streams.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/constructors/cons_2.ma".
  16 include "ground_2/lib/relations.ma".
  17
  18 (* STREAMS ******************************************************************)
  19
  20 coinductive stream (A:Type[0]): Type[0] ≝
  21 | seq: A → stream A → stream A
  22 .
  23
  24 interpretation "cons (nstream)" 'Cons b t = (seq ? b t).
  25
  26 (* Basic properties *********************************************************)
  27
  28 lemma stream_rew (A) (t:stream A): match t with [ seq a u ⇒ a @ u ] = t.
  29 #A * //
  30 qed.