matita/matita/contribs/lambdadelta/basic_2/relocation/frees.ma

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  14
  15 include "basic_2/notation/relations/freestar_3.ma".
  16 include "basic_2/grammar/trace_sor.ma".
  17 include "basic_2/grammar/lenv.ma".
  18
  19 (* CONTEXT-SENSITIVE FREE VARIABLES *****************************************)
  20
  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
  37 .
  38
  39 interpretation
  40    "context-sensitive free variables (term)"
  41    'FreeStar L T cs = (frees L T cs).