Monoids Cats

Monoid Type Class

cats.kernel.Monoid (aliased cats.Monoid) extends cats.external.Semigroup (alias cats.Semigroup).

Cats Kernel

A subproject of Cats to provide a small set of type classes for libraries that don't need the full Cats toolbox. They are in the cats.kernel package, but they are aliased as cats.

Monoid Instances

Monoid has the same Cats pattern for the user interface, a companion object has an apply method.

import cats.Monoid
import cats.instances.string._ // for Monoid

Monoid[String].combine("Hi ", "there")
// res0: String = Hi there

Monoid[String].empty
// res1: String = ""

is the same thing as:

Monoid.apply[String].combine("Hi ", "there")
// res2: String = Hi there

Monoid.apply[String].empty
// res3: String = ""

and if we don't need empty, then we can do this instead:

import cats.Semigroup

Semigroup[String].combine("Hi ", "there")
// res4: String = Hi there

Monoid Syntax

Cats provides syntax for combine with |+|. It technically comes from Semigroup, so we need cats.syntax.semigroup:

import cats.instances.string._ // for Monoid
import cats.syntax.semigroup._ // for |+|

val stringResult = "Hi " |+| "there" |+| Monoid[String].empty
// stringResult: String = Hi there

import cats.instances.int._ // for Monoid

val intResult = 1 |+| 2 |+| Monoid[Int].empty
// intResult: Int = 3

Example

A function that adds: def add(items: List[Int]): Int

def add(items: List[Int]): Int = items.foldLeft(0)(_ + _)

//or

import cats.Monoid
import cats.instances.int._
import cats.syntax.semigroup._

def add(items: List[Int]): Int =
  items.foldLeft(Monoid[Int].empty)(_ |+| _)

A function that now adds List[Option[Int]]:

//Make it generic!!

import cats.Monoid
import cats.syntax.semigroup._ // for |+|

def add[A](items: List[A])(implicit monoid: Monoid[A]): A =
  items.foldLeft(monoid.empty)(_ |+| _)

Equivalently with context bounds syntax:

def add[A: Monoid](items: List[A]): A =
  items.foldLeft(Monoid[A].empty)(_ |+| _)

import cats.instances.int._ // for Monoid

add(List(1, 2, 3))
// res9: Int = 6

import cats.instances.option._ // for Monoid

add(List(Some(1), None, Some(2), None, Some(3)))
// res10: Option[Int] = Some(6)

Now we want to sum of Order's

case class Order(totalCost: Double, quantity: Double)

implicit val monoid: Monoid[Order] = new Monoid[Order] {
  def combine(o1: Order, o2: Order) =
    Order(
      o1.totalCost + o2.totalCost,
      o1.quantity + o2.quantity
    )

  def empty = Order(0, 0)
}