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id="toc-Data_structures-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Comparison_to_imperative_programming" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Comparison_to_imperative_programming"> <div class="vector-toc-text"> 3 Comparison to imperative programming </div> </a> <button aria-controls="toc-Comparison_to_imperative_programming-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Comparison to imperative programming subsection </button> <ul id="toc-Comparison_to_imperative_programming-sublist" class="vector-toc-list"> <li id="toc-Imperative_vs._functional_programming" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Imperative_vs._functional_programming"> <div class="vector-toc-text"> 3.1 Imperative vs. functional programming </div> </a> <ul id="toc-Imperative_vs._functional_programming-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Simulating_state" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Simulating_state"> <div class="vector-toc-text"> 3.2 Simulating state </div> </a> <ul id="toc-Simulating_state-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Efficiency_issues" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Efficiency_issues"> <div class="vector-toc-text"> 3.3 Efficiency issues </div> </a> <ul id="toc-Efficiency_issues-sublist" class="vector-toc-list"> <li id="toc-Abstraction_cost" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Abstraction_cost"> <div class="vector-toc-text"> 3.3.1 Abstraction cost </div> </a> <ul id="toc-Abstraction_cost-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Functional_programming_in_non-functional_languages" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Functional_programming_in_non-functional_languages"> <div class="vector-toc-text"> 3.4 Functional programming in non-functional languages </div> </a> <ul id="toc-Functional_programming_in_non-functional_languages-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Comparison_to_logic_programming" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Comparison_to_logic_programming"> <div class="vector-toc-text"> 4 Comparison to logic programming </div> </a> <ul id="toc-Comparison_to_logic_programming-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Applications" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Applications"> <div class="vector-toc-text"> 5 Applications </div> </a> <button aria-controls="toc-Applications-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Applications subsection </button> <ul id="toc-Applications-sublist" class="vector-toc-list"> <li id="toc-Text_editors" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Text_editors"> <div class="vector-toc-text"> 5.1 Text editors </div> </a> <ul id="toc-Text_editors-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Spreadsheets" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Spreadsheets"> <div class="vector-toc-text"> 5.2 Spreadsheets </div> </a> <ul id="toc-Spreadsheets-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Microservices" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Microservices"> <div class="vector-toc-text"> 5.3 Microservices </div> </a> <ul id="toc-Microservices-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Academia" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Academia"> <div class="vector-toc-text"> 5.4 Academia </div> </a> <ul id="toc-Academia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Industry" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Industry"> <div class="vector-toc-text"> 5.5 Industry </div> </a> <ul id="toc-Industry-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Education" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Education"> <div class="vector-toc-text"> 5.6 Education </div> </a> <ul id="toc-Education-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> 6 See also </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes_and_references" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes_and_references"> <div class="vector-toc-text"> 7 Notes and references </div> </a> <ul id="toc-Notes_and_references-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> 8 Further reading </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> 9 External links </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" > Toggle the table of contents </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading">Functional programming</h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 53 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-53" aria-hidden="true" > 53 languages </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A8%D8%B1%D9%85%D8%AC%D8%A9_%D9%88%D8%B8%D9%8A%D9%81%D9%8A%D8%A9" title="برمجة وظيفية – Arabic" lang="ar" hreflang="ar" data-title="برمجة وظيفية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Programaci%C3%B3n_funcional" title="Programación funcional – Asturian" lang="ast" hreflang="ast" data-title="Programación funcional" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target">Asturianu</a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AB%E0%A6%BE%E0%A6%82%E0%A6%B6%E0%A6%A8%E0%A6%AD%E0%A6%BF%E0%A6%A4%E0%A7%8D%E0%A6%A4%E0%A6%BF%E0%A6%95_%E0%A6%AA%E0%A7%8D%E0%A6%B0%E0%A7%8B%E0%A6%97%E0%A7%8D%E0%A6%B0%E0%A6%BE%E0%A6%AE%E0%A6%BF%E0%A6%82" title="ফাংশনভিত্তিক প্রোগ্রামিং – Bangla" lang="bn" hreflang="bn" data-title="ফাংশনভিত্তিক প্রোগ্রামিং" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target">বাংলা</a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D1%8B%D1%8F%D0%BD%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0%D0%B5_%D0%BF%D1%80%D0%B0%D0%B3%D1%80%D0%B0%D0%BC%D0%B0%D0%B2%D0%B0%D0%BD%D0%BD%D0%B5" title="Функцыянальнае праграмаванне – Belarusian" lang="be" hreflang="be" data-title="Функцыянальнае праграмаванне" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target">Беларуская</a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D0%BE%D0%BD%D0%B0%D0%BB%D0%BD%D0%BE_%D0%BF%D1%80%D0%BE%D0%B3%D1%80%D0%B0%D0%BC%D0%B8%D1%80%D0%B0%D0%BD%D0%B5" title="Функционално програмиране – Bulgarian" lang="bg" hreflang="bg" data-title="Функционално програмиране" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target">Български</a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Programaci%C3%B3_funcional" title="Programació funcional – Catalan" lang="ca" hreflang="ca" data-title="Programació funcional" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target">Català</a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Funkcion%C3%A1ln%C3%AD_programov%C3%A1n%C3%AD" title="Funkcionální programování – Czech" lang="cs" hreflang="cs" data-title="Funkcionální programování" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target">Čeština</a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Funktionsprogrammering" title="Funktionsprogrammering – Danish" lang="da" hreflang="da" data-title="Funktionsprogrammering" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target">Dansk</a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Funktionale_Programmierung" title="Funktionale Programmierung – German" lang="de" hreflang="de" data-title="Funktionale Programmierung" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target">Deutsch</a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Funktsionaalne_programmeerimine" title="Funktsionaalne programmeerimine – Estonian" lang="et" hreflang="et" data-title="Funktsionaalne programmeerimine" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target">Eesti</a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A3%CF%85%CE%BD%CE%B1%CF%81%CF%84%CE%B7%CF%83%CE%B9%CE%B1%CE%BA%CF%8C%CF%82_%CF%80%CF%81%CE%BF%CE%B3%CF%81%CE%B1%CE%BC%CE%BC%CE%B1%CF%84%CE%B9%CF%83%CE%BC%CF%8C%CF%82" title="Συναρτησιακός προγραμματισμός – Greek" lang="el" hreflang="el" data-title="Συναρτησιακός προγραμματισμός" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target">Ελληνικά</a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Programaci%C3%B3n_funcional" title="Programación funcional – Spanish" lang="es" hreflang="es" data-title="Programación funcional" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Programazio_funtzional" title="Programazio funtzional – Basque" lang="eu" hreflang="eu" data-title="Programazio funtzional" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target">Euskara</a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A8%D8%B1%D9%86%D8%A7%D9%85%D9%87%E2%80%8C%D9%86%D9%88%DB%8C%D8%B3%DB%8C_%D8%AA%D8%A7%D8%A8%D8%B9%DB%8C" title="برنامه‌نویسی تابعی – Persian" lang="fa" hreflang="fa" data-title="برنامه‌نویسی تابعی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target">فارسی</a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Programmation_fonctionnelle" title="Programmation fonctionnelle – French" lang="fr" hreflang="fr" data-title="Programmation fonctionnelle" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/R%C3%ADomhchl%C3%A1r%C3%BA_feidhmi%C3%BAil" title="Ríomhchlárú feidhmiúil – Irish" lang="ga" hreflang="ga" data-title="Ríomhchlárú feidhmiúil" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target">Gaeilge</a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Programaci%C3%B3n_funcional" title="Programación funcional – Galician" lang="gl" hreflang="gl" data-title="Programación funcional" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target">Galego</a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%95%A8%EC%88%98%ED%98%95_%ED%94%84%EB%A1%9C%EA%B7%B8%EB%9E%98%EB%B0%8D" title="함수형 프로그래밍 – Korean" lang="ko" hreflang="ko" data-title="함수형 프로그래밍" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%96%D5%B8%D6%82%D5%B6%D5%AF%D6%81%D5%AB%D5%B8%D5%B6%D5%A1%D5%AC_%D5%AE%D6%80%D5%A1%D5%A3%D6%80%D5%A1%D5%BE%D5%B8%D6%80%D5%B8%D6%82%D5%B4" title="Ֆունկցիոնալ ծրագրավորում – Armenian" lang="hy" hreflang="hy" data-title="Ֆունկցիոնալ ծրագրավորում" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target">Հայերեն</a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Funkcijsko_programiranje" title="Funkcijsko programiranje – Croatian" lang="hr" hreflang="hr" data-title="Funkcijsko programiranje" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target">Hrvatski</a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Pemrograman_fungsional" title="Pemrograman fungsional – Indonesian" lang="id" hreflang="id" data-title="Pemrograman fungsional" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target">Bahasa Indonesia</a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Programmazione_funzionale" title="Programmazione funzionale – Italian" lang="it" hreflang="it" data-title="Programmazione funzionale" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target">Italiano</a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%AA%D7%9B%D7%A0%D7%95%D7%AA_%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%A0%D7%9C%D7%99" title="תכנות פונקציונלי – Hebrew" lang="he" hreflang="he" data-title="תכנות פונקציונלי" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target">עברית</a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Uprogramishaji_kikadhia" title="Uprogramishaji kikadhia – Swahili" lang="sw" hreflang="sw" data-title="Uprogramishaji kikadhia" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target">Kiswahili</a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Programmatura_functionalis" title="Programmatura functionalis – Latin" lang="la" hreflang="la" data-title="Programmatura functionalis" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target">Latina</a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Funkcinis_programavimas" title="Funkcinis programavimas – Lithuanian" lang="lt" hreflang="lt" data-title="Funkcinis programavimas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target">Lietuvių</a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Funkcion%C3%A1lis_programoz%C3%A1s" title="Funkcionális programozás – Hungarian" lang="hu" hreflang="hu" data-title="Funkcionális programozás" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target">Magyar</a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AB%E0%B4%99%E0%B5%8D%E0%B4%B7%E0%B4%A3%E0%B5%BD_%E0%B4%AA%E0%B5%8D%E0%B4%B0%E0%B5%8B%E0%B4%97%E0%B5%8D%E0%B4%B0%E0%B4%BE%E0%B4%AE%E0%B4%BF%E0%B4%82%E0%B4%97%E0%B5%8D" title="ഫങ്ഷണൽ പ്രോഗ്രാമിംഗ് – Malayalam" lang="ml" hreflang="ml" data-title="ഫങ്ഷണൽ പ്രോഗ്രാമിംഗ്" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target">മലയാളം</a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Pengaturcaraan_kefungsian" title="Pengaturcaraan kefungsian – Malay" lang="ms" hreflang="ms" data-title="Pengaturcaraan kefungsian" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target">Bahasa Melayu</a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/Porgrama%C3%A7on_funcional" title="Porgramaçon funcional – Mirandese" lang="mwl" hreflang="mwl" data-title="Porgramaçon funcional" data-language-autonym="Mirandés" data-language-local-name="Mirandese" class="interlanguage-link-target">Mirandés</a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Functioneel_programmeren" title="Functioneel programmeren – Dutch" lang="nl" hreflang="nl" data-title="Functioneel programmeren" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%96%A2%E6%95%B0%E5%9E%8B%E3%83%97%E3%83%AD%E3%82%B0%E3%83%A9%E3%83%9F%E3%83%B3%E3%82%B0" title="関数型プログラミング – Japanese" lang="ja" hreflang="ja" data-title="関数型プログラミング" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Funksjonell_programmering" title="Funksjonell 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class="mw-parser-output"><a href="/wiki/File:En-Functional_programming.ogg" title="Listen to this article"><img alt="Listen to this article" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Sound-icon.svg/20px-Sound-icon.svg.png" decoding="async" width="20" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Sound-icon.svg/30px-Sound-icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/47/Sound-icon.svg/40px-Sound-icon.svg.png 2x" data-file-width="128" data-file-height="96" /></a></div></div> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Programming paradigm based on applying and composing functions</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For subroutine-oriented programming, see <a href="/wiki/Procedural_programming" title="Procedural programming">Procedural programming</a>.