A Fold is an optic that can see into a structure and get 0 to N foci. It is a generalization of fold, and implements all operators that can be derived from it.

A structure S that has a focus A to which we can apply a function (A) -> R with Monoid<R> to S and get R. For example, S == List<Int> to which we apply (Int) -> String with Monoid<String> and we get R == String

Creating a Fold can be done by manually defining foldMap.

import arrow.core.*
import arrow.optics.*
import arrow.typeclasses.*

fun <T> nullableFold(): Fold<T?, T> = object : Fold<T?, T> {
    override fun <R> foldMap(M: Monoid<R>, s: T?, f: (T) -> R): R =
        s?.let(f) ?: M.empty()

Fold has an API similar to kotlin.collections, but because it’s defined in terms of foldMap, there are no associative fold functions available.

Fold.nonEmptyList<Int>().combineAll(, nonEmptyListOf(1, 2, 3))
Fold.nonEmptyList<Int>().firstOrNull(nonEmptyListOf(1, 2, 3, 4))


Composing Fold can be used for accessing foci in nested structures.

val nestedNelFold: Fold<NonEmptyList<NonEmptyList<Int>>, NonEmptyList<Int>> = Fold.nonEmptyList()

val nestedNel = nonEmptyListOf(1, 2, 3, 4).map {
    nonEmptyListOf(it, it)

(nestedNelFold compose Fold.nonEmptyList()).getAll(nestedNel)

Fold can be composed with all optics except Setter, and results in the following optics.

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

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