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<span>Examples</span> </div> </a> <button aria-controls="toc-Examples-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Examples subsection</span> </button> <ul id="toc-Examples-sublist" class="vector-toc-list"> <li id="toc-Factorial" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Factorial"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Factorial</span> </div> </a> <ul id="toc-Factorial-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-List_reverse" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#List_reverse"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>List reverse</span> </div> </a> <ul id="toc-List_reverse-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Modules" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Modules"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Modules</span> </div> </a> <ul id="toc-Modules-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"> <span class="vector-toc-numb">3</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>References</span> </div> </a> <ul id="toc-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"> <span class="vector-toc-numb">5</span> <span>Further reading</span> </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"> <span class="vector-toc-numb">6</span> <span>External links</span> </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" 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Available in 28 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-28" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">28 languages</span> </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%A3%D9%85_%D8%A3%D9%84_(%D9%84%D8%BA%D8%A9_%D8%A8%D8%B1%D9%85%D8%AC%D8%A9)" title="أم أل (لغة برمجة) – Arabic" lang="ar" hreflang="ar" data-title="أم أل (لغة برمجة)" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/ML" title="ML – Aragonese" lang="an" hreflang="an" data-title="ML" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/ML" title="ML – Catalan" lang="ca" hreflang="ca" data-title="ML" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/ML_(Programmiersprache)" title="ML (Programmiersprache) – German" lang="de" hreflang="de" data-title="ML (Programmiersprache)" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/ML_(%CE%B3%CE%BB%CF%8E%CF%83%CF%83%CE%B1_%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%CE%BF%CF%8D)" title="ML (γλώσσα προγραμματισμού) – Greek" lang="el" hreflang="el" data-title="ML (γλώσσα προγραμματισμού)" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/ML_(lenguaje_de_programaci%C3%B3n)" title="ML (lenguaje de programación) – Spanish" lang="es" hreflang="es" data-title="ML (lenguaje de programación)" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/ML_(programlingvo)" title="ML (programlingvo) – Esperanto" lang="eo" hreflang="eo" data-title="ML (programlingvo)" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D9%85%E2%80%8C%D8%A7%D9%84" title="ام‌ال – Persian" lang="fa" hreflang="fa" data-title="ام‌ال" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/ML_(langage)" title="ML (langage) – French" lang="fr" hreflang="fr" data-title="ML (langage)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/ML_(%ED%94%84%EB%A1%9C%EA%B7%B8%EB%9E%98%EB%B0%8D_%EC%96%B8%EC%96%B4)" title="ML (프로그래밍 언어) – Korean" lang="ko" hreflang="ko" data-title="ML (프로그래밍 언어)" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/ML_(programski_jezik)" title="ML (programski jezik) – Croatian" lang="hr" hreflang="hr" data-title="ML (programski jezik)" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/ML_(linguaggio_di_programmazione)" title="ML (linguaggio di programmazione) – Italian" lang="it" hreflang="it" data-title="ML (linguaggio di programmazione)" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/ML_(%D7%A9%D7%A4%D7%AA_%D7%AA%D7%9B%D7%A0%D7%95%D7%AA)" title="ML (שפת תכנות) – Hebrew" lang="he" hreflang="he" data-title="ML (שפת תכנות)" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/ML_(programoz%C3%A1si_nyelv)" title="ML (programozási nyelv) – Hungarian" lang="hu" hreflang="hu" data-title="ML (programozási nyelv)" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/ML_(programmeertaal)" title="ML (programmeertaal) – Dutch" lang="nl" hreflang="nl" data-title="ML (programmeertaal)" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/ML_(%E3%83%97%E3%83%AD%E3%82%B0%E3%83%A9%E3%83%9F%E3%83%B3%E3%82%B0%E8%A8%80%E8%AA%9E)" title="ML (プログラミング言語) – Japanese" lang="ja" hreflang="ja" data-title="ML (プログラミング言語)" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/MetaLanguage" title="MetaLanguage – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="MetaLanguage" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Meta_Language" title="Meta Language – Polish" lang="pl" hreflang="pl" data-title="Meta Language" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/ML_(linguagem_de_programa%C3%A7%C3%A3o)" title="ML (linguagem de programação) – Portuguese" lang="pt" hreflang="pt" data-title="ML (linguagem de programação)" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/ML" title="ML – Russian" lang="ru" hreflang="ru" data-title="ML" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/ML_(programski_jezik)" title="ML (programski jezik) – Serbian" lang="sr" hreflang="sr" data-title="ML (programski jezik)" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/ML_(programski_jezik)" title="ML (programski