Re: [Haskell-cafe] monadic plumbing

From: Alberto G. Corona Sent: Tue, February 22, 2011 3:03:56 PM

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. ... to summarize, given:

foo, : a -> m (Maybe b) bar : b -> m (Maybe c) baz : c -> m (Maybe d)

how to compose foo bar and baz? Or, at least, Are something out there to handle

it in the less painful way?.

Control.Monad.Trans.Maybe.MaybeT from mtl is defined as newtype MaybeT m a = MaybeT { runMaybeT :: m (Maybe a) } with (among others), instance Monad m => Monad (MaybeT m)

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)

The standard construction uses a distributive law - if you have an operation distribute :: n (m a) -> m (n a), then you can make m around n into a monad by m (n (m (n a))) == by fmap distribute => m (m (n (n a))) == by join (for m) => m (n (n a)) == by fmap join (n's join) => m (n a) Here, that's a function Maybe (m a) -> m (Maybe a), which can be distribute (Just ma) = fmap Just ma distribute Nothing = return Nothing Brandon