Support for additional type classes

[CK-LinoPro]

I think it would be a nice addition to this library to support some of the following type classes from Haskell:

• Comonad w
  • extract :: w a -> a
  • duplicate :: w a -> w (w a)
  • extend :: (w a -> b) -> w a -> w b
• Contravariant
  • contramap :: (a -> b) -> f a -> f b
• Profunctor
  • lmap :: (a -> b) -> p b c -> p b c
  • lmap :: (b -> c) -> p a b -> p a c
  • dimap :: (a -> b) -> (c -> d) -> p b c -> p a d
• Arrow
  • arr :: (b -> c) -> a b c
  • first :: a b c -> a (b, d) (c, d)
  • second :: a b c -> a (d, b) (d, c)
  • pair :: a b c -> a b' c' -> a (b, b') (c, c')
  • combine :: a b c -> a b c' -> a b (c, c')

Along with some comonad types:

• Env e a = (e, a) (reader comonad)
• Traced m a = m -> a (writer comonad)
• Store s a = (s -> a) -> s (state comonad)
• NonEmpty a = a | (a * (NonEmpty a)) (non-empty list)
• Stream a = a * Stream a (strictly infinite list)
• RoseTree a = a * [RoseTree a] (rose tree)

This list of type classes and types is meant as suggestions.
I think they might be benifitial for anyone and general enough for a functional base library.
I've written implementations of all of these types myself, but I don't think my implementation comes anywhere close to the quality of this library.
I could work on more elaborate implementations and provide them as a pull request if desired when I find time to re-implement them.

[louthy]

I was holding off for a while to see how the concepts/shapes proposal progressed with csharplang. The problem with the higher-order types is that they're very difficult to formulate and use effectively (with C# constraints), and so I doubt many are defining functions that can take any monad, or any functor, for example. Whereas it works well for the lower-kinds like monoids.

extend in co-monad is an example where it become difficult, because we can parameterise the w. And so it becomes generics hell.

In principle I'm all for bespoke implementations of the types, but the general story isn't so great.

Right now I'm unfortunately very time poor, so I probably won't be looking at this in the short term I'm afraid. But I'll keep this open, because I agree they're valuable.