Proposal: Add Compositor class as superclass of Arrow
Bertram Felgenhauer
bertram.felgenhauer at googlemail.com
Mon Oct 22 16:07:02 EDT 2007
Twan van Laarhoven wrote:
> My proposal would be the following. The important things are that:
> 1. It incorporates Conal's deep arrow,
> 2. as well as everything that is needed for functional references/lenses
> and bijective/invertible functions.
> I have chosen to reuse prelude names where possible.
This is a rather finely grained hierarchy, but it's still too coarse
to define a category of invertible functions. That category has pairs:
it supports first, second and (***), but not fst and snd.
> -- | 'cat' can work with pairs
> class Category cat => CategoryPair cat where
> fst :: cat (a,b) a
> snd :: cat (a,b) b
> swap :: cat (a,b) (b,a)
> first :: cat a b -> cat (a,c) (b,c)
> second :: cat a b -> cat (c,a) (c,b)
> (***) :: cat a b -> cat c d -> cat (a,c) (b,d)
A similar problem exists with inl and inr of CategoryChoice.
[snip]
> class Category cat => CategoryAssoc cat t where
> lAssoc :: cat (t a (t b c)) (t (t a b) c)
> rAssoc :: cat (t (t a b) c) (t a (t b c))
This one is nice. Have you thought about other laws, in particular
the distributive laws of sums and products (Either and (,))?
> I would further propose that all classes named Category* go into
> Control.Category, while Arrow* goes into Control.Arrow. The latter can
> re-export the Control.Category module.
For compatibility reasons, I don't like reusing the Control.Arrow
module name.
Bertram
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