[Haskell-cafe] Name for the following combinators?

[Tom Ellis]

On Sat, Dec 28, 2013 at 04:13:52PM +0000, Tom Ellis wrote:
> 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.

In fact, since is is 'n' that requires the 'Monad' constraint, I suspect
you'll need to swap the order of the type arguments to get a monad
transformer:

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

Anyway, my main point remains: your first check should be whether what you
have can be captured as a genuine monad.


> import Control.Monad.Trans (MonadTrans, lift)
> import Control.Monad (join)
> 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
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