</div> In <a href="/wiki/Computer_science" title="Computer science">computer science</a>, functional programming is a <a href="/wiki/Programming_paradigm" title="Programming paradigm">programming paradigm</a> where programs are constructed by <a href="/wiki/Function_application" title="Function application">applying</a> and <a href="/wiki/Function_composition_(computer_science)" title="Function composition (computer science)">composing</a> <a href="/wiki/Function_(computer_science)" class="mw-redirect" title="Function (computer science)">functions</a>. It is a <a href="/wiki/Declarative_programming" title="Declarative programming">declarative programming</a> paradigm in which function definitions are <a href="/wiki/Tree_(data_structure)" class="mw-redirect" title="Tree (data structure)">trees</a> of <a href="/wiki/Expression_(computer_science)" title="Expression (computer science)">expressions</a> that map <a href="/wiki/Value_(computer_science)" title="Value (computer science)">values</a> to other values, rather than a sequence of <a href="/wiki/Imperative_programming" title="Imperative programming">imperative</a> <a href="/wiki/Statement_(computer_science)" title="Statement (computer science)">statements</a> which update the <a href="/wiki/State_(computer_science)" title="State (computer science)">running state</a> of the program. In functional programming, functions are treated as <a href="/wiki/First-class_citizen" title="First-class citizen">first-class citizens</a>, meaning that they can be bound to names (including local <a href="/wiki/Identifier_(computer_languages)" title="Identifier (computer languages)">identifiers</a>), passed as <a href="/wiki/Parameter_(computer_programming)" title="Parameter (computer programming)">arguments</a>, and <a href="/wiki/Return_value" class="mw-redirect" title="Return value">returned</a> from other functions, just as any other <a href="/wiki/Data_type" title="Data type">data type</a> can. This allows programs to be written in a <a href="/wiki/Declarative_programming" title="Declarative programming">declarative</a> and <a href="/wiki/Composability" title="Composability">composable</a> style, where small functions are combined in a <a href="/wiki/Modular_programming" title="Modular programming">modular</a> manner. Functional programming is sometimes treated as synonymous with <a href="/wiki/Purely_functional_programming" title="Purely functional programming">purely functional programming</a>, a subset of functional programming that treats all functions as <a href="/wiki/Deterministic_system" title="Deterministic system">deterministic</a> mathematical <a href="/wiki/Function_(mathematics)" title="Function (mathematics)">functions</a>, or <a href="/wiki/Pure_function" title="Pure function">pure functions</a>. When a pure function is called with some given arguments, it will always return the same result, and cannot be affected by any mutable <a href="/wiki/State_(computer_science)" title="State (computer science)">state</a> or other <a href="/wiki/Side_effect_(computer_science)" title="Side effect (computer science)">side effects</a>. This is in contrast with impure <a href="/wiki/Procedure_(computer_science)" class="mw-redirect" title="Procedure (computer science)">procedures</a>, common in <a href="/wiki/Imperative_programming" title="Imperative programming">imperative programming</a>, which can have side effects (such as modifying the program's state or taking input from a user). Proponents of purely functional programming claim that by restricting side effects, programs can have fewer <a href="/wiki/Software_bug" title="Software bug">bugs</a>, be easier to <a href="/wiki/Debugging" title="Debugging">debug</a> and <a href="/wiki/Software_testing" title="Software testing">test</a>, and be more suited to <a href="/wiki/Formal_verification" title="Formal verification">formal verification</a>.<a href="#cite_note-hudak1989-1">[1]</a><a href="#cite_note-hughesWhyFPMatters-2">[2]</a> Functional programming has its roots in <a href="/wiki/Academia" class="mw-redirect" title="Academia">academia</a>, evolving from the <a href="/wiki/Lambda_calculus" title="Lambda calculus">lambda calculus</a>, a formal system of computation based only on functions. Functional programming has historically been less popular than imperative programming, but many functional languages are seeing use today in industry and education, including <a href="/wiki/Common_Lisp" title="Common Lisp">Common Lisp</a>, <a href="/wiki/Scheme_(programming_language)" title="Scheme (programming language)">Scheme</a>,<a href="#cite_note-clinger1987-3">[3]</a><a href="#cite_note-hartheimer1987-4">[4]</a><a href="#cite_note-kidd2007-5">[5]</a><a href="#cite_note-cleis2006-6">[6]</a> <a href="/wiki/Clojure" title="Clojure">Clojure</a>, <a href="/wiki/Wolfram_Language" title="Wolfram Language">Wolfram Language</a>,<a href="#cite_note-reference.wolfram.com-7">[7]</a><a href="#cite_note-Amath-CO-8">[8]</a> <a href="/wiki/Racket_(programming_language)" title="Racket (programming language)">Racket</a>,<a href="#cite_note-racket-video-games-9">[9]</a> <a href="/wiki/Erlang_(programming_language)" title="Erlang (programming language)">Erlang</a>,<a href="#cite_note-erlang-faq-10">[10]</a><a href="#cite_note-armstrong2007-11">[11]</a><a href="#cite_note-larson2009-12">[12]</a> <a href="/wiki/Elixir_(programming_language)" title="Elixir (programming language)">Elixir</a>,<a href="#cite_note-13">[13]</a> <a href="/wiki/OCaml" title="OCaml">OCaml</a>,<a href="#cite_note-minksy2008-14">[14]</a><a href="#cite_note-leroy2007-15">[15]</a> <a href="/wiki/Haskell" title="Haskell">Haskell</a>,<a href="#cite_note-haskell-industry-16">[16]</a><a href="#cite_note-hudak2007-17">[17]</a> and <a href="/wiki/F_Sharp_(programming_language)" title="F Sharp (programming language)">F#</a>.<a href="#cite_note-quantFSharp-18">[18]</a><a href="#cite_note-businessAppsFSharp-19">[19]</a> <a href="/wiki/Lean_(proof_assistant)" title="Lean (proof assistant)">Lean</a> is a functional programming language commonly used for verifying mathematical theorems.<a href="#cite_note-20">[20]</a> Functional programming is also key to some languages that have found success in specific domains, like <a href="/wiki/JavaScript" title="JavaScript">JavaScript</a> in the Web,<a href="#cite_note-21">[21]</a> <a href="/wiki/R_(programming_language)" title="R (programming language)">R</a> in statistics,<a href="#cite_note-useR-22">[22]</a><a href="#cite_note-Chambers-23">[23]</a> <a href="/wiki/J_(programming_language)" title="J (programming language)">J</a>, <a href="/wiki/K_(programming_language)" title="K (programming language)">K</a> and <a href="/wiki/Q_(programming_language_from_Kx_Systems)" title="Q (programming language from Kx Systems)">Q</a> in financial analysis, and <a href="/wiki/XQuery" title="XQuery">XQuery</a>/<a href="/wiki/XSLT" title="XSLT">XSLT</a> for <a href="/wiki/XML" title="XML">XML</a>.<a href="#cite_note-Novatchev-24">[24]</a><a href="#cite_note-Mertz-25">[25]</a> Domain-specific declarative languages like <a href="/wiki/SQL" title="SQL">SQL</a> and <a href="/wiki/Lex_(software)" title="Lex (software)">Lex</a>/<a href="/wiki/Yacc" title="Yacc">Yacc</a> use some elements of functional programming, such as not allowing <a href="/wiki/Mutable_object" class="mw-redirect" title="Mutable object">mutable values</a>.<a href="#cite_note-Chamberlin_Boyce-26">[26]</a> In addition, many other programming languages support programming in a functional style or have implemented features from functional programming, such as <a href="/wiki/C%2B%2B11" title="C++11">C++11</a>, <a href="/wiki/C_Sharp_(programming_language)" title="C Sharp (programming language)">C#</a>,<a href="#cite_note-27">[27]</a> <a href="/wiki/Kotlin_(programming_language)" title="Kotlin (programming language)">Kotlin</a>,<a href="#cite_note-:0-28">[28]</a> <a href="/wiki/Perl" title="Perl">Perl</a>,<a href="#cite_note-29">[29]</a> <a href="/wiki/PHP" title="PHP">PHP</a>,<a href="#cite_note-30">[30]</a> <a href="/wiki/Python_(programming_language)" title="Python (programming language)">Python</a>,<a href="#cite_note-AutoNT-13-31">[31]</a> <a href="/wiki/Go_(programming_language)" title="Go (programming language)">Go</a>,<a href="#cite_note-32">[32]</a> <a href="/wiki/Rust_(programming_language)" title="Rust (programming language)">Rust</a>,<a href="#cite_note-33">[33]</a> <a href="/wiki/Raku_(programming_language)" title="Raku (programming language)">Raku</a>,<a href="#cite_note-34">[34]</a> <a href="/wiki/Scala_(programming_language)" title="Scala (programming language)">Scala</a>,<a href="#cite_note-effective-scala-35">[35]</a> and <a href="/wiki/Java_(programming_language)" title="Java (programming language)">Java (since Java 8)</a>.<a href="#cite_note-java-8-javadoc-36">[36]</a> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2>[<a href="/w/index.php?title=Functional_programming&action=edit&section=1" title="Edit section: History">edit</a>]</div> The <a href="/wiki/Lambda_calculus" title="Lambda calculus">lambda calculus</a>, developed in the 1930s by <a href="/wiki/Alonzo_Church" title="Alonzo Church">Alonzo Church</a>, is a <a href="/wiki/Formal_system" title="Formal system">formal system</a> of <a href="/wiki/Computation" title="Computation">computation</a> built from <a href="/wiki/Function_application" title="Function application">function application</a>. In 1937 <a href="/wiki/Alan_Turing" title="Alan Turing">Alan Turing</a> proved that the lambda calculus and <a href="/wiki/Turing_machines" class="mw-redirect" title="Turing machines">Turing machines</a> are equivalent models of computation,<a href="#cite_note-37">[37]</a> showing that the lambda calculus is <a href="/wiki/Turing_complete" class="mw-redirect" title="Turing complete">Turing complete</a>. Lambda calculus forms the basis of all functional programming languages. An equivalent theoretical formulation, <a href="/wiki/Combinatory_logic" title="Combinatory logic">combinatory logic</a>, was developed by <a href="/wiki/Moses_Sch%C3%B6nfinkel" title="Moses Schönfinkel">Moses Schönfinkel</a> and <a href="/wiki/Haskell_Curry" title="Haskell Curry">Haskell Curry</a> in the 1920s and 1930s.<a href="#cite_note-38">[38]</a> Church later developed a weaker system, the <a href="/wiki/Simply-typed_lambda_calculus" class="mw-redirect" title="Simply-typed lambda calculus">simply-typed lambda calculus</a>, which extended the lambda calculus by assigning a <a href="/wiki/Data_type" title="Data type">data type</a> to all terms.<a href="#cite_note-39">[39]</a> This forms the basis for statically typed functional programming. The first <a href="/wiki/High-level_programming_language" title="High-level programming language">high-level</a> functional programming language, <a href="/wiki/Lisp_(programming_language)" title="Lisp (programming language)">Lisp</a>, was developed in the late 1950s for the <a href="/wiki/IBM_700/7000_series#Scientific_Architecture" title="IBM 700/7000 series">IBM 700/7000 series</a> of scientific computers by <a href="/wiki/John_McCarthy_(computer_scientist)" title="John McCarthy (computer scientist)">John McCarthy</a> while at <a href="/wiki/Massachusetts_Institute_of_Technology" title="Massachusetts Institute of Technology">Massachusetts Institute of Technology</a> (MIT).<a href="#cite_note-40">[40]</a> Lisp functions were defined using Church's lambda notation, extended with a label construct to allow <a href="/wiki/Recursion_(computer_science)" title="Recursion (computer science)">recursive</a> functions.<a href="#cite_note-41">[41]</a> Lisp first introduced many paradigmatic features of functional programming, though early Lisps were <a href="/wiki/Programming_paradigm#Multi-paradigm" title="Programming paradigm">multi-paradigm languages</a>, and incorporated support for numerous programming styles as new paradigms evolved. Later dialects, such as <a href="/wiki/Scheme_(programming_language)" title="Scheme (programming language)">Scheme</a> and <a href="/wiki/Clojure" title="Clojure">Clojure</a>, and offshoots such as <a href="/wiki/Dylan_(programming_language)" title="Dylan (programming language)">Dylan</a> and <a href="/wiki/Julia_(programming_language)" title="Julia (programming language)">Julia</a>, sought to simplify and rationalise Lisp around a cleanly functional core, while <a href="/wiki/Common_Lisp" title="Common Lisp">Common Lisp</a> was designed to preserve and update the paradigmatic features of the numerous older dialects it replaced.<a href="#cite_note-42">[42]</a> <a href="/wiki/Information_Processing_Language" title="Information Processing Language">Information Processing Language</a> (IPL), 1956, is sometimes cited as the first computer-based functional programming language.<a href="#cite_note-43">[43]</a> It is an <a href="/wiki/Assembly_language" title="Assembly language">assembly-style language</a> for manipulating lists of symbols. It does have a notion of generator, which amounts to a function that accepts a function as an argument, and, since it is an assembly-level language, code can be data, so IPL can be regarded as having higher-order functions. However, it relies heavily on the mutating list structure and similar imperative features. <a href="/wiki/Kenneth_E._Iverson" title="Kenneth E. Iverson">Kenneth E. Iverson</a> developed <a href="/wiki/APL_(programming_language)" title="APL (programming language)">APL</a> in the early 1960s, described in his 1962 book A Programming Language (<style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780471430148" title="Special:BookSources/9780471430148">9780471430148</a>). APL was the primary influence on <a href="/wiki/John_Backus" title="John Backus">John Backus</a>'s <a href="/wiki/FP_(programming_language)" title="FP (programming language)">FP</a>. In the early 1990s, Iverson and <a href="/wiki/Roger_Hui" title="Roger Hui">Roger Hui</a> created <a href="/wiki/J_(programming_language)" title="J (programming language)">J</a>. In the mid-1990s, <a href="/wiki/Arthur_Whitney_(computer_scientist)" title="Arthur Whitney (computer scientist)">Arthur Whitney</a>, who had previously worked with Iverson, created <a href="/wiki/K_(programming_language)" title="K (programming language)">K</a>, which is used commercially in financial industries along with its descendant <a href="/wiki/Q_(programming_language_from_Kx_Systems)" title="Q (programming language from Kx Systems)">Q</a>. In the mid-1960s, <a href="/wiki/Peter_Landin" title="Peter Landin">Peter Landin</a> invented <a href="/wiki/SECD_machine" title="SECD machine">SECD machine</a>,<a href="#cite_note-44">[44]</a> the first <a href="/wiki/Abstract_machine" title="Abstract machine">abstract machine</a> for a functional programming language,<a href="#cite_note-45">[45]</a> described a correspondence between <a href="/wiki/ALGOL_60" title="ALGOL 60">ALGOL 60</a> and the <a href="/wiki/Lambda_calculus" title="Lambda calculus">lambda calculus</a>,<a href="#cite_note-46">[46]</a><a href="#cite_note-47">[47]</a> and proposed the <a href="/wiki/ISWIM" title="ISWIM">ISWIM</a> programming language.<a href="#cite_note-48">[48]</a> <a href="/wiki/John_Backus" title="John Backus">John Backus</a> presented <a href="/wiki/FP_(programming_language)" title="FP (programming language)">FP</a> in his 1977 <a href="/wiki/Turing_Award" title="Turing Award">Turing Award</a> lecture "Can Programming Be Liberated From the <a href="/wiki/Von_Neumann_architecture" title="Von Neumann architecture">von Neumann</a> Style? A Functional Style and its Algebra of Programs".<a href="#cite_note-Backus_1977-49">[49]</a> He defines functional programs as being built up in a hierarchical way by means of "combining forms" that allow an "algebra of programs"; in modern language, this means that functional programs follow the <a href="/wiki/Principle_of_compositionality" title="Principle of compositionality">principle of compositionality</a>.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="I dont completely agree with this interpretation of John Backus definition of functional programs, which I feel is widely misunderstood. As he is very sadly no longer alive, we can't ask him, but a reference for this interpretation, especially if it includes a justification, would be very beneficial. (February 2017)">citation needed</a>] Backus's paper popularized research into functional programming, though it emphasized <a href="/wiki/Function-level_programming" title="Function-level programming">function-level programming</a> rather than the lambda-calculus style now associated with functional programming. The 1973 language <a href="/wiki/ML_(programming_language)" title="ML (programming language)">ML</a> was created by <a href="/wiki/Robin_Milner" title="Robin Milner">Robin Milner</a> at the <a href="/wiki/University_of_Edinburgh" title="University of Edinburgh">University of Edinburgh</a>, and <a href="/wiki/David_Turner_(computer_scientist)" title="David Turner (computer scientist)">David Turner</a> developed the language <a href="/wiki/SASL_(programming_language)" title="SASL (programming language)">SASL</a> at the <a href="/wiki/University_of_St_Andrews" title="University of St Andrews">University of St Andrews</a>. Also in Edinburgh in the 1970s, Burstall and Darlington developed the functional language <a href="/wiki/NPL_(programming_language)" title="NPL (programming language)">NPL</a>.