{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE UndecidableInstances #-}
module ReflectOrd where
import Data.Reflection
import Data.Proxy

newtype Ordable s a = Ordable { unordable :: a }

instance Reifies s (a -> a -> Ordering) => Eq (Ordable s a) where
  Ordable a == Ordable b = reflect (Proxy :: Proxy s) a b == EQ

instance Reifies s (a -> a -> Ordering) => Ord (Ordable s a) where
  compare (Ordable a) (Ordable b) = reflect (Proxy :: Proxy s) a b

f :: forall a x y. (Functor x, Functor y) => (a -> a -> Ordering) -> (forall b. Ord b => x b -> y b) -> x a -> y a
f f g xs =
  reify f $ \(Proxy :: Proxy s) ->
    fmap unordable (g (fmap (\x -> Ordable x :: Ordable s a) xs))