jezik) – Serbo-Croatian" lang="sh" hreflang="sh" data-title="ML (programski jezik)" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/ML_(ohjelmointikieli)" title="ML (ohjelmointikieli) – Finnish" lang="fi" hreflang="fi" data-title="ML (ohjelmointikieli)" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/ML_(programspr%C3%A5k)" title="ML (programspråk) – Swedish" lang="sv" hreflang="sv" data-title="ML (programspråk)" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/ML" title="ML – Tajik" lang="tg" hreflang="tg" data-title="ML" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/ML_(programlama_dili)" title="ML (programlama dili) – Turkish" lang="tr" hreflang="tr" data-title="ML (programlama dili)" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/ML" title="ML – Ukrainian" lang="uk" hreflang="uk" data-title="ML" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/ML%E8%AF%AD%E8%A8%80" title="ML语言 – Chinese" lang="zh" hreflang="zh" data-title="ML语言" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q860654#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div 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.ambox{display:none!important}}</style><table class="box-More_citations_needed plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span 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Unsourced material may be challenged and removed.<br /><small><span class="plainlinks"><i>Find sources:</i> <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22ML%22+programming+language">"ML" programming language</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22ML%22+programming+language+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22ML%22+programming+language&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22ML%22+programming+language+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22ML%22+programming+language">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22ML%22+programming+language&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">May 2015</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox vevent"><caption class="infobox-title summary">ML</caption><tbody><tr><th scope="row" class="infobox-label"><a href="/wiki/Programming_paradigm" title="Programming paradigm">Paradigm</a></th><td class="infobox-data"><a href="/wiki/Multi-paradigm_programming_language" class="mw-redirect" title="Multi-paradigm programming language">Multi-paradigm</a>: <a href="/wiki/Functional_programming" title="Functional programming">functional</a>, <a href="/wiki/Generic_programming" title="Generic programming">generic</a>, <a href="/wiki/Imperative_programming" title="Imperative programming">imperative</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Software_design" title="Software design">Designed by</a></th><td class="infobox-data"><a href="/wiki/Robin_Milner" title="Robin Milner">Robin Milner</a>, others at the <a href="/wiki/University_of_Edinburgh" title="University of Edinburgh">University of Edinburgh</a></td></tr><tr><th scope="row" class="infobox-label">First appeared</th><td class="infobox-data">1973<span class="noprint">; 51 years ago</span><span style="display:none"> (<span class="bday dtstart published updated">1973</span>)</span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Type_system" title="Type system">Typing discipline</a></th><td class="infobox-data"><a href="/wiki/Type_inference" title="Type inference">Inferred</a>, <a href="/wiki/Static_typing" class="mw-redirect" title="Static typing">static</a>, <a href="/wiki/Strong_typing" class="mw-redirect" title="Strong typing">strong</a></td></tr><tr><th colspan="2" class="infobox-header" style="background-color: #eee;"><a href="/wiki/Programming_language#Dialects,_flavors_and_implementations" title="Programming language">Dialects</a></th></tr><tr><td colspan="2" class="infobox-full-data"><a href="/wiki/OCaml" title="OCaml">OCaml</a>, <a href="/wiki/Standard_ML" title="Standard ML">Standard ML</a>, <a href="/wiki/F_Sharp_(programming_language)" title="F Sharp (programming language)">F#</a></td></tr><tr><th colspan="2" class="infobox-header" style="background-color: #eee;">Influenced by</th></tr><tr><td colspan="2" class="infobox-full-data"><a href="/wiki/ISWIM" title="ISWIM">ISWIM</a></td></tr><tr><th colspan="2" class="infobox-header" style="background-color: #eee;">Influenced</th></tr><tr><td colspan="2" class="infobox-full-data"><a href="/wiki/Clojure" title="Clojure">Clojure</a>, <a href="/wiki/Coq_(software)" title="Coq (software)">Coq</a>, <a href="/wiki/Cyclone_(programming_language)" title="Cyclone (programming language)">Cyclone</a>, <a href="/wiki/C%2B%2B" title="C++">C++</a>, <a href="/wiki/Elm_(programming_language)" title="Elm (programming language)">Elm</a>, <a href="/wiki/F_Sharp_(programming_language)" title="F Sharp (programming language)">F#</a>, <a href="/wiki/F*_(programming_language)" title="F* (programming language)">F*</a>, <a href="/wiki/Haskell" title="Haskell">Haskell</a>, <a href="/wiki/Idris_(programming_language)" title="Idris (programming language)">Idris</a>, <a href="/wiki/Kotlin_(programming_language)" title="Kotlin (programming language)">Kotlin</a>, <a href="/wiki/Miranda_(programming_language)" title="Miranda (programming language)">Miranda</a>, <a href="/wiki/Nemerle" title="Nemerle">Nemerle</a>, <a href="/wiki/OCaml" title="OCaml">OCaml</a>, <a href="/wiki/Opa_(programming_language)" title="Opa (programming language)">Opa</a>, <a