Robert Dockins wrote: [snip other points]
7) Finally, I somehow feel like there should be a nice categorical formulation of these datastructure abstractions which would help to drive a refactoring of the API typeclasses in a principled way, rather than on an ad-hoc I-sort-of-think-these-go-together sort of way. Unfortunately, my category-fu is quite weak, so all I have is this vague intuition that I can't substantiate. I'm sort of familiar with initial algebras, but I think they may be too concrete. I'm looking for some way to classify algebras that have, eg, the property of having folds, or of being set-like, etc. If anybody can point me in the right direction wrt this, that would be great.
I'd love to find out more about these categorical abstractions also, since Monads and Monoids (the only ones I know about) are an incredible source of power and expressiveness in Haskell programming, so I've got the feeling that I'm wasting tremendous amounts of time reinventing the wheel when other abstractions that may be equally useful are just waiting to be used... Can anyone recommend a good book or web tutorial about category theory that's not too difficult? I'm thinking about something which would have lots of diagrams and discussion about the relevance of the concepts to practical computing problems but not something loaded with complicated proofs or LaTeX symbols :-) Thanks, Brian. -- Logic empowers us and Love gives us purpose. Yet still phantoms restless for eras long past, congealed in the present in unthought forms, strive mightily unseen to destroy us. http://www.metamilk.com