From c7284415e4bdd3315c84c7d15d140d3fee000bc5 Mon Sep 17 00:00:00 2001 From: Jason Gross Date: Fri, 9 May 2014 10:13:32 -0400 Subject: Move opened bugs to bugs/opened --- test-suite/bugs/closed/HoTT_coq_014.v | 164 ---------------------------------- 1 file changed, 164 deletions(-) delete mode 100644 test-suite/bugs/closed/HoTT_coq_014.v (limited to 'test-suite/bugs/closed/HoTT_coq_014.v') diff --git a/test-suite/bugs/closed/HoTT_coq_014.v b/test-suite/bugs/closed/HoTT_coq_014.v deleted file mode 100644 index 1fd7e251f..000000000 --- a/test-suite/bugs/closed/HoTT_coq_014.v +++ /dev/null @@ -1,164 +0,0 @@ -Set Implicit Arguments. -Generalizable All Variables. - - -Polymorphic Record SpecializedCategory (obj : Type) := Build_SpecializedCategory' { - Object :> _ := obj; - Morphism' : obj -> obj -> Type; - - Identity' : forall o, Morphism' o o; - Compose' : forall s d d', Morphism' d d' -> Morphism' s d -> Morphism' s d' -}. - -Polymorphic Definition Morphism obj (C : @SpecializedCategory obj) : forall s d : C, _ := Eval cbv beta delta [Morphism'] in C.(Morphism'). - -(* eh, I'm not terribly happy. meh. *) -Polymorphic Definition SmallSpecializedCategory (obj : Set) (*mor : obj -> obj -> Set*) := SpecializedCategory obj. -Identity Coercion SmallSpecializedCategory_LocallySmallSpecializedCategory_Id : SmallSpecializedCategory >-> SpecializedCategory. - -Polymorphic Record Category := { - CObject : Type; - - UnderlyingCategory :> @SpecializedCategory CObject -}. - -Polymorphic Definition GeneralizeCategory `(C : @SpecializedCategory obj) : Category. - refine {| CObject := C.(Object) |}; auto. -Defined. - -Coercion GeneralizeCategory : SpecializedCategory >-> Category. - - - -Section SpecializedFunctor. - Set Universe Polymorphism. - Context `(C : @SpecializedCategory objC). - Context `(D : @SpecializedCategory objD). - Unset Universe Polymorphism. - - Polymorphic Record SpecializedFunctor := { - ObjectOf' : objC -> objD; - MorphismOf' : forall s d, C.(Morphism') s d -> D.(Morphism') (ObjectOf' s) (ObjectOf' d); - FCompositionOf' : forall s d d' (m1 : C.(Morphism') s d) (m2: C.(Morphism') d d'), - MorphismOf' _ _ (C.(Compose') _ _ _ m2 m1) = D.(Compose') _ _ _ (MorphismOf' _ _ m2) (MorphismOf' _ _ m1); - FIdentityOf' : forall o, MorphismOf' _ _ (C.(Identity') o) = D.(Identity') (ObjectOf' o) - }. -End SpecializedFunctor. - -Global Coercion ObjectOf' : SpecializedFunctor >-> Funclass. -(*Unset Universe Polymorphism.*) -Section Functor. - Variable C D : Category. - - Polymorphic Definition Functor := SpecializedFunctor C D. -End Functor. - -Identity Coercion Functor_SpecializedFunctor_Id : Functor >-> SpecializedFunctor. -Polymorphic Definition GeneralizeFunctor objC C objD D (F : @SpecializedFunctor objC C objD D) : Functor C D := F. -Coercion GeneralizeFunctor : SpecializedFunctor >-> Functor. - -Arguments SpecializedFunctor {objC} C {objD} D. - - -Polymorphic Record SmallCategory := { - SObject : Set; - - SUnderlyingCategory :> @SmallSpecializedCategory SObject -}. - -Polymorphic Definition GeneralizeSmallCategory `(C : @SmallSpecializedCategory obj) : SmallCategory. - refine {| SObject := obj |}; destruct C; econstructor; eassumption. -Defined. - -Coercion GeneralizeSmallCategory : SmallSpecializedCategory >-> SmallCategory. - -Bind Scope category_scope with SmallCategory. - - -Polymorphic Definition TypeCat : @SpecializedCategory Type := (@Build_SpecializedCategory' Type - (fun s d => s -> d) - (fun _ => (fun x => x)) - (fun _ _ _ f g => (fun x => f (g x)))). -(*Unset Universe Polymorphism.