<a href="#cite_note-50">[50]</a> NPL was based on <a href="/wiki/Kleene%27s_recursion_theorem" title="Kleene's recursion theorem">Kleene Recursion Equations</a> and was first introduced in their work on program transformation.<a href="#cite_note-51">[51]</a> Burstall, MacQueen and Sannella then incorporated the <a href="/wiki/Polymorphism_(computer_science)" title="Polymorphism (computer science)">polymorphic</a> type checking from ML to produce the language <a href="/wiki/Hope_(programming_language)" title="Hope (programming language)">Hope</a>.<a href="#cite_note-52">[52]</a> ML eventually developed into several dialects, the most common of which are now <a href="/wiki/OCaml" title="OCaml">OCaml</a> and <a href="/wiki/Standard_ML" title="Standard ML">Standard ML</a>. In the 1970s, <a href="/wiki/Guy_L._Steele" class="mw-redirect" title="Guy L. Steele">Guy L. Steele</a> and <a href="/wiki/Gerald_Jay_Sussman" title="Gerald Jay Sussman">Gerald Jay Sussman</a> developed <a href="/wiki/Scheme_(programming_language)" title="Scheme (programming language)">Scheme</a>, as described in the <a href="/wiki/Lambda_Papers" class="mw-redirect" title="Lambda Papers">Lambda Papers</a> and the 1985 textbook <a href="/wiki/Structure_and_Interpretation_of_Computer_Programs" title="Structure and Interpretation of Computer Programs">Structure and Interpretation of Computer Programs</a>. Scheme was the first dialect of lisp to use <a href="/wiki/Lexical_scope" class="mw-redirect" title="Lexical scope">lexical scoping</a> and to require <a href="/wiki/Tail-call_optimization" class="mw-redirect" title="Tail-call optimization">tail-call optimization</a>, features that encourage functional programming. In the 1980s, <a href="/wiki/Per_Martin-L%C3%B6f" title="Per Martin-Löf">Per Martin-Löf</a> developed <a href="/wiki/Intuitionistic_type_theory" title="Intuitionistic type theory">intuitionistic type theory</a> (also called constructive type theory), which associated functional programs with <a href="/wiki/Constructive_proof" title="Constructive proof">constructive proofs</a> expressed as <a href="/wiki/Dependent_type" title="Dependent type">dependent types</a>. This led to new approaches to <a href="/wiki/Interactive_theorem_proving" class="mw-redirect" title="Interactive theorem proving">interactive theorem proving</a> and has influenced the development of subsequent functional programming languages.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] The lazy functional language, <a href="/wiki/Miranda_(programming_language)" title="Miranda (programming language)">Miranda</a>, developed by David Turner, initially appeared in 1985 and had a strong influence on <a href="/wiki/Haskell" title="Haskell">Haskell</a>. With Miranda being proprietary, Haskell began with a consensus in 1987 to form an <a href="/wiki/Open_standard" title="Open standard">open standard</a> for functional programming research; implementation releases have been ongoing as of 1990. More recently it has found use in niches such as parametric <a href="/wiki/Computer_Aided_Design" class="mw-redirect" title="Computer Aided Design">CAD</a> in the <a href="/wiki/OpenSCAD" title="OpenSCAD">OpenSCAD</a> language built on the <a href="/wiki/CGAL" title="CGAL">CGAL</a> framework, although its restriction on reassigning values (all values are treated as constants) has led to confusion among users who are unfamiliar with functional programming as a concept.<a href="#cite_note-53">[53]</a> Functional programming continues to be used in commercial settings.<a href="#cite_note-54">[54]</a><a href="#cite_note-55">[55]</a><a href="#cite_note-56">[56]</a> <div class="mw-heading mw-heading2"><h2 id="Concepts">Concepts</h2>[<a href="/w/index.php?title=Functional_programming&action=edit&section=2" title="Edit section: Concepts">edit</a>]</div> A number of concepts<a href="#cite_note-57">[57]</a> and paradigms are specific to functional programming, and generally foreign to <a href="/wiki/Imperative_programming" title="Imperative programming">imperative programming</a> (including <a href="/wiki/Object-oriented_programming" title="Object-oriented programming">object-oriented programming</a>). However, programming languages often cater to several programming paradigms, so programmers using "mostly imperative" languages may have utilized some of these concepts.<a href="#cite_note-58">[58]</a> <div class="mw-heading mw-heading3"><h3 id="First-class_and_higher-order_functions">First-class and higher-order functions</h3>[<a href="/w/index.php?title=Functional_programming&action=edit&section=3" title="Edit section: First-class and higher-order functions">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/First-class_function" title="First-class function">First-class function</a> and <a href="/wiki/Higher-order_function" title="Higher-order function">Higher-order function</a></div> <a href="/wiki/Higher-order_function" title="Higher-order function">Higher-order functions</a> are functions that can either take other functions as arguments or return them as results. In calculus, an example of a higher-order function is the <a href="/wiki/Differential_operator" title="Differential operator">differential operator</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d/dx}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d/dx}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75a0e680edceb47b7d233535262fcacd931585f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.924ex; height:2.843ex;" alt="{\displaystyle d/dx}">, which returns the <a href="/wiki/Derivative" title="Derivative">derivative</a> of a function <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}">. Higher-order functions are closely related to <a href="/wiki/First-class_function" title="First-class function">first-class functions</a> in that higher-order functions and first-class functions both allow functions as arguments and results of other functions. The distinction between the two is subtle: "higher-order" describes a mathematical concept of functions that operate on other functions, while "first-class" is a computer science term for programming language entities that have no restriction on their use (thus first-class functions can appear anywhere in the program that other first-class entities like numbers can, including as arguments to other functions and as their return values). Higher-order functions enable <a href="/wiki/Partial_application" title="Partial application">partial application</a> or <a href="/wiki/Currying" title="Currying">currying</a>, a technique that applies a function to its arguments one at a time, with each application returning a new function that accepts the next argument. This lets a programmer succinctly express, for example, the <a href="/wiki/Successor_function" title="Successor function">successor function</a> as the addition operator partially applied to the <a href="/wiki/Natural_number" title="Natural number">natural number</a> one. <div class="mw-heading mw-heading3"><h3 id="Pure_functions">Pure functions</h3>[<a href="/w/index.php?title=Functional_programming&action=edit&section=4" title="Edit section: Pure functions">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Pure_function" title="Pure function">Pure function</a></div> <a href="/wiki/Pure_function" title="Pure function">Pure functions</a> (or expressions) have no <a href="/wiki/Side_effect_(computer_science)" title="Side effect (computer science)">side effects</a> (memory or I/O). This means that pure functions have several useful properties, many of which can be used to optimize the code: <ul><li>If the result of a pure expression is not used, it can be removed without affecting other expressions.</li> <li>If a pure function is called with arguments that cause no side-effects, the result is constant with respect to that argument list (sometimes called <a href="/wiki/Referential_transparency" title="Referential transparency">referential transparency</a> or <a href="/wiki/Idempotence" title="Idempotence">idempotence</a>), i.e., calling the pure function again with the same arguments returns the same result. (This can enable caching optimizations such as <a href="/wiki/Memoization" title="Memoization">memoization</a>.)</li> <li>If there is no data dependency between two pure expressions, their order can be reversed, or they can be performed in <a href="/wiki/Parallelization" class="mw-redirect" title="Parallelization">parallel</a> and they cannot interfere with one another (in other terms, the evaluation of any pure expression is <a href="/wiki/Thread-safe" class="mw-redirect" title="Thread-safe">thread-safe</a>).</li> <li>If the entire language does not allow side-effects, then any evaluation strategy can be used; this gives the compiler freedom to reorder or combine the evaluation of expressions in a program (for example, using <a href="/wiki/Deforestation_(computer_science)" title="Deforestation (computer science)">deforestation</a>).</li></ul> While most compilers for imperative programming languages detect pure functions and perform common-subexpression elimination for pure function calls, they cannot always do this for pre-compiled libraries, which generally do not expose this information, thus preventing optimizations that involve those external functions. Some compilers, such as <a href="/wiki/GNU_Compiler_Collection" title="GNU Compiler Collection">gcc</a>, add extra keywords for a programmer to explicitly mark external functions as pure, to enable such optimizations. <a href="/wiki/Fortran_95" class="mw-redirect" title="Fortran 95">Fortran 95</a> also lets functions be designated pure.<a href="#cite_note-fortran95-59">[59]</a> C++11 added <code>constexpr</code> keyword with similar semantics. <div class="mw-heading mw-heading3"><h3 id="Recursion">Recursion</h3>[<a href="/w/index.php?title=Functional_programming&action=edit&section=5" title="Edit section: Recursion">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Recursion_(computer_science)" title="Recursion (computer science)">Recursion (computer science)</a></div> <a href="/wiki/Iteration" title="Iteration">Iteration</a> (looping) in functional languages is usually accomplished via <a href="/wiki/Recursion" title="Recursion">recursion</a>. <a href="/wiki/Recursion_(computer_science)" title="Recursion (computer science)">Recursive functions</a> invoke themselves, letting an operation be repeated until it reaches the <a href="/wiki/Recursion_(computer_science)" title="Recursion (computer science)">base case</a>. In general, recursion requires maintaining a <a href="/wiki/Call_stack" title="Call stack">stack</a>, which consumes space in a linear amount to the depth of recursion. This could make recursion prohibitively expensive to use instead of imperative loops. However, a special form of recursion known as <a href="/wiki/Tail_recursion" class="mw-redirect" title="Tail recursion">tail recursion</a> can be recognized and optimized by a compiler into the same code used to implement iteration in imperative languages. Tail recursion optimization can be implemented by transforming the program into <a href="/wiki/Continuation_passing_style" class="mw-redirect" title="Continuation passing style">continuation passing style</a> during compiling, among other approaches. The <a href="/wiki/Scheme_(programming_language)" title="Scheme (programming language)">Scheme</a> language standard requires implementations to support proper tail recursion, meaning they must allow an unbounded number of active tail calls.<a href="#cite_note-SchemeProperTailRec-60">[60]</a><a href="#cite_note-61">[61]</a> Proper tail recursion is not simply an optimization; it is a language feature that assures users that they can use recursion to express a loop and doing so would be safe-for-space.<a href="#cite_note-62">[62]</a> Moreover, contrary to its name, it accounts for all tail calls, not just tail recursion. While proper tail recursion is usually implemented by turning code into imperative loops, implementations might implement it in other ways. For example, <a href="/wiki/Chicken_(Scheme_implementation)" title="Chicken (Scheme implementation)">Chicken</a> intentionally maintains a stack and lets the <a href="/wiki/Stack_overflow" title="Stack overflow">stack overflow</a>. However, when this happens, its <a href="/wiki/Garbage_collection_(computer_science)" title="Garbage collection (computer science)">garbage collector</a> will claim space back,<a href="#cite_note-63">[63]</a> allowing an unbounded number of active tail calls even though it does not turn tail recursion into a loop. Common patterns of recursion can be abstracted away using higher-order functions, with <a href="/wiki/Catamorphism" title="Catamorphism">catamorphisms</a> and <a href="/wiki/Anamorphism" title="Anamorphism">anamorphisms</a> (or "folds" and "unfolds") being the most obvious examples. Such recursion schemes play a role analogous to built-in control structures such as <a href="/wiki/Program_loops" class="mw-redirect" title="Program loops">loops</a> in <a href="/wiki/Imperative_languages" class="mw-redirect" title="Imperative languages">imperative languages</a>. Most general purpose functional programming languages allow unrestricted recursion and are <a href="/wiki/Turing_complete" class="mw-redirect" title="Turing complete">Turing complete</a>, which makes the <a href="/wiki/Halting_problem" title="Halting problem">halting problem</a> <a href="/wiki/Undecidable_problem" title="Undecidable problem">undecidable</a>, can cause unsoundness of <a href="/wiki/Equational_reasoning" class="mw-redirect" title="Equational reasoning">equational reasoning</a>, and generally requires the introduction of <a href="/wiki/Inconsistency" class="mw-redirect" title="Inconsistency">inconsistency</a> into the logic expressed by the language's <a href="/wiki/Type_system" title="Type system">type system</a>. Some special purpose languages such as <a href="/wiki/Coq_(software)" title="Coq (software)">Coq</a> allow only <a href="/wiki/Well-founded" class="mw-redirect" title="Well-founded">well-founded</a> recursion and are <a href="/wiki/Strongly_normalizing" class="mw-redirect" title="Strongly normalizing">strongly normalizing</a> (nonterminating computations can be expressed only with infinite streams of values called <a href="/wiki/Codata_(computer_science)" class="mw-redirect" title="Codata (computer science)">codata</a>). As a consequence, these languages fail to be Turing complete and expressing certain functions in them is impossible, but they can still express a wide class of interesting computations while avoiding the problems introduced by unrestricted recursion. Functional programming limited to well-founded recursion with a few other constraints is called <a href="/wiki/Total_functional_programming" title="Total functional programming">total functional programming</a>.