data Bool : Type where
     False : Bool
     True : Bool

not : Bool -> Bool
not False = True
not True = False

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

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

data Vect : ? -> Type -> Type where
     Nil : Vect Z a
     Cons : a -> Vect k a -> Vect (S k) a

data Fin : Nat -> Type where
     FZ : Fin (S k)
     FS : Fin k -> Fin (S k)

lookup : Fin n -> Vect n a -> a
lookup FZ (Cons x xs) = x
lookup (FS k) (Cons x xs) = lookup k xs

lookup' : Fin n -> Vect n a -> a
lookup' (FS k) (Cons x xs) = lookup' k xs

lookup'' : Fin n -> Vect n a -> a
lookup'' n xs = lookup' n xs