matita/matita/contribs/lambdadelta/basic_2/dynamic/ypr.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/reducibility/ltpr.ma".
  16 include "basic_2/dynamic/lsubsv.ma".
  17
  18 (* "BIG TREE" PARALLEL REDUCTION FOR CLOSURES *******************************)
  19
  20 inductive ypr (h) (g) (L1) (T1): relation2 lenv term ≝
  21 | ypr_fw    : ∀L2,T2. ♯{L2, T2} < ♯{L1, T1} → ypr h g L1 T1 L2 T2
  22 | ypr_ltpr  : ∀L2. L1 ➡ L2 → ypr h g L1 T1 L2 T1
  23 | ypr_cpr   : ∀T2. L1 ⊢ T1 ➡ T2 → ypr h g L1 T1 L1 T2
  24 | ypr_ssta  : ∀T2,l. ⦃h, L1⦄ ⊢ T1 •[g, l + 1] T2 → ypr h g L1 T1 L1 T2
  25 | ypr_lsubsv: ∀L2. h ⊢ L2 ⊩:⊑[g] L1 → ypr h g L1 T1 L2 T1
  26 .
  27
  28 interpretation
  29    "'big tree' parallel reduction (closure)"
  30    'BTPRed h g L1 T1 L2 T2 = (ypr h g L1 T1 L2 T2).
  31
  32 (* Basic properties *********************************************************)
  33
  34 lemma ypr_refl: ∀h,g. bi_reflexive … (ypr h g).
  35 /2 width=1/ qed.