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Diffstat (limited to 'test-suite/bugs/closed/HoTT_coq_014.v')
| -rw-r--r-- | test-suite/bugs/closed/HoTT_coq_014.v | 200 |
1 files changed, 200 insertions, 0 deletions
diff --git a/test-suite/bugs/closed/HoTT_coq_014.v b/test-suite/bugs/closed/HoTT_coq_014.v new file mode 100644 index 00000000..63548a64 --- /dev/null +++ b/test-suite/bugs/closed/HoTT_coq_014.v @@ -0,0 +1,200 @@ +Set Implicit Arguments. +Generalizable All Variables. +Set Universe Polymorphism. + +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@{Set Set} obj. +Polymorphic 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. + +Polymorphic 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 Polymorphic Coercion ObjectOf' : SpecializedFunctor >-> Funclass. +Set Universe Polymorphism. +Section Functor. + Variable C D : Category. + + Polymorphic Definition Functor := SpecializedFunctor C D. +End Functor. +Unset Universe Polymorphism. + +Polymorphic Identity Coercion Functor_SpecializedFunctor_Id : Functor >-> SpecializedFunctor. +Polymorphic Definition GeneralizeFunctor objC C objD D (F : @SpecializedFunctor objC C objD D) : Functor C D := F. +Polymorphic 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. + +Polymorphic 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. + +Set Universe Polymorphism. +Section GraphObj. + Context `(C : @SpecializedCategory objC). + + Inductive GraphIndex := GraphIndexSource | GraphIndexTarget. + + 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 /. + + Definition GraphIndex_Compose s d d' (m1 : GraphIndex_Morphism d d') (m2 : GraphIndex_Morphism s d) : + GraphIndex_Morphism s d'. + Admitted. + + Definition GraphIndexingCategory : @SpecializedCategory GraphIndex. + refine {| + Morphism' := GraphIndex_Morphism; + Identity' := (fun x => match x with GraphIndexSource => tt | GraphIndexTarget => tt end); + Compose' := GraphIndex_Compose + |}; + admit. + Defined. + + 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 /. + + Definition UnderlyingGraph_MorphismOf s d (m : Morphism GraphIndexingCategory s d) : + UnderlyingGraph_ObjectOf s -> UnderlyingGraph_ObjectOf d. + Admitted. + + 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. + +Set Printing Universes. +Set Printing All. + +Print Coercions. + +Section test. + +Fail Polymorphic Definition UnderlyingGraphFunctor_MorphismOf' (C D : SmallCategory) (F : SpecializedFunctor C D) : + Morphism (FunctorCategory TypeCat GraphIndexingCategory) + (@UnderlyingGraph (SObject C) + (SmallSpecializedCategory_LocallySmallSpecializedCategory_Id (SUnderlyingCategory C))) + (UnderlyingGraph D). + (* Toplevel input, characters 216-249: +Error: +In environment +C : SmallCategory (* Top.594 *) +D : SmallCategory (* Top.595 *) +F : +@SpecializedFunctor (* Top.25 Set Top.25 Set *) (SObject (* Top.25 *) C) + (SUnderlyingCategory (* Top.25 *) C) (SObject (* Top.25 *) D) + (SUnderlyingCategory (* Top.25 *) D) +The term + "SUnderlyingCategory (* Top.25 *) C + :SpecializedCategory (* Top.25 Set *) (SObject (* Top.25 *) C)" has type + "SpecializedCategory (* Top.618 Top.619 *) (SObject (* Top.25 *) C)" +while it is expected to have type + "SpecializedCategory (* Top.224 Top.225 *) (SObject (* Top.617 *) C)" +(Universe inconsistency: Cannot enforce Set = Top.225)). + *) +Fail Admitted. + +Fail Polymorphic Definition UnderlyingGraphFunctor_MorphismOf (C D : SmallCategory) (F : SpecializedFunctor C D) : + Morphism (FunctorCategory TypeCat GraphIndexingCategory) (UnderlyingGraph C) (UnderlyingGraph D). (* Anomaly: apply_coercion. Please report.*) +Fail Admitted. + +Polymorphic Definition UnderlyingGraphFunctor_MorphismOf (C D : SmallCategory) (F : SpecializedFunctor C D) : + Morphism (FunctorCategory GraphIndexingCategory TypeCat) (UnderlyingGraph C) (UnderlyingGraph D). (* Anomaly: apply_coercion. Please report.*) +Proof. +Admitted.
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