# [Haskell-cafe] Name for the following combinators?

Tom Ellis tom-lists-haskell-cafe-2013 at jaguarpaw.co.uk
Sat Dec 28 16:13:52 UTC 2013

```On Sat, Dec 28, 2013 at 03:58:10PM +0000, Tom Ellis wrote:
> On Sat, Dec 28, 2013 at 04:47:40PM +0100, Hans Höglund wrote:
> > Recently I have found myself using these two combinators a lot: http://lpaste.net/97643
>
> FYI it looks a lot like these give rise to a monad transformer.

Specifically, the following.  Careful though: I haven't made any effort to
check this satisfies the monad or transformer laws.

If 'Wrap m n' genuinely satisfies the monad laws then you don't need new
combinators.  Just Wrap the type constructors and get a real monad.  (If
'Wrap m' is genuinely a monad transformer, so much the better!)

Tom

import qualified Data.Traversable as T
import Data.Traversable (Traversable)

data Wrap m n a = Wrap (m (n a))

unwrap :: Wrap m n a -> m (n a)
unwrap (Wrap m) = m

mbind :: (Monad m, Monad n, Functor m, Traversable n)
=> (a -> m (n b)) -> m (n a) -> m (n b)
mbind = (join .) . fmap . (fmap join .) . T.mapM

instance (Functor m, Traversable n, Monad m, Monad n) => Monad (Wrap m n)
where
return = Wrap . return . return
m >>= f = Wrap (mbind (unwrap . f) (unwrap m))

instance Monad m => MonadTrans (Wrap m) where
lift = Wrap . return
```