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/notation/functions/drop_1.ma".
  16 include "ground_2/lib/streams_eq.ma".
  17 include "ground_2/lib/arith.ma".
  18
  19 (* STREAMS ******************************************************************)
  20
  21 definition hd (A:Type[0]): stream A → A ≝
  22               λt. match t with [ seq a _ ⇒ a ].
  23
  24 definition tl (A:Type[0]): stream A → stream A ≝
  25               λt. match t with [ seq _ t ⇒ t ].
  26
  27 interpretation "tail (streams)" 'Drop t = (tl ? t).
  28
  29 (* basic properties *********************************************************)
  30
  31 lemma hd_rew (A) (a) (t): a = hd A (a@t).
  32 // qed.
  33
  34 lemma tl_rew (A) (a) (t): t = tl A (a@t).
  35 // qed.
  36
  37 lemma eq_stream_split (A) (t): (hd … t) @ ↓t ≐⦋A⦌ t.
  38 #A * //
  39 qed.