- degree-based equivalene for terms

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / fpa / gcp.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/fpa/gcp.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/fpa/gcp.etc
new file mode 100644 (file)
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/grammar/genv.ma".
+include "basic_2/multiple/fpas.ma".
+
+(* GENERIC COMPUTATION PROPERTIES *******************************************)
+
+definition candidate: Type[0] ≝ relation3 genv lenv term.
+
+definition CP0 ≝ λRR:relation4 genv lenv term term. λRS:relation term.
+                 ∀G,L1,L2,T1,T2,s. ⦃L1, T1⦄ ⇳[s] ⦃L2, T2⦄ →
+                 NF … (RR G L1) RS T1 → NF … (RR G L2) RS T2.
+
+definition CP0s ≝ λRR:relation4 genv lenv term term. λRS:relation term.
+                  ∀G,L1,L2,T1,T2,s. ⦃L1, T1⦄ ⇳*[s] ⦃L2, T2⦄ →
+                  NF … (RR G L1) RS T1 → NF … (RR G L2) RS T2.
+
+definition CP1 ≝ λRR:relation4 genv lenv term term. λRS:relation term.
+                 ∀G,L. ∃k. NF … (RR G L) RS (⋆k).
+
+definition CP2 ≝ λRP:candidate.
+                 ∀G,L,T,k. RP G L (ⓐ⋆k.T) → RP G L T.
+
+(* requirements for generic computation properties *)
+record gcp (RR:relation4 genv lenv term term) (RS:relation term) (RP:candidate) : Prop ≝
+{ cp0: CP0 RR RS;
+  cp1: CP1 RR RS;
+  cp2: CP2 RP
+}.
+
+(* Basic properties *********************************************************)
+
+(* Basic_1: was just: nf2_lift1 *)
+lemma gcp_fpas: ∀RR,RS. CP0 RR RS → CP0s RR RS.
+#RR #RS #HRR #G #L1 #L2 #T1 #T2 #s #H @(fpas_ind … H) -L2 -T2 /3 width=5 by/
+qed.