[Haskell-cafe] Re: what is inverse of mzero and return?

[Daniel Fischer]

Am Sonntag, 23. Januar 2005 15:58 schrieb Jorge Adriano Aires:
>
> I'm not arguing that definition would be "wrong". It is a monoid. This is
> the instance for ():
>
> instance MonadPlus() where
>   mzero = ()
>   mplus a b = ()
>
Maybe I'm stupid, but:
class Monad m => MonadPlus m where
    mzero :: m a
    mplus :: m a -> m a -> m a

How does () fit into this, () isn't of kind * -> *, as far as I know
() Int is meaningless -- just checked, gives Kind Error.
>
> And this would be "correct" too:
>
> instance MonadPlus Maybe where
>   mzero = Nothing
>   mplus a b = Nothing
>> instance MonadPlus [] where
>   mzero = []
>   mplus a b = []
>
Both aren't correct, since mzero `mplus` x == x
doesn't hold (they're syntactically correct, though).

> Which are not really useful. I'm claiming that the fact that Maybe is a
> trivial Monoid doesn't mean we should "dumb" down other instances, like the
> one on lists. The usual definition of Monoid on lists is [] as identity and
> ++ as the monoid operation. That is how it's defined  in class monoid, and
> I expect this relation to hold:
>
> instance MonadPlus m => Monoid (m a) where
>    mempty = mzero
>    mappend = mplus
>
> > >Then, I'd say you're not thinking of monadic sums, but of catching
> > > errors, and the appropriate place for that is the class MonadError.
> >
> > I am thinking about how some monads are summed - like Maybe and
> > the Parser monad.
>
> But, this is not how monadic parsers are summed. Just look into the instace
> of MonadError for Text.ParserCombinators.ReadP.P. Again it would be the
> case for parsers that would return just one possible parsing, but not for
> parsers that return [(a,String)].
>
> J.A.
>
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Daniel