List as a newtype, using products and sums

Lists.hs

{-# LANGUAGE TypeOperators #-}

data (:+:) a b
  = Inl a
  | Inr b

data (:*:) a b
  = a :*: b

data One = One

newtype List a = List (One :+: (a :*: List a))

nil :: List a
nil = List $ Inl One

cons :: a -> List a -> List a
cons x xs = List $ Inr $ (x :*: xs)

sumList :: List Int -> Int
sumList (List (Inl One)) = 0
sumList (List (Inr (n :*: xs))) = n + sumList xs

-- > sumList (cons 1 (cons 2 (cons 3 nil)))
-- 6