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

parent a9173997
 ... @@ -229,30 +229,23 @@ Ltac setoid_subst := ... @@ -229,30 +229,23 @@ Ltac setoid_subst := | H : @equiv ?A ?e _ ?x |- _ => symmetry in H; setoid_subst_aux (@equiv A e) x | H : @equiv ?A ?e _ ?x |- _ => symmetry in H; setoid_subst_aux (@equiv A e) x end. end. (** f_equiv solves goals of the form "f _ = f _", for any relation and any (** f_equiv works on goals of the form "f _ = f _", for any relation and any number of arguments, by looking for appropriate "Proper" instances. number of arguments. It looks for an appropriate "Proper" instance, and If it cannot solve an equality, it will leave that to the user. *) applies it. *) Ltac f_equiv := Ltac f_equiv := (* Deal with "pointwise_relation" *) match goal with repeat lazymatch goal with | _ => reflexivity | |- 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] (* We support matches on both sides, *if* they concern the same (* We support matches on both sides, *if* they concern the same variable. variable. TODO: We should support different variables, provided that we can TODO: We should support different variables, provided that we can derive contradictions for the off-diagonal cases. *) derive contradictions for the off-diagonal cases. *) | |- ?R (match ?x with _ => _ end) (match ?x with _ => _ end) => | |- ?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 *) (* First assume that the arguments need the same relation as the result *) | |- ?R (?f ?x) (?f _) => | |- ?R (?f ?x) (?f _) => apply (_ : Proper (R ==> R) f); f_equiv apply (_ : Proper (R ==> R) f) | |- ?R (?f ?x ?y) (?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 (* Next, try to infer the relation. Unfortunately, there is an instance of Proper for (eq ==> _), which will always be matched. *) of Proper for (eq ==> _), which will always be matched. *) (* TODO: Can we exclude that instance? *) (* TODO: Can we exclude that instance? *) ... @@ -260,15 +253,28 @@ Ltac f_equiv := ... @@ -260,15 +253,28 @@ Ltac f_equiv := query for "pointwise_relation"'s. But that leads to a combinatorial query for "pointwise_relation"'s. But that leads to a combinatorial explosion about which arguments are and which are not the same. *) explosion about which arguments are and which are not the same. *) | |- ?R (?f ?x) (?f _) => | |- ?R (?f ?x) (?f _) => apply (_ : Proper (_ ==> R) f); f_equiv apply (_ : Proper (_ ==> R) f) | |- ?R (?f ?x ?y) (?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, (* In case the function symbol differs, but the arguments are the same, maybe we have a pointwise_relation in our context. *) maybe we have a pointwise_relation in our context. *) | H : pointwise_relation _ ?R ?f ?g |- ?R (?f ?x) (?g ?x) => | H : pointwise_relation _ ?R ?f ?g |- ?R (?f ?x) (?g ?x) => apply H; f_equiv apply H end. 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 (** solve_proper solves goals of the form "Proper (R1 ==> R2)", for any number of relations. All the actual work is done by f_equiv; number of relations. All the actual work is done by f_equiv; solve_proper just introduces the assumptions and unfolds the first solve_proper just introduces the assumptions and unfolds the first ... @@ -291,7 +297,7 @@ Ltac solve_proper := ... @@ -291,7 +297,7 @@ Ltac solve_proper := | |- ?R (?f _ _) (?f _ _) => unfold f | |- ?R (?f _ _) (?f _ _) => unfold f | |- ?R (?f _) (?f _) => unfold f | |- ?R (?f _) (?f _) => unfold f end; end; solve [ f_equiv ]. solve [ auto_proper ]. (** The tactic [intros_revert tac] introduces all foralls/arrows, performs tac, (** The tactic [intros_revert tac] introduces all foralls/arrows, performs tac, and then reverts them. *) and then reverts them. *) ... ...
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