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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/term_vector.ma".
+include "basic_2/grammar/genv.ma".
+
+(* REDUCTION AND TYPE MACHINE ***********************************************)
+
+(* machine local environment *)
+inductive xenv: Type[0] ≝
+| XAtom: xenv                                    (* empty *)
+| XQuad: xenv → bind2 → nat → xenv → term → xenv (* entry *)
+.
+
+interpretation "atom (ext. local environment)"
+   'Star = XAtom.
+
+interpretation "environment construction (quad)"
+   'DxItem4 L I u K V = (XQuad L I u K V).
+
+(* machine stack *)
+definition stack: Type[0] ≝ list2 xenv term.
+
+(* machine status *)
+record rtm: Type[0] ≝
+{ rg: genv;  (* global environment *)
+  ru: nat;   (* current de Bruijn's level *)
+  re: xenv;  (* extended local environment *)
+  rs: stack; (* application stack *)
+  rt: term   (* code *)
+}.
+
+(* initial state *)
+definition rtm_i: genv → term → rtm ≝
+                  λG,T. mk_rtm G 0 (⋆) (⟠) T.
+
+(* update code *)
+definition rtm_t: rtm → term → rtm ≝
+                  λM,T. match M with
+                  [ mk_rtm G u E _ _ ⇒ mk_rtm G u E (⟠) T
+                  ].
+
+(* update closure *)
+definition rtm_u: rtm → xenv → term → rtm ≝
+                  λM,E,T. match M with
+                  [ mk_rtm G u _ _ _ ⇒ mk_rtm G u E (⟠) T
+                  ].
+
+(* get global environment *)
+definition rtm_g: rtm → genv ≝
+                  λM. match M with
+                  [ mk_rtm G _ _ _ _ ⇒ G
+                  ].
+
+(* get local reference level *)
+definition rtm_l: rtm → nat ≝
+                  λM. match M with
+                  [ mk_rtm _ u E _ _ ⇒ match E with
+                     [ XAtom           ⇒ u
+                     | XQuad _ _ u _ _ ⇒ u
+                     ]
+                  ].
+
+(* get stack *)
+definition rtm_s: rtm → stack ≝
+                  λM. match M with
+                  [ mk_rtm _ _ _ S _ ⇒ S
+                  ].
+
+(* get code *)
+definition rtm_c: rtm → term ≝
+                  λM. match M with
+                  [ mk_rtm _ _ _ _ T ⇒ T
+                  ].