Tom Tom - 5 months ago 21
Scala Question

Why Is Functor a Higher-Kinded type

I have following functor definition

trait Functor[F[_]] {
def map[A, B](fa: F[A])(f: A => B): F[B]
object ListFunctor extends Functor[List] { //
def map[A, B](f: A => B)(data: List[A]): List[B] = data map f

In scala, it is very common that
is a collection type, such as List,Seq,Option, I would ask why Functor has to be higher kinded type, and what does the type parameter
really mean?

Answer Source

why Functor has to be higher kinded type

Functor has to be higher kinded because we want to abstract over a type parameter which itself takes a type parameter.

The types that Functor deals with are called "first order kinds" and their kind is of * -> *. When you look at the implementations you provide for a Functor, it makes sense, we're basically abstracting over the inner type parameter, for example when you define a functor for List, as you did in your example, you define it as a Functor[List]. As you see, we're not creating a functor for a specific List[Int], but rather any type parameter which is contained inside a List. This abstraction brings great power because once you define such a type class, you can use it for any List type, be it List[String] or List[Int].

I always like to refer to the image drawn by Adriaan Moore in his paper "Genrics Of A Higher Kind":

Higher Kinds

What does the type parameter F really mean

Fs sole purpose is to define a contract with the implementer of the Functor. By the signature of F we can deduce what kind of type Functor expects. When we see that it has one "placeholder" ([_]) we know, by convention, that this means that F should take a single type parameter. If we think about all the types that take a single type parameter, we can see that there are many, for example List, Option, Try, Future, Task, etc.

For a more broad explanation regarding higher kinded types, see What is a higher kinded type in Scala?

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