Merge branch 'ralf/f_equiv' into 'master'

f_equiv optimizations

See merge request !325

CHANGELOG.md

@@ -165,6 +165,11 @@ API-breaking change is listed.
 - Enable `f_equiv` (and by extension `solve_proper`) to handle goals of the form
   `f x ≡ g x` when `f ≡ g` is in scope, where `f` has a type like Iris's `-d>`
   and `-n>`.
+- Optimize `f_equiv` by doing more syntactic checking before handing off to
+  unification. This can make some uses 50x faster, but also makes the tactic
+  slightly weaker in case the left-hand side and right-hand side of the relation
+  call a function with arguments that are convertible but not syntactically
+  equal.
 
 The following `sed` script should perform most of the renaming
 (on macOS, replace `sed` by `gsed`, installed via e.g. `brew install gnu-sed`).

theories/tactics.v

@@ -374,46 +374,60 @@ Ltac f_equiv :=
     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 *)
-  | |- ?R (?f _) _ => simple apply (_ : Proper (R ==> R) f)
-  | |- ?R (?f _ _) _ => simple apply (_ : Proper (R ==> R ==> R) f)
-  | |- ?R (?f _ _ _) _ => simple apply (_ : Proper (R ==> R ==> R ==> R) f)
-  | |- ?R (?f _ _ _ _) _ => simple apply (_ : Proper (R ==> R ==> R ==> R ==> R) f)
-  | |- ?R (?f _ _ _ _ _) _ => simple apply (_ : Proper (R ==> R ==> R ==> R ==> R ==> R) f)
+  (* First assume that the arguments need the same relation as the result. We
+  check the most restrictive pattern first: [(?f _) (?f _)] requires all but the
+  last argument to be syntactically equal. *)
+  | |- ?R (?f _) (?f _) => simple apply (_ : Proper (R ==> R) f)
+  | |- ?R (?f _ _) (?f _ _) => simple apply (_ : Proper (R ==> R ==> R) f)
+  | |- ?R (?f _ _ _) (?f _ _ _) => simple apply (_ : Proper (R ==> R ==> R ==> R) f)
+  | |- ?R (?f _ _ _ _) (?f _ _ _ _) => simple apply (_ : Proper (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,
   like equiv. *)
-  | |- (?R _) (?f _) _ => simple apply (_ : Proper (R _ ==> _) f)
-  | |- (?R _ _) (?f _) _ => simple apply (_ : Proper (R _ _ ==> _) f)
-  | |- (?R _ _ _) (?f _) _ => simple apply (_ : Proper (R _ _ _ ==> _) f)
-  | |- (?R _) (?f _ _) _ => simple apply (_ : Proper (R _ ==> R _ ==> _) f)
-  | |- (?R _ _) (?f _ _) _ => simple apply (_ : Proper (R _ _ ==> R _ _ ==> _) f)
-  | |- (?R _ _ _) (?f _ _) _ => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ ==> _) f)
-  | |- (?R _) (?f _ _ _) _ => simple apply (_ : Proper (R _ ==> R _ ==> R _ ==> _) f)
-  | |- (?R _ _) (?f _ _ _) _ => simple apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _ ==> _) f)
-  | |- (?R _ _ _) (?f _ _ _) _ => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ R _ _ _ ==> _) f)
-  | |- (?R _) (?f _ _ _ _) _ => simple apply (_ : Proper (R _ ==> R _ ==> R _ ==> R _ ==> _) f)
-  | |- (?R _ _) (?f _ _ _ _) _ => simple apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _ ==> R _ _ ==> _) f)
-  | |- (?R _ _ _) (?f _ _ _ _) _ => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> _) f)
-  | |- (?R _) (?f _ _ _ _ _) _ => simple apply (_ : Proper (R _ ==> R _ ==> R _ ==> R _ ==> R _ ==> _) f)
-  | |- (?R _ _) (?f _ _ _ _ _) _ => simple apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _ ==> R _ _ ==> R _ _ ==> _) f)
-  | |- (?R _ _ _) (?f _ _ _ _ _) _ => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> _) f)
-  (* Next, try to infer the relation. Unfortunately, very often, it will turn
-     the goal into a Leibniz equality so we get stuck. *)
-  (* TODO: Can we exclude that instance? *)
+  | |- (?R _) (?f _) (?f _) => simple apply (_ : Proper (R _ ==> R _) f)
+  | |- (?R _ _) (?f _) (?f _) => simple apply (_ : Proper (R _ _ ==> R _ _) f)
+  | |- (?R _ _ _) (?f _) (?f _) => simple apply (_ : Proper (R _ _ _ ==> R _ _ _) f)
+
