# [Haskell-cafe] Combining computations

Tillmann Rendel rendel at cs.au.dk
Sun May 3 07:33:31 EDT 2009

```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
```