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 "ground_2/notation/constructors/nil_0.ma".
  16 include "ground_2/notation/constructors/cons_3.ma".
  17 include "ground_2/notation/functions/append_2.ma".
  18 include "ground_2/lib/arith.ma".
  19
  20 (* LISTS OF PAIRS ***********************************************************)
  21
  22 inductive list2 (A1,A2:Type[0]) : Type[0] :=
  23   | nil2 : list2 A1 A2
  24   | cons2: A1 → A2 → list2 A1 A2 → list2 A1 A2.
  25
  26 interpretation "nil (list of pairs)" 'Nil = (nil2 ? ?).
  27
  28 interpretation "cons (list of pairs)" 'Cons hd1 hd2 tl = (cons2 ? ? hd1 hd2 tl).
  29
  30 rec definition append2 (A1,A2:Type[0]) (l1,l2:list2 A1 A2) on l1 ≝ match l1 with
  31 [ nil2           ⇒ l2
  32 | cons2 a1 a2 tl ⇒ {a1, a2} @ append2 A1 A2 tl l2
  33 ].
  34
  35 interpretation "append (list of pairs)"
  36    'Append l1 l2 = (append2 ? ? l1 l2).
  37
  38 rec definition length2 (A1,A2:Type[0]) (l:list2 A1 A2) on l ≝ match l with
  39 [ nil2        ⇒ 0
  40 | cons2 _ _ l ⇒ ⫯(length2 A1 A2 l)
  41 ].
  42
  43 interpretation "length (list of pairs)"
  44    'card l = (length2 ? ? l).