Haskell type class hierarchy in Java

Question

I write a library with Java interfaces resembling Haskell type classes, and abstract classes implementing all "derivable" methods (eg Monad.join can be written using >>= and return ). This is my planned structure ([] means the interface doesn't exist yet):

                      Applicative <= Alternative <-,     
Functor <= Pointed <= Applicative <= Monad <= MondPlus
Functor <= Copointed <= Comonad      Monad <= [MonadFix]

Category <= Arrow <= ArrowChoice   
            Arrow <= [ArrowApply]
            Arrow <= [ArrowLoop] 
            Arrow <= [ArrowZero] <= [ArrowPlus]
Bifunctor

• Is this hierarchy "correct"?
• Particularly, is it correct that MonadPlus implements Alternative?
• Should I split MonadZero from MonadPlus? Same question for ArrowZero and ArrowPlus
• How can I reduce code duplication when a class implements multiple "endpoints" (eg Maybe is a MonadPlus and a MonadFix, Kleisli is ArrowEverything)
• Arrow could theoretically extend Applicative as well. Currently I have a method on Arrow returning that Applicative, because it looks like type curring makes inheritance impossible here.
• Are there other non-obvious "connections" (like Arrow->Applicative) I'm missing?
• Which "useful" type classes are missing in this hierarchy?

Answer 1

1. You should make sure to consult the typeclassopedia .

2. Edward Kmett has been doing yeoman's work in trying to construct a rich, sane, hierarchy of core classes, starting with semigroups and moving forward. It's worth corresponding with him directly, but take a look at semigroupoids and the many related packages he's uploaded for some pointers: