data Nat : Type where
     Z : Nat
     S : Nat -> Nat

AdderTy : Nat -> Type
AdderTy Z = Nat
AdderTy (S $k) = Nat -> AdderTy k

plus : Nat -> Nat -> Nat
plus Z $y = y
plus (S $k) $y = S (plus k y)

adder : (i : Nat) -> (acc : Nat) -> AdderTy i
adder Z $acc = acc
adder (S $k) $acc = \x => adder k (plus x acc)