SemigroupK 

Semigroup we saw on day 4 is a bread and butter of functional programming that shows up in many places.

import cats._, cats.syntax.all._

List(1, 2, 3) |+| List(4, 5, 6)
// res0: List[Int] = List(1, 2, 3, 4, 5, 6)

"one" |+| "two"
// res1: String = "onetwo"

There’s a similar typeclass called SemigroupK for type constructors F[_].

@typeclass trait SemigroupK[F[_]] { self =>

  /**
   * Combine two F[A] values.
   */
  @simulacrum.op("<+>", alias = true)
  def combineK[A](x: F[A], y: F[A]): F[A]

  /**
   * Given a type A, create a concrete Semigroup[F[A]].
   */
  def algebra[A]: Semigroup[F[A]] =
    new Semigroup[F[A]] {
      def combine(x: F[A], y: F[A]): F[A] = self.combineK(x, y)
    }
}

This enables combineK operator and its symbolic alias <+>. Let’s try using this.

List(1, 2, 3) <+> List(4, 5, 6)
// res2: List[Int] = List(1, 2, 3, 4, 5, 6)

Unlike Semigroup, SemigroupK works regardless of the type parameter of F[_].

Option as SemigroupK 

Option[A] forms a Semigroup only when the type parameter A forms a Semigroup. Let’s disrupt that by creating a datatype does not form a Semigroup:

case class Foo(x: String)

So this won’t work:

Foo("x").some |+| Foo("y").some
// error: value |+| is not a member of Option[repl.MdocSession.App.Foo]
// Foo("x").some |+| Foo("y").some
// ^^^^^^^^^^^^^^^^^

But this works fine:

Foo("x").some <+> Foo("y").some
// res4: Option[Foo] = Some(value = Foo(x = "x"))

There’s also a subtle difference in the behaviors of two typeclasses.

1.some |+| 2.some
// res5: Option[Int] = Some(value = 3)

1.some <+> 2.some
// res6: Option[Int] = Some(value = 1)

The Semigroup will combine the inner value of the Option whereas SemigroupK will just pick the first one.

SemigroupK laws 

trait SemigroupKLaws[F[_]] {
  implicit def F: SemigroupK[F]

  def semigroupKAssociative[A](a: F[A], b: F[A], c: F[A]): IsEq[F[A]] =
    F.combineK(F.combineK(a, b), c) <-> F.combineK(a, F.combineK(b, c))
}