Add Divisible and Decideable (contravariant Applicative and co.)

[adelbertc]

https://hackage.haskell.org/package/contravariant-1.4/docs/Data-Functor-Contravariant-Divisible.html

Example use case: divide can be seen as a way of deriving behavior by splitting a "larger" type in two

[iravid]

Yes please! Very useful for encoders

[LukaJCB]

Can you expand a bit on the example use case? I'm not really seeing its usefulness right now

[iravid]

Divisible is to Applicative as Contravariant is to Functor.

Let's say that we have an encoder trait:

trait Encoder[T] {
  def encode(t: T): String
}

Encoder has a contravariant functor as it is isomorphic to ? => String.

Given this definition of divisible:

trait Divisible[F[_]] extends Contravariant[F[_]] {
  def contramap2[A, B, C](fa: F[A], fb: F[B])(f: C => (A, B): F[C]
}

I could derive an encoder given two other encoders:

case class Record(i: Int, s: String)
val recEnc: Encoder[Record] = Divisible[Record].contramap2(Encoder[Int], Encoder[String])((rec: Record) => (rec.i, rec.s))

[LukaJCB]

Thanks @iravid, that indeed seems like a useful addition. However, I'm not sure that we'd have a lot of instances. The only one I can come up with right now would be Show and Order. I'm not really sure these are common enough to warrant adding them to core.

Maybe we could add them in some other module? WDYT?

[iravid]

I wouldn't mind that, as long as they're available :-)

[adelbertc]

Looking at https://hackage.haskell.org/package/contravariant-1.4/docs/Data-Functor-Contravariant-Divisible.html we can define instances for Const, the usual transformer "induction"/"back chaining", Nested, Tuple2K

[stephen-lazaro]

Would anyone object if I were to try my hand at this? I'd be happy to give it a shot. I can always open it against cats-core for now and then move it over to cats-more if that's the direction folks go.

[kailuowang]

This one is more likely to goto cats.more.

[LukaJCB]

This can be closed now after #2034

[LukaJCB]

Actually I closed to early as we do have an analogue to Divisible, but not to Decidable, so I'll reopen this :)