Commit ab9f921d authored by Ralf Jung's avatar Ralf Jung

improve f_equiv and solve_proper; use them in a few more places

parent c64b9a55
......@@ -257,22 +257,28 @@ Ltac f_equiv :=
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 *)
(* Next, try to infer the relation. Unfortunately, there is an instance
of Proper for (eq ==> _), which will always be matched. *)
(* TODO: Can we exclude that instance? *)
(* 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 R1 := fresh "R" in let H := fresh "HProp" 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 H := fresh "HProp" 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
(* In case the function symbol differs, but the arguments are the same,
maybe we have a pointwise_relation in our context. *)
| H : pointwise_relation _ ?R ?f ?g |- ?R (?f ?x) (?g ?x) =>
apply H; f_equiv
end | idtac (* Let the user solve this goal *)
].
......@@ -289,6 +295,10 @@ Ltac solve_proper :=
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
| |- ?R (?f _ _ _ _) (?f _ _ _ _) => unfold f
| |- ?R (?f _ _ _) (?f _ _ _) => unfold f
| |- ?R (?f _ _) (?f _ _) => unfold f
......@@ -296,6 +306,7 @@ Ltac solve_proper :=
end;
solve [ f_equiv ].
(** Given a tactic [tac2] generating a list of terms, [iter tac1 tac2]
runs [tac x] for each element [x] until [tac x] succeeds. If it does not
suceed for any element of the generated list, the whole tactic wil fail. *)
......
......@@ -40,7 +40,7 @@ Section auth.
Implicit Types γ : gname.
Global Instance auth_own_ne n γ : Proper (dist n ==> dist n) (auth_own γ).
Proof. by rewrite auth_own_eq /auth_own_def=> a b ->. Qed.
Proof. rewrite auth_own_eq; solve_proper. Qed.
Global Instance auth_own_proper γ : Proper (() ==> ()) (auth_own γ).
Proof. by rewrite auth_own_eq /auth_own_def=> a b ->. Qed.
Global Instance auth_own_timeless γ a : TimelessP (auth_own γ a).
......
......@@ -52,22 +52,20 @@ Section sts.
(** Setoids *)
Global Instance sts_inv_ne n γ :
Proper (pointwise_relation _ (dist n) ==> dist n) (sts_inv γ).
Proof. by intros φ1 φ2 Hφ; rewrite /sts_inv; setoid_rewrite Hφ. Qed.
Proof. solve_proper. Qed.
Global Instance sts_inv_proper γ :
Proper (pointwise_relation _ () ==> ()) (sts_inv γ).
Proof. by intros φ1 φ2 Hφ; rewrite /sts_inv; setoid_rewrite Hφ. Qed.
Proof. solve_proper. Qed.
Global Instance sts_ownS_proper γ : Proper (() ==> () ==> ()) (sts_ownS γ).
Proof.
intros S1 S2 HS T1 T2 HT. by rewrite !sts_ownS_eq /sts_ownS_def HS HT.
Qed.
Proof. rewrite sts_ownS_eq. solve_proper. Qed.
Global Instance sts_own_proper γ s : Proper (() ==> ()) (sts_own γ s).
Proof. intros T1 T2 HT. by rewrite !sts_own_eq /sts_own_def HT. Qed.
Proof. rewrite sts_own_eq. solve_proper. Qed.
Global Instance sts_ctx_ne n γ N :
Proper (pointwise_relation _ (dist n) ==> dist n) (sts_ctx γ N).
Proof. by intros φ1 φ2 Hφ; rewrite /sts_ctx Hφ. Qed.
Proof. solve_proper. Qed.
Global Instance sts_ctx_proper γ N :
Proper (pointwise_relation _ () ==> ()) (sts_ctx γ N).
Proof. by intros φ1 φ2 Hφ; rewrite /sts_ctx Hφ. Qed.
Proof. solve_proper. Qed.
(* The same rule as implication does *not* hold, as could be shown using
sts_frag_included. *)
......
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