matita/matita/contribs/lambdadelta/apps_2/models/tm.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 "basic_2/rt_equivalence/cpcs.ma".
  16 include "apps_2/functional/mf.ma".
  17 include "apps_2/models/model.ma".
  18
  19 (* TERM MODEL ***************************************************************)
  20
  21 definition tm_dd ≝ term.
  22
  23 definition tm_sq (h) (T1) (T2) ≝  ❨⋆,⋆❩ ⊢ T1 ⬌*[h] T2.
  24
  25 definition tm_sv (s) ≝ ⋆s.
  26
  27 definition tm_co (p) (V) (T) ≝ ⓓ[p]V.(↑[1]T).
  28
  29 definition tm_ap (V) (T) ≝ ⓐV.T.
  30
  31 definition tm_ti (gv) (lv) (T) ≝ ■[gv,lv]T.
  32
  33 definition TM (h): model ≝ mk_model … .
  34 [ @tm_dd
  35 | @(tm_sq h) |7,8: skip
  36 | @tm_sv
  37 | @tm_co
  38 | @tm_ap
  39 | @tm_ti
  40 ].
  41 defined-.
  42
  43 (* Basic properties *********************************************************)
  44
  45 lemma tm_co_rw (h) (p) (V) (T): V⊕{TM h}[p]T = ⓓ[p]V.(↑[1]T).
  46 // qed.
  47
  48 lemma tm_ti_sort (h) (gv) (lv): ∀s. ⟦⋆s⟧{TM h}[gv,lv] = sv … s.
  49 // qed.
  50
  51 lemma tm_ti_lref (h): ∀gv,lv,i. ⟦#i⟧{TM h}[gv,lv] = lv i.
  52 // qed.
  53
  54 lemma tm_ti_gref (h): ∀gv,lv,l. ⟦§l⟧{TM h}[gv,lv] = gv l.
  55 // qed.
  56
  57 lemma tm_ti_bind (h) (p) (I): ∀gv,lv,V,T.
  58                               ⟦ⓑ[p,I]V.T⟧{TM h}[gv,lv] = ⓑ[p,I]⟦V⟧[gv,lv].⟦T⟧{TM h}[⇡[0]gv,⇡[0←#0]lv].
  59 // qed.