instance Applicative Data.Map

[Roman Cheplyaka]

* Henning Thielemann <lemming at henning-thielemann.de> [2012-11-14 21:28:06+0100]
> 
> On Wed, 14 Nov 2012, Roman Cheplyaka wrote:
> 
> >* Henning Thielemann <lemming at henning-thielemann.de> [2012-11-14 20:46:29+0100]
> >>An ZipList-like Applicative instance for Data.Map would be nice. I
> >>have an application where I like to write
> >>   liftA3 f amap bmap cmap
> >> meaning
> >>   Map.intersectionWith ($) (Map.intersectionWith f amap bmap) cmap
> >>
> >>But I cannot complete the instance implementation because there is no
> >>sensible definition for 'pure' for Data.Map. :-(
> >
> >You can lift Map like this:
> >
> >   data ZipMap k a
> >     = Pure a -- a "Map" that maps every possible key to 'a'
> >     | Zip (Map k a)
> 
> Yes, that would work. It is only annoying that for liftA3 I do not
> need 'pure', at all. Thus we may note in the record that Data.Map is
> an example where <*> and liftAn make sense (for n>0) but 'pure' (i.e.
> Pointed) cannot be defined.

True. It's like being a semigroup but not a monoid.

Roman