<a href="#cite_note-totalfp-64">[64]</a> <div class="mw-heading mw-heading3"><h3 id="Strict_versus_non-strict_evaluation">Strict versus non-strict evaluation</h3>[<a href="/w/index.php?title=Functional_programming&action=edit&section=6" title="Edit section: Strict versus non-strict evaluation">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Evaluation_strategy" title="Evaluation strategy">Evaluation strategy</a></div> Functional languages can be categorized by whether they use strict (eager) or non-strict (lazy) evaluation, concepts that refer to how function arguments are processed when an expression is being evaluated. The technical difference is in the <a href="/wiki/Denotational_semantics" title="Denotational semantics">denotational semantics</a> of expressions containing failing or divergent computations. Under strict evaluation, the evaluation of any term containing a failing subterm fails. For example, the expression: <pre>print length([2+1, 3*2, 1/0, 5-4]) </pre> fails under strict evaluation because of the division by zero in the third element of the list. Under lazy evaluation, the length function returns the value 4 (i.e., the number of items in the list), since evaluating it does not attempt to evaluate the terms making up the list. In brief, strict evaluation always fully evaluates function arguments before invoking the function. Lazy evaluation does not evaluate function arguments unless their values are required to evaluate the function call itself. The usual implementation strategy for lazy evaluation in functional languages is <a href="/wiki/Graph_reduction" title="Graph reduction">graph reduction</a>.<a href="#cite_note-65">[65]</a> Lazy evaluation is used by default in several pure functional languages, including <a href="/wiki/Miranda_(programming_language)" title="Miranda (programming language)">Miranda</a>, <a href="/wiki/Clean_(programming_language)" title="Clean (programming language)">Clean</a>, and <a href="/wiki/Haskell" title="Haskell">Haskell</a>. <a href="#CITEREFHughes1984">Hughes 1984</a> argues for lazy evaluation as a mechanism for improving program modularity through <a href="/wiki/Separation_of_concerns" title="Separation of concerns">separation of concerns</a>, by easing independent implementation of producers and consumers of data streams.<a href="#cite_note-hughesWhyFPMatters-2">[2]</a> Launchbury 1993 describes some difficulties that lazy evaluation introduces, particularly in analyzing a program's storage requirements, and proposes an <a href="/wiki/Operational_semantics" title="Operational semantics">operational semantics</a> to aid in such analysis.<a href="#cite_note-launchbury1993-66">[66]</a> Harper 2009 proposes including both strict and lazy evaluation in the same language, using the language's type system to distinguish them.<a href="#cite_note-67">[67]</a> <div class="mw-heading mw-heading3"><h3 id="Type_systems">Type systems</h3>[<a href="/w/index.php?title=Functional_programming&action=edit&section=7" title="Edit section: Type systems">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Type_system" title="Type system">Type system</a></div> Especially since the development of <a href="/wiki/Hindley%E2%80%93Milner_type_inference" class="mw-redirect" title="Hindley–Milner type inference">Hindley–Milner type inference</a> in the 1970s, functional programming languages have tended to use <a href="/wiki/Typed_lambda_calculus" title="Typed lambda calculus">typed lambda calculus</a>, rejecting all invalid programs at compilation time and risking <a href="/wiki/False_positives_and_false_negatives#False_positive_error" title="False positives and false negatives">false positive errors</a>, as opposed to the <a href="/wiki/Untyped_lambda_calculus" class="mw-redirect" title="Untyped lambda calculus">untyped lambda calculus</a>, that accepts all valid programs at compilation time and risks <a href="/wiki/False_positives_and_false_negatives#False_negative_error" title="False positives and false negatives">false negative errors</a>, used in Lisp and its variants (such as <a href="/wiki/Scheme_(programming_language)" title="Scheme (programming language)">Scheme</a>), as they reject all invalid programs at runtime when the information is enough to not reject valid programs. The use of <a href="/wiki/Algebraic_data_type" title="Algebraic data type">algebraic data types</a> makes manipulation of complex data structures convenient; the presence of strong compile-time type checking makes programs more reliable in absence of other reliability techniques like <a href="/wiki/Test-driven_development" title="Test-driven development">test-driven development</a>, while <a href="/wiki/Type_inference" title="Type inference">type inference</a> frees the programmer from the need to manually declare types to the compiler in most cases. Some research-oriented functional languages such as <a href="/wiki/Coq_(software)" title="Coq (software)">Coq</a>, <a href="/wiki/Agda_(programming_language)" title="Agda (programming language)">Agda</a>, <a href="/wiki/Lennart_Augustsson" title="Lennart Augustsson">Cayenne</a>, and <a href="/wiki/Epigram_(programming_language)" title="Epigram (programming language)">Epigram</a> are based on <a href="/wiki/Intuitionistic_type_theory" title="Intuitionistic type theory">intuitionistic type theory</a>, which lets types depend on terms. Such types are called <a href="/wiki/Dependent_type" title="Dependent type">dependent types</a>. These type systems do not have decidable type inference and are difficult to understand and program with.<a href="#cite_note-68">[68]</a><a href="#cite_note-69">[69]</a><a href="#cite_note-70">[70]</a><a href="#cite_note-71">[71]</a> But dependent types can express arbitrary propositions in <a href="/wiki/Higher-order_logic" title="Higher-order logic">higher-order logic</a>. Through the <a href="/wiki/Curry%E2%80%93Howard_isomorphism" class="mw-redirect" title="Curry–Howard isomorphism">Curry–Howard isomorphism</a>, then, well-typed programs in these languages become a means of writing formal <a href="/wiki/Mathematical_proof" title="Mathematical proof">mathematical proofs</a> from which a compiler can generate <a href="/wiki/Formal_verification" title="Formal verification">certified code</a>. While these languages are mainly of interest in academic research (including in <a href="/wiki/Formalized_mathematics" class="mw-redirect" title="Formalized mathematics">formalized mathematics</a>), they have begun to be used in engineering as well. <a href="/wiki/Compcert" class="mw-redirect" title="Compcert">Compcert</a> is a <a href="/wiki/Compiler" title="Compiler">compiler</a> for a subset of the language <a href="/wiki/C_(programming_language)" title="C (programming language)">C</a> that is written in Coq and formally verified.<a href="#cite_note-72">[72]</a> A limited form of dependent types called <a href="/wiki/Generalized_algebraic_data_type" title="Generalized algebraic data type">generalized algebraic data types</a> (GADT's) can be implemented in a way that provides some of the benefits of dependently typed programming while avoiding most of its inconvenience.<a href="#cite_note-73">[73]</a> GADT's are available in the <a href="/wiki/Glasgow_Haskell_Compiler" title="Glasgow Haskell Compiler">Glasgow Haskell Compiler</a>, in <a href="/wiki/OCaml" title="OCaml">OCaml</a><a href="#cite_note-74">[74]</a> and in <a href="/wiki/Scala_(programming_language)" title="Scala (programming language)">Scala</a>,<a href="#cite_note-75">[75]</a> and have been proposed as additions to other languages including Java and C#.<a href="#cite_note-76">[76]</a> <div class="mw-heading mw-heading3"><h3 id="Referential_transparency">Referential transparency</h3>[<a href="/w/index.php?title=Functional_programming&action=edit&section=8" title="Edit section: Referential transparency">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Referential_transparency" title="Referential transparency">Referential transparency</a></div> Functional programs do not have assignment statements, that is, the value of a variable in a functional program never changes once defined. This eliminates any chances of side effects because any variable can be replaced with its actual value at any point of execution. So, functional programs are referentially transparent.<a href="#cite_note-77">[77]</a> Consider <a href="/wiki/C_(programming_language)" title="C (programming language)">C</a> assignment statement <code>x=x*10</code>, this changes the value assigned to the variable <code>x</code>. Let us say that the initial value of <code>x</code> was <code>1</code>, then two consecutive evaluations of the variable <code>x</code> yields <code>10</code> and <code>100</code> respectively. Clearly, replacing <code>x=x*10</code> with either <code>10</code> or <code>100</code> gives a program a different meaning, and so the expression is not referentially transparent. In fact, assignment statements are never referentially transparent. Now, consider another function such as <code class="mw-highlight mw-highlight-lang-c mw-content-ltr" dir="ltr">int plusone(int x) {return x+1;}</code> is transparent, as it does not implicitly change the input x and thus has no such <a href="/wiki/Side_effect_(computer_science)" title="Side effect (computer science)">side effects</a>. Functional programs exclusively use this type of function and are therefore referentially transparent. <div class="mw-heading mw-heading3"><h3 id="Data_structures">Data structures</h3>[<a href="/w/index.php?title=Functional_programming&action=edit&section=9" title="Edit section: Data structures">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Purely_functional_data_structure" title="Purely functional data structure">Purely functional data structure</a></div> Purely functional <a href="/wiki/Data_structure" title="Data structure">data structures</a> are often represented in a different way to their <a href="/wiki/Imperative_programming" title="Imperative programming">imperative</a> counterparts.<a href="#cite_note-78">[78]</a> For example, the <a href="/wiki/Array_data_structure" class="mw-redirect" title="Array data structure">array</a> with constant access and update times is a basic component of most imperative languages, and many imperative data-structures, such as the <a href="/wiki/Hash_table" title="Hash table">hash table</a> and <a href="/wiki/Binary_heap" title="Binary heap">binary heap</a>, are based on arrays. Arrays can be replaced by <a href="/wiki/Map_(computer_science)" class="mw-redirect" title="Map (computer science)">maps</a> or random access lists, which admit purely functional implementation, but have <a href="/wiki/Logarithm" title="Logarithm">logarithmic</a> access and update times. Purely functional data structures have <a href="/wiki/Persistent_data_structure" title="Persistent data structure">persistence</a>, a property of keeping previous versions of the data structure unmodified. In Clojure, persistent data structures are used as functional alternatives to their imperative counterparts. Persistent vectors, for example, use trees for partial updating. Calling the insert method will result in some but not all nodes being created.<a href="#cite_note-79">[79]</a> <div class="mw-heading mw-heading2"><h2 id="Comparison_to_imperative_programming">Comparison to imperative programming</h2>[<a href="/w/index.php?title=Functional_programming&action=edit&section=10" title="Edit section: Comparison to imperative programming">edit</a>]</div> Functional programming is very different from <a href="/wiki/Imperative_programming" title="Imperative programming">imperative programming</a>. The most significant differences stem from the fact that functional programming avoids <a href="/wiki/Side_effect_(computer_science)" title="Side effect (computer science)">side effects</a>, which are used in imperative programming to implement state and I/O. Pure functional programming completely prevents side-effects and provides referential transparency. Higher-order functions are rarely used in older imperative programming. A traditional imperative program might use a loop to traverse and modify a list. A functional program, on the other hand, would probably use a higher-order "map" function that takes a function and a list, generating and returning a new list by applying the function to each list item. <div class="mw-heading mw-heading3"><h3 id="Imperative_vs._functional_programming">Imperative vs. functional programming</h3>[<a href="/w/index.php?title=Functional_programming&action=edit&section=11" title="Edit section: Imperative vs. functional programming">edit</a>]</div> The following two examples (written in <a href="/wiki/JavaScript_(programming_language)" class="mw-redirect" title="JavaScript (programming language)">JavaScript</a>) achieve the same effect: they multiply all even numbers in an array by 10 and add them all, storing the final sum in the variable "result". Traditional imperative loop: <div class="mw-highlight mw-highlight-lang-javascript mw-content-ltr" dir="ltr"><pre>const numList = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]; let result = 0; for (let i = 0; i < numList.length; i++) { if (numList[i] % 2 === 0) { result += numList[i] * 10; } } </pre></div> Functional programming with higher-order functions: <div class="mw-highlight mw-highlight-lang-javascript mw-content-ltr" dir="ltr"><pre>const result = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] .filter(n => n % 2 === 0) .map(a => a * 10) .reduce((a, b) => a + b, 0); </pre></div>Sometimes the abstractions offered by functional programming might lead to development of more robust code that avoids certain issues that might arise when building upon large amount of complex, imperative code, such as <a href="/wiki/Off-by-one_error" title="Off-by-one error">off-by-one errors</a> (see <a href="/wiki/Greenspun%27s_tenth_rule" title="Greenspun's tenth rule">Greenspun's tenth rule</a>). <div class="mw-heading mw-heading3"><h3 id="Simulating_state">Simulating state</h3>[<a href="/w/index.php?title=Functional_programming&action=edit&section=12" title="Edit section: Simulating state">edit</a>]</div> There are tasks (for example, maintaining a bank account balance) that often seem most naturally implemented with state. Pure functional programming performs these tasks, and I/O tasks such as accepting user input and printing to the screen, in a different way. The pure functional programming language <a href="/wiki/Haskell" title="Haskell">Haskell</a> implements them using <a href="/wiki/Monad_(functional_programming)" title="Monad (functional programming)">monads</a>, derived from <a href="/wiki/Category_theory" title="Category theory">category theory</a>.<a href="#cite_note-80">[80]</a> Monads offer a way to abstract certain types of computational patterns, including (but not limited to) modeling of computations with mutable state (and other side effects such as I/O) in an imperative manner without losing purity. While existing monads may be easy to apply in a program, given appropriate templates and examples, many students find them difficult to understand conceptually, e.g., when asked to define new monads (which is sometimes needed for certain types of libraries).<a href="#cite_note-81">[81]</a> Functional languages also simulate states by passing around immutable states. This can be done by making a function accept the state as one of its parameters, and return a new state together with the result, leaving the old state unchanged.<a href="#cite_note-82">[82]</a> Impure functional languages usually include a more direct method of managing mutable state. <a href="/wiki/Clojure" title="Clojure">Clojure</a>, for example, uses managed references that can be updated by applying pure functions to the current state. This kind of approach enables mutability while still promoting the use of pure functions as the preferred way to express computations.