### Improve solve_proper a bit.

```This is very experimental. It should now deal better with stuff like:

match x with .. end = match y with .. end

In case there is a hypothesis H : R x y, it will try to destruct it.```
parent b46746a9
Pipeline #1631 passed with stage
 ... @@ -260,12 +260,12 @@ favor the second. *) ... @@ -260,12 +260,12 @@ favor the second. *) Ltac f_equiv := Ltac f_equiv := match goal with match goal with | _ => reflexivity | _ => reflexivity (* We support matches on both sides, *if* they concern the same (* We support matches on both sides, *if* they concern the same variable, or variable. variables in some relation. *) 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) => | |- ?R (match ?x with _ => _ end) (match ?x with _ => _ end) => destruct x destruct x | H : ?R ?x ?y |- ?R2 (match ?x with _ => _ end) (match ?y with _ => _ end) => destruct H (* 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 _) => apply (_ : Proper (R ==> R) f) | |- ?R (?f ?x) (?f _) => apply (_ : Proper (R ==> R) f) (* For the case in which R is polymorphic, or an operational type class, (* For the case in which R is polymorphic, or an operational type class, ... @@ -283,14 +283,11 @@ Ltac f_equiv := ... @@ -283,14 +283,11 @@ Ltac f_equiv := (* TODO: If some of the arguments are the same, we could also (* TODO: If some of the arguments are the same, we could also 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) apply (_ : Proper (_ ==> R) f) | |- ?R (?f ?x ?y) (?f _ _) => apply (_ : Proper (_ ==> _ ==> R) f) | |- ?R (?f ?x ?y) (?f _ _) => 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 apply H end. end. (** auto_proper solves goals of the form "f _ = f _", for any relation and any (** auto_proper solves goals of the form "f _ = f _", for any relation and any ... @@ -317,7 +314,8 @@ Ltac solve_proper := ... @@ -317,7 +314,8 @@ Ltac solve_proper := | |- Proper _ _ => intros ??? | |- Proper _ _ => intros ??? | |- (_ ==> _)%signature _ _ => intros ??? | |- (_ ==> _)%signature _ _ => intros ??? | |- pointwise_relation _ _ _ _ => intros ? | |- pointwise_relation _ _ _ _ => intros ? end; | |- ?R ?f _ => try let f' := constr:(λ x, f x) in intros ? end; simpl; (* Unfold the head symbol, which is the one we are proving a new property about *) (* Unfold the head symbol, which is the one we are proving a new property about *) lazymatch goal with lazymatch goal with | |- ?R (?f _ _ _ _ _ _ _ _) (?f _ _ _ _ _ _ _ _) => unfold f | |- ?R (?f _ _ _ _ _ _ _ _) (?f _ _ _ _ _ _ _ _) => unfold f ... ...
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