[Haskell-cafe] monadic plumbing

[Luke Palmer]

On Tue, Feb 22, 2011 at 2:03 PM, Alberto G. Corona <agocorona at gmail.com> wrote:
> Recently I had to navigatate trough data structures chained with mutable
> referenes in th STM monad. The problem is that their values are enveloped in
>  Either or Maybe results.
> functional compositions in the Either of Maybe , or list  monads are not
> possible when the values are  embedded inside effect monads (i.e. STM or IO)
> . I tried  to find some trick to handle it.
> to summarize, given:
>  foo, :  a -> m (Maybe b)
>  bar :   b -> m (Maybe c)
>  baz :  c -> m (Maybe d)

These are isomorphic to:

   foo :: a -> MaybeT m a

And so on (from the MaybeT package on hackage). So to compose these
three, lift them into MaybeT and then use Kleisli composition:

    MaybeT . foo >=> MaybeT . bar >=> MaybeT . baz

Luke

> how to compose foo bar and baz? Or, at least,  Are something out there to
> handle it in the less painful way?.
>
> I solved the generalized problem  (chaining  any double monadic combination)
> with a sort of monadic connector that acts as a " double monadic" operator
>>>>>==  so that
> return. return (x :: a) >>>>== foo >>>== bar >>>== baz
> can be possible. Although I don't know if  it is the best solution. I wonder
> why nobody has written about it before:
> class (Monad m, Monad n) => Bimonad m n where
>  (>>>=)   ::  n a -> (a -> m(n b)) -> m(n b)
> (>>>>==) :: (Bimonad m n) => m (n a) -> (a -> m(n b)) -> m (n b)
> (>>>>==) x  f =  x >>= \y -> y >>>=  f
> x >>>> f = x >>>>== \ _-> f
> infixl 1 >>>>==, >>>>
> The instance for handling the Maybe monad under any other monad is very
> similar to the definition of the "normal" monad:
> instance (Monad m) => Bimonad m Maybe where
>    Just x  >>>= f = f x
>    Nothing >>>= _ = return $ Nothing
>
>
>
>
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