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] Alternative methods such as <a href="/wiki/Hoare_logic" title="Hoare logic">Hoare logic</a> and <a href="/wiki/Uniqueness_type" title="Uniqueness type">uniqueness</a> have been developed to track side effects in programs. Some modern research languages use <a href="/wiki/Effect_system" title="Effect system">effect systems</a> to make the presence of side effects explicit.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] <div class="mw-heading mw-heading3"><h3 id="Efficiency_issues">Efficiency issues</h3>[<a href="/w/index.php?title=Functional_programming&action=edit&section=13" title="Edit section: Efficiency issues">edit</a>]</div> Functional programming languages are typically less efficient in their use of <a href="/wiki/Central_processing_unit" title="Central processing unit">CPU</a> and memory than imperative languages such as <a href="/wiki/C_(programming_language)" title="C (programming language)">C</a> and <a href="/wiki/Pascal_(programming_language)" title="Pascal (programming language)">Pascal</a>.<a href="#cite_note-83">[83]</a> This is related to the fact that some mutable data structures like arrays have a very straightforward implementation using present hardware. Flat arrays may be accessed very efficiently with deeply pipelined CPUs, prefetched efficiently through caches (with no complex <a href="/w/index.php?title=Pointer_chasing&action=edit&redlink=1" class="new" title="Pointer chasing (page does not exist)">pointer chasing</a>), or handled with SIMD instructions. It is also not easy to create their equally efficient general-purpose immutable counterparts. For purely functional languages, the worst-case slowdown is logarithmic in the number of memory cells used, because mutable memory can be represented by a purely functional data structure with logarithmic access time (such as a balanced tree).<a href="#cite_note-Spiewak-84">[84]</a> However, such slowdowns are not universal. For programs that perform intensive numerical computations, functional languages such as <a href="/wiki/OCaml" title="OCaml">OCaml</a> and <a href="/wiki/Clean_(programming_language)" title="Clean (programming language)">Clean</a> are only slightly slower than C according to <a href="/wiki/The_Computer_Language_Benchmarks_Game" title="The Computer Language Benchmarks Game">The Computer Language Benchmarks Game</a>.<a href="#cite_note-85">[85]</a> For programs that handle large <a href="/wiki/Matrix_(mathematics)" title="Matrix (mathematics)">matrices</a> and multidimensional <a href="/wiki/Database" title="Database">databases</a>, <a href="/wiki/Array_programming" title="Array programming">array</a> functional languages (such as <a href="/wiki/J_(programming_language)" title="J (programming language)">J</a> and <a href="/wiki/K_(programming_language)" title="K (programming language)">K</a>) were designed with speed optimizations. Immutability of data can in many cases lead to execution efficiency by allowing the compiler to make assumptions that are unsafe in an imperative language, thus increasing opportunities for <a href="/wiki/Inline_expansion" title="Inline expansion">inline expansion</a>.<a href="#cite_note-86">[86]</a> Even if the involved copying that may seem implicit when dealing with persistent immutable data structures might seem computationally costly, some functional programming languages, like <a href="/wiki/Clojure" title="Clojure">Clojure</a> solve this issue by implementing mechanisms for safe memory sharing between formally immutable data.<a href="#cite_note-87">[87]</a> <a href="/wiki/Rust_(programming_language)" title="Rust (programming language)">Rust</a> distinguishes itself by its approach to data immutability which involves immutable <a href="/wiki/Reference_(computer_science)" title="Reference (computer science)">references</a><a href="#cite_note-88">[88]</a> and a concept called lifetimes.<a href="#cite_note-89">[89]</a> Immutable data with separation of identity and state and <a href="/wiki/Shared-nothing_architecture" title="Shared-nothing architecture">shared-nothing</a> schemes can also potentially be more well-suited for <a href="/wiki/Parallel_computing" title="Parallel computing">concurrent and parallel</a> programming by the virtue of reducing or eliminating the risk of certain concurrency hazards, since concurrent operations are usually <a href="/wiki/Linearizability" title="Linearizability">atomic</a> and this allows eliminating the need for locks. This is how for example <code>java.util.concurrent</code> classes are implemented, where some of them are immutable variants of the corresponding classes that are not suitable for concurrent use.<a href="#cite_note-90">[90]</a> Functional programming languages often have a concurrency model that instead of shared state and synchronization, leverages <a href="/wiki/Message_passing" title="Message passing">message passing</a> mechanisms (such as the <a href="/wiki/Actor_model" title="Actor model">actor model</a>, where each actor is a container for state, behavior, child actors and a message queue).<a href="#cite_note-91">[91]</a><a href="#cite_note-92">[92]</a> This approach is common in <a href="/wiki/Erlang_(programming_language)" title="Erlang (programming language)">Erlang</a>/<a href="/wiki/Elixir_(programming_language)" title="Elixir (programming language)">Elixir</a> or <a href="/wiki/Akka_(toolkit)" title="Akka (toolkit)">Akka</a>. <a href="/wiki/Lazy_evaluation" title="Lazy evaluation">Lazy evaluation</a> may also speed up the program, even asymptotically, whereas it may slow it down at most by a constant factor (however, it may introduce <a href="/wiki/Memory_leak" title="Memory leak">memory leaks</a> if used improperly). Launchbury 1993<a href="#cite_note-launchbury1993-66">[66]</a> discusses theoretical issues related to memory leaks from lazy evaluation, and O'Sullivan et al. 2008<a href="#cite_note-93">[93]</a> give some practical advice for analyzing and fixing them. However, the most general implementations of lazy evaluation making extensive use of dereferenced code and data perform poorly on modern processors with deep pipelines and multi-level caches (where a cache miss may cost hundreds of cycles) [<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>]. <div class="mw-heading mw-heading4"><h4 id="Abstraction_cost">Abstraction cost</h4>[<a href="/w/index.php?title=Functional_programming&action=edit&section=14" title="Edit section: Abstraction cost">edit</a>]</div> Some functional programming languages might not optimize abstractions such as higher order functions like "<a href="/wiki/Map_(higher-order_function)" title="Map (higher-order function)">map</a>" or "<a href="/wiki/Filter_(higher-order_function)" title="Filter (higher-order function)">filter</a>" as efficiently as the underlying imperative operations. Consider, as an example, the following two ways to check if 5 is an even number in <a href="/wiki/Clojure" title="Clojure">Clojure</a>: <div class="mw-highlight mw-highlight-lang-clojure mw-content-ltr" dir="ltr"><pre>(even? 5) (.equals (mod 5 2) 0) </pre></div> When <a href="/wiki/Benchmarking" title="Benchmarking">benchmarked</a> using the <a rel="nofollow" class="external text" href="https://clojars.org/criterium">Criterium</a> tool on a <a href="/wiki/Zen_3" title="Zen 3">Ryzen 7900X</a> GNU/Linux PC in a <a href="/wiki/Leiningen_(software)" title="Leiningen (software)">Leiningen</a> <a href="/wiki/REPL" class="mw-redirect" title="REPL">REPL</a> 2.11.2, running on <a href="/wiki/JVM" class="mw-redirect" title="JVM">Java VM</a> version 22 and Clojure version 1.11.1, the first implementation, which is implemented as: <div class="mw-highlight mw-highlight-lang-clojure mw-content-ltr" dir="ltr"><pre>(defn even? "Returns true if n is even, throws an exception if n is not an integer" {:added "1.0" :static true} [n] (if (integer? n) (zero? (bit-and (clojure.lang.RT/uncheckedLongCast n) 1)) (throw (IllegalArgumentException. (str "Argument must be an integer: " n))))) </pre></div> has the mean execution time of 4.76 ms, while the second one, in which <code class="mw-highlight mw-highlight-lang-clojure mw-content-ltr" dir="ltr">.equals</code> is a direct invocation of the underlying <a href="/wiki/Java_(programming_language)" title="Java (programming language)">Java</a> method, has a mean execution time of 2.8 μs – roughly 1700 times faster. Part of that can be attributed to the type checking and exception handling involved in the implementation of <code class="mw-highlight mw-highlight-lang-clojure mw-content-ltr" dir="ltr">even?</code>, so let's take for instance the <a rel="nofollow" class="external text" href="https://github.com/samber/lo">lo library</a> for <a href="/wiki/Go_(programming_language)" title="Go (programming language)">Go</a>, which implements various higher-order functions common in functional programming languages using <a href="/wiki/Generic_programming" title="Generic programming">generics</a>. In a benchmark provided by the library's author, calling <code>map</code> is 4% slower than an equivalent <code>for</code> loop and has the same <a href="/wiki/Memory_management" title="Memory management">allocation</a> profile,<a href="#cite_note-94">[94]</a> which can be attributed to various compiler optimizations, such as <a href="/wiki/Inlining" class="mw-redirect" title="Inlining">inlining</a>.<a href="#cite_note-95">[95]</a> One distinguishing feature of <a href="/wiki/Rust_(programming_language)" title="Rust (programming language)">Rust</a> are zero-cost abstractions. This means that using them imposes no additional runtime overhead. This is achieved thanks to the compiler using <a href="/wiki/Loop_unrolling" title="Loop unrolling">loop unrolling</a>, where each iteration of a loop, be it imperative or using iterators, is converted into a standalone <a href="/wiki/Assembly_language" title="Assembly language">Assembly</a> instruction, without the overhead of the loop controlling code. If an iterative operation writes to an array, the resulting array's elements <a href="/wiki/Register_allocation" title="Register allocation">will be stored in specific CPU registers</a>, allowing for <a href="/wiki/Time_complexity" title="Time complexity">constant-time access</a> at runtime.<a href="#cite_note-96">[96]</a> <div class="mw-heading mw-heading3"><h3 id="Functional_programming_in_non-functional_languages">Functional programming in non-functional languages</h3>[<a href="/w/index.php?title=Functional_programming&action=edit&section=15" title="Edit section: Functional programming in non-functional languages">edit</a>]</div> It is possible to use a functional style of programming in languages that are not traditionally considered functional languages.<a href="#cite_note-97">[97]</a> For example, both <a href="/wiki/D_(programming_language)" title="D (programming language)">D</a><a href="#cite_note-98">[98]</a> and <a href="/wiki/Fortran_95" class="mw-redirect" title="Fortran 95">Fortran 95</a><a href="#cite_note-fortran95-59">[59]</a> explicitly support pure functions. <a href="/wiki/JavaScript" title="JavaScript">JavaScript</a>, <a href="/wiki/Lua_(programming_language)" title="Lua (programming language)">Lua</a>,<a href="#cite_note-99">[99]</a> <a href="/wiki/Python_(programming_language)" title="Python (programming language)">Python</a> and <a href="/wiki/Go_(programming_language)" title="Go (programming language)">Go</a><a href="#cite_note-100">[100]</a> had <a href="/wiki/First-class_function" title="First-class function">first class functions</a> from their inception.<a href="#cite_note-101">[101]</a> Python had support for "<a href="/wiki/Anonymous_function" title="Anonymous function">lambda</a>", "<a href="/wiki/Map_(higher-order_function)" title="Map (higher-order function)">map</a>", "<a href="/wiki/Fold_(higher-order_function)" title="Fold (higher-order function)">reduce</a>", and "<a href="/wiki/Filter_(higher-order_function)" title="Filter (higher-order function)">filter</a>" in 1994, as well as closures in Python 2.2,<a href="#cite_note-102">[102]</a> though Python 3 relegated "reduce" to the <code>functools</code> standard library module.<a href="#cite_note-103">[103]</a> First-class functions have been introduced into other mainstream languages such as <a href="/wiki/PHP" title="PHP">PHP</a> 5.3, <a href="/wiki/Visual_Basic_9" class="mw-redirect" title="Visual Basic 9">Visual Basic 9</a>, <a href="/wiki/C_Sharp_(programming_language)" title="C Sharp (programming language)">C#</a> 3.0, <a href="/wiki/C%2B%2B11" title="C++11">C++11</a>, and <a href="/wiki/Kotlin_(programming_language)" title="Kotlin (programming language)">Kotlin</a>.<a href="#cite_note-:0-28">[28]</a>[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] In PHP, <a href="/wiki/Anonymous_class" class="mw-redirect" title="Anonymous class">anonymous classes</a>, <a href="/wiki/Closure_(computer_science)" class="mw-redirect" title="Closure (computer science)">closures</a> and lambdas are fully supported. Libraries and language extensions for immutable data structures are being developed to aid programming in the functional style. In <a href="/wiki/Java_(programming_language)" title="Java (programming language)">Java</a>, anonymous classes can sometimes be used to simulate closures;<a href="#cite_note-104">[104]</a> however, anonymous classes are not always proper replacements to closures because they have more limited capabilities.<a href="#cite_note-105">[105]</a> Java 8 supports lambda expressions as a replacement for some anonymous classes.<a href="#cite_note-106">[106]</a> In <a href="/wiki/C_Sharp_(programming_language)" title="C Sharp (programming language)">C#</a>, anonymous classes are not necessary, because closures and lambdas are fully supported. Libraries and language extensions for immutable data structures are being developed to aid programming in the functional style in C#. Many <a href="/wiki/Object-oriented" class="mw-redirect" title="Object-oriented">object-oriented</a> <a href="/wiki/Design_pattern_(computer_science)" class="mw-redirect" title="Design pattern (computer science)">design patterns</a> are expressible in functional programming terms: for example, the <a href="/wiki/Strategy_pattern" title="Strategy pattern">strategy pattern</a> simply dictates use of a higher-order function, and the <a href="/wiki/Visitor_(design_pattern)" class="mw-redirect" title="Visitor (design pattern)">visitor</a> pattern roughly corresponds to a <a href="/wiki/Catamorphism" title="Catamorphism">catamorphism</a>, or <a href="/wiki/Fold_(higher-order_function)" title="Fold (higher-order function)">fold</a>. Similarly, the idea of immutable data from functional programming is often included in imperative programming languages,<a href="#cite_note-107">[107]</a> for example the tuple in Python, which is an immutable array, and Object.freeze() in JavaScript.<a href="#cite_note-108">[108]</a> <div class="mw-heading mw-heading2"><h2 id="Comparison_to_logic_programming">Comparison to logic programming</h2>[<a href="/w/index.php?title=Functional_programming&action=edit&section=16" title="Edit section: Comparison to logic programming">edit</a>]</div> <a href="/wiki/Logic_programming" title="Logic programming">Logic programming</a> can be viewed as a generalisation of functional programming, in which functions are a special case of relations.