Diving into Scala Cats - Functors

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If you’re new to the concept of type classes I suggest you read my other article explaining them. The Cats library makes extensive use of type classes and a basic understanding is a prerequisite for this article.

In previous articles, we talked about Semigroups and Monoids, which are abstractions that let us combine values of the same type together.

In this post, we’ll take a look at Functors, which allow us to operate on values inside containers without having to know any of the implementation details of the containers themselves.

What are Functors?

In terms of functional programming, a Functor is simply something that can be mapped over, or we can call it a Mappable instead.

It is basically an abstraction that allows us to
represent sequences of operations within a context such as Collections, Futures and Options.

Cats’ Functor type class provides a base class for mappable types that allow us to write generic code for Futures, Options, Lists and more.

Standard Scala has no base type/trait to represent following generically:

def calcBudget(orders: List[LineItem]) = orders.map(...)
def calcBudget(maybeOrder: Option[LineItem]) = maybeOrder.map(...)
def calcBudget(eventualOrder: Future[LineItem]) = eventualOrder.map(...)

However using cats’ Functor type class we can write a generic method like this:

def calcBudget(order: Functor[LineItem]) = order.map(...)

Definition of a Functor

A Functor is a type F[A] with a map operation (A => B) => F[B]:

package cats

trait Functor[F[_]] {
  def map[A, B](fa: F[A])(f: A => B): F[B]
}

It accepts the initial F[A] as a parameter alongside the transformation function.

Let’s rewrite calcBudget using Functor:

import cats.Functor

case class LineItem(price: Double)

def calcBudget[F[_]](order: F[LineItem])(implicit ev: Functor[F]): F[LineItem] = {
  Functor[F].map(order)(o => o.copy(price = o.price * 1.2))
}

The Functor[F].map(...) method is parameterized based on a type of F[_]. Here F[_] means any type constructor (type wrapping another type) that has a map method e.g. Option, List, Future etc.

The implicit parameter ev: Functor[F] means that we must have a type class implementation in place that allows us to treat F as a cats Functor.

Functor Laws

If we are creating our own Functors, then the Functor must follow these laws.

Identity : If we pass an identity function to the Functor map method, then the Functor must get back the original Functor.
Composition : If two functions execute sequentially like (f andThen g)(x) or map(f).map(g) then the output must be equal to g(f(x)).

Functor Type Class and Instances

The Functor type class is cats.Functor. Cats library provide us with inbuilt Functors and their implementation for predefined types like Option, List, Future etc.

So far so good, let’s try to use type class implementation of Functor for List:

import cats.Functor

object ListFunctor {
  def transformList(list: List[Int]): List[Int] = {
    Functor[List].map(list)(_ * 2)
  }
}

val list: List[Int] = List(1, 2, 3, 4, 5)
val transformedList = List(2, 4, 6, 8, 10)
assert(ListFunctor.transformList(list) == transformedList)

Now let’s try to use type class implementation of Functor for Option:

import cats.Functor

object OptionFunctor {
  def transformOption(option: Option[Int]): Option[String] = {
    Functor[Option].map(option)(_.toString)
  }
}

val option: Option[Int] = Some(10)
val transformedOption = Some("10")
assert(OptionFunctor.transformOption(option) == transformedOption)

Now let’s try to use type class implementation of Functor for Future:

import cats.Functor

object FutureFunctor {
  def transformFuture(future: Future[Int]): Future[Int] = {
    Functor[Future].map(future)(_ + 1)
  }
}

val future: Future[Int] = Future{10}
val transformedFutureResult = 11
FutureFunctor.transformFuture(future).map(result => assert(result == transformedFutureResult))

Whenever we summon a Functor for Future, the compiler will
locate futureFunctor by implicit resolution and recursively search for an
ExecutionContext at the call site. This is what the expansion might look
like:

// We write this:
Functor[Future]

// The compiler expands to this first:
Functor[Future](futureFunctor)

// And then to this:
Functor[Future](futureFunctor(executionContext))

Functor Syntax

By using the Functor type class we can abstract over anything that can be mapped. We’re not restricted to the types in the standard library, we could add a map method to our own types.

Cats allows us to do this by using the concept of syntax or extension methods.

This concept is implemented using implicit classes and allows us to write order.map(...) instead of Functor[F].map(order)(...). We can also drop the implicit parameter by specifying that type F[_] is a Functor:

import cats.syntax.functor._ //for map

def calcBudget[F[_]: Functor](order: F[LineItem]): F[LineItem] = {
  order.map(o => o.copy(price = o.price * 1.2))
}

But we can also build a higher order function which can deal with any type and perform any mapping operation:

def withFunctor[A, B, F[_]](item: F[A], op: A => B)(implicit ev: Functor[F]): F[_] = Functor[F].map(item)(op)

val lineItemsList = List(LineItem(10.0), LineItem(20.0))
val result = FunctorSyntax.withFunctor(lineItemsList, calcBudget)
assert(result == List(LineItem(10.0), LineItem(20.0)))

Of course this is a contrived example as withFunctor adds no value over a simple inline call but it illustrates the point that A, B & F can be anything so long as the caller of the method:

Supplies evidence that F is a Functor (an implementation)
Knows how to map from A to B

Summary

In this article, we’ve looked at Functors provided by Scala Cats library. Functors represent sequencing behaviors. We talked about why do we need Functors and how can we define them. For a type class to be a Functor it must obey two laws: Firstly it should be possible to compose two map calls. Secondly mapping with the identity function should have no effect. We saw that we can write Functor type class implementation for all the mappable types present in Scala ecosystem like Futures, Options, Lists, etc. We’re not restricted to the types in the standard library, we can also add map method to our own types by using the concept of syntax or extension methods.