initial definition of λδ model

[helm.git] / matita / matita / contribs / lambdadelta / apps_2 / models / model.ma

diff --git a/matita/matita/contribs/lambdadelta/apps_2/models/model.ma b/matita/matita/contribs/lambdadelta/apps_2/models/model.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 "ground_2/notation/relations/ringeq_3.ma".
+include "apps_2/notation/models/at_3.ma".
+include "apps_2/notation/models/wbrackets_4.ma".
+include "basic_2/syntax/term.ma".
+
+(* MODEL ********************************************************************)
+
+record model: Type[1] ≝ {
+   dd: Type[0];                            (* denotations domain *)
+   sq: relation2 dd dd;                    (* structural equivalence *)
+   sv: nat → dd;                           (* sort evaluation *)
+   ap: dd → dd → dd;                       (* application *)
+   ti: (nat → dd) → (nat → dd) → term → dd (* term interperpretation *)
+}.
+
+interpretation "structural equivalence (model)"
+   'RingEq M d1 d2 = (sq M d1 d2).
+
+interpretation "application (model)"
+   'At M d1 d2 = (ap M d1 d2).
+
+interpretation "term interpretation (model)"
+   'WBrackets M gv lv T = (ti M gv lv T).
+
+definition evaluation: model → Type[0] ≝ λM. nat → dd M.