matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.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 "delayed_updating/syntax/path_depth.ma".
  16 include "delayed_updating/syntax/path_structure.ma".
  17 include "delayed_updating/syntax/path_balanced.ma".
  18 include "delayed_updating/substitution/fsubst.ma".
  19 include "delayed_updating/substitution/lift_preterm.ma".
  20 include "delayed_updating/notation/relations/black_rightarrow_f_4.ma".
  21
  22 (* IMMEDIATE FOCUSED REDUCTION ************************************************)
  23
  24 inductive ifr (p) (q) (t): predicate preterm ≝
  25 | ifr_beta (b):
  26   let r ≝ p●𝗔◗b●𝗟◗q in
  27   r◖𝗱(↑❘q❘) ϵ t → ⊓(⊗b) → ifr p q t (t[⋔r←↑[𝐮❨↑❘q❘❩]t⋔(p◖𝗦)])
  28 .
  29
  30 interpretation
  31   "focused balanced reduction with immediate updating (preterm)"
  32   'BlackRightArrowF t1 p q t2 = (ifr p q t1 t2).