+  | |- (?R _) (?f _ _) (?f _ _) => simple apply (_ : Proper (R _ ==> R _ ==> R _) f)
+  | |- (?R _ _) (?f _ _) (?f _ _) => simple apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _) f)
+  | |- (?R _ _ _) (?f _ _) (?f _ _) => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ ==> R _ _ _) f)
+
+  | |- (?R _) (?f _ _ _) (?f _ _ _) => simple apply (_ : Proper (R _ ==> R _ ==> R _ ==> R _) f)
+  | |- (?R _ _) (?f _ _ _) (?f _ _ _) => simple apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _ ==> R _ _) f)
+  | |- (?R _ _ _) (?f _ _ _) (?f _ _ _) => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> R _ _ _) f)
+
+  | |- (?R _) (?f _ _ _ _) (?f _ _ _ _) => simple apply (_ : Proper (R _ ==> R _ ==> R _ ==> R _ ==> R _) f)
+  | |- (?R _ _) (?f _ _ _ _) (?f _ _ _ _) => simple apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _ ==> R _ _ ==> R _ _) f)
+  | |- (?R _ _ _) (?f _ _ _ _) (?f _ _ _ _) => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> R _ _ _) f)
+
+  | |- (?R _) (?f _ _ _ _ _) (?f _ _ _ _ _) => simple apply (_ : Proper (R _ ==> R _ ==> R _ ==> R _ ==> R _ ==> R _) f)
+  | |- (?R _ _) (?f _ _ _ _ _) (?f _ _ _ _ _) => simple apply (_ : Proper (R _ _ ==> R _ _ ==> R _ _ ==> R _ _ ==> R _ _ ==> R _ _) f)
+  | |- (?R _ _ _) (?f _ _ _ _ _) (?f _ _ _ _ _) => simple apply (_ : Proper (R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> R _ _ _ ==> R _ _ _) f)
+  (* In case the function symbol differs, but the arguments are the same, maybe
+     we have a relation about those functions in our context that we can simply
+     apply. (The case where the arguments differ is a lot more complicated; with
+     the way we typically define the relations on function spaces it further
+     requires [Proper]ness of [f] or [g]). *)
+  | H : _ ?f ?g |- ?R (?f ?x) (?g ?x) => solve [simple apply H]
+  | H : _ ?f ?g |- ?R (?f ?x ?y) (?g ?x ?y) => solve [simple apply H]
+
+  (* Fallback case: try to infer the relation, and allow the function to not be
+     syntactically the same on both sides. Unfortunately, very often, it will
+     turn the goal into a Leibniz equality so we get stuck. Furthermore, looking
+     for instances in this order will mean that Coq will try to unify the
+     remaining arguments that we have not explicitly generalized, which can be
+     very slow -- but if we go for the opposite order, we will hit the Leibniz
+     equality fallback instance even more often. *)
+  (* TODO: Can we exclude that Leibniz equality instance? *)
   | |- ?R (?f _) _ => simple apply (_ : Proper (_ ==> R) f)
   | |- ?R (?f _ _) _ => simple apply (_ : Proper (_ ==> _ ==> R) f)
   | |- ?R (?f _ _ _) _ => simple apply (_ : Proper (_ ==> _ ==> _ ==> R) f)
   | |- ?R (?f _ _ _ _) _ => simple apply (_ : Proper (_ ==> _ ==> _ ==> _ ==> R) f)
   | |- ?R (?f _ _ _ _ _) _ => simple apply (_ : Proper (_ ==> _ ==> _ ==> _ ==> _ ==> R) f)
-  (* In case the function symbol differs, but the arguments are the same,
-     maybe we have a relation about those functions in our context. *)
-  (* TODO: If only some of the arguments are the same, we could also
-     query for such relations. But that leads to a combinatorial
-     explosion about which arguments are and which are not the same. *)
-  | H : _ ?f ?g |- ?R (?f ?x) (?g ?x) => solve [simple apply H]
-  | H : _ ?f ?g |- ?R (?f ?x ?y) (?g ?x ?y) => solve [simple apply H]
   end;
-  try simple apply reflexivity.
+  (* Only try reflexivity if the terms are syntactically equal. This avoids
+     very expensive failing unification. *)
+  try match goal with  |- _ ?x ?x => simple apply reflexivity end.
 Tactic Notation "f_equiv" "/=" := csimpl in *; f_equiv.
 
 (** The tactic [solve_proper_unfold] unfolds the first head symbol, so that