By the way, you can use this stuff to solve the restricted monad problem (e.g. make Set an instance of Monad). This is not that useful until we find out what the mother of all MonadPlus is, though, because we really need a MonadPlus Set instance. Code below. Cheers, Max \begin{code} {-# LANGUAGE RankNTypes #-} import Control.Applicative import Data.Set (Set) import qualified Data.Set as S newtype CodensityOrd m a = CodensityOrd { runCodensityOrd :: forall b. Ord b => (a -> m b) -> m b } -- liftCodensityOrd :: Monad m => m a -> CodensityOrd m a -- liftCodensityOrd m = CodensityOrd ((>>=) m) -- lowerCodensityOrd :: (Ord a, Monad m) => CodensityOrd m a -> m a -- lowerCodensityOrd m = runCodensityOrd m return instance Functor (CodensityOrd f) where fmap f m = CodensityOrd (\k -> runCodensityOrd m (k . f)) instance Applicative (CodensityOrd f) where pure x = CodensityOrd (\k -> k x) mf <*> mx = CodensityOrd (\k -> runCodensityOrd mf (\f -> runCodensityOrd mx (\x -> k (f x)))) instance Monad (CodensityOrd f) where return = pure m >>= k = CodensityOrd (\c -> runCodensityOrd m (\a -> runCodensityOrd (k a) c)) liftSet :: Ord a => Set a -> CodensityOrd Set a liftSet m = CodensityOrd (bind m) where bind :: (Ord a, Ord b) => Set a -> (a -> Set b) -> Set b mx `bind` fxmy = S.fold (\x my -> fxmy x `S.union` my) S.empty mx lowerSet :: Ord a => CodensityOrd Set a -> Set a lowerSet m = runCodensityOrd m S.singleton main = print $ lowerSet $ monadicPlus (liftSet $ S.fromList [1, 2, 3]) (liftSet $ S.fromList [1, 2, 3]) monadicPlus :: Monad m => m Int -> m Int -> m Int monadicPlus mx my = do x <- mx y <- my return (x + y) \end{code}