Commit 6fe27bb5 authored by Ralf Jung's avatar Ralf Jung

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

parent eb091d1d
......@@ -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. *)
......
Markdown is supported
0%
or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment