Quellcode-Bibliothek

^© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: bug_4221.v Sprache: Coq

Original von: Coq^©

Universes a b c ω ω'.
Definition Typeω := Type@{ω}.
Definition Type2 : Typeω := Type@{c}.
Definition Type1 : Type2 := Type@{b}.
Definition Type0 : Type1 := Type@{a}.

Set Universe Polymorphism.
Set Printing Universes.

Definition Typei' (n : nat)
  := match n return Type@{ω'} with
     | 0 => Type0
     | 1 => Type1
     | 2 => Type2
     | _ => Typeω
     end.
Definition TypeOfTypei' {n} (x : Typei' n) : Type@{ω'}
  := match n return Typei' n -> Type@{ω'} with
     | 0 | 1 | 2 | _ => fun x => x
     end x.
Definition Typei (n : nat) : Typei' (S n)
  := match n return Typei' (S n) with
     | 0 => Type0
     | 1 => Type1
     | _ => Type2
     end.
Definition TypeOfTypei {n} (x : TypeOfTypei' (Typei n)) : Type@{ω'}
  := match n return TypeOfTypei' (Typei n) -> Type@{ω'} with
     | 0 | 1 | _ => fun x => x
     end x.
Check Typei 0 : Typei 1.
Check Typei 1 : Typei 2.

Definition lift' {n} : TypeOfTypei' (Typei n) -> TypeOfTypei' (Typei (S n))
  := match n return TypeOfTypei' (Typei n) -> TypeOfTypei' (Typei (S n)) with
     | 0 | 1 | 2 | _ => fun x => (x : Type)
     end.
Definition lift'' {n} : TypeOfTypei' (Typei n) -> TypeOfTypei' (Typei (S n))
  := match n return TypeOfTypei' (Typei n) -> TypeOfTypei' (Typei (S n)) with
     | 0 | 1 | 2 | _ => fun x => x
     end. (* The command has indeed failed with message:
In environment
n : nat
x : TypeOfTypei' (Typei 0)
The term "x" has type "TypeOfTypei' (Typei 0)" while it is expected to have type
"TypeOfTypei' (Typei 1)" (universe inconsistency: Cannot enforce b = a because  a < b).
*)
Check (fun x : TypeOfTypei' (Typei 0) => TypeOfTypei' (Typei 1)).

Definition lift''' {n} : TypeOfTypei' (Typei n) -> TypeOfTypei' (Typei (S n)).
  refine match n return TypeOfTypei' (Typei n) -> TypeOfTypei' (Typei (S n))  with
         | 0 | 1 | 2 | _ => fun x => _
         end.
  exact x.
  Undo.
  (* The command has indeed failed with message:
In environment
n : nat
x : TypeOfTypei' (Typei 0)
The term "x" has type "TypeOfTypei' (Typei 0)" while it is expected to have type
"TypeOfTypei' (Typei 1)" (universe inconsistency: Cannot enforce b = a because  a < b).
*)
  all:compute in *.
  all:exact x.
Abort.

¤ Dauer der Verarbeitung: 0.1 Sekunden (vorverarbeitet) ¤

Download des Quellennavigators
Download des sprechenden Kalenders
Eigene Datei ansehen

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.