*) -Polymorphic Definition FunctorCategory objC (C : @SpecializedCategory objC) objD (D : @SpecializedCategory objD) : - @SpecializedCategory (SpecializedFunctor C D). -Admitted. - -Polymorphic Definition DiscreteCategory (O : Type) : @SpecializedCategory O. -Admitted. - -Polymorphic Definition ComputableCategory (I : Type) (Index2Object : I -> Type) (Index2Cat : forall i : I, @SpecializedCategory (@Index2Object i)) : - @SpecializedCategory I. -Admitted. - -Polymorphic Definition is_unique (A : Type) (x : A) := forall x' : A, x' = x. - -Polymorphic Definition InitialObject obj {C : SpecializedCategory obj} (o : C) := - forall o', { m : C.(Morphism) o o' | is_unique m }. - -Polymorphic Definition SmallCat := ComputableCategory _ SUnderlyingCategory. - -Lemma InitialCategory_Initial : InitialObject (C := SmallCat) (DiscreteCategory Empty_set : SmallSpecializedCategory _). - admit. -Qed. - - -Section GraphObj. - Context `(C : @SpecializedCategory objC). - - Inductive GraphIndex := GraphIndexSource | GraphIndexTarget. - - Polymorphic Definition GraphIndex_Morphism (a b : GraphIndex) : Set := - match (a, b) with - | (GraphIndexSource, GraphIndexSource) => unit - | (GraphIndexTarget, GraphIndexTarget) => unit - | (GraphIndexTarget, GraphIndexSource) => Empty_set - | (GraphIndexSource, GraphIndexTarget) => GraphIndex - end. - - Global Arguments GraphIndex_Morphism a b /. - - Polymorphic Definition GraphIndex_Compose s d d' (m1 : GraphIndex_Morphism d d') (m2 : GraphIndex_Morphism s d) : - GraphIndex_Morphism s d'. - Admitted. - - Polymorphic Definition GraphIndexingCategory : @SpecializedCategory GraphIndex. - refine {| - Morphism' := GraphIndex_Morphism; - Identity' := (fun x => match x with GraphIndexSource => tt | GraphIndexTarget => tt end); - Compose' := GraphIndex_Compose - |}; - admit. - Defined. - - Polymorphic Definition UnderlyingGraph_ObjectOf x := - match x with - | GraphIndexSource => { sd : objC * objC & C.(Morphism) (fst sd) (snd sd) } - | GraphIndexTarget => objC - end. - - Global Arguments UnderlyingGraph_ObjectOf x /. - - Polymorphic Definition UnderlyingGraph_MorphismOf s d (m : Morphism GraphIndexingCategory s d) : - UnderlyingGraph_ObjectOf s -> UnderlyingGraph_ObjectOf d. - Admitted. - - Polymorphic Definition UnderlyingGraph : SpecializedFunctor GraphIndexingCategory TypeCat. - Proof. - match goal with - | [ |- SpecializedFunctor ?C ?D ] => - refine (Build_SpecializedFunctor C D - UnderlyingGraph_ObjectOf - UnderlyingGraph_MorphismOf - _ - _ - ) - end; - admit. - Defined. -End GraphObj. - - -Polymorphic Definition UnderlyingGraphFunctor_MorphismOf (C D : SmallCategory) (F : SpecializedFunctor C D) : - Morphism (FunctorCategory TypeCat GraphIndexingCategory) (UnderlyingGraph C) (UnderlyingGraph D). (* Anomaly: apply_coercion. Please report.*) -Admitted. -- cgit v1.2.3