refactoring to park the notions:

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / scpds.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/scpds.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/scpds.ma
new file mode 100644 (file)
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@@ -0,0 +1,48 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2/notation/relations/dpredstar_7.ma".
+include "basic_2/static/da.ma".
+include "basic_2/computation/cprs.ma".
+
+(* STRATIFIED DECOMPOSED PARALLEL COMPUTATION ON TERMS **********************)
+
+definition scpds: ∀h. sd h → nat → relation4 genv lenv term term ≝
+                  λh,o,d2,G,L,T1,T2.
+                  ∃∃T,d1. d2 ≤ d1 & ⦃G, L⦄ ⊢ T1 ▪[h, o] d1 & ⦃G, L⦄ ⊢ T1 •*[h, d2] T & ⦃G, L⦄ ⊢ T ➡* T2.
+
+interpretation "stratified decomposed parallel computation (term)"
+   'DPRedStar h o d G L T1 T2 = (scpds h o d G L T1 T2).
+
+(* Basic properties *********************************************************)
+
+lemma sta_cprs_scpds: ∀h,o,G,L,T1,T,T2,d. ⦃G, L⦄ ⊢ T1 ▪[h, o] d+1 → ⦃G, L⦄ ⊢ T1 •*[h, 1] T →
+                      ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, o, 1] T2.
+/2 width=6 by ex4_2_intro/ qed.
+
+lemma lstas_scpds: ∀h,o,G,L,T1,T2,d1. ⦃G, L⦄ ⊢ T1 ▪[h, o] d1 →
+                   ∀d2. d2 ≤ d1 → ⦃G, L⦄ ⊢ T1 •*[h, d2] T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, o, d2] T2.
+/2 width=6 by ex4_2_intro/ qed.
+
+lemma scpds_strap1: ∀h,o,G,L,T1,T,T2,d.
+                    ⦃G, L⦄ ⊢ T1 •*➡*[h, o, d] T → ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, o, d] T2.
+#h #o #G #L #T1 #T #T2 #d * /3 width=8 by cprs_strap1, ex4_2_intro/
+qed.
+
+(* Basic forward lemmas *****************************************************)
+
+lemma scpds_fwd_cprs: ∀h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 •*➡*[h, o, 0] T2 →
+                      ⦃G, L⦄ ⊢ T1 ➡* T2.
+#h #o #G #L #T1 #T2 * /3 width=3 by cprs_strap2, lstas_cpr/
+qed-.