matita/matita/contribs/lambdadelta/ground/lib/list.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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  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/circled_element_e_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_empty: list A
  23 | list_lcons: A → list A → list A
  24 .
  25
  26 interpretation
  27   "empty (lists)"
  28   'CircledElementE A = (list_empty A).
  29
  30 interpretation
  31   "left cons (lists)"
  32   'OPlusRight A hd tl = (list_lcons A hd tl).
  33
  34 rec definition list_all A (R:predicate A) (l:list A) on l ≝ match l with
  35 [ list_empty       ⇒ ⊤
  36 | list_lcons hd tl ⇒ ∧∧ R hd & list_all A R tl
  37 ].