From 7cfc4e5146be5666419451bdd516f1f3f264d24a Mon Sep 17 00:00:00 2001 From: Enrico Tassi Date: Sun, 25 Jan 2015 14:42:51 +0100 Subject: Imported Upstream version 8.5~beta1+dfsg --- test-suite/bugs/closed/HoTT_coq_007.v | 112 ++++++++++++++++++++++++++++++++++ 1 file changed, 112 insertions(+) create mode 100644 test-suite/bugs/closed/HoTT_coq_007.v (limited to 'test-suite/bugs/closed/HoTT_coq_007.v') diff --git a/test-suite/bugs/closed/HoTT_coq_007.v b/test-suite/bugs/closed/HoTT_coq_007.v new file mode 100644 index 00000000..8592c729 --- /dev/null +++ b/test-suite/bugs/closed/HoTT_coq_007.v @@ -0,0 +1,112 @@ +Module Comment1. + Set Implicit Arguments. + + Polymorphic Record Category (obj : Type) := + { + Morphism : obj -> obj -> Type; + Identity : forall o, Morphism o o + }. + + Polymorphic Record Functor objC (C :Category objC) objD (D : Category objD) := + { + ObjectOf :> objC -> objD; + MorphismOf : forall s d, C.(Morphism) s d -> D.(Morphism) (ObjectOf s) (ObjectOf d); + FIdentityOf : forall o, MorphismOf _ _ (C.(Identity) o) = D.(Identity) (ObjectOf o) + }. + + Create HintDb functor discriminated. + + Hint Rewrite @FIdentityOf : functor. + + Polymorphic Definition ComposeFunctors objC C objD D objE E (G : @Functor objD D objE E) (F : @Functor objC C objD D) : Functor C E. + refine {| ObjectOf := (fun c => G (F c)); + MorphismOf := (fun _ _ m => G.(MorphismOf) _ _ (F.(MorphismOf) _ _ m)) + |}; + intros; autorewrite with functor; reflexivity. + Defined. + + Definition Cat0 : Category@{i j} Empty_set. + refine {| + Morphism := fun s d : Empty_set => s = d; + Identity := fun o : Empty_set => eq_refl + |}; + admit. + Defined. + + Set Printing All. + Set Printing Universes. + + Lemma foo objC (C : @Category objC) (C0 : Category (Functor Cat0 C)) (x : Functor Cat0 Cat0) + : forall (y : Functor C0 Cat0) z, (ComposeFunctors y z = x). + intro. intro. + unfold ComposeFunctors. + Abort. +End Comment1. + +Module Comment2. + Set Implicit Arguments. + + Polymorphic Record Category (obj : Type) := + { + Morphism : obj -> obj -> Type; + + Identity : forall o, Morphism o o; + Compose : forall s d d2, Morphism d d2 -> Morphism s d -> Morphism s d2; + + LeftIdentity : forall a b (f : Morphism a b), Compose (Identity b) f = f + }. + + Polymorphic Record Functor objC (C : Category objC) objD (D : Category objD) := + { + ObjectOf : objC -> objD; + MorphismOf : forall s d, C.(Morphism) s d -> D.(Morphism) (ObjectOf s) (ObjectOf d) + }. + + Create HintDb morphism discriminated. + + Polymorphic Hint Resolve @LeftIdentity : morphism. + + Polymorphic Definition ProductCategory objC (C : Category objC) objD (D : Category objD) : @Category (objC * objD)%type. + refine {| + Morphism := (fun s d => (C.(Morphism) (fst s) (fst d) * D.(Morphism) (snd s) (snd d))%type); + Identity := (fun o => (Identity _ (fst o), Identity _ (snd o))); + Compose := (fun (s d d2 : (objC * objD)%type) m2 m1 => (C.(Compose) _ _ _ (fst m2) (fst m1), D.(Compose) _ _ _ (snd m2) (snd m1))) + |}; + intros; apply injective_projections; simpl; auto with morphism. (* Replacing [auto with morphism] with [apply @LeftIdentity] removes the error *) + Defined. + + Polymorphic Definition Cat0 : Category Empty_set. + refine {| + Morphism := fun s d : Empty_set => s = d; + Identity := fun o : Empty_set => eq_refl; + Compose := fun s d d2 m0 m1 => eq_trans m1 m0 + |}; + admit. + Defined. + + Set Printing All. + Set Printing Universes. + Polymorphic Definition ProductLaw0Functor (objC : Type) (C : Category objC) : Functor (ProductCategory C Cat0) Cat0. + refine (Build_Functor (ProductCategory C Cat0) Cat0 _ _). (* Toplevel input, characters 15-71: +Error: Refiner was given an argument + "prod (* Top.2289 Top.2289 *) objC Empty_set" of type +"Type (* Top.2289 *)" instead of "Set". *) + Abort. + Polymorphic Definition ProductLaw0Functor (objC : Type) (C : Category objC) : Functor (ProductCategory C Cat0) Cat0. + econstructor. (* Toplevel input, characters 0-12: +Error: No applicable tactic. + *) + Abort. +End Comment2. + + +Module Comment3. + Polymorphic Lemma foo {obj : Type} : 1 = 1. + trivial. + Qed. + + Polymorphic Hint Resolve foo. (* success *) + Polymorphic Hint Rewrite @foo. (* Success *) + Polymorphic Hint Resolve @foo. (* Error: @foo is a term and cannot be made a polymorphic hint, only global references can be polymorphic hints. *) + Fail Polymorphic Hint Rewrite foo. (* Error: Cannot infer the implicit parameter obj of foo. *) +End Comment3. -- cgit v1.2.3