From a4c7f8bd98be2a200489325ff7c5061cf80ab4f3 Mon Sep 17 00:00:00 2001 From: Enrico Tassi Date: Tue, 27 Dec 2016 16:53:30 +0100 Subject: Imported Upstream version 8.6 --- test-suite/bugs/closed/3209.v | 75 +++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 75 insertions(+) create mode 100644 test-suite/bugs/closed/3209.v (limited to 'test-suite/bugs/closed/3209.v') diff --git a/test-suite/bugs/closed/3209.v b/test-suite/bugs/closed/3209.v new file mode 100644 index 00000000..855058b0 --- /dev/null +++ b/test-suite/bugs/closed/3209.v @@ -0,0 +1,75 @@ +(* Avoiding some occur-check *) + +(* 1. Original example *) + +Inductive eqT {A} (x : A) : A -> Type := + reflT : eqT x x. +Definition Bi_inv (A B : Type) (f : (A -> B)) := + sigT (fun (g : B -> A) => + sigT (fun (h : B -> A) => + sigT (fun (α : forall b : B, eqT (f (g b)) b) => + forall a : A, eqT (h (f a)) a))). +Definition TEquiv (A B : Type) := sigT (fun (f : A -> B) => Bi_inv _ _ f). + +Axiom UA : forall (A B : Type), TEquiv (TEquiv A B) (eqT A B). +Definition idtoeqv {A B} (e : eqT A B) : TEquiv A B := + sigT_rect (fun _ => TEquiv A B) + (fun (f : TEquiv A B -> eqT A B) H => + sigT_rect _ (* (fun _ => TEquiv A B) *) + (fun g _ => g e) + H) + (UA A B). + +(* 2. Alternative example by Guillaume *) + +Inductive foo (A : Prop) : Prop := Foo : foo A. +Axiom bar : forall (A : Prop) (P : foo A -> Prop), (A -> P (Foo A)) -> Prop. + +(* This used to fail with a Not_found, we fail more graciously but a + heuristic could be implemented, e.g. in some smart occur-check + function, to find a solution of then form ?P := fun _ => ?P' *) + +Fail Check (fun e : ?[T] => bar ?[A] ?[P] (fun g : ?[A'] => g e)). + +(* This works and tells which solution we could have inferred *) + +Check (fun e : ?[T] => bar ?[A] (fun _ => ?[P]) (fun g : ?[A'] => g e)). + +(* For the record, here is the trace in the failing example: + +In (fun e : ?T => bar ?[A] ?[P] (fun g : ?A' => g e)), we have the existential variables + +e:?T |- ?A : Prop +e:?T |- ?P : foo ?A -> Prop +e:?T |- ?A' : Type + +with constraints + +?A' == ?A +?A' == ?T -> ?P (Foo ?A) + +To type (g e), unification first defines + +?A := forall x:?B, ?P'{e:=e,x:=x} +with ?T <= ?B +and ?P'@{e:=e,x:=e} <= ?P@{e:=e} (Foo (forall x:?B, ?P'{e:=e,x:=x})) + +Then, since ?P'@{e:=e,x:=e} may use "e" in two different ways, it is +not a pattern and we define a new + +e:?T x:?B|- ?P'' : foo (?B' -> ?P''') -> Prop + +for some ?B' and ?P''', together with + +?P'@{e,x} := ?P''{e:=e,x:=e} (Foo (?B -> ?P') +?P@{e} := ?P''{e:=e,x:=e} + +Moreover, ?B' and ?P''' have to satisfy + +?B'@{e:=e,x:=e} == ?B@{e:=e} +?P'''@{e:=e,x:=e} == ?P'@{e:=e,x:=x} + +and this leads to define ?P' which was the initial existential +variable to define. +*) + -- cgit v1.2.3