[Haskell-cafe] Re: The mother of all functors/monads/categories

[Sebastian Fischer]

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}


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