Section AppendEntriesRequestLeaderLogs.
Context {orig_base_params : BaseParams}.
Context {one_node_params : OneNodeParams orig_base_params}.
Context {raft_params : RaftParams orig_base_params}.
Context {lhllsi : leaders_have_leaderLogs_strong_interface}.
Context {rri : raft_refinement_interface}.
Context {si : sorted_interface}.
Context {lmi : log_matching_interface}.
Context {nisi : nextIndex_safety_interface}.
Proof using si rri.
intros.
eapply lift_prop; eauto using logs_sorted_invariant.
Qed.
Proof using si rri.
intros.
find_apply_lem_hyp lift_sorted.
unfold logs_sorted, logs_sorted_host in *.
intuition.
unfold deghost in *. simpl in *. break_match; eauto.
Qed.
Proof using lmi rri.
intros.
eapply lift_prop; eauto using log_matching_invariant.
Qed.
Proof using.
unfold update_elections_data_client_request in *.
intros. repeat break_match; repeat find_inversion; auto.
Qed.
Proof using.
unfold update_elections_data_timeout.
intros.
repeat break_match; simpl in *; auto.
Qed.
Proof using.
intros.
unfold update_elections_data_appendEntries.
repeat break_match; subst; simpl in *; auto.
Qed.
Proof using.
unfold update_elections_data_requestVote.
intros.
repeat break_match; auto.
Qed.
Proof using.
unfold update_elections_data_requestVoteReply.
intros.
repeat break_match; auto.
simpl in *. intuition.
Qed.
Ltac start :=
red; unfold append_entries_leaderLogs; intros;
subst; simpl in *; find_higher_order_rewrite;
update_destruct; subst; rewrite_update; eauto; simpl in *.
Ltac prove_in :=
match goal with
| [ _ : nwPackets ?net = _,
_ : In (?p : packet) _ |- _] =>
assert (In p (nwPackets net)) by (repeat find_rewrite; do_in_app; intuition)
| [ _ : nwPackets ?net = _,
_ : pBody ?p = _ |- _] =>
assert (In p (nwPackets net)) by (repeat find_rewrite; intuition)
end.
Proof using.
red. unfold append_entries_leaderLogs. intros.
subst. simpl in *.
find_apply_hyp_hyp. intuition eauto.
- prove_in. eapply_prop_hyp In In; break_exists. intuition; eauto.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto;
rewrite update_elections_data_appendEntries_leaderLogs; eauto;
subst; auto.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto;
rewrite update_elections_data_appendEntries_leaderLogs; eauto;
subst; auto.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto;
rewrite update_elections_data_appendEntries_leaderLogs; eauto;
subst; auto.
+ eauto.
- subst. simpl in *.
unfold handleAppendEntries in *.
repeat break_match; find_inversion; congruence.
Qed.
Proof using.
red. unfold append_entries_leaderLogs. intros.
subst. simpl in *.
find_apply_hyp_hyp. intuition eauto.
- prove_in. eapply_prop_hyp In In; break_exists. intuition; eauto.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto;
subst; auto.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto;
subst; auto.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto;
subst; auto.
+ eauto.
- do_in_map. subst. simpl in *.
unfold handleAppendEntriesReply in *.
repeat break_match; find_inversion; simpl in *; intuition.
Qed.
Proof using.
red. unfold append_entries_leaderLogs. intros.
subst. simpl in *.
find_apply_hyp_hyp. intuition eauto.
- prove_in. eapply_prop_hyp In In; break_exists. intuition; eauto.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto;
rewrite update_elections_data_requestVote_leaderLogs; eauto;
subst; auto.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto;
rewrite update_elections_data_requestVote_leaderLogs; eauto;
subst; auto.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto;
rewrite update_elections_data_requestVote_leaderLogs; eauto;
subst; auto.
+ eauto.
- subst. simpl in *.
unfold handleRequestVote in *.
repeat break_match; find_inversion; congruence.
Qed.
Proof using.
red. unfold append_entries_leaderLogs. intros.
subst. simpl in *.
find_apply_hyp_hyp. intuition eauto.
- prove_in. eapply_prop_hyp In In; break_exists. intuition; eauto.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto.
subst; auto using update_elections_data_requestVoteReply_leaderLogs.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto.
subst; auto using update_elections_data_requestVoteReply_leaderLogs.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto.
subst; auto using update_elections_data_requestVoteReply_leaderLogs.
+ eauto.
Qed.
Proof using.
red. unfold append_entries_leaderLogs. intros.
subst. simpl in *.
find_apply_hyp_hyp. intuition eauto.
- eapply_prop_hyp In In; break_exists. intuition; eauto.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto.
subst. rewrite update_elections_data_client_request_leaderLogs.
eauto.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto.
subst. rewrite update_elections_data_client_request_leaderLogs.
eauto.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto.
subst. rewrite update_elections_data_client_request_leaderLogs.
eauto.
