matita/matita/lib/lambda/terms/size.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 "lambda/terms/relocation.ma".
  16 include "basics/core_notation/card_1.ma".
  17
  18 (* SIZE *********************************************************************)
  19
  20 (* Note: this gives the number of abstractions and applications in M *)
  21 let rec size M on M ≝ match M with
  22 [ VRef i   ⇒ 0
  23 | Abst A   ⇒ size A + 1
  24 | Appl B A ⇒ (size B) + (size A) + 1
  25 ].
  26
  27 interpretation "term size"
  28    'card M = (size M).
  29
  30 lemma size_lift: ∀h,M,d. |↑[d, h] M| = |M|.
  31 #h #M elim M -M normalize //
  32 qed.