Functors in Scala

Let us debunk this major, but simple functional abstraction called the Functor

Intuition behind Functors

The idea stems from category theory and can be readily applied to elegantly look inside a container that contains a certain category and apply a function to the contents, thereby producing another category wrapped inside the same container. The name of a functor sounds very much similar to that of a function and in fact it is indeed the same, but there is this additional thingy called the container or in other words a context.

You might already be familiar with such contexts like List[A], Seq[A] that can hold zero to many values of type A. List or Seq can be said that they are the containers for holding elements or types of type A. Other containers or contexts like Option, Either, Future etc., also can be cited. Henceforth, we will use the term context instead of a container, but both mean the same.

Hitting the ground

To manipulate the data inside a context could be done like this:

1  // Let us use the Option as our context
2  val somePerson = Some(Person("firstName", "lastName", salary = 1000000))
3  if (somePerson.isDefined) {
4    somePerson.get.map(person => person.copy(salary = 20000000))
5  }


So, with that example., we simply checked if a Person exists and if yes, we manipulated his salary. That piece of code is like telling to scala how to do, which is basically an imperative style of programming. We instead would want to say to Scala just what to do and, the programming language should figure out how to do. This is where our Functor intuition could help us out.

Most of scala's context have built in functor like capabilities. Let us get to the following example:

1  val listOfSalary = List(200000, 100000, 400000, 600000, 700000, 350000)
2  val bonusFunction: Int => Int = baseSalary => baseSalary + 100000
3  val finalSalaries = listOfSalary.map(bonusFunction)


With that code snippet, we have instructed Scala what we want which is to map the salaries to bonuses. The map function figures out how to get the job done. Its signature is like this:

1  trait F[A] {
2    def map[A, B](f: A => B): F[B]
3  }


Here F[A] is our container or context in which we have defined a map function that should know how to map from A -> B

Let us now define a simple Functor. You need three things to do that:

1. The container / context that you will plug in (List, Try, Either, Option etc.,) - F[_]
2. The Type from which you want to go from - A
3. The Type to which you want to go to - B

With that said, let us implement a Functor interface:

1  import scala.language.higherKinds
2  trait Functor[F[_]] {
3    def map[A, B](fa: F[A])(f: A => B): F[B]
4  }


What we have basically done is, we have created a trait that operates on a generic context which is the F[_]. If you follow what higher kinded types in Scala mean, that signature should be straight forward. It basically says that in the place of F[_], I can plugin any context which itself is a context around a certain type. For example., List, Option, Try, Either all are contexts that around a certain type. So they qualify to be the F[_] which can be exemplified as F[List], F[Option], F[Try], F[Either] and so on. Have a lok here for some basic understanding of higher kinded types

For the sake of this blog, let us implement a List Functor as below:

1  val listFunctor: Functor[List] = new Functor[List] {
2    def map[A, B](fa: List[A])(f: A => B): List[B] = fa.map(f)
3  }


With that, we have now defined a context around List that knows how to map one category in a List to another category. I hope this was clear enough.

Functor laws

To qualify for Functorship, the following laws should be respected:

Identity

This basically states that when a map is called on a Functor with an identity function, you get the same Functor back. Remember that an identity function is one that returns the exact same input. So basically, we are saying that:

1  Functor[X].map(identity) "should be equal to" Functor[X]


Associativity

If f and g are two independent functions, then calling a map on f anf then g is as good as calling a map with g composed f or in other words calling g(f(x)). So basically, we are saying that:

1Functor[X].map(f).map(g) == Functor[X].map(x => g(f(x))


Wrap up

So essentially a Functor is just doing this:

1. Unwrap a value from a context
2. Apply a function to that context
3. Rewrap that value back into that context
4. Return the new context

That is all what is to Functors. Really simple indeed!