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[helm.git] / matita / tests / coercions_nonuniform.ma

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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+
+
+axiom A : Type.
+axiom B : A -> Type.
+axiom f : A -> A.
+axiom f1 : A -> A.
+
+axiom k : ∀a:A.B (f a).
+
+coercion cic:/matita/tests/coercions_nonuniform/k.con.
+
+axiom C : Type.
+
+(* axiom c1 : ∀a:A. B (f a) -> C. *) (* COQ NO: non uniform *)
+(* axiom c1 : ∀a:A. B (f1 a) -> C. *) (* non si compongono, ma almeno ho le 2 non composte le ho e le posso usare *)
+(* axiom c1 : ∀f.∀a:A.B (f a) -> C. *) (* COQ NO: non uniform *)
+
+(* COQ NO: non uniform *)
+axiom c2 : ∀a.B (f a) -> B (f1 a).
+axiom c1 : ∀a:A. B (f1 a) -> C.
+
+coercion cic:/matita/tests/coercions_nonuniform/c1.con.
+coercion cic:/matita/tests/coercions_nonuniform/c2.con.
+
+axiom g : C -> C.
+
+definition test := λa:A.g a.
+
+(*
+Coq < Coercion c1 : B >-> C.                
+User error: c1 does not respect the inheritance uniform condition
+*)