Re: instance Applicative Data.Map

On Wed, Nov 14, 2012 at 10:31:06PM +0200, Roman Cheplyaka wrote:

* Henning Thielemann [2012-11-14 21:28:06+0100]

...

On Wed, 14 Nov 2012, Roman Cheplyaka wrote:

...

* Henning Thielemann [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.

Precisely. See edwardk's package http://hackage.haskell.org/package/semigroupoids which defines this and many other related things. -Brent