<a href="#cite_note-109">[109]</a> For example, the function, mother(X) = Y, (every X has only one mother Y) can be represented by the relation mother(X, Y). Whereas functions have a strict input-output pattern of arguments, relations can be queried with any pattern of inputs and outputs. Consider the following logic program: <div class="mw-highlight mw-highlight-lang-prolog mw-content-ltr" dir="ltr"><pre>mother(charles, elizabeth). mother(harry, diana). </pre></div> The program can be queried, like a functional program, to generate mothers from children: <div class="mw-highlight mw-highlight-lang-prolog mw-content-ltr" dir="ltr"><pre>?- mother(harry, X). X = diana. ?- mother(charles, X). X = elizabeth. </pre></div> But it can also be queried backwards, to generate children: <div class="mw-highlight mw-highlight-lang-prolog mw-content-ltr" dir="ltr"><pre>?- mother(X, elizabeth). X = charles. ?- mother(X, diana). X = harry. </pre></div> It can even be used to generate all instances of the mother relation: <div class="mw-highlight mw-highlight-lang-prolog mw-content-ltr" dir="ltr"><pre>?- mother(X, Y). X = charles, Y = elizabeth. X = harry, Y = diana. </pre></div> Compared with relational syntax, functional syntax is a more compact notation for nested functions. For example, the definition of maternal grandmother in functional syntax can be written in the nested form: <div class="mw-highlight mw-highlight-lang-prolog mw-content-ltr" dir="ltr"><pre>maternal_grandmother(X) = mother(mother(X)). </pre></div> The same definition in relational notation needs to be written in the unnested form: <div class="mw-highlight mw-highlight-lang-prolog mw-content-ltr" dir="ltr"><pre>maternal_grandmother(X, Y) :- mother(X, Z), mother(Z, Y). </pre></div> Here <code>:-</code> means if and <code> , </code>means and. However, the difference between the two representations is simply syntactic. In <a href="/wiki/Ciao_(programming_language)" title="Ciao (programming language)">Ciao</a> Prolog, relations can be nested, like functions in functional programming:<a href="#cite_note-110">[110]</a> <div class="mw-highlight mw-highlight-lang-prolog mw-content-ltr" dir="ltr"><pre>grandparent(X) := parent(parent(X)). parent(X) := mother(X). parent(X) := father(X). mother(charles) := elizabeth. father(charles) := phillip. mother(harry) := diana. father(harry) := charles. ?- grandparent(X,Y). X = harry, Y = elizabeth. X = harry, Y = phillip. </pre></div> Ciao transforms the function-like notation into relational form and executes the resulting logic program using the standard Prolog execution strategy. <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2>[<a href="/w/index.php?title=Functional_programming&action=edit&section=17" title="Edit section: Applications">edit</a>]</div> <div class="mw-heading mw-heading3"><h3 id="Text_editors">Text editors</h3>[<a href="/w/index.php?title=Functional_programming&action=edit&section=18" title="Edit section: Text editors">edit</a>]</div> <a href="/wiki/Emacs" title="Emacs">Emacs</a>, a highly extensible text editor family uses its own <a href="/wiki/Emacs_Lisp" title="Emacs Lisp">Lisp dialect</a> for writing plugins. The original author of the most popular Emacs implementation, <a href="/wiki/GNU_Emacs" title="GNU Emacs">GNU Emacs</a> and Emacs Lisp, <a href="/wiki/Richard_Stallman" title="Richard Stallman">Richard Stallman</a> considers Lisp one of his favorite programming languages.<a href="#cite_note-111">[111]</a> <a href="/w/index.php?title=Helix_(text_editor)&action=edit&redlink=1" class="new" title="Helix (text editor) (page does not exist)">Helix</a>, since version 24.03 supports previewing <a href="/wiki/Abstract_syntax_tree" title="Abstract syntax tree">AST</a> as <a href="/wiki/S-expression" title="S-expression">S-expressions</a>, which are also the core feature of the Lisp programming language family.<a href="#cite_note-112">[112]</a> <div class="mw-heading mw-heading3"><h3 id="Spreadsheets">Spreadsheets</h3>[<a href="/w/index.php?title=Functional_programming&action=edit&section=19" title="Edit section: Spreadsheets">edit</a>]</div> <a href="/wiki/Spreadsheet" title="Spreadsheet">Spreadsheets</a> can be considered a form of pure, <a href="/wiki/Higher-order_function" title="Higher-order function">zeroth-order</a>, strict-evaluation functional programming system.<a href="#cite_note-Wakeling2007-113">[113]</a> However, spreadsheets generally lack higher-order functions as well as code reuse, and in some implementations, also lack recursion. Several extensions have been developed for spreadsheet programs to enable higher-order and reusable functions, but so far remain primarily academic in nature.<a href="#cite_note-excel-114">[114]</a> <div class="mw-heading mw-heading3"><h3 id="Microservices">Microservices</h3>[<a href="/w/index.php?title=Functional_programming&action=edit&section=20" title="Edit section: Microservices">edit</a>]</div> Due to their <a href="/wiki/Composability" title="Composability">composability</a>, functional programming paradigms can be suitable for <a href="/wiki/Microservices" title="Microservices">microservices</a>-based architectures.<a href="#cite_note-115">[115]</a> <div class="mw-heading mw-heading3"><h3 id="Academia">Academia</h3>[<a href="/w/index.php?title=Functional_programming&action=edit&section=21" title="Edit section: Academia">edit</a>]</div> Functional programming is an active area of research in the field of <a href="/wiki/Programming_language_theory" title="Programming language theory">programming language theory</a>. There are several <a href="/wiki/Peer-review" class="mw-redirect" title="Peer-review">peer-reviewed</a> publication venues focusing on functional programming, including the <a href="/wiki/International_Conference_on_Functional_Programming" title="International Conference on Functional Programming">International Conference on Functional Programming</a>, the <a href="/wiki/Journal_of_Functional_Programming" title="Journal of Functional Programming">Journal of Functional Programming</a>, and the <a href="/wiki/Symposium_on_Trends_in_Functional_Programming" title="Symposium on Trends in Functional Programming">Symposium on Trends in Functional Programming</a>. <div class="mw-heading mw-heading3"><h3 id="Industry">Industry</h3>[<a href="/w/index.php?title=Functional_programming&action=edit&section=22" title="Edit section: Industry">edit</a>]</div> Functional programming has been employed in a wide range of industrial applications. For example, <a href="/wiki/Erlang_(programming_language)" title="Erlang (programming language)">Erlang</a>, which was developed by the <a href="/wiki/Sweden" title="Sweden">Swedish</a> company <a href="/wiki/Ericsson" title="Ericsson">Ericsson</a> in the late 1980s, was originally used to implement <a href="/wiki/Fault_tolerance" title="Fault tolerance">fault-tolerant</a> <a href="/wiki/Telecommunications" title="Telecommunications">telecommunications</a> systems,<a href="#cite_note-armstrong2007-11">[11]</a> but has since become popular for building a range of applications at companies such as <a href="/wiki/Nortel" title="Nortel">Nortel</a>, <a href="/wiki/Facebook" title="Facebook">Facebook</a>, <a href="/wiki/%C3%89lectricit%C3%A9_de_France" title="Électricité de France">Électricité de France</a> and <a href="/wiki/WhatsApp" title="WhatsApp">WhatsApp</a>.<a href="#cite_note-erlang-faq-10">[10]</a><a href="#cite_note-larson2009-12">[12]</a><a href="#cite_note-116">[116]</a><a href="#cite_note-Sim-Diasca-117">[117]</a><a href="#cite_note-whatsapp.blog.2012-118">[118]</a> <a href="/wiki/Scheme_(programming_language)" title="Scheme (programming language)">Scheme</a>, a dialect of <a href="/wiki/Lisp_(programming_language)" title="Lisp (programming language)">Lisp</a>, was used as the basis for several applications on early <a href="/wiki/Apple_Macintosh" class="mw-redirect" title="Apple Macintosh">Apple Macintosh</a> computers<a href="#cite_note-clinger1987-3">[3]</a><a href="#cite_note-hartheimer1987-4">[4]</a> and has been applied to problems such as training-<a href="/wiki/Computer_simulation" title="Computer simulation">simulation software</a><a href="#cite_note-kidd2007-5">[5]</a> and <a href="/wiki/Telescope" title="Telescope">telescope</a> control.<a href="#cite_note-cleis2006-6">[6]</a> <a href="/wiki/OCaml" title="OCaml">OCaml</a>, which was introduced in the mid-1990s, has seen commercial use in areas such as financial analysis,<a href="#cite_note-minksy2008-14">[14]</a> <a href="/wiki/Software_driver" class="mw-redirect" title="Software driver">driver</a> verification, industrial <a href="/wiki/Robot" title="Robot">robot</a> programming and static analysis of <a href="/wiki/Embedded_software" title="Embedded software">embedded software</a>.<a href="#cite_note-leroy2007-15">[15]</a> <a href="/wiki/Haskell" title="Haskell">Haskell</a>, though initially intended as a research language,<a href="#cite_note-hudak2007-17">[17]</a> has also been applied in areas such as aerospace systems, hardware design and web programming.<a href="#cite_note-haskell-industry-16">[16]</a><a href="#cite_note-hudak2007-17">[17]</a> Other functional programming languages that have seen use in industry include <a href="/wiki/Scala_(programming_language)" title="Scala (programming language)">Scala</a>,<a href="#cite_note-119">[119]</a> <a href="/wiki/F_Sharp_(programming_language)" title="F Sharp (programming language)">F#</a>,<a href="#cite_note-quantFSharp-18">[18]</a><a href="#cite_note-businessAppsFSharp-19">[19]</a> <a href="/wiki/Wolfram_Language" title="Wolfram Language">Wolfram Language</a>,<a href="#cite_note-reference.wolfram.com-7">[7]</a> <a href="/wiki/Lisp_(programming_language)" title="Lisp (programming language)">Lisp</a>,<a href="#cite_note-120">[120]</a> <a href="/wiki/Standard_ML" title="Standard ML">Standard ML</a><a href="#cite_note-121">[121]</a><a href="#cite_note-122">[122]</a> and Clojure.<a href="#cite_note-123">[123]</a> Scala has been widely used in <a href="/wiki/Data_science" title="Data science">Data science</a>,<a href="#cite_note-124">[124]</a> while <a href="/wiki/ClojureScript" class="mw-redirect" title="ClojureScript">ClojureScript</a>,<a href="#cite_note-125">[125]</a> <a href="/wiki/Elm_(programming_language)" title="Elm (programming language)">Elm</a><a href="#cite_note-126">[126]</a> or <a href="/wiki/PureScript" title="PureScript">PureScript</a><a href="#cite_note-127">[127]</a> are some of the functional frontend programming languages used in production. <a href="/wiki/Elixir_(programming_language)" title="Elixir (programming language)">Elixir</a>'s Phoenix framework is also used by some relatively popular commercial projects, such as <a href="/wiki/Font_Awesome" title="Font Awesome">Font Awesome</a> or <a href="/wiki/Allegro_Platform" class="mw-redirect" title="Allegro Platform">Allegro</a> (one of the biggest e-commerce platforms in Poland)<a href="#cite_note-128">[128]</a>'s classified ads platform Allegro Lokalnie.<a href="#cite_note-129">[129]</a> Functional "platforms" have been popular in finance for risk analytics (particularly with large investment banks). Risk factors are coded as functions that form interdependent graphs (categories) to measure correlations in market shifts, similar in manner to <a href="/wiki/Gr%C3%B6bner_basis" title="Gröbner basis">Gröbner basis</a> optimizations but also for regulatory frameworks such as <a href="/wiki/Comprehensive_Capital_Analysis_and_Review" title="Comprehensive Capital Analysis and Review">Comprehensive Capital Analysis and Review</a>. Given the use of OCaml and <a href="/wiki/Caml" title="Caml">Caml</a> variations in finance, these systems are sometimes considered related to a <a href="/wiki/Categorical_abstract_machine" title="Categorical abstract machine">categorical abstract machine</a>. Functional programming is heavily influenced by <a href="/wiki/Category_theory" title="Category theory">category theory</a>.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] <div class="mw-heading mw-heading3"><h3 id="Education">Education</h3>[<a href="/w/index.php?title=Functional_programming&action=edit&section=23" title="Edit section: Education">edit</a>]</div> Many <a href="/wiki/University" title="University">universities</a> teach functional programming.<a href="#cite_note-oxfordFP-130">[130]</a><a href="#cite_note-imperialFP-131">[131]</a><a href="#cite_note-nottinghamFP-132">[132]</a><a href="#cite_note-mitFP-133">[133]</a> Some treat it as an introductory programming concept<a href="#cite_note-mitFP-133">[133]</a> while others first teach imperative programming methods.<a href="#cite_note-nottinghamFP-132">[132]</a><a href="#cite_note-61A-134">[134]</a> Outside of computer science, functional programming is used to teach problem-solving, algebraic and geometric concepts.<a href="#cite_note-bootstrapworld-135">[135]</a> It has also been used to teach classical mechanics, as in the book <a href="/wiki/Structure_and_Interpretation_of_Classical_Mechanics" title="Structure and Interpretation of Classical Mechanics">Structure and Interpretation of Classical Mechanics</a>. In particular, <a href="/wiki/Scheme_(programming_language)" title="Scheme (programming language)">Scheme</a> has been a relatively popular choice for teaching programming for years.<a href="#cite_note-136">[136]</a><a href="#cite_note-137">[137]</a> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2>[<a href="/w/index.php?title=Functional_programming&action=edit&section=24" title="Edit section: See also">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1239009302">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{clear:left;float:left;margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><a href="/wiki/File:Octicons-terminal.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Octicons-terminal.svg/24px-Octicons-terminal.svg.png" decoding="async" width="24" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Octicons-terminal.svg/37px-Octicons-terminal.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Octicons-terminal.svg/49px-Octicons-terminal.svg.png 2x" data-file-width="896" data-file-height="1024" /></a><a href="/wiki/Portal:Computer_programming" title="Portal:Computer programming">Computer programming portal</a></li></ul> <ul><li><a href="/wiki/Eager_evaluation" class="mw-redirect" title="Eager evaluation">Eager evaluation</a></li> <li><a href="/wiki/Functional_reactive_programming" title="Functional reactive programming">Functional reactive programming</a></li> <li><a href="/wiki/Inductive_functional_programming" class="mw-redirect" title="Inductive functional programming">Inductive functional programming</a></li> <li><a href="/wiki/List_of_functional_programming_languages" class="mw-redirect" title="List of functional programming languages">List of functional programming languages</a></li> <li><a href="/wiki/List_of_functional_programming_topics" title="List of functional programming topics">List of functional programming topics</a></li> <li><a href="/wiki/Nested_function" title="Nested function">Nested function</a></li> <li><a href="/wiki/Purely_functional_programming" title="Purely functional programming">Purely functional programming</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes_and_references">Notes and references</h2>[<a href="/w/index.php?title=Functional_programming&action=edit&section=25" title="Edit section: Notes and references">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-lower-alpha"> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-hudak1989-1"><a href="#cite_ref-hudak1989_1-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHudak1989" class="citation journal cs1"><a href="/wiki/Paul_Hudak" title="Paul Hudak">Hudak, Paul</a> (September 1989). