partial update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / reduction / dbfr.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr.ma
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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 "delayed_updating/substitution/fsubst.ma".
+include "delayed_updating/syntax/prototerm_constructors.ma".
+include "delayed_updating/syntax/prototerm_eq.ma".
+include "delayed_updating/syntax/path_head.ma".
+include "delayed_updating/syntax/path_balanced.ma".
+include "delayed_updating/syntax/path_structure.ma".
+include "delayed_updating/notation/relations/black_rightarrow_dbf_3.ma".
+include "ground/arith/nat_rplus.ma".
+include "ground/xoa/ex_6_5.ma".
+
+(* DELAYED BALANCED FOCUSED REDUCTION ***************************************)
+
+(**) (* explicit ninj because we cannot declare the expectd type of k *)
+definition dbfr (r): relation2 prototerm prototerm ≝
+           λt1,t2.
+           ∃∃p,b,q,h,k. p●𝗔◗b●𝗟◗q = r &
+           ⊗b ϵ 𝐁 & b = ↳[h]b &
+           (𝗟◗q) = ↳[ninj k](𝗟◗q) & r◖𝗱k ϵ t1 &
+           t1[⋔r←𝛕(k+h).(t1⋔(p◖𝗦))] ⇔ t2
+.
+
+interpretation
+  "balanced focused reduction with delayed updating (prototerm)"
+  'BlackRightArrowDBF t1 r t2 = (dbfr r t1 t2).