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.)
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