diff options
author | Jason Gross <jgross@mit.edu> | 2014-05-09 10:13:32 -0400 |
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committer | Matthieu Sozeau <mattam@mattam.org> | 2014-05-10 15:39:39 +0200 |
commit | c7284415e4bdd3315c84c7d15d140d3fee000bc5 (patch) | |
tree | cc8ded3feba7e1da0dd4f7d17b7e5f974de752c3 /test-suite/bugs/closed/HoTT_coq_064.v | |
parent | 3f64bd23a343bcd7be0ef07afa7d9e3249df24ec (diff) |
Move opened bugs to bugs/opened
Diffstat (limited to 'test-suite/bugs/closed/HoTT_coq_064.v')
-rw-r--r-- | test-suite/bugs/closed/HoTT_coq_064.v | 187 |
1 files changed, 0 insertions, 187 deletions
diff --git a/test-suite/bugs/closed/HoTT_coq_064.v b/test-suite/bugs/closed/HoTT_coq_064.v deleted file mode 100644 index fae954f81..000000000 --- a/test-suite/bugs/closed/HoTT_coq_064.v +++ /dev/null @@ -1,187 +0,0 @@ -(* File reduced by coq-bug-finder from 279 lines to 219 lines. *) - -Set Implicit Arguments. -Set Universe Polymorphism. -Definition admit {T} : T. -Admitted. -Module Export Overture. - Reserved Notation "g 'o' f" (at level 40, left associativity). - - Inductive paths {A : Type} (a : A) : A -> Type := - idpath : paths a a. - - Arguments idpath {A a} , [A] a. - - Notation "x = y :> A" := (@paths A x y) : type_scope. - - Notation "x = y" := (x = y :>_) : type_scope. - - Delimit Scope path_scope with path. - - Local Open Scope path_scope. - - Definition ap {A B:Type} (f:A -> B) {x y:A} (p:x = y) : f x = f y - := match p with idpath => idpath end. - - Definition apD10 {A} {B:A->Type} {f g : forall x, B x} (h:f=g) - : forall x, f x = g x - := fun x => match h with idpath => idpath end. - - Class IsEquiv {A B : Type} (f : A -> B) := BuildIsEquiv { equiv_inv : B -> A }. - - Delimit Scope equiv_scope with equiv. - Local Open Scope equiv_scope. - - Notation "f ^-1" := (@equiv_inv _ _ f _) (at level 3) : equiv_scope. - - Class Funext := - { isequiv_apD10 :> forall (A : Type) (P : A -> Type) f g, IsEquiv (@apD10 A P f g) }. - - Definition path_forall `{Funext} {A : Type} {P : A -> Type} (f g : forall x : A, P x) : - (forall x, f x = g x) -> f = g - := - (@apD10 A P f g)^-1. - -End Overture. - -Module Export Core. - - Set Implicit Arguments. - Delimit Scope morphism_scope with morphism. - Delimit Scope category_scope with category. - Delimit Scope object_scope with object. - - Record PreCategory := - { - object :> Type; - morphism : object -> object -> Type; - - compose : forall s d d', - morphism d d' - -> morphism s d - -> morphism s d' - where "f 'o' g" := (compose f g); - - associativity : forall x1 x2 x3 x4 - (m1 : morphism x1 x2) - (m2 : morphism x2 x3) - (m3 : morphism x3 x4), - (m3 o m2) o m1 = m3 o (m2 o m1) - }. - Bind Scope category_scope with PreCategory. - Arguments compose [!C%category s%object d%object d'%object] m1%morphism m2%morphism : rename. - - Infix "o" := compose : morphism_scope. - -End Core. - -Local Open Scope morphism_scope. -Record Functor (C D : PreCategory) := - { - object_of :> C -> D; - morphism_of : forall s d, morphism C s d - -> morphism D (object_of s) (object_of d) - }. - -Inductive Unit : Set := - tt : Unit. - -Definition indiscrete_category (X : Type) : PreCategory - := @Build_PreCategory X - (fun _ _ => Unit) - (fun _ _ _ _ _ => tt) - (fun _ _ _ _ _ _ _ => idpath). - - -Record NaturalTransformation C D (F G : Functor C D) := { components_of :> forall c, morphism D (F c) (G c) }. -Section path_natural_transformation. - Context `{Funext}. - Variable C : PreCategory. - Variable D : PreCategory. - Variables F G : Functor C D. - - Section path. - Variables T U : NaturalTransformation F G. - Lemma path'_natural_transformation - : components_of T = components_of U - -> T = U. - admit. - Defined. - Lemma path_natural_transformation - : (forall x, T x = U x) - -> T = U. - Proof. - intros. - apply path'_natural_transformation. - apply path_forall; assumption. - Qed. - End path. -End path_natural_transformation. -Ltac path_natural_transformation := - repeat match goal with - | _ => intro - | _ => apply path_natural_transformation; simpl - end. -Definition comma_category A B C (S : Functor A C) (T : Functor B C) -: PreCategory. - admit. -Defined. -Definition compose C D (F F' F'' : Functor C D) - (T' : NaturalTransformation F' F'') (T : NaturalTransformation F F') -: NaturalTransformation F F'' - := Build_NaturalTransformation F F'' - (fun c => T' c o T c). - -Infix "o" := compose : natural_transformation_scope. - -Local Open Scope natural_transformation_scope. - -Definition associativity `{fs : Funext} - C D F G H I - (V : @NaturalTransformation C D F G) - (U : @NaturalTransformation C D G H) - (T : @NaturalTransformation C D H I) -: (T o U) o V = T o (U o V). -Proof. - path_natural_transformation. - - apply associativity. -Qed. -Definition functor_category `{Funext} (C D : PreCategory) : PreCategory - := @Build_PreCategory (Functor C D) - (@NaturalTransformation C D) - (@compose C D) - (@associativity _ C D). - -Notation "C -> D" := (functor_category C D) : category_scope. - -Definition compose_functor `{Funext} (C D E : PreCategory) : object ((C -> D) -> ((D -> E) -> (C -> E))). - admit. - -Defined. - -Definition pullback_along `{Funext} (C C' D : PreCategory) (p : Functor C C') -: object ((C' -> D) -> (C -> D)) - := Eval hnf in compose_functor _ _ _ p. - -Definition IsColimit `{Funext} C D (F : Functor D C) (x : object - (@comma_category (indiscrete_category Unit) - (@functor_category H (indiscrete_category Unit) C) - (@functor_category H D C) - admit - (@pullback_along H D (indiscrete_category Unit) C - admit))) : Type - := admit. - -Generalizable All Variables. -Axiom fs : Funext. - -Section bar. - - Variable D : PreCategory. - - Context `(has_colimits - : forall F : Functor D C, - @IsColimit _ C D F (colimits F)). -(* Error: Unsatisfied constraints: Top.3773 <= Set - (maybe a bugged tactic). *) |