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'd opt for more research for that proposal to answer the following essential questions: - Do the classes correspond to already-known categories, i.e. are the class names optimal? - What laws do we expect to hold? - Are the signatures minimal, i.e. does there exist a smaller set of combinators that still achieves the intended effect? Are the signatures complete, i.e. can the intended effect always expressed with the given combinators? - Plenty and useful examples? At least enough examples that fit in the fine grained hierarchy but cannot be fit into a coarser grained one so as to demonstrate the necessity of a fine grained hierarchy. These questions likely have nice answers for many of the classes, but CategoryZero, CategoryPlus, CategoryChoice and in particular CategoryFun may be hard nuts. Also, the proposed subclass chain InvArrow => RefArrow => FunArrow may be cumbersome in practice since it would mean to define three functions instead of just arr when declaring an Arrow. Btw, a better implementation type for functional references / lenses is Lens s a = Lens { focus :: s -> (a, a -> s) } since that allows a more efficient implementation of modify than modify f s = put (f (get s)) s The latter deconstructs s twice whereas the focus primitive works like a zipper. Regards, apfelmus