[Haskell-cafe] Re: (liftM join .) . mapM

[Conor McBride]

Hi Maciej

On 29 Dec 2009, at 20:52, Maciej Piechotka wrote:

> On Tue, 2009-12-29 at 18:20 +0000, Conor McBride wrote:
>>
>>   ala AppLift foldMap
>
> What is benefit of it over:
> concatMapA f = foldr (liftA2 mappend . f) (pure mempty)

Given that applicative functors take monoids to monoids, it's
nice to exploit that property by name, rather than reconstructing
it by engineered coincidence. I reuse the "library" pattern once
(AppLift) that you reinvent in two places (liftA2 mappend)
(pure mempty).

(Ironically, foldr is defined in terms of foldMap by code that
amounts to, modulo a flip,

   ala Endo foldMap

appealing to the monoid of endomorphisms.)

The result is an operation which

   (a) points out the essential mechanism, foldMap;
   (b) points out the structures on which it works, lifted monoids;
   (c) is short enough not to bother naming.

More structure, less code,

Conor