[Haskell-cafe] Name for the following combinators?

[Hans Höglund]

On 29 dec 2013, at 18:40, Hans Höglund wrote:

> > On Sat, Dec 28, 2013 at 5:13 PM, Tom Ellis
> > <tom-lists-haskell-cafe-2013 at jaguarpaw.co.uk> wrote:
> > > data Wrap m n a = Wrap (m (n a))
> > 
> > This is Compose [0] from traversable. It doesn't have a Monad
> > instance, though...
> > 
> > Erik
> > 
> > [0] http://hackage.haskell.org/package/transformers-0.3.0.0/docs/Data-Functor-Compose.html
> According to [1], Wrap/Compose does indeed have a Monad instance terms of traverse (here called 'swap'). As far as I understand the paper includes a proof that all the Monad laws holds for such as composition, however there is no mention of transformers as the paper predates them. Personally I am not sure that the transformer composition is useful.
> 
> Would it be as simple as adding this instance to Data.Functor.Compose:
> 
> > instance (Functor m, Traversable n, Monad m, Monad n) => Monad (Compose m n)
> 
> or can anyone spot a problem with this approach?
> 
> Hans
> 
> [1]: http://web.cecs.pdx.edu/~mpj/pubs/RR-1004.pdf, page 9
> [2]: http://strictlypositive.org/IdiomLite.pdf

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