matita/matita/contribs/lambdadelta/ground/lib/stream_hdtl.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/notation/functions/downdashedarrow_2.ma".
  16 include "ground/lib/stream.ma".
  17
  18 (* HEAD AND TAIL FOR STREAMS ************************************************)
  19
  20 definition stream_hd (A:Type[0]): stream A → A.
  21 #A * #a #_ @a
  22 defined.
  23
  24 definition stream_tl (A:Type[0]): stream A → stream A.
  25 #A * #_ #t @t
  26 defined.
  27
  28 interpretation
  29   "tail (streams)"
  30   'DownDashedArrow A t = (stream_tl A t).
  31
  32 (* Basic constructions ******************************************************)
  33
  34 lemma stream_hd_cons (A) (a) (t):
  35       a = stream_hd A (a⨮t).
  36 // qed.
  37
  38 lemma stream_tl_cons (A) (a) (t):
  39       t = ⇣{A}(a⨮t).
  40 // qed.
  41
  42 lemma stream_split_tl (A) (t):
  43       stream_hd A t ⨮ ⇣t = t.
  44 #A * //
  45 qed.