matita/matita/contribs/lambdadelta/ground/lib/list.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 include "ground/notation/functions/circledE_1.ma".
  16 include "ground/notation/functions/oplusright_3.ma".
  17 include "ground/lib/relations.ma".
  18
  19 (* LISTS ********************************************************************)
  20
  21 inductive list (A:Type[0]) : Type[0] :=
  22 | list_nil : list A
  23 | list_cons: A → list A → list A
  24 .
  25
  26 interpretation
  27   "nil (lists)"
  28   'CircledE A = (list_nil A).
  29
  30 interpretation
  31   "cons (lists)"
  32   'OPlusRight A hd tl = (list_cons A hd tl).
  33
  34 rec definition list_all A (R:predicate A) (l:list A) on l ≝
  35 match l with
  36 [ list_nil        ⇒ ⊤
  37 | list_cons hd tl ⇒ ∧∧ R hd & list_all A R tl
  38 ].