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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "basic_2/notation/relations/freestar_3.ma".
16 include "basic_2/grammar/trace_sor.ma".
17 include "basic_2/grammar/lenv.ma".
19 (* CONTEXT-SENSITIVE FREE VARIABLES *****************************************)
21 inductive frees: relation3 lenv term trace ≝
22 | frees_atom: ∀I. frees (⋆) (⓪{I}) (◊)
23 | frees_sort: ∀L,k,cs. frees L (⋆k) cs →
24 ∀I,T. frees (L.ⓑ{I}T) (⋆k) (Ⓕ @ cs)
25 | frees_zero: ∀L,T,cs. frees L T cs →
26 ∀I. frees (L.ⓑ{I}T) (#0) (Ⓣ @ cs)
27 | frees_lref: ∀L,i,cs. frees L (#i) cs →
28 ∀I,T. frees (L.ⓑ{I}T) (#(S i)) (Ⓕ @ cs)
29 | frees_gref: ∀L,p,cs. frees L (§p) cs →
30 ∀I,T. frees (L.ⓑ{I}T) (§p) (Ⓕ @ cs)
31 | frees_bind: ∀cv,ct,cs. cv ⋓ ct ≡ cs →
32 ∀L,V. frees L V cv → ∀I,T,b. frees (L.ⓑ{I}V) T (b @ ct) →
33 ∀a. frees L (ⓑ{a,I}V.T) cs
34 | frees_flat: ∀cv,ct,cs. cv ⋓ ct ≡ cs →
35 ∀L,V. frees L V cv → ∀T. frees L T ct →
36 ∀I. frees L (ⓕ{I}V.T) cs
40 "context-sensitive free variables (term)"
41 'FreeStar L T cs = (frees L T cs).