewrite; in_crush)
end.
eapply_prop msg_refined_raft_net_invariant_state_same_packet_subset'; [|eauto|idtac|]; eauto.
+ match goal with
| [ H : nwPackets ?net = _ |- _ {| nwPackets := ?ps ; nwState := ?st |} ] =>
assert (forall p, In p (nwPackets {| nwPackets := ps ; nwState := st |}) ->
In p (nwPackets net)) by (intros; simpl in *; find_rewrite; in_crush)
end.
eapply_prop msg_refined_raft_net_invariant_state_same_packet_subset'; [|eauto|idtac|];
eauto.
+ auto.
+ eapply_prop msg_refined_raft_net_invariant_reboot'; eauto;
intros; simpl in *; repeat break_if; intuition; subst; intuition eauto.
* econstructor. eauto. eapply StepFailure_reboot; eauto.
* destruct (nwState net h); auto.
- eapply msg_refined_raft_invariant_handle_input'; eauto.
eapply MRRIR_handleInput; eauto.
- eapply msg_refined_raft_invariant_handle_message'; eauto.
eapply MRRIR_handleMessage; eauto.
- eapply_prop msg_refined_raft_net_invariant_do_leader'; eauto.
eapply MRRIR_doLeader; eauto.
- eapply_prop msg_refined_raft_net_invariant_do_generic_server'; eauto.
eapply MRRIR_doGenericServer; eauto.
Qed.
Ltac workhorse :=
try match goal with
| [ |- mkNetwork _ _ = mkNetwork _ _ ] => f_equal
end;
try match goal with
| [ |- (fun _ => _) = (fun _ => _) ] => apply functional_extensionality; intros
end;
repeat break_match;
repeat match goal with
| [ H : (_, _) = (_, _) |- _ ] => invc H
end;
repeat (simpl in *; subst);
repeat rewrite map_app;
repeat rewrite map_map.
Notation mgv_deghost := (@mgv_deghost _ _ ghost_log_params).
Proof using.
intros.
induction H.
- constructor.
- simpl in *.
pose proof (RRIR_step_failure).
specialize (H1 failed (mgv_deghost net) failed' (mgv_deghost net') out).
apply H1; auto.
apply (@mgv_ghost_simulation_1 _ _ _ ghost_log_params); auto.
- unfold mgv_deghost in *. simpl in *.
eapply RRIR_handleInput; eauto.
+ simpl in *. repeat break_match. simpl in *. eauto.
+ intros. simpl in *.
repeat break_match; subst; simpl in *;
repeat find_higher_order_rewrite; break_if; subst; simpl in *;
congruence.
+ intros. simpl in *. in_crush.
find_apply_hyp_hyp.
in_crush.
right.
unfold add_ghost_msg in *.
do_in_map. subst. simpl in *.
apply in_map_iff. eauto.
- unfold mgv_deghost in *. simpl in *.
pose proof (RRIR_handleMessage).
specialize
(H5 (@mkPacket _ raft_refined_multi_params
(pSrc p)
(pDst p)
(snd (pBody p)))).
eapply H5; eauto.
+ simpl in *. repeat break_match. simpl in *.
repeat find_rewrite. eauto.
+ simpl in *.
unfold mgv_refined_base_params, raft_refined_base_params, refined_base_params, raft_msg_refined_multi_params, raft_refined_multi_params in *.
simpl in *.
unfold mgv_refined_base_params, raft_refined_base_params, refined_base_params, raft_msg_refined_multi_params, raft_refined_multi_params in *.
simpl in *. repeat find_rewrite.
map_crush. eauto.
+ intros. repeat break_match. simpl in *.
repeat find_higher_order_rewrite.
repeat break_match; congruence.
+ in_crush.
find_apply_hyp_hyp. in_crush.
right.
unfold add_ghost_msg in *.
do_in_map. subst. simpl in *.
apply in_map_iff. eauto.
- unfold mgv_deghost in *. simpl in *.
eapply RRIR_doLeader; eauto.
+ simpl in *. repeat break_match. simpl in *. eauto.
+ simpl in *.
intros. repeat break_match; simpl in *;
repeat find_higher_order_rewrite;
repeat break_match; congruence.
+ in_crush.
find_apply_hyp_hyp. in_crush.
right.
unfold add_ghost_msg in *.
do_in_map. subst. simpl in *.
apply in_map_iff. eauto.
- unfold mgv_deghost in *. simpl in *.
eapply RRIR_doGenericServer; eauto.
+ simpl in *. repeat break_match. simpl in *. eauto.
+ simpl in *.
intros. repeat break_match; simpl in *;
repeat find_higher_order_rewrite;
repeat break_match; congruence.
+ in_crush.
find_apply_hyp_hyp. in_crush.
right.
unfold add_ghost_msg in *.
do_in_map. subst. simpl in *.
apply in_map_iff. eauto.
Qed.
Proof using.
intros.
eauto using simulation_1.
Qed.
Proof using.
intros.
prep_induction H.
induction H using refl_trans_1n_trace_n1_ind; intros; subst.
- find_inversion. auto.
- destruct x'. simpl in *.
eapply MRRIR_step_failure; [|eauto].
eauto.
Qed.
Proof using raft_params one_node_params orig_base_params.
induction l'; simpl; intros.
- exists nil. simpl in *. intuition.
- assert (exists x, In x l /\ f x = f a).
{ specialize (H (f a)). concludes.
find_apply_lem_hyp in_map_iff.
firstorder.
}
specialize (IHl' ltac:(intuition)).
repeat break_exists.
break_and.
exists (x :: x0).
simpl. intuition; congruence.
Qed.
Proof using.
intros.
unfold mgv_deghost_packet, mgv_ghost_packet.
simpl. destruct p; auto.
Qed.

Theorem simulation_2 :
forall net,
refined_raft_intermediate_reachable net ->
exists rnet,
net = mgv_deghost rnet /\
msg_refined_raft_intermediate_reachable rnet.