matita/matita/contribs/lambda/terms/length.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 "terms/lift.ma".
  16
  17 (* LENGTH *******************************************************************)
  18
  19 (* Note: this gives the number of abstractions and applications in M *)
  20 let rec length M on M ≝ match M with
  21 [ VRef i   ⇒ 0
  22 | Abst A   ⇒ length A + 1
  23 | Appl B A ⇒ (length B) + (length A) + 1
  24 ].
  25
  26 interpretation "term length"
  27    'card M = (length M).
  28
  29 lemma length_lift: ∀h,M,d. |↑[d, h] M| = |M|.
  30 #h #M elim M -M normalize //
  31 qed.