ParametrizedOrd.hs

{-# LANGUAGE MultiParamTypeClasses, ScopedTypeVariables #-}

import Prelude hiding (compare)

data Order f = Lt | Gt | Eq

class OrdI a f where
    compare :: a -> a -> Order f -- Could use a proxy too

data IntOrd

instance OrdI Int IntOrd where
    compare x y
        | x == y = Eq
        | x <  y = Lt
        | x >  y = Gt

data FlippedIntOrd

instance OrdI Int FlippedIntOrd where
    compare x y
        | x == y = Eq
        | x <  y = Gt
        | x >  y = Lt

data Minimizer f a = Minimizer a deriving Show

combine :: forall a f . OrdI a f => Minimizer f a -> Minimizer f a -> Minimizer f a
combine (Minimizer x) (Minimizer y) = case compare x y :: Order f of
    Lt -> Minimizer x
    Eq -> Minimizer x
    Gt -> Minimizer y

main = do
    print $ combine (Minimizer 0) (Minimizer 1 :: Minimizer IntOrd Int)
    print $ combine (Minimizer 0) (Minimizer 1 :: Minimizer FlippedIntOrd Int)