Commit d0c9c6c8 authored by Ralf Jung's avatar Ralf Jung

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

parent e38e903b
Pipeline #174 passed with stage
......@@ -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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