Section LeaderCompleteness.
Context {orig_base_params : BaseParams}.
Context {one_node_params : OneNodeParams orig_base_params}.
Context {raft_params : RaftParams orig_base_params}.
Context {rri : raft_refinement_interface}.
Context {pwti : prefix_within_term_interface}.
Context {lltsi : leaderLogs_term_sanity_interface}.
Context {llpi : leaderLogs_preserved_interface}.
Context {eewci : every_entry_was_created_interface}.
Context {llvwli : leaderLogs_votesWithLog_interface}.
Context {aevwli : allEntries_votesWithLog_interface}.
Context {vwlsi : votesWithLog_sorted_interface}.
Context {taifoi : terms_and_indices_from_one_interface}.
Context {lllmi : leaderLogs_entries_match_interface}.
Fixpoint contradicting_leader_logs_on_leader l t e :=
match l with
| (t', log') :: l' =>
if (sumbool_and _ _ _ _
(lt_dec t t')
(sumbool_not _ _
(in_dec entry_eq_dec e log'))) then
(t', log') :: contradicting_leader_logs_on_leader l' t e
else
contradicting_leader_logs_on_leader l' t e
| [] => []
end.
Fixpoint contradicting_leader_logs net nodes t e : list (term * name * list entry) :=
match nodes with
| h :: nodes' => (map (fun l => (fst l, h, snd l))
(contradicting_leader_logs_on_leader (leaderLogs (fst (nwState net h))) t e))
++ contradicting_leader_logs net nodes' t e
| [] => []
end.
Definition minimal_contradicting_leader_log net t e :=
argmin (fun l => fst (fst l)) (contradicting_leader_logs net nodes t e).
Proof using.
induction l; intros; simpl in *; intuition; subst;
repeat break_match; subst; simpl in *; intuition eauto;
congruence.
Qed.
Proof using.
intros.
induction nodes; simpl in *; intuition; subst;
find_apply_lem_hyp app_eq_nil; intuition;
find_apply_lem_hyp map_eq_nil; auto.
Qed.
Proof using.
intros.
find_apply_lem_hyp argmin_None.
eapply contradicting_leader_logs_on_leader_empty; eauto.
eapply contradicting_leader_logs_empty; eauto.
apply all_fin_all.
Qed.
Proof using.
intros; induction l; simpl in *; intuition;
repeat break_match; subst; simpl in *; intuition;
find_inversion; intuition.
Qed.
Proof using.
induction nodes; intros; simpl in *; intuition.
do_in_app. intuition.
do_in_map. find_inversion. rewrite <- surjective_pairing. auto.
Qed.
Proof using.
induction ll; intros; simpl in *; intuition.
repeat break_match; simpl in *; intuition eauto.
Qed.
Proof using.
induction ll; intros; simpl in *; intuition.
repeat break_match; simpl in *; intuition eauto.
find_inversion. auto.
Qed.
Proof using.
induction ll; intros; simpl in *; intuition.
repeat break_match; simpl in *; intuition; repeat find_inversion; eauto.
Qed.
Proof using.
induction ll; intros; simpl in *; intuition;
repeat break_match; repeat find_inversion; simpl in *; intuition.
Qed.
Proof using.
induction nodes; intros; simpl in *; intuition.
apply in_or_app.
subst. left. apply in_map_iff. eexists. intuition eauto. simpl. auto.
Qed.
Proof using.
unfold minimal_contradicting_leader_log.
intros.
find_apply_lem_hyp argmin_elim. intuition.
- eauto using in_contradicting_leader_logs_on_leader_term_lt,
in_contradicting_leader_logs.
- eauto using in_contradicting_leader_logs,
in_contradicting_leader_logs_on_leader_in_leaderLog.
- eauto using in_contradicting_leader_logs,
in_contradicting_leader_logs_on_leader_not_in_log.
- destruct (le_lt_dec t'' t); auto.
destruct (le_lt_dec t' t''); auto.
destruct (in_dec entry_eq_dec e l'); auto.
find_eapply_lem_hyp contradicting_leader_logs_on_leader_complete; eauto.
find_eapply_lem_hyp contradicting_leader_logs_complete; [|solve [apply all_fin_all]].
find_apply_hyp_hyp. simpl in *. lia.
Qed.
Proof using.
destruct l; simpl; eauto.
Qed.
Proof using.
destruct l; simpl; eauto.
Qed.
