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In functional programming, fold (also termed reduce, accumulate, aggregate, compress, or inject) refers to a family of higher-order functions that analyze a recursive data structure and through use of a given combining operation, recombine the results of recursively processing its constituent parts, building up a return value. Typically, a fold is presented with a combining function, a top node of a data structure, and possibly some default values to be used under certain conditions. The fold then proceeds to combine elements of the data structure's hierarchy, using the function in a systematic way.

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  • Fold (higher-order function) (en)
  • Fold (it)
  • Fold (고차 함수) (ko)
  • Fold (nl)
  • Fold (pl)
  • Свёртка списка (ru)
  • Fold (高阶函数) (zh)
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  • Fold, anche conosciuta come reduce, accumulate, compress o inject, nella programmazione funzionale è una funzione che itera una funzione arbitraria su una struttura dati in un certo ordine e costruisce un valore di ritorno.Tipicamente una fold, dialoga con due cose: una funzione combinante e una lista di elementi di una struttura dati.La fold poi procede a combinare elementi della struttura dati usando la funzione in modo sistematico. Le due principali tipologie di fold sono foldr e foldl, dove 'r' ed 'l' stanno, rispettivamente, per 'right' e 'left'. (it)
  • 함수형 프로그래밍에서 fold란 고차 함수의 계열 중 하나이다. reduce, accumulate, compress 혹은 inject 등 다양하게 알려져 있다. 재귀적인 자료 구조를 분석하고, 전달받은 결합된 명령들을 사용하여 재결합하며, 재귀적으로 수행된 그 결과들로 반환 값(return value)을 만들어낸다. 보통 fold는 함수를 자료 구조의 최상위 노드의 조합 함수의 형태로 표현되며, 특정 조건 하에서 사용할 수 있는 어떤 기본 값(default values)을 가질 수 있다. 그리고 계통적인 방식으로 그 함수를 사용하여 자료 구조의 위계 상의 요소들을 조합하는 과정을 진행한다. (ko)
  • 在函数式编程中，折叠（fold），也称为归约（reduce）、积累（accumulate）、聚集（aggregate）、压缩（compress）或注入（inject），指称一组高阶函数，它们分析递归数据结构并通过使用给定组合运算，将递归的处理它的构成部件、建造一个返回值的结果重组起来。典型的，要向折叠提供一个组合函数，一个数据结构的顶端，和可能的在特定条件下使用的某些缺省值。折叠接着以系统性方式使用这个函数，进行组合这个数据结构的层级中的元素。 折叠在某种意义上是（unfold）的对偶，它接受一个种子值并共递归的应用一个函数，来确定如何进一步的构造一个共递归的数据结构。折叠递归的分解这个数据结构，在每个节点应用一个组合函数于它的终结值和递归结果之上，用得到这个结果替代它。折叠是，而展开是。 (zh)
  • In functional programming, fold (also termed reduce, accumulate, aggregate, compress, or inject) refers to a family of higher-order functions that analyze a recursive data structure and through use of a given combining operation, recombine the results of recursively processing its constituent parts, building up a return value. Typically, a fold is presented with a combining function, a top node of a data structure, and possibly some default values to be used under certain conditions. The fold then proceeds to combine elements of the data structure's hierarchy, using the function in a systematic way. (en)
  • In functionele programmeertalen is een fold (of reduce) een hogere-ordefunctie waarmee een recursieve datastructuur geanalyseerd kan worden. In veel gevallen wordt een lijst in een bepaalde volgorde doorlopen en wordt gaandeweg een bepaalde waarde berekend. Een fold maakt gebruik van twee zaken: een functie die elementen van de datastructuur combineert en de datastructuur zelf. Een voorbeeld: fold (+) [1,2,3,4,5] (nl)
  • Fold (z ang. składać, zwijać) to rodzina funkcji wyższego rzędu występująca w językach funkcyjnych. Znana jest również jako reduce, accumulate, compress bądź inject. Funkcje fold przetwarzają uporządkowane kolekcje danych (zazwyczaj listy) w celu zbudowania końcowego wyniku przy pomocy jakiejś funkcji łączącej elementy. Dwie najbardziej popularne funkcje z tej rodziny to foldr (fold right) i foldl (fold left). (pl)
  • Свёртка списка (англ. folding, также известна как reduce, accumulate) в программировании — функция высшего порядка, которая производит преобразование структуры данных к единственному значению при помощи заданной функции. Операция свёртки часто используется в функциональном программировании при обработке списков. Свёртка может быть обобщена на произвольный алгебраический тип данных при помощи понятия из теории категорий. (ru)
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