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/downspoon_2.ma".
  16 include "ground/lib/stream_eq.ma".
  17
  18 (* HEAD AND TAIL FOR STREAMS ************************************************)
  19
  20 definition stream_hd (A:Type[0]): stream A → A ≝
  21            λt. match t with [ stream_cons a _ ⇒ a ].
  22
  23 definition stream_tl (A:Type[0]): stream A → stream A ≝
  24            λt. match t with [ stream_cons _ t ⇒ t ].
  25
  26 interpretation
  27   "tail (streams)"
  28   'DownSpoon A t = (stream_tl A t).
  29
  30 (* Basic constructions ******************************************************)
  31
  32 lemma stream_hd_cons (A) (a) (t):
  33       a = stream_hd A (a⨮t).
  34 // qed.
  35
  36 lemma stream_tl_cons (A) (a) (t):
  37       t = ⫰{A}(a⨮t).
  38 // qed.
  39
  40 lemma eq_stream_split_hd_tl (A) (t):
  41       stream_hd … t ⨮ ⫰t ≗{A} t.
  42 #A * //
  43 qed.