### make f_equiv behaior more like the original f_equiv: It applies a *single* Proper

parent e38e903b
 ... ... @@ -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. move =>s1 s2 Hs. simpl in HT. by apply up_preserving. f_equiv; last done. 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. ... ...
 ... ... @@ -229,30 +229,23 @@ 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. *) (** f_equiv works on goals of the form "f _ = f _", for any relation and any number of arguments. It looks for an appropriate "Proper" instance, and applies it. *) Ltac f_equiv := (* Deal with "pointwise_relation" *) repeat lazymatch goal with | |- pointwise_relation _ _ _ _ => intros ? end; (* Normalize away equalities. *) simplify_eq; (* repeatedly apply congruence lemmas and use the equalities in the hypotheses. *) try match goal with | _ => first [ reflexivity | assumption | symmetry; assumption] match goal with | _ => reflexivity (* We support matches on both sides, *if* they concern the same variable. 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 destruct x (* First assume that the arguments need the same relation as the result *) | |- ?R (?f ?x) (?f _) => apply (_ : Proper (R ==> R) f); f_equiv apply (_ : Proper (R ==> R) f) | |- ?R (?f ?x ?y) (?f _ _) => apply (_ : Proper (R ==> R ==> R) f); f_equiv apply (_ : Proper (R ==> R ==> R) f) (* 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? *) ... ... @@ -260,15 +253,28 @@ Ltac f_equiv := 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 _) => apply (_ : Proper (_ ==> R) f); f_equiv apply (_ : Proper (_ ==> R) f) | |- ?R (?f ?x ?y) (?f _ _) => apply (_ : Proper (_ ==> _ ==> R) f); f_equiv apply (_ : Proper (_ ==> _ ==> R) f) (* 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 apply H end. (** auto_proper solves goals of the form "f _ = f _", for any relation and any number of arguments, by repeatedly apply f_equiv and handling trivial cases. If it cannot solve an equality, it will leave that to the user. *) Ltac auto_proper := (* Deal with "pointwise_relation" *) repeat lazymatch goal with | |- pointwise_relation _ _ _ _ => intros ? end; (* Normalize away equalities. *) simplify_eq; (* repeatedly apply congruence lemmas and use the equalities in the hypotheses. *) try (f_equiv; assumption || (symmetry; assumption) || auto_proper). (** 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 ... ... @@ -291,7 +297,7 @@ Ltac solve_proper := | |- ?R (?f _ _) (?f _ _) => unfold f | |- ?R (?f _) (?f _) => unfold f end; solve [ f_equiv ]. solve [ auto_proper ]. (** The tactic [intros_revert tac] introduces all foralls/arrows, performs tac, and then reverts them. *) ... ...
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