matita/matita/contribs/lambda_delta/basic_2/grammar/term_weight.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 "basic_2/grammar/term.ma".
  16
  17 (* WEIGHT OF A TERM *********************************************************)
  18
  19 let rec tw T ≝ match T with
  20 [ TAtom _     ⇒ 1
  21 | TPair _ V T ⇒ tw V + tw T + 1
  22 ].
  23
  24 interpretation "weight (term)" 'Weight T = (tw T).
  25
  26 (* Basic properties *********************************************************)
  27
  28 (* Basic_1: was: tweight_lt *)
  29 lemma tw_pos: ∀T. 1 ≤ #{T}.
  30 #T elim T -T //
  31 qed.
  32
  33 (* Basic eliminators ********************************************************)
  34
  35 axiom tw_ind: ∀R:predicate term.
  36               (∀T2. (∀T1. #{T1} < #{T2} → R T1) → R T2) →
  37               ∀T. R T.
  38
  39 (* Basic_1: removed theorems 11:
  40             wadd_le wadd_lt wadd_O weight_le weight_eq weight_add_O
  41             weight_add_S tlt_trans tlt_head_sx tlt_head_dx tlt_wf_ind
  42             removed local theorems 1: q_ind
  43 *)