+ eauto.
- subst. simpl in *.
unfold handleClientRequest in *.
repeat break_match; find_inversion; do_in_map; simpl in *; intuition.
Qed.
Proof using.
red. unfold append_entries_leaderLogs. intros.
subst. simpl in *.
find_apply_hyp_hyp. intuition eauto.
- eapply_prop_hyp In In; break_exists. intuition; eauto.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto.
subst. rewrite update_elections_data_timeout_leaderLogs.
eauto.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto.
subst. rewrite update_elections_data_timeout_leaderLogs.
eauto.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto.
subst. rewrite update_elections_data_timeout_leaderLogs.
eauto.
+ eauto.
- subst. simpl in *.
unfold handleTimeout, tryToBecomeLeader in *.
repeat break_match; find_inversion; do_in_map; simpl in *; intuition;
subst; simpl in *; do_in_map; subst; simpl in *; congruence.
Qed.
Proof using.
red. unfold append_entries_leaderLogs. intros.
subst. simpl in *.
find_apply_hyp_hyp. intuition eauto.
- eapply_prop_hyp In In; break_exists. intuition; eauto.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto.
subst. replace gd with (fst (nwState net x)); eauto; repeat find_rewrite; reflexivity.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto.
subst. replace gd with (fst (nwState net x)); eauto; repeat find_rewrite; reflexivity.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto.
subst. replace gd with (fst (nwState net x)); eauto; repeat find_rewrite; reflexivity.
+ eauto.
- unfold doGenericServer in *;
repeat break_match; find_inversion; do_in_map; simpl in *; intuition;
subst; simpl in *; do_in_map; subst; simpl in *; congruence.
Qed.
Proof using.
intros. unfold doLeader, advanceCommitIndex in *.
break_match; try solve [find_inversion; simpl in *; intuition].
break_if; try solve [find_inversion; simpl in *; intuition].
find_inversion. simpl. do_in_map. subst.
simpl in *. find_inversion. intuition.
match goal with
| |- context [pred ?x] =>
remember (pred x) as index
end. break_match; simpl in *.
- right. left. eauto.
-  destruct index; intuition.
right. right. exists x.
match goal with
| _ : S _ = pred ?x |- context [pred ?y] =>
assert (pred x = pred y) by auto
end.
repeat find_rewrite. intuition.
Qed.
Proof using nisi rri.
intros.
eapply lift_prop; eauto using nextIndex_safety_invariant.
Qed.
Proof using nisi lmi si rri.
intros.
find_copy_apply_lem_hyp lift_log_matching.
find_copy_apply_lem_hyp lift_nextIndex_safety.
assert (pred (getNextIndex (snd (nwState net h)) h') > 0) by lia.
unfold log_matching, log_matching_hosts in *.
unfold nextIndex_safety in *.
match goal with
| H : forall _ _, type _ = _ -> _ |- _ => specialize (H h h')
end.
intuition.
match goal with
| H : forall _ _, _ <= _ <= _ -> _ |- _ =>
specialize (H h (pred (getNextIndex (snd (nwState net h)) h')))
end.
unfold raft_refined_base_params in *.
repeat find_rewrite_lem deghost_spec. intuition.
break_exists_exists. intuition.
apply findAtIndex_intro; eauto using lift_logs_sorted, sorted_uniqueIndices.
Qed.
Proof using.
induction l; intros; simpl in *; intuition.
break_if; intuition.
- f_equal. auto.
- do_bool. specialize (H a); intuition; lia.
Qed.
Proof using lmi rri.
intros.
find_apply_lem_hyp lift_log_matching.
unfold log_matching, log_matching_hosts in *. intuition.
unfold raft_refined_base_params in *.
match goal with
| H : In _ _ |- _ =>
rewrite <- deghost_spec in H
end. eauto.
Qed.
Proof using.
intros. induction l; simpl in *; auto.
Qed.
Proof using.
induction l1; intros; simpl in *; intuition.
- subst. break_if; do_bool; try lia.
eexists; repeat (simpl in *; intuition).
- specialize (H1 e); intuition. conclude H1 ltac:(apply in_app_iff; intuition).
break_if; do_bool; try lia. eexists; intuition; eauto.
simpl in *. intuition.
eapply_prop_hyp sorted sorted; eauto. break_exists; intuition.
find_rewrite. eauto.
Qed.
Proof using.
induction l1; intros; simpl in *; intuition.
subst. destruct l2; simpl in *; auto.
specialize (H2 e0); conclude_using eauto; intuition.
Qed.
Proof using.
induction l; intros; simpl in *; intuition.
break_if; simpl in *; intuition.
Qed.