href="/wiki/Erlang_(programming_language)" title="Erlang (programming language)">Erlang</a>, <a href="/wiki/Rust_(programming_language)" title="Rust (programming language)">Rust</a>, <a href="/wiki/Scala_(programming_language)" title="Scala (programming language)">Scala</a>, <a href="/wiki/Standard_ML" title="Standard ML">Standard ML</a></td></tr></tbody></table> <p><b>ML</b> (<b>Meta Language</b>) is a <a href="/wiki/General-purpose_programming_language" title="General-purpose programming language">general-purpose</a>, <a href="/wiki/High-level_programming_language" title="High-level programming language">high-level</a>, <a href="/wiki/Functional_programming" title="Functional programming">functional</a> <a href="/wiki/Programming_language" title="Programming language">programming language</a>. It is known for its use of the polymorphic <a href="/wiki/Hindley%E2%80%93Milner_type_system" title="Hindley–Milner type system">Hindley–Milner type system</a>, which automatically assigns the <a href="/wiki/Data_type" title="Data type">data types</a> of most <a href="/wiki/Expression_(programming)" class="mw-redirect" title="Expression (programming)">expressions</a> without requiring explicit type annotations (<a href="/wiki/Type_inference" title="Type inference">type inference</a>), and ensures type safety; there is a <a href="/wiki/Formal_proof" title="Formal proof">formal proof</a> that a well-typed ML program does not cause runtime type errors.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> ML provides pattern matching for function arguments, <a href="/wiki/Garbage_collection_(computer_science)" title="Garbage collection (computer science)">garbage collection</a>, <a href="/wiki/Imperative_programming" title="Imperative programming">imperative programming</a>, <a href="/wiki/Call-by-value" class="mw-redirect" title="Call-by-value">call-by-value</a> and <a href="/wiki/Currying" title="Currying">currying</a>. While a <a href="/wiki/General-purpose_programming_language" title="General-purpose programming language">general-purpose programming language</a>, ML is used heavily in <a href="/wiki/Programming_language_theory" title="Programming language theory">programming language research</a> and is one of the few languages to be completely specified and verified using <a href="/wiki/Formal_semantics_of_programming_languages" class="mw-redirect" title="Formal semantics of programming languages">formal semantics</a>. Its types and pattern matching make it well-suited and commonly used to operate on other formal languages, such as in <a href="/wiki/Compiler_writing" class="mw-redirect" title="Compiler writing">compiler writing</a>, <a href="/wiki/Automated_theorem_proving" title="Automated theorem proving">automated theorem proving</a>, and <a href="/wiki/Formal_verification" title="Formal verification">formal verification</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Overview">Overview</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=ML_(programming_language)&action=edit&section=1" title="Edit section: Overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Features of ML include a call-by-value <a href="/wiki/Evaluation_strategy" title="Evaluation strategy">evaluation strategy</a>, <a href="/wiki/First-class_function" title="First-class function">first-class functions</a>, automatic memory management through garbage collection, <a href="/wiki/Parametric_polymorphism" title="Parametric polymorphism">parametric polymorphism</a>, <a href="/wiki/Type_system#Static_typing" title="Type system">static typing</a>, <a href="/wiki/Type_inference" title="Type inference">type inference</a>, <a href="/wiki/Algebraic_data_types" class="mw-redirect" title="Algebraic data types">algebraic data types</a>, <a href="/wiki/Pattern_matching" title="Pattern matching">pattern matching</a>, and <a href="/wiki/Exception_handling" title="Exception handling">exception handling</a>. ML uses <a href="/wiki/Scope_(computer_science)#Lexical_scoping" title="Scope (computer science)">static scoping</a> rules.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>ML can be referred to as an <i>impure</i> functional language, because although it encourages functional programming, it does allow <a href="/wiki/Side-effect_(computer_science)" class="mw-redirect" title="Side-effect (computer science)">side-effects</a><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> (like languages such as <a href="/wiki/Lisp_(programming_language)" title="Lisp (programming language)">Lisp</a>, but unlike a <a href="/wiki/Purely_functional_language" class="mw-redirect" title="Purely functional language">purely functional language</a> such as <a href="/wiki/Haskell" title="Haskell">Haskell</a>). Like most programming languages, ML uses <a href="/wiki/Eager_evaluation" class="mw-redirect" title="Eager evaluation">eager evaluation</a>, meaning that all subexpressions are always evaluated, though <a href="/wiki/Lazy_evaluation" title="Lazy evaluation">lazy evaluation</a> can be achieved through the use of <a href="/wiki/Closure_(computer_science)" class="mw-redirect" title="Closure (computer science)">closures</a>. Thus, infinite streams can be created and used as in Haskell, but their expression is indirect. </p><p>ML's strengths are mostly applied in language design and manipulation (compilers, analyzers, theorem provers), but it is a general-purpose language also used in <a href="/wiki/Bioinformatics" title="Bioinformatics">bioinformatics</a> and