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160131083528/http://www.dbnet.ece.ntua.gr/~adamo/languages/books/p359-hudak.pdf">"Conception, evolution, and application of functional programming languages"</a> (PDF). 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History of Programming Languages. Los Angeles, CA. pp. 173–185. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F800025.808387">10.1145/800025.808387</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=conference&rft.jtitle=History+of+Programming+Languages&rft.atitle=History+of+Lisp&rft.pages=173-185&rft.date=1978-06&rft_id=info%3Adoi%2F10.1145%2F800025.808387&rft.aulast=McCarthy&rft.aufirst=John&rft_id=http%3A%2F%2Fjmc.stanford.edu%2Farticles%2Flisp%2Flisp.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFunctional+programming" class="Z3988"> </li> <li id="cite_note-41"><a href="#cite_ref-41">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJohn_McCarthy1960" class="citation journal cs1"><a href="/wiki/John_McCarthy_(computer_scientist)" title="John McCarthy (computer scientist)">John McCarthy</a> (1960). <a rel="nofollow" class="external text" href="http://jmc.stanford.edu/articles/recursive/recursive.pdf">"Recursive functions of symbolic expressions and their computation by machine, Part I."</a> (PDF). 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ACM New York, NY, US: 184–195. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F367177.367199">10.1145/367177.367199</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:1489409">1489409</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Communications+of+the+ACM&rft.atitle=Recursive+functions+of+symbolic+expressions+and+their+computation+by+machine%2C+Part+I.&rft.volume=3&rft.issue=4&rft.pages=184-195&rft.date=1960&rft_id=info%3Adoi%2F10.1145%2F367177.367199&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A1489409%23id-name%3DS2CID&rft.au=John+McCarthy&rft_id=http%3A%2F%2Fjmc.stanford.edu%2Farticles%2Frecursive%2Frecursive.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFunctional+programming" class="Z3988"> </li> <li id="cite_note-42"><a href="#cite_ref-42">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGuy_L._SteeleRichard_P._Gabriel1996" class="citation book cs1">Guy L. 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Retrieved 2024-04-29.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=IMACS+%E2%80%93+Making+Better+Thinkers+for+Life&rft.atitle=What+Is+Scheme+%26+Why+Is+it+Beneficial+for+Students%3F&rft.date=2011-06-03&rft.aulast=Staff&rft.aufirst=IMACS&rft_id=https%3A%2F%2Fwww.imacs.org%2Flearn-computer-programming-using-scheme%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFunctional+programming" class="Z3988"> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2>[<a href="/w/index.php?title=Functional_programming&action=edit&section=26" title="Edit section: Further reading">edit</a>]</div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAbelsonSussman1985" class="citation book cs1"><a href="/wiki/Hal_Abelson" title="Hal Abelson">Abelson, Hal</a>; <a href="/wiki/Gerald_Jay_Sussman" title="Gerald Jay Sussman">Sussman, Gerald Jay</a> (1985). <a rel="nofollow" class="external text" href="https://mitpress.mit.edu/9780262510363/structure-and-interpretation-of-computer-programs/">Structure and Interpretation of Computer Programs</a>. MIT Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Structure+and+Interpretation+of+Computer+Programs&rft.pub=MIT+Press&rft.date=1985&rft.aulast=Abelson&rft.aufirst=Hal&rft.au=Sussman%2C+Gerald+Jay&rft_id=https%3A%2F%2Fmitpress.mit.edu%2F9780262510363%2Fstructure-and-interpretation-of-computer-programs%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFunctional+programming" class="Z3988"></li> <li>Cousineau, Guy and Michel Mauny. The Functional Approach to Programming. Cambridge, UK: <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>, 1998.</li> <li>Curry, Haskell Brooks and Feys, Robert and Craig, William. Combinatory Logic. Volume I. North-Holland Publishing Company, Amsterdam, 1958.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCurryHindleySeldin1972" class="citation book cs1"><a href="/wiki/Haskell_Curry" title="Haskell Curry">Curry, Haskell B.</a>; <a href="/wiki/J._Roger_Hindley" title="J. Roger Hindley">Hindley, J. Roger</a>; <a href="/w/index.php?title=Jonathan_P._Seldin&action=edit&redlink=1" class="new" title="Jonathan P. Seldin (page does not exist)">Seldin, Jonathan P.</a> (1972). Combinatory Logic. Vol. II. Amsterdam: North Holland. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7204-2208-5" title="Special:BookSources/978-0-7204-2208-5"><bdi>978-0-7204-2208-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Combinatory+Logic&rft.place=Amsterdam&rft.pub=North+Holland&rft.date=1972&rft.isbn=978-0-7204-2208-5&rft.aulast=Curry&rft.aufirst=Haskell+B.&rft.au=Hindley%2C+J.+Roger&rft.au=Seldin%2C+Jonathan+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFunctional+programming" class="Z3988"></li> <li>Dominus, Mark Jason. <a rel="nofollow" class="external text" href="http://hop.perl.plover.com/book/pdf/HigherOrderPerl.pdf">Higher-Order Perl</a>. <a href="/wiki/Morgan_Kaufmann" class="mw-redirect" title="Morgan Kaufmann">Morgan Kaufmann</a>. 2005.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFelleisenFindlerFlattKrishnamurthi2018" class="citation book cs1">Felleisen, Matthias; Findler, Robert; Flatt, Matthew; Krishnamurthi, Shriram (2018). <a rel="nofollow" class="external text" href="http://www.htdp.org">How to Design Programs</a>. MIT Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=How+to+Design+Programs&rft.pub=MIT+Press&rft.date=2018&rft.aulast=Felleisen&rft.aufirst=Matthias&rft.au=Findler%2C+Robert&rft.au=Flatt%2C+Matthew&rft.au=Krishnamurthi%2C+Shriram&rft_id=http%3A%2F%2Fwww.htdp.org&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFunctional+programming" class="Z3988"></li> <li>Graham, Paul. ANSI Common LISP. Englewood Cliffs, New Jersey: <a href="/wiki/Prentice_Hall" title="Prentice Hall">Prentice Hall</a>, 1996.</li> <li>MacLennan, Bruce J. Functional Programming: Practice and Theory. Addison-Wesley, 1990.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMichaelson2013" class="citation book cs1">Michaelson, Greg (10 April 2013). An Introduction to Functional Programming Through Lambda Calculus. Courier Corporation. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-28029-5" title="Special:BookSources/978-0-486-28029-5"><bdi>978-0-486-28029-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Introduction+to+Functional+Programming+Through+Lambda+Calculus&rft.pub=Courier+Corporation&rft.date=2013-04-10&rft.isbn=978-0-486-28029-5&rft.aulast=Michaelson&rft.aufirst=Greg&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFunctional+programming" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFO'SullivanStewartGoerzen2008" class="citation book cs1">O'Sullivan, Brian; Stewart, Don; Goerzen, John (2008). <a rel="nofollow" class="external text" href="http://book.realworldhaskell.org/read/">Real World Haskell</a>. O'Reilly.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Real+World+Haskell&rft.pub=O%27Reilly&rft.date=2008&rft.aulast=O%27Sullivan&rft.aufirst=Brian&rft.au=Stewart%2C+Don&rft.au=Goerzen%2C+John&rft_id=http%3A%2F%2Fbook.realworldhaskell.org%2Fread%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFunctional+programming" class="Z3988"></li> <li>Pratt, Terrence W. and <a href="/wiki/Marvin_Victor_Zelkowitz" class="mw-redirect" title="Marvin Victor Zelkowitz">Marvin Victor Zelkowitz</a>. Programming Languages: Design and Implementation. 3rd ed. Englewood Cliffs, New Jersey: <a href="/wiki/Prentice_Hall" title="Prentice Hall">Prentice Hall</a>, 1996.</li> <li>Salus, Peter H. Functional and Logic Programming Languages. Vol. 4 of Handbook of Programming Languages. Indianapolis, Indiana: <a href="/w/index.php?title=Macmillan_Technical_Publishing&action=edit&redlink=1" class="new" title="Macmillan Technical Publishing (page does not exist)">Macmillan Technical Publishing</a>, 1998.</li> <li>Thompson, Simon. Haskell: The Craft of Functional Programming. Harlow, England: <a href="/w/index.php?title=Addison-Wesley_Longman_Limited&action=edit&redlink=1" class="new" title="Addison-Wesley Longman Limited (page does not exist)">Addison-Wesley Longman Limited</a>, 1996.</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2>[<a href="/w/index.php?title=Functional_programming&action=edit&section=27" title="Edit section: External links">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1235611614">.mw-parser-output .spoken-wikipedia{border:1px solid #a2a9b1;background-color:var(--background-color-interactive-subtle,#f8f9fa);margin:0.5em 0;padding:0.2em;line-height:1.5em;font-size:90%}.mw-parser-output .spoken-wikipedia-header{text-align:center}.mw-parser-output .spoken-wikipedia-listen-to{font-weight:bold}.mw-parser-output .spoken-wikipedia-files{text-align:center;margin-top:10px;margin-bottom:0.4em}.mw-parser-output .spoken-wikipedia-icon{float:left;margin-left:5px;margin-top:10px}.mw-parser-output .spoken-wikipedia-disclaimer{margin-left:60px;margin-top:10px;font-size:95%;line-height:1.4em}.mw-parser-output .spoken-wikipedia-footer{margin-top:10px;text-align:center}@media(min-width:720px){.mw-parser-output .spoken-wikipedia{width:20em;float:right;clear:right;margin-left:1em}}</style><div class="spoken-wikipedia noprint haudio"><div class="spoken-wikipedia-header">Listen to this article (28 minutes)</div><div class="spoken-wikipedia-files"><figure class="mw-halign-center" typeof="mw:File"><audio id="mwe_player_0" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="200" style="width:200px;" data-durationhint="1679" data-mwtitle="En-Functional_programming.ogg" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/8/83/En-Functional_programming.ogg" type="audio/ogg; codecs="vorbis"" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/83/En-Functional_programming.ogg/En-Functional_programming.ogg.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio><figcaption></figcaption></figure> </div><div class="spoken-wikipedia-icon"><img alt="Spoken Wikipedia icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Sound-icon.svg/45px-Sound-icon.svg.png" decoding="async" width="45" height="34" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Sound-icon.svg/68px-Sound-icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/47/Sound-icon.svg/90px-Sound-icon.svg.png 2x" data-file-width="128" data-file-height="96" /></div><div class="spoken-wikipedia-disclaimer"><a href="/wiki/File:En-Functional_programming.ogg" title="File:En-Functional programming.ogg">This audio file</a> was created from a revision of this article dated 25 August 2011 (2011-08-25), and does not reflect subsequent edits.</div><div class="spoken-wikipedia-footer">(<a href="/wiki/Wikipedia:Media_help" class="mw-redirect" title="Wikipedia:Media help">Audio help</a> · <a href="/wiki/Wikipedia:Spoken_articles" title="Wikipedia:Spoken articles">More spoken articles</a>)</div></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFord" class="citation web cs1">Ford, Neal. <a rel="nofollow" class="external text" href="http://nealford.com/functionalthinking.html">"Functional thinking"</a>. Retrieved 2021-11-10.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Functional+thinking&rft.aulast=Ford&rft.aufirst=Neal&rft_id=http%3A%2F%2Fnealford.com%2Ffunctionalthinking.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFunctional+programming" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAkhmechet2006" class="citation web cs1">Akhmechet, Slava (2006-06-19). <a rel="nofollow" class="external text" href="http://www.defmacro.org/ramblings/fp.html">"defmacro – Functional Programming For The Rest of Us"</a>. Retrieved 2013-02-24.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=defmacro+%E2%80%93+Functional+Programming+For+The+Rest+of+Us&rft.date=2006-06-19&rft.aulast=Akhmechet&rft.aufirst=Slava&rft_id=http%3A%2F%2Fwww.defmacro.org%2Framblings%2Ffp.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFunctional+programming" class="Z3988"> An introduction</li> <li>Functional programming in Python (by David Mertz): <a rel="nofollow" class="external text" href="http://gnosis.cx/publish/programming/charming_python_13.html">part 1</a>, <a rel="nofollow" class="external text" href="http://gnosis.cx/publish/programming/charming_python_16.html">part 2</a>, <a rel="nofollow" class="external text" href="http://gnosis.cx/publish/programming/charming_python_19.html">part 3</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output 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language</a>)</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Imperative_programming" title="Imperative programming">Imperative</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Structured_programming" title="Structured programming">Structured</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Jackson_structured_programming" title="Jackson structured programming">Jackson structures</a></li> <li><a href="/wiki/Block_(programming)" title="Block (programming)">Block-structured</a></li> <li><a href="/wiki/Modular_programming" title="Modular programming">Modular</a></li> <li><a href="/wiki/Non-structured_programming" title="Non-structured programming">Non-structured</a></li> <li><a href="/wiki/Procedural_programming" title="Procedural programming">Procedural</a></li> <li><a href="/wiki/Programming_in_the_large_and_programming_in_the_small" title="Programming in the large and programming in the small">Programming in the large and in the small</a></li> <li><a href="/wiki/Design_by_contract" title="Design by contract">Design by contract</a></li> <li><a href="/wiki/Invariant-based_programming" title="Invariant-based programming">Invariant-based</a></li> <li><a href="/wiki/Nested_function" title="Nested function">Nested function</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Object-oriented_programming" title="Object-oriented programming">Object-oriented</a> (<a href="/wiki/Comparison_of_programming_languages_(object-oriented_programming)" title="Comparison of programming languages (object-oriented programming)">comparison</a>, <a href="/wiki/List_of_object-oriented_programming_languages" title="List of object-oriented programming languages">list</a>)</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Class-based_programming" title="Class-based programming">Class-based</a>, <a href="/wiki/Prototype-based_programming" title="Prototype-based programming">Prototype-based</a>, <a href="/wiki/Object-based_language" title="Object-based language">Object-based</a></li> <li><a href="/wiki/Agent-oriented_programming" title="Agent-oriented programming">Agent</a></li> <li><a href="/wiki/Immutable_object" title="Immutable object">Immutable object</a></li> <li><a href="/wiki/Persistent_programming_language" title="Persistent programming language">Persistent</a></li> <li><a href="/wiki/Uniform_Function_Call_Syntax" title="Uniform Function Call Syntax">Uniform Function Call Syntax</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Declarative_programming" title="Declarative programming">Declarative</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a class="mw-selflink selflink">Functional</a> (<a href="/wiki/Comparison_of_functional_programming_languages" title="Comparison of functional programming languages">comparison</a>)</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Recursion_(computer_science)" title="Recursion (computer