matita/matita/contribs/lambda-delta/Basic-2/reduction/cpr.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/reduction/tpr.ma".
  16
  17 (* CONTEXT-SENSITIVE PARALLEL REDUCTION ON TERMS ****************************)
  18
  19 definition cpr: lenv → term → term → Prop ≝
  20    λL,T1,T2. ∃∃T. T1 ⇒ T & L ⊢ T [0, |L|] ≫ T2.
  21
  22 interpretation
  23    "context-sensitive parallel reduction (term)"
  24    'PRed L T1 T2 = (cpr L T1 T2).
  25
  26 (* Basic properties *********************************************************)
  27
  28 lemma cpr_pr: ∀T1,T2. T1 ⇒ T2 → ∀L. L ⊢ T1 ⇒ T2.
  29 /2/ qed.
  30
  31 lemma cpr_tps: ∀L,T1,T2,d,e. L ⊢ T1 [d, e] ≫ T2 → L ⊢ T1 ⇒ T2.
  32 /3 width=5/ qed.
  33
  34 lemma cpr_refl: ∀L,T. L ⊢ T ⇒ T.
  35 /2/ qed.
  36
  37 (* NOTE: new property *)
  38 lemma cpr_flat: ∀I,L,V1,V2,T1,T2.
  39                 L ⊢ V1 ⇒ V2 → L ⊢ T1 ⇒ T2 → L ⊢ 𝕗{I} V1. T1 ⇒ 𝕗{I} V2. T2.
  40 #I #L #V1 #V2 #T1 #T2 * #V #HV1 #HV2 * /3 width=5/
  41 qed.
  42
  43 lemma cpr_delta: ∀L,K,V1,V2,V,i.
  44                  ↓[0, i] L ≡ K. 𝕓{Abbr} V1 → K ⊢ V1 [0, |L| - i - 1] ≫ V2 →
  45                  ↑[0, i + 1] V2 ≡ V → L ⊢ #i ⇒ V.
  46 #L #K #V1 #V2 #V #i #HLK #HV12 #HV2
  47 @ex2_1_intro [2: // | skip ] /3 width=8/ (**) (* /4/ is too slow *)
  48 qed.
  49
  50 lemma cpr_cast: ∀L,V,T1,T2.
  51                 L ⊢ T1 ⇒ T2 → L ⊢ 𝕗{Cast} V. T1 ⇒ T2.
  52 #L #V #T1 #T2 * /3/
  53 qed.
  54
  55 (* Basic inversion lemmas ***************************************************)