MaybeT to transformers

[David Menendez]

On Fri, Feb 6, 2009 at 12:40 PM, Benja Fallenstein
<benja.fallenstein at gmail.com> wrote:
> On Fri, Feb 6, 2009 at 5:56 PM, Sittampalam, Ganesh
> <ganesh.sittampalam at credit-suisse.com> wrote:
>> I tend to agree that this is the right one to use, but I think care
>> should be taken when adding this to what is/is expected to be a widely
>> used package, as it could make it difficult for people who want the
>> alternate behaviour, and it might imply a degree of standardisation/
>> canonicity that is not really justified.
>>
>> On the other hand, perhaps there are no real uses for the other one.
>
> ErrorT has had the equivalent MonadPlus instance for a while, hasn't
> it? Anybody run into problems with that?

In my own monad implementations, I prefer to keep exception handling
distinct from nondeterminism. From that perspective, Maybe and MaybeT
are better suited to MonadError than MonadPlus.

There are also times where it would be nice if you could assume that
>>= distributed over mplus, as it does in a nondeterminism monad.

Let's say I have a state monad implemented using CPS.

    newtype StateT s m a = C { unC :: forall b. (a -> s -> m b) -> s -> m b }

The simple way to promote mplus is to do:

    mplus a b = C (\k s -> unC a k s `mplus` unC b k s)

But that version always distributes, regardless of what the underlying
mplus does. In particular, it does not satisfy this equation:

    lift (mplus a b) = mplus (lift a) (lift b)

So intead, you have to do something like

    mplus a b = C (\k s -> unC a (uncurry return) s `mplus` unC b
(uncurry return) s >>= curry k)

which is more complicated and involves four operations in the
underlying monad, instead of just one.



Here's an easy way to test whether a monad's mplus distributes:

    test = mplus (return 0) (return 1) >>= \x -> guard (odd x) >> return x

If the monad distributes over mplus, then test = return 1. Otherwise,
test = mzero.

-- 
Dave Menendez <dave at zednenem.com>
<http://www.eyrie.org/~zednenem/>