science)">Recursive</a></li> <li><a href="/wiki/Anonymous_function" title="Anonymous function">Anonymous function</a> (<a href="/wiki/Partial_application" title="Partial application">Partial application</a>)</li> <li><a href="/wiki/Higher-order_programming" title="Higher-order programming">Higher-order</a></li> <li><a href="/wiki/Purely_functional_programming" title="Purely functional programming">Purely functional</a></li> <li><a href="/wiki/Total_functional_programming" title="Total functional programming">Total</a></li> <li><a href="/wiki/Strict_programming_language" title="Strict programming language">Strict</a></li> <li><a href="/wiki/Generalized_algebraic_data_type" title="Generalized algebraic data type">GADTs</a></li> <li><a href="/wiki/Dependent_type" title="Dependent type">Dependent types</a></li> <li><a href="/wiki/Functional_logic_programming" title="Functional logic programming">Functional logic</a></li> <li><a href="/wiki/Tacit_programming" title="Tacit programming">Point-free style</a></li> <li><a href="/wiki/Expression-oriented_programming_language" title="Expression-oriented programming language">Expression-oriented</a></li> <li><a href="/wiki/Applicative_programming_language" title="Applicative programming language">Applicative</a>, <a href="/wiki/Concatenative_programming_language" title="Concatenative programming language">Concatenative</a></li> <li><a href="/wiki/Function-level_programming" title="Function-level programming">Function-level</a>, <a href="/wiki/Value-level_programming" title="Value-level programming">Value-level</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Dataflow_programming" title="Dataflow programming">Dataflow</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Flow-based_programming" title="Flow-based programming">Flow-based</a></li> <li><a href="/wiki/Reactive_programming" title="Reactive programming">Reactive</a> (<a href="/wiki/Functional_reactive_programming" title="Functional reactive programming">Functional reactive</a>)</li> <li><a href="/wiki/Signal_programming" class="mw-redirect" title="Signal programming">Signals</a></li> <li><a href="/wiki/Stream_processing" title="Stream processing">Streams</a></li> <li><a href="/wiki/Synchronous_programming_language" title="Synchronous programming language">Synchronous</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Logic_programming" title="Logic programming">Logic</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Abductive_logic_programming" title="Abductive logic programming">Abductive logic</a></li> <li><a href="/wiki/Answer_set_programming" title="Answer set programming">Answer set</a></li> <li><a href="/wiki/Constraint_programming" title="Constraint programming">Constraint</a> (<a href="/wiki/Constraint_logic_programming" title="Constraint logic programming">Constraint logic</a>)</li> <li><a href="/wiki/Inductive_logic_programming" title="Inductive logic programming">Inductive logic</a></li> <li><a href="/wiki/Nondeterministic_programming" title="Nondeterministic programming">Nondeterministic</a></li> <li><a href="/wiki/Ontology_language" title="Ontology language">Ontology</a></li> <li><a href="/wiki/Probabilistic_logic_programming" title="Probabilistic logic programming">Probabilistic logic</a></li> <li><a href="/wiki/Query_language" title="Query language">Query</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Domain-specific_language" title="Domain-specific language">DSL</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Algebraic_modeling_language" title="Algebraic modeling language">Algebraic modeling</a></li> <li><a href="/wiki/Array_programming" title="Array programming">Array</a></li> <li><a href="/wiki/Automata-based_programming" title="Automata-based programming">Automata-based</a> (<a href="/wiki/Action_language" title="Action language">Action</a>)</li> <li><a href="/wiki/Command_language" title="Command language">Command</a> (<a href="/wiki/Spacecraft_command_language" title="Spacecraft command language">Spacecraft</a>)</li> <li><a href="/wiki/Differentiable_programming" title="Differentiable programming">Differentiable</a></li> <li><a href="/wiki/End-user_development" title="End-user development">End-user</a></li> <li><a href="/wiki/Grammar-oriented_programming" title="Grammar-oriented programming">Grammar-oriented</a></li> <li><a href="/wiki/Interface_description_language" title="Interface description language">Interface description</a></li> <li><a href="/wiki/Language-oriented_programming" title="Language-oriented programming">Language-oriented</a></li> <li><a href="/wiki/List_comprehension" title="List comprehension">List comprehension</a></li> <li><a href="/wiki/Low-code_development_platform" title="Low-code development platform">Low-code</a></li> <li><a href="/wiki/Modeling_language" title="Modeling language">Modeling</a></li> <li><a href="/wiki/Natural-language_programming" title="Natural-language programming">Natural language</a></li> <li><a href="/wiki/Non-English-based_programming_languages" title="Non-English-based programming languages">Non-English-based</a></li> <li><a href="/wiki/Page_description_language" title="Page description language">Page description</a></li> <li><a href="/wiki/Pipeline_(software)" title="Pipeline (software)">Pipes</a> and <a href="/wiki/Filter_(software)" title="Filter (software)">filters</a></li> <li><a href="/wiki/Probabilistic_programming" title="Probabilistic programming">Probabilistic</a></li> <li><a href="/wiki/Quantum_programming" title="Quantum programming">Quantum</a></li> <li><a href="/wiki/Scientific_programming_language" title="Scientific programming language">Scientific</a></li> <li><a href="/wiki/Scripting_language" title="Scripting language">Scripting</a></li> <li><a href="/wiki/Set_theoretic_programming" title="Set theoretic programming">Set-theoretic</a></li> <li><a href="/wiki/Simulation_language" title="Simulation language">Simulation</a></li> <li><a href="/wiki/Stack-oriented_programming" title="Stack-oriented programming">Stack-based</a></li> <li><a href="/wiki/System_programming_language" title="System programming language">System</a></li> <li><a href="/wiki/Tactile_programming_language" title="Tactile programming language">Tactile</a></li> <li><a href="/wiki/Template_processor" title="Template processor">Templating</a></li> <li><a href="/wiki/Transformation_language" title="Transformation language">Transformation</a> (<a href="/wiki/Graph_rewriting" title="Graph rewriting">Graph rewriting</a>, <a href="/wiki/Production_system_(computer_science)" title="Production system (computer science)">Production</a>, <a href="/wiki/Pattern_matching" title="Pattern matching">Pattern</a>)</li> <li><a href="/wiki/Visual_programming_language" title="Visual programming language">Visual</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Concurrent_computing" title="Concurrent computing">Concurrent</a>, <a href="/wiki/Distributed_computing" title="Distributed computing">distributed</a>, <a href="/wiki/Parallel_computing" title="Parallel computing">parallel</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Actor_model" title="Actor model">Actor-based</a></li> <li><a href="/wiki/Automatic_mutual_exclusion" title="Automatic mutual exclusion">Automatic mutual exclusion</a></li> <li><a href="/wiki/Choreographic_programming" title="Choreographic programming">Choreographic programming</a></li> <li><a href="/wiki/Concurrent_logic_programming" title="Concurrent logic programming">Concurrent logic</a> (<a href="/wiki/Concurrent_constraint_logic_programming" title="Concurrent constraint logic programming">Concurrent constraint logic</a>)</li> <li><a href="/wiki/Concurrent_object-oriented_programming" title="Concurrent object-oriented programming">Concurrent OO</a></li> <li><a href="/wiki/Macroprogramming" title="Macroprogramming">Macroprogramming</a></li> <li><a href="/wiki/Multitier_programming" title="Multitier programming">Multitier programming</a></li> <li><a href="/wiki/Organic_computing" title="Organic computing">Organic computing</a></li> <li><a href="/wiki/Parallel_programming_model" title="Parallel programming model">Parallel programming models</a></li> <li><a href="/wiki/Partitioned_global_address_space" title="Partitioned global address space">Partitioned global address space</a></li> <li><a href="/wiki/Process-oriented_programming" title="Process-oriented programming">Process-oriented</a></li> <li><a href="/wiki/Relativistic_programming" title="Relativistic programming">Relativistic programming</a></li> <li><a href="/wiki/Service-oriented_programming" title="Service-oriented programming">Service-oriented</a></li> <li><a href="/wiki/Structured_concurrency" title="Structured concurrency">Structured concurrency</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Metaprogramming" title="Metaprogramming">Metaprogramming</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Attribute-oriented_programming" title="Attribute-oriented programming">Attribute-oriented</a></li> <li><a href="/wiki/Automatic_programming" title="Automatic programming">Automatic</a> (<a href="/wiki/Inductive_programming" title="Inductive programming">Inductive</a>)</li> <li><a href="/wiki/Dynamic_programming_language" title="Dynamic programming language">Dynamic</a></li> <li><a href="/wiki/Extensible_programming" title="Extensible programming">Extensible</a></li> <li><a href="/wiki/Generic_programming" title="Generic programming">Generic</a></li> <li><a href="/wiki/Homoiconicity" title="Homoiconicity">Homoiconicity</a></li> <li><a href="/wiki/Interactive_programming" title="Interactive programming">Interactive</a></li> <li><a href="/wiki/Macro_(computer_science)" title="Macro (computer science)">Macro</a> (<a href="/wiki/Hygienic_macro" title="Hygienic macro">Hygienic</a>)</li> <li><a href="/wiki/Metalinguistic_abstraction" title="Metalinguistic abstraction">Metalinguistic abstraction</a></li> <li><a href="/wiki/Multi-stage_programming" title="Multi-stage programming">Multi-stage</a></li> <li><a href="/wiki/Program_synthesis" title="Program synthesis">Program synthesis</a> (<a href="/wiki/Bayesian_program_synthesis" title="Bayesian program synthesis">Bayesian</a>, <a href="/wiki/Inferential_programming" title="Inferential programming">Inferential</a>, <a href="/wiki/Programming_by_demonstration" title="Programming by demonstration">by demonstration</a>, <a href="/wiki/Programming_by_example" title="Programming by example">by example</a>)</li> <li><a href="/wiki/Reflective_programming" title="Reflective programming">Reflective</a></li> <li><a href="/wiki/Self-modifying_code" title="Self-modifying code">Self-modifying code</a></li> <li><a href="/wiki/Symbolic_programming" title="Symbolic programming">Symbolic</a></li> <li><a href="/wiki/Template_metaprogramming" title="Template metaprogramming">Template</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Separation_of_concerns" title="Separation of concerns">Separation of concerns</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Aspect-oriented_programming" title="Aspect-oriented programming">Aspects</a></li> <li><a href="/wiki/Component-based_software_engineering" title="Component-based software engineering">Components</a></li> <li><a href="/wiki/Data-driven_programming" title="Data-driven programming">Data-driven</a></li> <li><a href="/wiki/Data-oriented_design" title="Data-oriented design">Data-oriented</a></li> <li><a href="/wiki/Event-driven_programming" title="Event-driven programming">Event-driven</a></li> <li><a href="/wiki/Feature-oriented_programming" title="Feature-oriented programming">Features</a></li> <li><a href="/wiki/Intentional_programming" title="Intentional programming">Intentional</a></li> <li><a href="/wiki/Literate_programming" title="Literate programming">Literate</a></li> <li><a href="/wiki/Role-oriented_programming" title="Role-oriented programming">Roles</a></li> <li><a href="/wiki/Subject-oriented_programming" title="Subject-oriented programming">Subjects</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Types_of_programming_languages" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Types_of_programming_languages" title="Template:Types of programming languages"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a 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language">Compiled</a></li> <li><a href="/wiki/Interpreted_language" class="mw-redirect" title="Interpreted language">Interpreted</a></li></ul> <ul><li><a href="/wiki/Low-level_programming_language" title="Low-level programming language">Low-level</a></li> <li><a href="/wiki/High-level_programming_language" title="High-level programming language">High-level</a></li> <li><a href="/wiki/Very_high-level_programming_language" title="Very high-level programming language">Very high-level</a></li> <li><a href="/wiki/Esoteric_programming_language" title="Esoteric programming language">Esoteric</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Programming_language_generations" title="Programming language generations">Generation</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/First-generation_programming_language" title="First-generation programming language">First</a></li> <li><a href="/wiki/Second-generation_programming_language" title="Second-generation programming language">Second</a></li> <li><a href="/wiki/Third-generation_programming_language" title="Third-generation programming language">Third</a></li> <li><a href="/wiki/Fourth-generation_programming_language" title="Fourth-generation programming language">Fourth</a></li> <li><a href="/wiki/Fifth-generation_programming_language" title="Fifth-generation programming language">Fifth</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"><style data-mw-deduplicate="TemplateStyles:r1038841319">.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}</style></div><div role="navigation" class="navbox authority-control" aria-label="Navbox" style="padding:3px"><table 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= 1,\n [\"CITEREFKennedyRusso2005\"] = 1,\n [\"CITEREFKidd\"] = 1,\n [\"CITEREFLandin1964\"] = 1,\n [\"CITEREFLandin1965a\"] = 1,\n [\"CITEREFLandin1965b\"] = 1,\n [\"CITEREFLandin1966b\"] = 1,\n [\"CITEREFLarson2009\"] = 1,\n [\"CITEREFLaunchbury1993\"] = 1,\n [\"CITEREFLaurikari2007\"] = 1,\n [\"CITEREFLeo_Cheung2017\"] = 1,\n [\"CITEREFLeroy\"] = 1,\n [\"CITEREFLeroy2018\"] = 1,\n [\"CITEREFLorimer2009\"] = 1,\n [\"CITEREFL’orange\"] = 1,\n [\"CITEREFMansell2008\"] = 1,\n [\"CITEREFMcCarthy1978\"] = 1,\n [\"CITEREFMertz\"] = 1,\n [\"CITEREFMichaelson2013\"] = 1,\n [\"CITEREFMinskyWeeks2008\"] = 1,\n [\"CITEREFMomtahan2009\"] = 1,\n [\"CITEREFNewbern\"] = 1,\n [\"CITEREFNovatchev\"] = 1,\n [\"CITEREFO\u0026#039;SullivanStewartGoerzen2008\"] = 1,\n [\"CITEREFPaulson1996\"] = 1,\n [\"CITEREFPeake2009\"] = 1,\n [\"CITEREFPeter_Bright2018\"] = 1,\n [\"CITEREFPeyton_JonesBurnettBlackwell2003\"] = 1,\n [\"CITEREFPeyton_JonesVytiniotisWeirichGeoffrey_Washburn2006\"] = 1,\n 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3,\n [\"Main\"] = 7,\n [\"Notelist\"] = 1,\n [\"Portal\"] = 1,\n [\"Programming paradigms navbox\"] = 1,\n [\"Reflist\"] = 1,\n [\"Short description\"] = 1,\n [\"Spoken Wikipedia\"] = 1,\n [\"Triangulation\"] = 1,\n [\"Types of programming languages\"] = 1,\n [\"Webarchive\"] = 1,\n}\narticle_whitelist = table#1 {\n}\n","limitreport-profile":[["dataWrapper \u003Cmw.lua:672\u003E","180","17.0"],["MediaWiki\\Extension\\Scribunto\\Engines\\LuaSandbox\\LuaSandboxCallback::callParserFunction","180","17.0"],["?","140","13.2"],["type","80","7.5"],["recursiveClone 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