Hi Max, very interesting observations!
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.
I'm not sure whether this is TMOA MonadPlus, but here is a set monad with MonadPlus instance (code below). Cheers, Sebastian \begin{code} {-# LANGUAGE RankNTypes #-} module SetMonad where import Data.Set ( Set ) import qualified Data.Set as Set import Control.Monad ( MonadPlus(..) ) newtype SetMonad a = SetMonad { (>>-) :: forall b . Ord b => (a -> Set b) -> Set b } fromSet :: Set a -> SetMonad a fromSet = Set.fold (mplus . return) mzero toSet :: Ord a => SetMonad a -> Set a toSet s = s >>- Set.singleton instance Monad SetMonad where return x = SetMonad ($x) a >>= f = SetMonad (\k -> a >>- \x -> f x >>- k) instance MonadPlus SetMonad where mzero = SetMonad (\_ -> Set.empty) a `mplus` b = SetMonad (\k -> Set.union (a >>- k) (b >>- k)) \end{code} -- Underestimating the novelty of the future is a time-honored tradition. (D.G.)