Thanks for all the help, everyone.
I think this stuff is starting to come together.
Michael
--- On Sun, 5/3/09, Tillmann Rendel <ren...@cs.au.dk> wrote:
From: Tillmann Rendel <ren...@cs.au.dk>
Subject: Re: [Haskell-cafe] Combining computations
To: "michael rice" <nowg...@yahoo.com>
Cc: haskell-cafe@haskell.org
Date: Sunday, May 3, 2009, 7:33 AM
Hi,
normally, one uses monads to express and combine computations in the same
monad. However, you can convert between some monads, e.g. from Maybe to List:
import Data.Maybe (maybeToList)
> let m1 = Nothing
> let m2 = [1]
> let m3 = maybeToList m1 `mplus` m2
> let m1 = Just 1
> let m2 = []
> let m3 = maybeToList m1 `mplus` m2
In fact, you can convert from Maybe to any MonadPlus.
maybeToMonadPlus Nothing = mzero
maybeToMonadPlus (Just x) = return x
And you can convert from List to any MonadPlus:
listToMonadPlus Nothing = []
listToMonadPlus (x : xs) = return x `mplus` listToMonadPlus xs
Now you should be able to do:
m1 = maybeToMonadPlus (Just 1)
m2 = listtoMonadPlus [2, 3]
m3 = m1 `mplus` m2 :: Just Int -- Just 1
m4 = m1 `mplus` m2 :: [Int] -- [1, 2, 3]
The reason this is possible is that Maybe and List do not support additional
effects beyond what is common to all MonadPlus instances.
Another option is to never specify which monad your computations are in in the
first place. Instead, only specify which computational effects the monad should
support.
m1 = mzero :: MonadPlus m => m a
m2 = return 1 :: (Monad m, Num a) => m a
m3 = m1 `mplus` m2 `mplus` Just 2 -- Just 1
m4 = m1 `mplus` m2 `mplus` [2, 3] -- [1, 2, 3]
In this version, m1 and m2 are polymorphic computations, which can be used
together with List computations, Maybe computations, or any other MonadPlus
instances. m1 needs MonadPlus, while m2 is happy with any Monad instance. This
fact is encoded in their type.
Tillmann
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