A Setter is an optic that can see into a structure and set or modify its focus.

It is a generalization of Functor#map. Given a Functor<F>, we can apply a function (A) -> B to Kind<F, A> and get Kind<F, B>. We can think of Kind<F, A> as a structure S that has a focus A. So, given a PSetter<S, T, A, B>, we can apply a function (A) -> B to S and get T.

  • Kind<F, A>, f: (A) -> B) -> Kind<F, B>
  • PSetter.modify(s: S, f: (A) -> B): T

You can get a Setter for any existing Functor.

import arrow.*
import arrow.optics.*
import arrow.core.*
import arrow.mtl.*
import arrow.core.extensions.listk.functor.*

val setter: Setter<ListKOf<Int>, Int> = Setter.fromFunctor(ListK.functor())
setter.set(listOf(1, 2, 3, 4).k(), 5)
// [5, 5, 5, 5]
setter.modify(listOf(1, 2, 3, 4).k()) { int -> int + 1 }
// [2, 3, 4, 5]

To create your own Setter, you need to define how to apply (A) -> B to S.

A Setter<Player, Int> can set and modify the value of Player. So we need to define how to apply a function (Int) -> Int to Player.

data class Player(val health: Int)

val playerSetter: Setter<Player, Int> = Setter { player: Player, f: (Int) -> Int ->
  val fHealth= f(
  player.copy(health = fHealth)
val increment: (Int) -> Int = Int::inc
playerSetter.modify(Player(75), increment)
// Player(health=76)
val lift = playerSetter.lift(increment)
// Player(health=76)

There are also some convenience methods to make working with State easier. This can make working with nested structures in stateful computations significantly more elegant.

import arrow.optics.mtl.*

val takeDamage = playerSetter.update_ { it - 15 }
// (Player(health=60), kotlin.Unit)
val restoreHealth = playerSetter.assign_(100)
// (Player(health=100), kotlin.Unit)


Unlike a regular set function, a Setter composes. Similar to a Lens, we can compose Setters to focus into nested structures and set or modify a value.

data class Bar(val player: Player)

val barSetter: Setter<Bar, Player> = Setter { bar, modifyPlayer ->
  val modifiedPlayer = modifyPlayer(bar.player)
  bar.copy(player = modifiedPlayer)

(barSetter compose playerSetter).modify(Bar(Player(75)), Int::inc)
// Bar(player=Player(health=76))

Setter can be composed with all optics but Getter and Fold. It results in the following optics:

  Iso Lens Prism Optional Getter Setter Fold Traversal
Setter Setter Setter Setter Setter X Setter X Setter

Polymorphic setter

When dealing with polymorphic types, we can also have polymorphic setters that allow us to morph the type of the focus. Previously, when we used a Setter<ListKOf<Int>, Int>, it was able to morph the Int values in the constructed type ListK<Int>. With a PSetter<ListKOf<Int>, ListKOf<String>, Int, String>, we can morph an Int value to a String value and thus also morph the type from ListK<Int> to ListK<String>.

val pSetter: PSetter<ListKOf<Int>, ListKOf<String>, Int, String> = PSetter.fromFunctor(ListK.functor())
pSetter.set(listOf(1, 2, 3, 4).k(), "Constant")
// [Constant, Constant, Constant, Constant]
pSetter.modify(listOf(1, 2, 3, 4).k()) {
    "Value at $it"
// [Value at 1, Value at 2, Value at 3, Value at 4]


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

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