financial systems. </p><p>ML was developed by <a href="/wiki/Robin_Milner" title="Robin Milner">Robin Milner</a> and others in the early 1970s at the <a href="/wiki/University_of_Edinburgh" title="University of Edinburgh">University of Edinburgh</a>,<sup id="cite_ref-Gordon1996_4-0" class="reference"><a href="#cite_note-Gordon1996-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> and its syntax is inspired by <a href="/wiki/ISWIM" title="ISWIM">ISWIM</a>. Historically, ML was conceived to develop proof tactics in the <a href="/wiki/Logic_for_Computable_Functions" title="Logic for Computable Functions">LCF theorem prover</a> (whose language, <i>pplambda</i>, a combination of the <a href="/wiki/First-order_logic" title="First-order logic">first-order predicate calculus</a> and the simply-typed <a href="/wiki/Polymorphism_(computer_science)" title="Polymorphism (computer science)">polymorphic</a> <a href="/wiki/Lambda_calculus" title="Lambda calculus">lambda calculus</a>, had ML as its metalanguage). </p><p>Today there are several languages in the ML family; the three most prominent are <a href="/wiki/Standard_ML" title="Standard ML">Standard ML</a> (SML), <a href="/wiki/OCaml" title="OCaml">OCaml</a> and <a href="/wiki/F_Sharp_(programming_language)" title="F Sharp (programming language)">F#</a>. Ideas from ML have influenced numerous other languages, like <a href="/wiki/Haskell" title="Haskell">Haskell</a>, <a href="/wiki/Cyclone_(programming_language)" title="Cyclone (programming language)">Cyclone</a>, <a href="/wiki/Nemerle" title="Nemerle">Nemerle</a>,<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> <a href="/wiki/ATS_(programming_language)" title="ATS (programming language)">ATS</a>, and <a href="/wiki/Elm_(programming_language)" title="Elm (programming language)">Elm</a>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Examples">Examples</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=ML_(programming_language)&action=edit&section=2" title="Edit section: Examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The following examples use the syntax of Standard ML. Other ML dialects such as OCaml and F# differ in small ways. </p> <div class="mw-heading mw-heading3"><h3 id="Factorial">Factorial</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=ML_(programming_language)&action=edit&section=3" title="Edit section: Factorial"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Factorial" title="Factorial">factorial</a> function expressed as pure ML: </p> <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre><span></span><span class="kr">fun</span> <span class="nf">fac</span> <span class="p">(</span><span class="mi">0</span> <span class="p">:</span> <span class="n">int</span><span class="p">)</span> <span class="p">:</span> <span class="n">int</span> <span class="p">=</span> <span class="mi">1</span> <span class="p">|</span> <span class="nf">fac</span> <span class="p">(</span><span class="n">n</span> <span class="p">:</span> <span class="n">int</span><span class="p">)</span> <span class="p">:</span> <span class="n">int</span> <span class="p">=</span> <span class="n">n</span> <span class="n">*</span> <span class="n">fac</span> <span class="p">(</span><span class="n">n</span> <span class="n">-</span> <span class="mi">1</span><span class="p">)</span> </pre></div> <p>This describes the factorial as a recursive function, with a single terminating base case. It is similar to the descriptions of factorials found in mathematics textbooks. Much of ML code is similar to mathematics in facility and syntax. </p><p>Part of the definition shown is optional, and describes the <i>types</i> of this function. The notation E : t can be read as <i>expression E has type t</i>. For instance, the argument n is assigned type <i>integer</i> (int), and fac (n : int), the result of applying fac to the integer n, also has type integer. The function fac as a whole then has type <i>function from integer to integer</i> (int -> int), that is, fac accepts an integer as an argument and returns an integer result. Thanks to type inference, the type annotations can be omitted and will be derived by the compiler. Rewritten without the type annotations, the example looks like: </p> <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre><span></span><span class="kr">fun</span> <span class="nf">fac</span> <span class="mi">0</span> <span class="p">=</span> <span class="mi">1</span> <span class="p">|</span> <span class="nf">fac</span> <span class="n">n</span> <span class="p">=</span> <span class="n">n</span> <span class="n">*</span> <span class="n">fac</span> <span class="p">(</span><span class="n">n</span> <span class="n">-</span> <span class="mi">1</span><span class="p">)</span> </pre></div> <p>The function also relies on pattern matching, an important part of ML programming. Note that parameters of a function are not necessarily in parentheses but separated by spaces. When the function's argument is 0 (zero) it will return the integer 1 (one). For all other cases the second line is tried. This is the <a href="/wiki/Recursion_(computer_science)" title="Recursion (computer science)">recursion</a>, and executes the function again until the base case is reached. </p><p>This implementation of the factorial function is not guaranteed to terminate, since a negative argument causes an <a href="/wiki/Infinite_descending_chain" class="mw-redirect" title="Infinite descending