helm/software/matita/contribs/ng_assembly/common/option.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 (* ********************************************************************** *)
  16 (*                          Progetto FreeScale                            *)
  17 (*                                                                        *)
  18 (*   Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it              *)
  19 (*   Sviluppo: 2008-2010                                                  *)
  20 (*                                                                        *)
  21 (* ********************************************************************** *)
  22
  23 include "num/bool.ma".
  24
  25 (* ****** *)
  26 (* OPTION *)
  27 (* ****** *)
  28
  29 ninductive option (A:Type) : Type ≝
  30   None : option A
  31 | Some : A → option A.
  32
  33 ndefinition eq_option ≝
  34 λT.λf:T → T → bool.λop1,op2:option T.
  35  match op1 with
  36   [ None ⇒ match op2 with [ None ⇒ true | Some _ ⇒ false ]
  37   | Some x1 ⇒ match op2 with [ None ⇒ false | Some x2 ⇒ f x1 x2 ]
  38   ].
  39
  40 (* option map = match ... with [ None ⇒ None ? | Some .. ⇒ .. ] *)
  41 ndefinition opt_map ≝
  42 λT1,T2:Type.λt:option T1.λf:T1 → option T2.
  43  match t with [ None ⇒ None ? | Some x ⇒ (f x) ].