weblib/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 \ 5img class="anchor" src="icons/tick.png" id="length"\ 6let rec length (A:Type[0]) (l:\ 5a href="cic:/matita/basics/list/list.ind(1,0,1)"\ 6list\ 5/a\ 6 A) on l ≝
  19   match l with
  20     [ nil ⇒ \ 5a title="natural number" href="cic:/fakeuri.def(1)"\ 60\ 5/a\ 6
  21     | cons a tl ⇒ \ 5a href="cic:/matita/arithmetics/nat/nat.con(0,2,0)"\ 6S\ 5/a\ 6 (length A tl)].
  22
  23 notation "|M|" non associative with precedence 60 for @{'norm $M}.
  24 interpretation "norm" 'norm l = (length ? l).
  25
  26 \ 5img class="anchor" src="icons/tick.png" id="nth"\ 6let rec nth n (A:Type[0]) (l:\ 5a href="cic:/matita/basics/list/list.ind(1,0,1)"\ 6list\ 5/a\ 6 A) (d:A)  ≝
  27   match n with
  28     [O ⇒ \ 5a href="cic:/matita/basics/list/hd.def(1)"\ 6hd\ 5/a\ 6 A l d
  29     |S m ⇒ nth m A (\ 5a href="cic:/matita/basics/list/tail.def(1)"\ 6tail\ 5/a\ 6 A l) d].