matita/matita/contribs/lambdadelta/apps_2/models/model.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "ground_2/notation/relations/ringeq_3.ma".
  16 include "apps_2/notation/models/at_3.ma".
  17 include "apps_2/notation/models/wbrackets_4.ma".
  18 include "static_2/syntax/term.ma".
  19
  20 (* MODEL ********************************************************************)
  21
  22 record model: Type[1] ≝ {
  23    dd: Type[0];                            (* denotations domain *)
  24    sq: relation2 dd dd;                    (* structural equivalence *)
  25    sv: nat → dd;                           (* sort evaluation *)
  26    ap: dd → dd → dd;                       (* application *)
  27    ti: (nat → dd) → (nat → dd) → term → dd (* term interperpretation *)
  28 }.
  29
  30 interpretation "structural equivalence (model)"
  31    'RingEq M d1 d2 = (sq M d1 d2).
  32
  33 interpretation "application (model)"
  34    'At M d1 d2 = (ap M d1 d2).
  35
  36 interpretation "term interpretation (model)"
  37    'WBrackets M gv lv T = (ti M gv lv T).
  38
  39 definition evaluation: model → Type[0] ≝ λM. nat → dd M.