Proof using.
induction l1; intros; simpl in *; intuition.
- eexists; intuition eauto using findGtIndex_Prefix.
- break_if; simpl in *; intuition.
+ eapply_prop_hyp sorted sorted; eauto.
break_exists; intuition; find_rewrite; eauto.
+ do_bool. specialize (H1 e); conclude H1 ltac:(apply in_app_iff; intuition).
lia.
Qed.
Proof using.
induction l1; intros; simpl in *.
- destruct l2; simpl in *; intuition; subst; auto.
break_if; try congruence. do_bool.
find_apply_hyp_hyp. intuition. lia.
- simpl in *. break_if; try congruence.
do_bool. find_inversion. intuition.
Qed.
Proof using nisi lmi si rri lhllsi.
red. unfold append_entries_leaderLogs. intros.
subst. simpl in *.
find_apply_hyp_hyp. intuition eauto.
- eapply_prop_hyp In In; break_exists. intuition; eauto.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto.
subst. replace gd with (fst (nwState net x)); eauto; repeat find_rewrite; reflexivity.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto.
subst. replace gd with (fst (nwState net x)); eauto; repeat find_rewrite; reflexivity.
+ repeat eexists; intuition eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto.
subst. replace gd with (fst (nwState net x)); eauto; repeat find_rewrite; reflexivity.
+ eauto.
- do_in_map. subst.
assert (sorted (log (snd (nwState net h)))) by eauto using lift_logs_sorted.
assert (forall e, In e (log (snd (nwState net h))) -> eIndex e > 0) by eauto using entries_gt_0.
simpl in *.
find_eapply_lem_hyp doLeader_spec; [|eauto|eauto]. intuition.
+ subst.
match goal with
| H : doLeader ?d ?h = _, H' : type ?d = _ |- _ =>
replace d with (snd (nwState net h)) in H by (repeat find_rewrite; reflexivity);
replace d with (snd (nwState net h)) in H' by (repeat find_rewrite; reflexivity)
end.
find_eapply_lem_hyp leaders_have_leaderLogs_strong_invariant; eauto.
exists h.
break_exists_exists. repeat find_rewrite.
eexists; intuition eauto using Prefix_refl; auto.
* simpl in *. repeat find_rewrite.
eapply sorted_findGtIndex_0; eauto.
* simpl in *. repeat find_higher_order_rewrite. rewrite_update. eauto.
+ subst. break_exists. intuition.
find_apply_lem_hyp findAtIndex_elim. intuition. subst.
match goal with
| H : doLeader ?d ?h = _, H' : type ?d = _, H'' : context [log ?d] |- _ =>
replace d with (snd (nwState net h)) in H by (repeat find_rewrite; reflexivity);
replace d with (snd (nwState net h)) in H' by (repeat find_rewrite; reflexivity);
replace d with (snd (nwState net h)) in H'' by (repeat find_rewrite; reflexivity);
replace d with (snd (nwState net h)) by (repeat find_rewrite; reflexivity)
end.
find_copy_apply_lem_hyp lift_log_matching.
unfold log_matching, log_matching_hosts in *. intuition.
match goal with
| H : forall _ _, In _ _ -> _ |- _ =>
specialize (H h x0);
conclude H ltac:(unfold deghost in *;
repeat (break_match; simpl in *);
repeat (simpl in *; find_rewrite);
auto)
end.
find_eapply_lem_hyp leaders_have_leaderLogs_strong_invariant; eauto.
exists h.
break_exists. intuition. exists x1.
repeat (find_rewrite; simpl in *).
do_in_app. intuition.
* find_copy_eapply_lem_hyp findGtIndex_app_in_1; eauto.
break_exists_exists. exists nil.
intuition; simpl in *; auto; eauto using sorted_app_in_1;
[rewrite app_nil_r; auto|].
clear H18.
find_higher_order_rewrite.
rewrite_update.
simpl in *. auto.
* { find_copy_eapply_lem_hyp findGtIndex_app_in_2; eauto.
exists x2. break_exists_exists.
intuition; simpl in *; auto; intuition eauto.
- clear H18. find_higher_order_rewrite. rewrite_update. auto.
- right. left. eexists; intuition; eauto.
match goal with
| |- Prefix_sane ?l _ _ =>
unfold Prefix_sane; destruct l; intuition
end;
try rewrite app_nil_r in *; eauto using findGtIndex_app_eq.
left. intuition. congruence.
}
+ exfalso.
break_exists. intuition.
replace d with (snd (nwState net h)) in * by (repeat find_rewrite; reflexivity).
find_eapply_lem_hyp nextIndex_sanity; eauto. break_exists. congruence.
Qed.

Lemma append_entries_leaderLogs_init :
refined_raft_net_invariant_init append_entries_leaderLogs.