chain">infinite descending chain</a> of recursive calls. A more robust implementation would check for a nonnegative argument before recursing, as follows: </p> <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre><span></span><span class="kr">fun</span> <span class="nf">fact</span> <span class="n">n</span> <span class="p">=</span> <span class="kr">let</span> <span class="kr">fun</span> <span class="nf">fac</span> <span class="mi">0</span> <span class="p">=</span> <span class="mi">1</span> <span class="p">|</span> <span class="nf">fac</span> <span class="n">n</span> <span class="p">=</span> <span class="n">n</span> <span class="n">*</span> <span class="n">fac</span> <span class="p">(</span><span class="n">n</span> <span class="n">-</span> <span class="mi">1</span><span class="p">)</span> <span class="kr">in</span> <span class="kr">if</span> <span class="p">(</span><span class="n">n</span> <span class="n"><</span> <span class="mi">0</span><span class="p">)</span> <span class="kr">then</span> <span class="kr">raise</span> <span class="n">Domain</span> <span class="kr">else</span> <span class="n">fac</span> <span class="n">n</span> <span class="kr">end</span> </pre></div> <p>The problematic case (when n is negative) demonstrates a use of ML's exception system. </p><p>The function can be improved further by writing its inner loop as a <a href="/wiki/Tail_call" title="Tail call">tail call</a>, such that the <a href="/wiki/Call_stack" title="Call stack">call stack</a> need not grow in proportion to the number of function calls. This is achieved by adding an extra, <i>accumulator</i>, parameter to the inner function. At last, we arrive at </p> <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre><span></span><span class="kr">fun</span> <span class="nf">fact</span> <span class="n">n</span> <span class="p">=</span> <span class="kr">let</span> <span class="kr">fun</span> <span class="nf">fac</span> <span class="mi">0</span> <span class="n">acc</span> <span class="p">=</span> <span class="n">acc</span> <span class="p">|</span> <span class="nf">fac</span> <span class="n">n</span> <span class="n">acc</span> <span class="p">=</span> <span class="n">fac</span> <span class="p">(</span><span class="n">n</span> <span class="n">-</span> <span class="mi">1</span><span class="p">)</span> <span class="p">(</span><span class="n">n</span> <span class="n">*</span> <span class="n">acc</span><span class="p">)</span> <span class="kr">in</span> <span class="kr">if</span> <span class="p">(</span><span class="n">n</span> <span class="n"><</span> <span class="mi">0</span><span class="p">)</span> <span class="kr">then</span> <span class="kr">raise</span> <span class="n">Domain</span> <span class="kr">else</span> <span class="n">fac</span> <span class="n">n</span> <span class="mi">1</span> <span class="kr">end</span> </pre></div> <div class="mw-heading mw-heading3"><h3 id="List_reverse">List reverse</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=ML_(programming_language)&action=edit&section=4" title="Edit section: List reverse"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The following function <i>reverses</i> the elements in a list. More precisely, it returns a new list whose elements are in reverse order compared to the given list. </p> <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre><span></span><span class="kr">fun</span> <span class="nf">reverse</span> <span class="p">[]</span> <span class="p">=</span> <span class="p">[]</span> <span class="p">|</span> <span class="nf">reverse</span> <span class="p">(</span><span class="n">x</span> <span class="n">::</span> <span class="n">xs</span><span class="p">)</span> <span class="p">=</span> <span class="p">(</span><span class="n">reverse</span> <span class="n">xs</span><span class="p">)</span> <span class="n">@</span> <span class="p">[</span><span class="n">x</span><span class="p">]</span> </pre></div> <p>This implementation of reverse, while correct and clear, is inefficient, requiring <a href="/wiki/Quadratic_time" class="mw-redirect" title="Quadratic time">quadratic time</a> for execution. The function can be rewritten to execute in <a href="/wiki/Linear_time" class="mw-redirect" title="Linear time">linear time</a>: </p> <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre><span></span><span class="kr">fun</span> <span class="nd">'a</span> <span class="nf">reverse</span> <span class="n">xs</span> <span class="p">:</span> <span class="nd">'a</span> <span class="n">list</span> <span class="p">=</span> <span class="nn">List</span><span class="p">.</span><span class="n">foldl</span> <span class="p">(</span><span class="kr">op</span> <span class="n">::</span><span class="p">)</span> <span class="p">[]</span> <span class="n">xs</span> </pre></div> <p>This function is an example of parametric polymorphism. That is, it can consume lists whose elements have any type, and return lists of the same type. </p> <div class="mw-heading mw-heading3"><h3 id="Modules">Modules</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=ML_(programming_language)&action=edit&section=5" title="Edit section: Modules"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Modules are ML's system for structuring large projects and libraries. A module consists of a signature file and one or more structure files. The signature file specifies the <a href="/wiki/API" title="API">API</a> to be implemented (like a C header file, or <a href="/wiki/Interface_(Java)" title="Interface (Java)">Java interface</a> file). The structure implements the signature (like a C source file or Java class file). For example, the following define an Arithmetic signature and an implementation of it using Rational numbers: </p> <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre><span></span><span class="kr">signature</span> <span class="nn">ARITH</span> <span class="p">=</span> <span class="kr">sig</span> <span class="kr">type</span> <span class="kt">t</span> <span class="kr">val</span> <span class="nv">zero</span> <span class="p">:</span> <span class="n">t</span> <span class="kr">val</span> <span class="nv">succ</span> <span class="p">:</span> <span class="n">t</span> <span class="p">-></span> <span class="n">t</span> <span class="kr">val</span> <span class="nv">sum</span> <span class="p">:</span> <span class="n">t</span> <span class="n">*</span> <span class="n">t</span> <span class="p">-></span> <span class="n">t</span> <span class="kr">end</span> </pre></div> <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre><span></span><span class="kr">structure</span> <span class="nn">Rational</span> <span class="p">:</span> <span class="n">ARITH</span> <span class="p">=</span> <span class="kr">struct</span> <span class="kr">datatype</span> <span class="kt">t</span> <span class="p">=</span> <span class="nc">Rat</span> <span class="kr">of</span> <span class="n">int</span> <span class="n">*</span> <span class="n">int</span> <span class="kr">val</span> <span class="nv">zero</span> <span class="p">=</span> <span class="n">Rat</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> <span class="kr">fun</span> <span class="nf">succ</span> <span class="p">(</span><span class="n">Rat</span> <span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">))</span> <span class="p">=</span> <span class="n">Rat</span> <span class="p">(</span><span class="n">a</span> <span class="n">+</span> <span class="n">b</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="kr">fun</span> <span class="nf">sum</span> <span class="p">(</span><span class="n">Rat</span> <span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">),</span> <span class="n">Rat</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">d</span><span class="p">))</span> <span class="p">=</span> <span class="n">Rat</span> <span class="p">(</span><span class="n">a</span> <span class="n">*</span> <span class="n">d</span> <span class="n">+</span> <span class="n">c</span> <span class="n">*</span> <span class="n">b</span> <span class="p">,</span> <span class="n">b</span> <span class="n">*</span> <span class="n">d</span><span class="p">)</span> <span class="kr">end</span> </pre></div> <p>These are imported into the interpreter by the 'use' command. Interaction with the implementation is only allowed via the signature functions, for example it is not possible to create a 'Rat' data object directly via this code. The 'structure' block hides all the implementation detail from outside. </p><p>ML's standard libraries are implemented as modules in this way. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=ML_(programming_language)&action=edit&section=6" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Standard_ML" title="Standard ML">Standard ML</a> and <a href="/wiki/Standard_ML#Implementations" title="Standard ML">Standard ML § Implementations</a></li> <li><a href="/wiki/Dependent_ML" title="Dependent ML">Dependent ML</a>: a dependently typed extension of ML <ul><li><a href="/wiki/ATS_(programming_language)" title="ATS (programming language)">ATS</a>: a further development of dependent ML</li></ul></li> <li><a href="/wiki/Lazy_ML" class="mw-redirect" title="Lazy ML">Lazy ML</a>: an experimental lazily evaluated ML dialect from the early 1980s</li> <li><a href="/wiki/PAL_(programming_language)" title="PAL (programming language)">PAL (programming language)</a>: an educational language related to ML</li> <li><a href="/wiki/OCaml" title="OCaml">OCaml</a>: an ML dialect used to implement <a href="/wiki/Coq_(software)" title="Coq (software)">Coq</a> and <a href="/wiki/OCaml#Software_written_in_OCaml" title="OCaml">various softwares</a></li> <li><a href="/wiki/F_Sharp_(programming_language)" title="F Sharp (programming language)">F#</a>: an open-source cross-platform functional-first language for the <a href="/wiki/.NET" title=".NET">.NET</a> framework</li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=ML_(programming_language)&action=edit&section=7" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">Robin Milner. A theory of type polymorphism in programming. Journal of Computer and System Sciences, 17(3):348–375, 1978.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><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><cite id="CITEREFMilnerTofte1991" class="citation book cs1">Milner, Robin; Tofte, Mads (1991). "4.1 Contexts, environments and scope". <i>Commentary on Standard ML</i>. The MIT Press. pp. 35–36. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-262-63137-7" title="Special:BookSources/0-262-63137-7"><bdi>0-262-63137-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=4.1+Contexts%2C+environments+and+scope&rft.btitle=Commentary+on+Standard+ML&rft.pages=35-36&rft.pub=The+MIT+Press&rft.date=1991&rft.isbn=0-262-63137-7&rft.aulast=Milner&rft.aufirst=Robin&rft.au=Tofte%2C+Mads&rfr_id=info%3Asid%2Fen.wikipedia.org%3AML+%28programming+language%29" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSebesta1999" class="citation book cs1">Sebesta, Robert (1999). <i>Concepts of Programming Languages</i> (4th ed.). Addison-Westley. p. 54. