Typeclasses as datatypes

typeclass.hs

-- Standard Prelude definitions
-- data Ordering = LT | EQ | GT
-- class Eq a => Ord a where
--   compare :: a -> a -> Ordering

isOrdered :: Ord a => [a] -> Bool
isOrdered (x:y:xs) = case compare x y of
    GT -> False
    _  -> isOrdered (y:xs)
isOrdered _ = True

-- isOrdered [1,2,3] = True
-- isOrdered [3,3,1] = False


-- *But* we could also define a datatype for the "Ord" typeclass, and pass
-- the instances as arguments.

newtype Ord' a = Ord' (a -> a -> Ordering)

isOrdered' :: Ord' a -> [a] -> Bool
isOrdered' c@(Ord' compare) (x:y:xs) = case compare x y of
    GT -> False
    _  -> isOrdered' c (y:xs)
isOrdered' _ _ = True