matita/matita/contribs/lambdadelta/ground_2/lib/streams_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_2/lib/streams.ma".
  16 include "ground_2/lib/arith.ma".
  17
  18 (* STREAMS ******************************************************************)
  19
  20 definition hd (A:Type[0]): stream A → A ≝
  21               λt. match t with [ seq a _ ⇒ a ].
  22
  23 definition tl (A:Type[0]): stream A → stream A ≝
  24               λt. match t with [ seq _ t ⇒ t ].
  25
  26 let rec tln (A:Type[0]) (i:nat) on i: stream A → stream A ≝ ?.
  27 cases i -i [ #t @t | #i * #_ #t @(tln … i t) ]
  28 qed.
  29
  30 (* basic properties *********************************************************)
  31
  32 lemma eq_stream_split (A) (t): (hd … t) @ (tl … t) ≐⦋A⦌ t.
  33 #A * //
  34 qed.