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-201-38596-1" title="Special:BookSources/0-201-38596-1"><bdi>0-201-38596-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Concepts+of+Programming+Languages&rft.pages=54&rft.edition=4th&rft.pub=Addison-Westley&rft.date=1999&rft.isbn=0-201-38596-1&rft.aulast=Sebesta&rft.aufirst=Robert&rfr_id=info%3Asid%2Fen.wikipedia.org%3AML+%28programming+language%29" class="Z3988"></span></span> </li> <li id="cite_note-Gordon1996-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-Gordon1996_4-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGordon1996" class="citation web cs1"><a href="/wiki/Michael_J._C._Gordon" title="Michael J. C. Gordon">Gordon, Michael J. C.</a> (1996). <a rel="nofollow" class="external text" href="http://www.cl.cam.ac.uk/~mjcg/papers/HolHistory.html">"From LCF to HOL: a short history"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2007-10-11</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=From+LCF+to+HOL%3A+a+short+history&rft.date=1996&rft.aulast=Gordon&rft.aufirst=Michael+J.+C.&rft_id=http%3A%2F%2Fwww.cl.cam.ac.uk%2F~mjcg%2Fpapers%2FHolHistory.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AML+%28programming+language%29" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="http://nemerle.org/About"><i>Programming language for "special forces" of developers</i></a>, Russian Software Development Network: Nemerle Project Team<span class="reference-accessdate">, retrieved <span class="nowrap">January 24,</span> 2021</span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Programming+language+for+%22special+forces%22+of+developers&rft.place=Russian+Software+Development+Network&rft.pub=Nemerle+Project+Team&rft_id=http%3A%2F%2Fnemerle.org%2FAbout&rfr_id=info%3Asid%2Fen.wikipedia.org%3AML+%28programming+language%29" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTateDaoudDeesMoffitt2014" class="citation book cs1">Tate, Bruce A.; Daoud, Fred; Dees, Ian; Moffitt, Jack (2014). "3. Elm". <i>Seven More Languages in Seven Weeks</i> (Book version: P1.0-November 2014 ed.). The Pragmatic Programmers, LLC. pp. 97, 101. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-941222-15-7" title="Special:BookSources/978-1-941222-15-7"><bdi>978-1-941222-15-7</bdi></a>. <q>On page 101, Elm creator Evan Czaplicki says: 'I tend to say "Elm is an ML-family language" to get at the shared heritage of all these languages.' ["these languages" is referring to Haskell, OCaml, SML, and F#.]</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=3.+Elm&rft.btitle=Seven+More+Languages+in+Seven+Weeks&rft.pages=97%2C+101&rft.edition=Book+version%3A+P1.0-November+2014&rft.pub=The+Pragmatic+Programmers%2C+LLC&rft.date=2014&rft.isbn=978-1-941222-15-7&rft.aulast=Tate&rft.aufirst=Bruce+A.&rft.au=Daoud%2C+Fred&rft.au=Dees%2C+Ian&rft.au=Moffitt%2C+Jack&rfr_id=info%3Asid%2Fen.wikipedia.org%3AML+%28programming+language%29" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=ML_(programming_language)&action=edit&section=8" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <ul><li><i>The Definition of Standard ML</i>, Robin Milner, <a href="/wiki/Mads_Tofte" title="Mads Tofte">Mads Tofte</a>, <a href="/wiki/Robert_Harper_(computer_scientist)" title="Robert Harper (computer scientist)">Robert Harper</a>, MIT Press 1990; (revised edition adds author David MacQueen), MIT Press 1997, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-262-63181-4" title="Special:BookSources/0-262-63181-4">0-262-63181-4</a> <a rel="nofollow" class="external text" href="https://smlfamily.github.io/sml97-defn.pdf">The Definition of Standard ML (Revised)</a>.</li> <li><i>Commentary on Standard ML</i>, <a href="/wiki/Robin_Milner" title="Robin Milner">Robin Milner</a>, <a href="/wiki/Mads_Tofte" title="Mads Tofte">Mads Tofte</a>, MIT Press 1997, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-262-63137-7" title="Special:BookSources/0-262-63137-7">0-262-63137-7</a>.</li> <li><i>ML for the Working Programmer</i>, <a href="/wiki/Lawrence_Paulson" title="Lawrence Paulson">Lawrence Paulson</a>, Cambridge University Press 1991, 1996, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-57050-6" title="Special:BookSources/0-521-57050-6">0-521-57050-6</a>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHarper2011" class="citation book cs1">Harper, Robert (2011). <a rel="nofollow" class="external text" href="https://www.cs.cmu.edu/~rwh/isml/book.pdf"><i>Programming in Standard ML</i></a> <span class="cs1-format">(PDF)</span>. Carnegie Mellon University.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Programming+in+Standard+ML&rft.pub=Carnegie+Mellon+University&rft.date=2011&rft.aulast=Harper&rft.aufirst=Robert&rft_id=https%3A%2F%2Fwww.cs.cmu.edu%2F~rwh%2Fisml%2Fbook.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AML+%28programming+language%29" class="Z3988"></span></li> <li><i>Elements of ML Programming</i>, <a href="/wiki/Jeffrey_D._Ullman" class="mw-redirect" title="Jeffrey D. Ullman">Jeffrey D. Ullman</a>, Prentice-Hall 1994, 1998, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-13-790387-1" title="Special:BookSources/0-13-790387-1">0-13-790387-1</a>.