module Core.Term

import Core.Thinning

import public Data.Fin

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

public export
data Term : Nat -> Type where
  Var : Fin n -> Term n

  Set : Term n

  Pi : Term n -> Term (S n) -> Term n
  Abs : Term (S n) -> Term n
  App : Term n -> Term n -> Term n

%name Term t, u, v

-- Weakening -------------------------------------------------------------------

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