Functor

The Functor typeclass abstracts the ability to map over the computational context of a type constructor. Examples of type constructors that can implement instances of the Functor typeclass include Option, NonEmptyList, List, and many other datatypes that include a map function with the shape fun F<A>.map(f: (A) -> B): F<B> where F refers to Option, List, or any other type constructor whose contents can be transformed.

Example

Oftentimes we find ourselves in situations where we need to transform the contents of some datatype. Functor#map allows us to safely compute over values under the assumption that they’ll be there returning the transformation encapsulated in the same context.

Consider both Option and Either:

Option<A> allows us to model absence and has two possible states: Some(a: A) if the value is not absent, and None to represent an empty case.

In a similar fashion, Either<A, B> may have two possible cases: Right(b: B) for computations that succeed, and Left(a: A) for exceptional cases.

Both Either and Option are example datatypes that can be computed over transforming their inner results.

import arrow.*
import arrow.core.*

Either.right(1).map { it * 2 }
Option(1).map { it * 2 }
// Option.Some(2)

Both Either and Option include ready-to-use Functor instances:

import arrow.core.extensions.option.functor.*

val optionFunctor = Option.functor()

import arrow.core.extensions.either.functor.*

val eitherFunctor = Either.functor<Int>()

Mapping over the empty/failed cases is always safe since the map operation in both Either and Option operate under the bias of those containing success values.

(None as Option<Int>).map { it * 2 }
(Either.left(IllegalArgumentException("")) as Either<Throwable, Int>).map { it * 2 }
// Either.Left(java.lang.IllegalArgumentException: )

Main Combinators

Kind<F, A>#map

Transforms the inner contents.

fun <A, B> Kind<F, A>.map(f: (A) -> B): Kind<F, B>

optionFunctor.run { Option(1).map { it + 1 } }
// Option.Some(2)

lift

Lift a function to the Functor context so it can be applied over values of the implementing datatype.

fun <A, B> lift(f: (A) -> B): (Kind<F, A>) -> Kind<F, B>

val lifted = optionFunctor.lift({ n: Int -> n + 1 })
lifted(Option(1))
// Option.Some(2)

Other combinators

For a full list of other useful combinators available in Functor, see the Source

Laws

Arrow provides FunctorLaws in the form of test cases for internal verification of lawful instances and third party apps creating their own Functor instances.

Creating your own Functor instances

Arrow already provides Functor instances for most common datatypes both in Arrow and the Kotlin stdlib. Oftentimes, you may find the need to provide your own for unsupported datatypes.

You may create or automatically derive instances of Functor for your own datatypes which you will be able to use in the context of abstract polymorphic code as demonstrated in the example above.

See Deriving and creating custom typeclass

Data types

Additionally, all instances of Applicative, Monad, and their MTL variants, implement the Functor typeclass directly since they are all subtypes of Functor