data Nat : Type where
	Zero : Nat
  	Succ : (n:Nat) -> Nat

plus : Nat -> Nat -> Nat
plus Zero y = y
plus (Succ x) y = Succ (plus x y)

pred : Nat -> Nat
pred Zero = Zero
pred (Succ n) = n

natToInt : Nat -> Int
natToInt Zero = 0
natToInt (Succ n) = 1 + natToInt n

plus : Nat -> Nat -> Nat
plus Zero y = y
plus (Succ x) y = Succ (plus x y)

intToNat : Int -> Nat
intToNat n = if n == 0 then Zero else Succ (intToNat (n-1))