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