matita/matita/nlibrary/basics/list2.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 "basics/list.ma".
  16 include "arithmetics/nat.ma".
  17
  18 nlet rec length (A:Type) (l:list A) on l ≝
  19   match l with
  20     [ nil ⇒ 0
  21     | cons a tl ⇒ S (length A tl)].
  22
  23 notation "|M|" non associative with precedence 65 for @{'norm $M}.
  24 interpretation "norm" 'norm l = (length ? l).
  25
  26 nlet rec nth n (A:Type) (l:list A) (d:A)  ≝
  27   match n with
  28     [O ⇒ hd A l d
  29     |S m ⇒ nth m A (tail A l) d].
  30