Add a different MonoidK and SemigroupK instance for Kleisli

[peterneyens]

I was just looking at a StackOverflow question and was thinking this could be solved using SemigroupK.combineK, but while there is a SemigroupK[Option] there is nothing to give us a SemigroupK[λ[α => Int => Option[α]]]. So I have added a SemigroupK and MonoidK for a function A => F[B] if there is a MonoidK[F].

I am not exactly sure how useful this is in practice. This is probably not something used very often (so I am not sure if this warrants inclusion in cats ?). It also seems you will always need to write a type lambda :

import cats.implicits._
val foo: Int => Option[Int] = x => if (x % 2 == 0) Some(x) else None
val bar: Int => Option[Int] = x => if (x % 3 == 0) Some(x) else None
SemigroupK[λ[α => Int => Option[α]]].combineK(foo, bar)

It would of course be nicer if you could write foo <+> bar. I'm not sure if that would be possible using the existing semigroupSyntaxU or using the SI-2712 fix (I tried with a locally published cats version with this PR and Miles' compiler plugin, but couldn't get it working) ?

[codecov-io]

Codecov Report

Merging #1098 into master will increase coverage by <.01%.
The diff coverage is 100%.

@@            Coverage Diff             @@
##           master    #1098      +/-   ##
==========================================
+ Coverage   96.07%   96.07%   +<.01%     
==========================================
  Files         273      273              
  Lines        4538     4539       +1     
  Branches      119      117       -2     
==========================================
+ Hits         4360     4361       +1     
  Misses        178      178

Impacted Files	Coverage Δ
core/src/main/scala/cats/data/Kleisli.scala	100% <100%> (ø)	⬆️

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[peterneyens]

I got the syntax working with a type alias (so it can use the semigroupSyntaxU syntax with an Unapply)

type T[f[_], a, b] = Function[a, f[b]]
val foo: T[Option, Int, Int] = x => if (x % 2 == 0) Some(x) else None
val bar: T[Option, Int, Int] = x => if (x % 3 == 0) Some(x) else None

foo <+> bar

This looks quite a lot like Kleisli 😛 , so I should probably change this PR to add these instances to Kleisli instead of Function1.

[non]

Looks good to me! 👍

[ceedubs]

@peterneyens thanks!

It seems like it could potentially be problematic to have two different SemigroupK instances for Kleisli. Would there be ambiguity in the case of something like Kleilsi[List, Int, Int]?

[peterneyens]

@ceedubs You are right, with this PR you will always get the newly added Kleisli[F, A, ?] instances. The existing SemigroupK[F, α, α] will probably be used more and is also consistent with the SemigroupK from Function1.

I'm not sure how often these new instances which combine Kleislis into one with the combined result will be used. Do I leave them in and only make them explicitly available (dropping the implicit from the functions) ?

[edmundnoble]

Any updates on this? I don't see an issue with providing these instances explicitly, provided they're documented.

[peterneyens]

Made this instances explicit (notreally sure about the naming of the instances and the traits) and added doctests for both instances.

Anything else you were thinking of @edmundnoble?

[kailuowang]

@peterneyens do you still have time to work on this PR? If you want, I can continue this one or asking @ChristopherDavenport for the favor

[peterneyens]

Could come back to this in the weekend, but if anybody else wants to go ahead in the mean time, I don't mind.

[kailuowang]

LGTM

[kailuowang]

Thanks so much @peterneyens

[aeons]

Awesome!