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Higher Kinds and Type Constructors

Kinds are like types for types. They describe the number of "holes" (or type parameters) in a type.

Regular types have no "holes" while type constructors have holes that need to be "filled" to produce a type.

  • List is a type constructor with one hole, takes one parameter
  • List[A] is a type, produced using a type parameter

This is analogous to functions and values. Functions are "value constructors"

  • math.abs is a function, takes one parameter
  • math.abs(x) is a value, produced using a value parameter

In Scala, we declare type constructors using underscores.

// Declare F using underscores:
def myMethod[F[_]] = {

    // Reference F without underscores:
    val functor = Functor.apply[F]

    // ...
}

Analously, we define a function's parameters in its definition and omit them when referring to it.

// Declare f specifying parameters:
val f = (x: Int) => x * 2

// Reference f without parameters:
val f2 = f andThen f

This is an advanced feature, so in Scala we have to enable support. Either by importing it or adding in the scalacOptions in build.sbt

import scala.language.higherKinds

scalacOptions += "-language:higherKinds"