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Commit 875dacf5 authored by Ralf Jung's avatar Ralf Jung
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f_equiv: do more syntactic matching before handing off to unification

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theories/tactics.v
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...@@ -375,36 +375,36 @@ Ltac f_equiv := ...@@ -375,36 +375,36 @@ Ltac f_equiv :=
| H : ?R ?x ?y |- ?R2 (match ?x with _ => _ end) (match ?y with _ => _ end) => | H : ?R ?x ?y |- ?R2 (match ?x with _ => _ end) (match ?y with _ => _ end) =>
destruct H 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 _) _ => simple apply (_ : Proper (R ==> R) f) | |- ?R (?f _) (?f _) => simple apply (_ : Proper (R ==> R) f)
| |- ?R (?f _ _) _ => simple apply (_ : Proper (R ==> R ==> R) f) | |- ?R (?f _ _) (?f _ _) => simple apply (_ : Proper (R ==> R ==> R) f)
| |- ?R (?f _ _ _) _ => simple apply (_ : Proper (R ==> R ==> R ==> R) f) | |- ?R (?f _ _ _) (?f _ _ _) => simple apply (_ : Proper (R ==> R ==> R ==> R) f)
| |- ?R (?f _ _ _ _) _ => simple apply (_ : Proper (R ==> R ==> R ==> R ==> R) f) | |- ?R (?f _ _ _ _) (?f _ _ _ _) => simple apply (_ : Proper (R ==> R ==> R ==> R ==> R) f)
| |- ?R (?f _ _ _ _ _) _ => simple apply (_ : Proper (R ==> R ==> R ==> R ==> R ==> R) f) | |- ?R (?f _ _ _ _ _) (?f _ _ _ _ _) => simple apply (_ : Proper (R ==> R ==> R ==> R ==> 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,
like equiv. *) like equiv. *)
| |- (?R _) (?f _) _ => simple apply (_ : Proper (R _ ==> _) f) | |- (?R _) (?f _) (?f _) => simple apply (_ : Proper (R _ ==> _) f)
| |- (?R _ _) (?f _) _ => simple apply (_ : Proper (R _ _ ==> _) f) | |- (?R _ _) (?f _) (?f _) => simple apply (_ : Proper (R _ _ ==> _) f)
| |- (?R _ _ _) (?f _) _ => simple apply (_ : Proper (R _ _ _ ==> _) f) | |- (?R _ _ _) (?f _) (?f _) => simple apply (_ : Proper (R _ _ _ ==> _) f)
| |- (?R _) (?f _ _) _ => simple apply (_ : Proper (R _ ==> R _ ==> _) f) | |- (?R _) (?f _ _) (?f _ _) => simple apply (_ : Proper (R _ ==> R _ ==> _) f)
| |- (?R _ _) (?f _ _) _ => simple apply (_ : Proper (R _ _ ==> R _ _ ==> _) f) | |- (?R _ _) (?f _ _) (?f _ _) => simple apply (_ : Proper (R _ _ ==> R _ _ ==> _) f)
| |- (?R _ _ _) (?f _ _) _ => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ ==> _) f) | |- (?R _ _ _) (?f _ _) (?f _ _) => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ ==> _) f)
| |- (?R _) (?f _ _ _) _ => simple apply (_ : Proper (R _ ==> R _ ==> R _ ==> _) f) | |- (?R _) (?f _ _ _) (?f _ _ _) => simple apply (_ : Proper (R _ ==> R _ ==> R _ ==> _) f)
| |- (?R _ _) (?f _ _ _) _ => simple apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _ ==> _) f) | |- (?R _ _) (?f _ _ _) (?f _ _ _) => simple apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _ ==> _) f)
| |- (?R _ _ _) (?f _ _ _) _ => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ R _ _ _ ==> _) f) | |- (?R _ _ _) (?f _ _ _) (?f _ _ _) => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ R _ _ _ ==> _) f)
| |- (?R _) (?f _ _ _ _) _ => simple apply (_ : Proper (R _ ==> R _ ==> R _ ==> R _ ==> _) f) | |- (?R _) (?f _ _ _ _) (?f _ _ _ _) => simple apply (_ : Proper (R _ ==> R _ ==> R _ ==> R _ ==> _) f)
| |- (?R _ _) (?f _ _ _ _) _ => simple apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _ ==> R _ _ ==> _) f) | |- (?R _ _) (?f _ _ _ _) (?f _ _ _ _) => simple apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _ ==> R _ _ ==> _) f)
| |- (?R _ _ _) (?f _ _ _ _) _ => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> _) f) | |- (?R _ _ _) (?f _ _ _ _) (?f _ _ _ _) => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> _) f)
| |- (?R _) (?f _ _ _ _ _) _ => simple apply (_ : Proper (R _ ==> R _ ==> R _ ==> R _ ==> R _ ==> _) f) | |- (?R _) (?f _ _ _ _ _) (?f _ _ _ _ _) => simple apply (_ : Proper (R _ ==> R _ ==> R _ ==> R _ ==> R _ ==> _) f)
| |- (?R _ _) (?f _ _ _ _ _) _ => simple apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _ ==> R _ _ ==> R _ _ ==> _) f) | |- (?R _ _) (?f _ _ _ _ _) (?f _ _ _ _ _) => simple apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _ ==> R _ _ ==> R _ _ ==> _) f)
| |- (?R _ _ _) (?f _ _ _ _ _) _ => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> _) f) | |- (?R _ _ _) (?f _ _ _ _ _) (?f _ _ _ _ _) => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> _) f)
(* Next, try to infer the relation. Unfortunately, very often, it will turn (* Next, try to infer the relation. Unfortunately, very often, it will turn
the goal into a Leibniz equality so we get stuck. *) the goal into a Leibniz equality so we get stuck. *)
(* TODO: Can we exclude that instance? *) (* TODO: Can we exclude that instance? *)
| |- ?R (?f _) _ => simple apply (_ : Proper (_ ==> R) f) | |- ?R (?f _) (?f _) => simple apply (_ : Proper (_ ==> R) f)
| |- ?R (?f _ _) _ => simple apply (_ : Proper (_ ==> _ ==> R) f) | |- ?R (?f _ _) (?f _ _) => simple apply (_ : Proper (_ ==> _ ==> R) f)
| |- ?R (?f _ _ _) _ => simple apply (_ : Proper (_ ==> _ ==> _ ==> R) f) | |- ?R (?f _ _ _) (?f _ _ _) => simple apply (_ : Proper (_ ==> _ ==> _ ==> R) f)
| |- ?R (?f _ _ _ _) _ => simple apply (_ : Proper (_ ==> _ ==> _ ==> _ ==> R) f) | |- ?R (?f _ _ _ _) (?f _ _ _ _) => simple apply (_ : Proper (_ ==> _ ==> _ ==> _ ==> R) f)
| |- ?R (?f _ _ _ _ _) _ => simple apply (_ : Proper (_ ==> _ ==> _ ==> _ ==> _ ==> R) f) | |- ?R (?f _ _ _ _ _) (?f _ _ _ _ _) => simple 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 relation about those functions in our context. *) maybe we have a relation about those functions in our context. *)
(* TODO: If only some of the arguments are the same, we could also (* TODO: If only some of the arguments are the same, we could also
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