Commit 2ee38008 authored by Robbert Krebbers's avatar Robbert Krebbers

Merge branch 'master' of gitlab.mpi-sws.org:FP/iris-coq

Conflicts:
	prelude/tactics.v
parents df7f6381 77a15fea
Pipeline #160 passed with stage
......@@ -40,8 +40,6 @@ Tactic Notation "cofe_subst" :=
| H:@dist ?A ?d ?n _ ?x |- _ => symmetry in H;setoid_subst_aux (@dist A d n) x
end.
Tactic Notation "solve_ne" := intros; solve_proper.
Record chain (A : Type) `{Dist A} := {
chain_car :> nat A;
chain_cauchy n i : n < i chain_car i {n} chain_car (S n)
......
......@@ -77,7 +77,7 @@ Proof. by intros ??? ?? [??]; split; apply up_preserving. Qed.
Global Instance up_set_preserving : Proper (() ==> flip () ==> ()) up_set.
Proof.
intros S1 S2 HS T1 T2 HT. rewrite /up_set.
f_equiv; last done. move =>s1 s2 Hs. simpl in HT. by apply up_preserving.
f_equiv. move =>s1 s2 Hs. simpl in HT. by apply up_preserving.
Qed.
Global Instance up_set_proper : Proper (() ==> () ==> ()) up_set.
Proof. by intros S1 S2 [??] T1 T2 [??]; split; apply up_set_preserving. Qed.
......
......@@ -648,7 +648,7 @@ Proof. intros; apply (anti_symm _); auto using const_intro. Qed.
Lemma equiv_eq {A : cofeT} P (a b : A) : a b P (a b).
Proof. intros ->; apply eq_refl. Qed.
Lemma eq_sym {A : cofeT} (a b : A) : (a b) (b a).
Proof. apply (eq_rewrite a b (λ b, b a)%I); auto using eq_refl. solve_ne. Qed.
Proof. apply (eq_rewrite a b (λ b, b a)%I); auto using eq_refl. solve_proper. Qed.
(* BI connectives *)
Lemma sep_mono P P' Q Q' : P Q P' Q' (P P') (Q Q').
......
......@@ -52,19 +52,17 @@ Definition recv (l : loc) (R : iProp) : iProp :=
saved_prop_own i Q (Q - R))%I.
(** Setoids *)
(* These lemmas really ought to be doable by just calling a tactic.
It is just application of already registered congruence lemmas. *)
Global Instance waiting_ne n : Proper (dist n ==> (=) ==> dist n) waiting.
Proof. intros P P' HP I ? <-. rewrite /waiting. by setoid_rewrite HP. Qed.
Proof. solve_proper. Qed.
Global Instance barrier_inv_ne n l :
Proper (dist n ==> pointwise_relation _ (dist n)) (barrier_inv l).
Proof. intros P P' HP [[]]; rewrite /barrier_inv //=. by setoid_rewrite HP. Qed.
Proper (dist n ==> eq ==> dist n) (barrier_inv l).
Proof. solve_proper. Qed.
Global Instance barrier_ctx_ne n γ l : Proper (dist n ==> dist n) (barrier_ctx γ l).
Proof. intros P P' HP. rewrite /barrier_ctx. by setoid_rewrite HP. Qed.
Proof. solve_proper. Qed.
Global Instance send_ne n l : Proper (dist n ==> dist n) (send l).
Proof. intros P P' HP. rewrite /send. by setoid_rewrite HP. Qed.
Proof. solve_proper. Qed.
Global Instance recv_ne n l : Proper (dist n ==> dist n) (recv l).
Proof. intros R R' HR. rewrite /recv. by setoid_rewrite HR. Qed.
Proof. solve_proper. Qed.
(** Helper lemmas *)
Lemma waiting_split i i1 i2 Q R1 R2 P I :
......
......@@ -228,6 +228,73 @@ Ltac setoid_subst :=
| H : @equiv ?A ?e _ ?x |- _ => symmetry in H; setoid_subst_aux (@equiv A e) x
end.
(** f_equiv solves goals of the form "f _ = f _", for any relation and any
number of arguments, by looking for appropriate "Proper" instances.
If it cannot solve an equality, it will leave that to the user. *)
Ltac f_equiv :=
(* Deal with "pointwise_relation" *)
try lazymatch goal with
| |- pointwise_relation _ _ _ _ => intros ?
end;
(* repeatedly apply congruence lemmas and use the equalities in the hypotheses. *)
first [ reflexivity | assumption | symmetry; assumption |
match goal with
(* We support matches on both sides, *if* they concern the same
or provably equal variables.
TODO: We should support different variables, provided that we can
derive contradictions for the off-diagonal cases. *)
| |- ?R (match ?x with _ => _ end) (match ?x with _ => _ end) =>
destruct x; f_equiv
| |- ?R (match ?x with _ => _ end) (match ?y with _ => _ end) =>
subst y; f_equiv
(* First assume that the arguments need the same relation as the result *)
| |- ?R (?f ?x) (?f _) =>
let H := fresh "Proper" in
assert (Proper (R ==> R) f) as H by (eapply _);
apply H; clear H; f_equiv
| |- ?R (?f ?x ?y) (?f _ _) =>
let H := fresh "Proper" in
assert (Proper (R ==> R ==> R) f) as H by (eapply _);
apply H; clear H; f_equiv
(* Next, try to infer the relation *)
(* TODO: If some of the arguments are the same, we could also
query for "pointwise_relation"'s. But that leads to a combinatorial
explosion about which arguments are and which are not the same. *)
| |- ?R (?f ?x) (?f _) =>
let R1 := fresh "R" in let H := fresh "Proper" in
let T := type of x in evar (R1: relation T);
assert (Proper (R1 ==> R) f) as H by (subst R1; eapply _);
subst R1; apply H; clear H; f_equiv
| |- ?R (?f ?x ?y) (?f _ _) =>
let R1 := fresh "R" in let R2 := fresh "R" in
let H := fresh "Proper" in
let T1 := type of x in evar (R1: relation T1);
let T2 := type of y in evar (R2: relation T2);
assert (Proper (R1 ==> R2 ==> R) f) as H by (subst R1 R2; eapply _);
subst R1 R2; apply H; clear H; f_equiv
end | idtac (* Let the user solve this goal *)
].
(** solve_proper solves goals of the form "Proper (R1 ==> R2)", for any
number of relations. All the actual work is done by f_equiv;
solve_proper just introduces the assumptions and unfolds the first
head symbol. *)
Ltac solve_proper :=
(* Introduce everything *)
intros;
repeat lazymatch goal with
| |- Proper _ _ => intros ???
| |- (_ ==> _)%signature _ _ => intros ???
end;
(* Unfold the head symbol, which is the one we are proving a new property about *)
lazymatch goal with
| |- ?R (?f _ _ _ _) (?f _ _ _ _) => unfold f
| |- ?R (?f _ _ _) (?f _ _ _) => unfold f
| |- ?R (?f _ _) (?f _ _) => unfold f
| |- ?R (?f _) (?f _) => unfold f
end;
solve [ f_equiv ].
(** The tactic [intros_revert tac] introduces all foralls/arrows, performs tac,
and then reverts them. *)
Ltac intros_revert tac :=
......
......@@ -43,6 +43,6 @@ Section saved_prop.
rewrite agree_equivI later_equivI /=; apply later_mono.
rewrite -{2}(iProp_fold_unfold P) -{2}(iProp_fold_unfold Q).
apply (eq_rewrite (iProp_unfold P) (iProp_unfold Q) (λ Q' : iPreProp Λ _,
iProp_fold (iProp_unfold P) iProp_fold Q')%I); solve_ne || auto with I.
iProp_fold (iProp_unfold P) iProp_fold Q')%I); solve_proper || auto with I.
Qed.
End saved_prop.
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