matita/matita/contribs/lambdadelta/ground_2/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_2/notation/functions/circledE_1.ma".
  16 include "ground_2/notation/functions/oplusright_3.ma".
  17 include "ground_2/lib/relations.ma".
  18
  19 (* LISTS ********************************************************************)
  20
  21 inductive list (A:Type[0]) : Type[0] :=
  22   | nil : list A
  23   | cons: A → list A → list A.
  24
  25 interpretation "nil (list)" 'CircledE A = (nil A).
  26
  27 interpretation "cons (list)" 'OPlusRight A hd tl = (cons A hd tl).
  28
  29 rec definition all A (R:predicate A) (l:list A) on l ≝
  30   match l with
  31   [ nil        ⇒ ⊤
  32   | cons hd tl ⇒ ∧∧ R hd & all A R tl
  33   ].