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_054.v | 94 ----------------------------------- 1 file changed, 94 deletions(-) delete mode 100644 test-suite/bugs/closed/HoTT_coq_054.v (limited to 'test-suite/bugs/closed/HoTT_coq_054.v') diff --git a/test-suite/bugs/closed/HoTT_coq_054.v b/test-suite/bugs/closed/HoTT_coq_054.v deleted file mode 100644 index f79fe1c1e..000000000 --- a/test-suite/bugs/closed/HoTT_coq_054.v +++ /dev/null @@ -1,94 +0,0 @@ -(* -*- mode: coq; coq-prog-args: ("-emacs" "-indices-matter") -*- *) -Inductive Empty : Prop := . - -Inductive paths {A : Type} (a : A) : A -> Type := - idpath : paths a a. - -Notation "x = y :> A" := (@paths A x y) : type_scope. -Notation "x = y" := (x = y :>_) : type_scope. - -Arguments idpath {A a} , [A] a. - -Definition idmap {A : Type} : A -> A := fun x => x. - -Definition path_sum {A B : Type} (z z' : A + B) - (pq : match z, z' with - | inl z0, inl z'0 => z0 = z'0 - | inr z0, inr z'0 => z0 = z'0 - | _, _ => Empty - end) -: z = z'. - destruct z, z', pq; exact idpath. -Defined. - -Definition ap {A B:Type} (f:A -> B) {x y:A} (p:x = y) : f x = f y - := match p with idpath => idpath end. - -Theorem ex2_8 {A B A' B' : Type} (g : A -> A') (h : B -> B') (x y : A + B) - (* Fortunately, this unifies properly *) - (pq : match (x, y) with (inl x', inl y') => x' = y' | (inr x', inr y') => x' = y' | _ => Empty end) : - let f z := match z with inl z' => inl (g z') | inr z' => inr (h z') end in - ap f (path_sum x y pq) = path_sum (f x) (f y) - (* Coq appears to require *ALL* of the annotations *) - ((match x as x return match (x, y) with - (inl x', inl y') => x' = y' - | (inr x', inr y') => x' = y' - | _ => Empty - end -> match (f x, f y) with - | (inl x', inl y') => x' = y' - | (inr x', inr y') => x' = y' - | _ => Empty end with - | inl x' => match y as y return match y with - inl y' => x' = y' - | _ => Empty - end -> match f y with - | inl y' => g x' = y' - | _ => Empty end with - | inl y' => ap g - | inr y' => idmap - end - | inr x' => match y as y return match y with - inr y' => x' = y' - | _ => Empty - end -> match f y with - | inr y' => h x' = y' - | _ => Empty end with - | inl y' => idmap - | inr y' => ap h - end - end) pq). - destruct x; destruct y; destruct pq; reflexivity. -Qed. -(* Toplevel input, characters 1367-1374: -Error: -In environment -A : Type -B : Type -A' : Type -B' : Type -g : A -> A' -h : B -> B' -x : A + B -y : A + B -pq : -match x with -| inl x' => match y with - | inl y' => x' = y' - | inr _ => Empty - end -| inr x' => match y with - | inl _ => Empty - | inr y' => x' = y' - end -end -f := -fun z : A + B => -match z with -| inl z' => inl (g z') -| inr z' => inr (h z') -end : A + B -> A' + B' -x' : B -y0 : A + B -y' : B -The term "x' = y'" has type "Type" while it is expected to have type -"Prop" (Universe inconsistency). *) -- cgit v1.2.3