Option Monoid with deep combine

[Joe San]

Let's say that I have a Monoid trait as below:

 trait Monoid[A] {
   def combine(a1: A, a2: A): A
   def identity: A
 }

Now if I want to write an optionMonoid for this, I could write it like this:

 val optionMonoid1 = new Monoid[Option[A]] {
   def combine(a1: Option[A], a2: Option[A2]) a1 orElse a2
   def identity = None
 }

This given the fact that I do not know anything about the inner type in the Option. But what if I want to have the combine operator in such a way that I want to really combine the inner types in the Option?

[Jasper-M]

That probably means a Monoid[A] needs to exist. You can encode that dependency with an implicit parameter or context bound. Assuming you encode typeclass instances with implicits.

For instance:

implicit def optionMonoid[A](implicit monoidA: Monoid[A]): Monoid[Option[A]] = new Monoid[Option[A]] {

  def combine(a1: Option[A], a2: Option[A]) = a1.flatMap(aa1 => a2.map(aa2 => monoidA.combine(aa1, aa2)))

  def identity = Option(monoidA.identity)

}

Cats implements it a bit differently: https://github.com/typelevel/cats/blob/v0.9.0/kernel/src/main/scala/cats/kernel/instances/option.scala#L61

They only require a Semigroup[A].

Op donderdag 20 april 2017 12:29:34 UTC+2 schreef Joe San:

[Joe San]

It makes sense with the cats implementation because a Semigroup already defines a combine operator!

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[Jasper-M]

Yes if you define empty to be None, you only need the combine method so Semigroup is enough then.