[Haskell-cafe] Composing monads (sort of)

[Pepe Iborra]

Wait, there are two monads in scene here, IO and Maybe.
The right solution is to compose them indeed. One could use the  
MaybeT monad transformer defined in the 'All about monads' tutorial 
[1], or we could just define the IOmaybe monad:

 > import Data.Traversable (mapM)
 >
 > newtype IOMaybe a = IOM { iom :: IO (Maybe a) }
 >
 > instance Monad IOMaybe where
 >     return = IOM . return . Just
 >     c >>= f = IOM$ do
 >        mb_v <- iom c
 >        mapM (iom.f) mb_v >>= return . join

Now we can define:

 > t1 = IOM . return . f1
 > t2 = IOM . f2
 > t3 = IOM . return . f3
 > traverse rec1 = t1 rec1 >>= t2 >>= t3

And this scheme lends itself very well to define any kind of traversal.
Note that I used the more general version of mapM defined in  
Data.Traversable in the definition of the (>>=) combinator. A more  
conventional definition is given the 'All about monads' tutorial.

Cheers
pepe

1- http://www.nomaware.com/monads/html/index.html

On 16/12/2006, at 15:35, Chris Eidhof wrote:

> Hey Mark,
>
>> How can I concisely compose these functions without having to  
>> write a cascade of case statements such as:
>>
>> case f1 rec1 of
>>     Nothing -> return Nothing
>>     Just id1 -> do
>>                     rec2 <- f2 id2
>>                     return $ case rec2 of
>>                                 Nothing -> return Nothing
>>                                 Just rec2' -> case f3 rec2' of
>>                                                 ....
>> I understand that if I was just dealing with Maybe I could use the  
>> fact that Maybe is a monad.
> Yes, you can write like this:
>
>> id2 <- f1 rec1
>> rec2 <- f2 id2
>> rec3 <- f3 rec2
>> return rec3
> or, even shorter:
>> id2 <- f1 rec1
>> rec2 <- f2 id2
>> f3 rec2
>
> The cool thing of the Maybe monad is that it combines a result in  
> such a way that it removes the plumbing of constantly checking for  
> Nothing. I can definitely recommand you the following tutorials:
>
> http://www.nomaware.com/monads/html/index.html
> http://uebb.cs.tu-berlin.de/~magr/pub/Transformers.en.html
>
> Those two tutorials really helped me.
>
> Good luck,
> Chris
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