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11 (*        v         GNU General Public License Version 2                  *)
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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.