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/downharpoonleft_2.ma".
  16 include "ground/notation/functions/downharpoonright_2.ma".
  17 include "ground/lib/stream.ma".
  18
  19 (* HEAD AND TAIL FOR STREAMS ************************************************)
  20
  21 definition stream_hd (A:Type[0]): stream A → A.
  22 #A * #a #_ @a
  23 defined.
  24
  25 interpretation
  26   "head (streams)"
  27   'DownHarpoonLeft A t = (stream_hd A t).
  28
  29 definition stream_tl (A:Type[0]): stream A → stream A.
  30 #A * #_ #t @t
  31 defined.
  32
  33 interpretation
  34   "tail (streams)"
  35   'DownHarpoonRight A t = (stream_tl A t).
  36
  37 (* Basic constructions ******************************************************)
  38
  39 lemma stream_hd_cons (A) (a) (t):
  40       a = ⇃{A}(a⨮t).
  41 // qed.
  42
  43 lemma stream_tl_cons (A) (a) (t):
  44       t = ⇂{A}(a⨮t).
  45 // qed.
  46
  47 lemma stream_split_tl (A) (t):
  48       ⇃{A}t ⨮ ⇂t = t.
  49 #A * //
  50 qed.