helm/software/matita/nlibrary/datatypes/sums.ma

   1 (**************************************************************************)
   2 (*       ___                                                                *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||       A.Asperti, C.Sacerdoti Coen,                          *)
   8 (*      ||A||       E.Tassi, S.Zacchiroli                                 *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU Lesser General Public License Version 2.1         *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "datatypes/pairs.ma".
  16
  17 ninductive void : Type[0] ≝.
  18
  19 ninductive unit : Type[0] ≝ something: unit.
  20
  21 ninductive Sum (A,B:Type[0]) : Type[0] ≝
  22 | inl : A → Sum A B
  23 | inr : B → Sum A B.
  24
  25 interpretation "Disjoint union" 'plus A B = (Sum A B).
  26
  27 ninductive option (A:Type[0]) : Type[0] ≝
  28  | None : option A
  29  | Some : A → option A.