Proof using taifoi vwlsi aevwli llvwli eewci llpi lltsi pwti.
unfold leader_completeness_directly_committed in *.
intros.
unfold directly_committed in *.
destruct (minimal_contradicting_leader_log net (eTerm e) e) eqn:?;
eauto using minimal_contradicting_leader_log_None.
repeat destruct p.
find_apply_lem_hyp minimal_contradicting_leader_log_elim.
match goal with
| [ H : exists _, _ |- _ ] => destruct H as [quorum]
end.
intuition.
destruct (le_lt_dec n t).
- exfalso.
assert (forall e', In e' l -> (eTerm e' < eTerm e) \/ (eTerm e' = eTerm e /\ eIndex e' < eIndex e)).
{
intros.
destruct (lt_eq_lt_dec (eTerm e') (eTerm e)).
- intuition. destruct (le_lt_dec (eIndex e) (eIndex e')); auto.
assert (exists x, In x quorum).
{
destruct quorum.
- simpl in *. lia.
- simpl. eauto.
}
break_exists.
assert (prefix_within_term (map snd (allEntries (fst (nwState net x)))) l) by (eapply allEntries_leaderLogs_prefix_within_term_invariant; eauto).
unfold prefix_within_term in *.
exfalso.
find_false.
match goal with
| [ H : _ |- _ ] => eapply H; try eassumption; auto;
[apply in_map_iff; eexists; split; [|eauto]; auto]
end.
- assert (leaderLogs_term_sanity net) by eauto using leaderLogs_term_sanity_invariant.
unfold leaderLogs_term_sanity in *.
assert (eTerm e' < n) by eauto.
assert (every_entry_was_created net) by eauto using every_entry_was_created_invariant.
unfold every_entry_was_created in *.
find_insterU. find_insterU. find_insterU. find_insterU.
conclude_using eauto.
conclude_using eauto.
unfold term_was_created in *.
break_exists.
find_copy_apply_hyp_hyp. repeat break_or_hyp; try lia.
assert (leaderLogs_preserved net) by eauto using leaderLogs_preserved_invariant.
unfold leaderLogs_preserved in *.
exfalso. eauto.
}
assert (leaderLogs_votesWithLog net) by eauto using leaderLogs_votesWithLog_invariant.
unfold leaderLogs_votesWithLog in *.
find_apply_hyp_hyp.
match goal with
| [ H : exists _, _ |- _ ] => destruct H as [quorum']
end.
break_and.
assert (NoDup nodes) by eauto using all_fin_NoDup.
match goal with
| H : NoDup nodes, _ : NoDup ?l1, _ : NoDup ?l2 |- _ =>
eapply pigeon with (l := nodes) (sub1 := l1) (sub2 := l2) in H
end; eauto using all_fin_all, name_eq_dec, div2_correct.
match goal with
| [ H : exists _, _ |- _ ] => destruct H as [a]
end.
break_and.
find_apply_hyp_hyp.
find_apply_hyp_hyp.
break_exists. break_and.
assert (In e x).
{
assert (allEntries_votesWithLog net) by eauto using allEntries_votesWithLog_invariant.
unfold allEntries_votesWithLog in *.
eapply_prop_hyp In In; eauto.
break_or_hyp; auto.
break_exists. break_and.
match goal with
| [ H : context [ In _ _ -> _ \/ _ ],
H' : In _ _ |- _ ] =>
eapply H in H'
end.
repeat (try break_or_hyp; break_and); try lia.
congruence.
}
assert (sorted x) by (eapply votesWithLog_sorted_invariant; eauto).
assert (maxTerm x >= eTerm e) by eauto using maxTerm_is_max.
assert (maxIndex x >= eIndex e) by eauto using maxIndex_is_max.
assert (exists e', In e' l /\
eTerm e' = maxTerm l /\
eIndex e' = maxIndex l).
{
assert (eTerm e >= 1 /\ eIndex e >= 1) by
match goal with
| [ H : In _ (votesWithLog _) |- _ ] =>
solve [eapply terms_and_indices_from_one_invariant in H; eauto]
end.
destruct l.
- simpl in *.
unfold moreUpToDate in *. do_bool.
repeat (intuition; do_bool); try lia.
- simpl in *. eauto.
}
match goal with
| [ H : exists _, _ |- _ ] => destruct H as [e']
end.
break_and.
find_apply_hyp_hyp.
unfold moreUpToDate in *.
do_bool; repeat (try break_or_hyp; break_and; do_bool); lia.
- match goal with
| [ H : context [In], H' : context [In] |- _ ] => apply H in H'; intuition; lia
end.
Qed.

Theorem leader_completeness_committed_invariant :
forall net,
refined_raft_intermediate_reachable net ->
leader_completeness_committed net.