[Haskell-cafe] MonadPlus

[Derek Elkins]

On Fri, 2008-05-09 at 12:48 -0700, Bryan O'Sullivan wrote:
> Andrew Coppin wrote:
> > But here's a
> > question: what is the purpose of the MonadPlus class?
> 
> It gives you a way of working with monads as monoids. 

I find this description mostly useless.  Monads form monoids without
being MonadPlus.

instance Monad m => Monoid (m ()) where
    mempty = return ()
    mappend = (<<)

You can form monoids out of Kleisli arrows,

instance Monad m => Monoid (a -> m a) where
    mempty = return
    mappend = (<=<)

You could form monads into a monoid in another way,

instance (Monad m, Monoid a) => Monoid (m a)
    mempty = return mempty
    mappend = liftM2 mappend

So "It gives you a way of working with monads as monoids." is
significantly underspecified and doesn't actually say what MonadPlus
means, let alone what it is intended for.

A more interesting statement in that vein is:
It gives you a way of working with monads as (distributive) near-rigs.

This statement does actually encode some (all?) of the intended meaning
of MonadPlus, e.g. mzero is intended to be a zero of (>>) beyond simply
being a unit for mplus.