module Core.Term

import Core.Context
import Core.Var
import Core.Thinning

%prefix_record_projections off

-- Definition ------------------------------------------------------------------

public export
data Term : Context -> Type where
  Var : Var sx -> Term sx

  Set : Term sx

  Pi : (n : Name) -> Term sx -> Term (sx :< n) -> Term sx
  Abs : (n : Name) -> Term (sx :< n) -> Term sx
  App : Term sx -> Term sx -> Term sx

%name Term t, u, v

-- Operations ------------------------------------------------------------------

public export
wkn : Term sx -> sx `Thins` sy -> Term sy
wkn (Var i) thin = Var $ wkn i thin
wkn Set thin = Set
wkn (Pi n t u) thin = Pi n (wkn t thin) (wkn u $ keep thin n)
wkn (Abs n t) thin = Abs n (wkn t $ keep thin n)
wkn (App t u) thin = App (wkn t thin) (wkn u thin)