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/oplus_4.ma".
  18 include "apps_2/notation/models/wbrackets_4.ma".
  19 include "static_2/syntax/term.ma".
  20
  21 (* MODEL ********************************************************************)
  22
  23 record model: Type[1] ≝ {
  24 (* Note: denotations domain *)
  25    dd: Type[0];
  26 (* Note: structural equivalence *)
  27    sq: relation2 dd dd;
  28 (* Note: sort evaluation *)
  29    sv: nat → dd;
  30 (* Note: conjunction *)
  31    co: bool → dd → dd → dd;
  32 (* Note: application *)
  33    ap: dd → dd → dd;
  34 (* Note: term interperpretation *)
  35    ti: (nat → dd) → (nat → dd) → term → dd
  36 }.
  37
  38 interpretation "structural equivalence (model)"
  39    'RingEq M d1 d2 = (sq M d1 d2).
  40
  41 interpretation "application (model)"
  42    'At M d1 d2 = (ap M d1 d2).
  43
  44 interpretation "conjunction (model)"
  45    'OPlus M p d1 d2 = (co M p d1 d2).
  46
  47 interpretation "term interpretation (model)"
  48    'WBrackets M gv lv T = (ti M gv lv T).
  49
  50 definition evaluation: model → Type[0] ≝ λM. nat → dd M.