</li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=ML_(programming_language)&action=edit&section=9" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://smlnj.org">Standard ML of New Jersey, another popular implementation</a></li> <li><a rel="nofollow" class="external text" href="http://msdn.microsoft.com/en-us/fsharp/default.aspx">F#, an ML implementation using the Microsoft .NET framework</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100218004857/http://msdn.microsoft.com/en-us/fsharp/default.aspx">Archived</a> 2010-02-18 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a rel="nofollow" class="external text" href="http://mlton.org">MLton, a whole-program optimizing Standard ML compiler</a></li> <li><a rel="nofollow" class="external text" href="https://cakeml.org">CakeML, a read-eval-print loop version of ML with formally verified runtime and translation to assembler</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 .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline 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implementation">Implementations</a>,<br /><a href="/wiki/Dialect_(computing)" class="mw-redirect" title="Dialect (computing)">dialects</a></th><td class="navbox-list-with-group navbox-list navbox-odd" 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/Caml" title="Caml">Caml</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/OCaml" title="OCaml">OCaml</a>° <ul><li><a href="/wiki/Eff_(programming_language)" title="Eff (programming language)">Eff</a></li> <li><a href="/wiki/F*_(programming_language)" title="F* (programming language)">F*</a>°</li> <li><a href="/wiki/F_Sharp_(programming_language)" title="F Sharp (programming language)">F#</a>°</li> <li><a href="/wiki/JoCaml" title="JoCaml">JoCaml</a>°</li> <li><a href="/wiki/Reason_(programming_language)" title="Reason (programming language)">Reason</a>°</li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Standard_ML" title="Standard ML">Standard ML</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><i><a href="/wiki/Alice_(programming_language)" title="Alice (programming language)">Alice</a></i>°</li> <li><a href="/wiki/Concurrent_ML" title="Concurrent ML">Concurrent ML</a></li> <li><a href="/wiki/Extended_ML" title="Extended ML">Extended ML</a></li> <li><a href="/wiki/MLton" title="MLton">MLton</a>°</li> <li><a href="/wiki/Standard_ML_of_New_Jersey" title="Standard ML of New Jersey">Standard ML of New Jersey</a>° (SML/NJ)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><i><a href="/wiki/Dependent_ML" title="Dependent ML">Dependent ML</a></i></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/ATS_(programming_language)" title="ATS (programming language)">ATS</a>°</li></ul> </div></td></tr></tbody></table><div> <ul><li><a href="/wiki/Futhark_(programming_language)" title="Futhark (programming language)">Futhark</a>°</li> <li><a href="/wiki/Lennart_Augustsson#Languages" title="Lennart Augustsson">Lazy ML</a></li> <li><a href="/wiki/MacroML" title="MacroML">MacroML</a></li> <li><a href="/wiki/Ur_(programming_language)" title="Ur (programming language)">Ur</a>°</li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Programming_tool" title="Programming tool">Programming tools</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <li><a href="/wiki/Alt-Ergo" title="Alt-Ergo">Alt-Ergo</a>°</li> <li><a href="/wiki/Astr%C3%A9e_(static_analysis)" title="Astrée (static analysis)">Astrée</a></li> <li><a href="/wiki/Camlp4" title="Camlp4">Camlp4</a>°</li> <li><a href="/wiki/FFTW" title="FFTW">FFTW</a>°</li> <li><a href="/wiki/Frama-C" title="Frama-C">Frama-C</a>°</li> <li><a href="/wiki/Haxe" title="Haxe">Haxe</a>°</li> <li><a href="/wiki/Marionnet" title="Marionnet">Marionnet</a>°</li> <li><a href="/wiki/MTASC" title="MTASC">MTASC</a>°</li> <li><a href="/wiki/Poplog" title="Poplog">Poplog</a>°</li> <li><a href="/wiki/Semgrep" title="Semgrep">Semgrep</a>°</li> <li><a href="/wiki/SLAM_project" title="SLAM project">SLAM project</a></li> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Automated_theorem_proving" title="Automated theorem proving">Theorem provers</a>,<br /><a href="/wiki/Proof_assistant" title="Proof assistant">proof assistants</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/Coq_(software)" title="Coq (software)">Coq</a>°</li> <li><a href="/wiki/HOL_(proof_assistant)" title="HOL (proof assistant)">HOL</a>° <ul><li><a href="/wiki/HOL_Light" title="HOL Light">HOL Light</a>°</li></ul></li> <li><a href="/wiki/Isabelle_(proof_assistant)" title="Isabelle (proof assistant)">Isabelle</a>°</li> <li><a href="/wiki/LEGO_(proof_assistant)" title="LEGO (proof assistant)">LEGO</a></li> <li><i><a href="/wiki/Logic_for_Computable_Functions" title="Logic for Computable Functions">Logic for Computable Functions</a></i></li> <li><a href="/wiki/Matita" title="Matita">Matita</a>°</li> <li><a href="/wiki/Twelf" title="Twelf">Twelf</a>°</li></ul> </div></td></tr></tbody></table><div> <ul><li><a href="/wiki/GeneWeb" title="GeneWeb">GeneWeb</a>°</li></ul></div></td><td class="noviewer navbox-image" rowspan="2" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:OCaml_Logo.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/OCaml_Logo.svg/110px-OCaml_Logo.svg.png" decoding="async" width="110" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/OCaml_Logo.svg/165px-OCaml_Logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/OCaml_Logo.svg/220px-OCaml_Logo.svg.png 2x" data-file-width="525" data-file-height="144" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Community_of_practice" title="Community of practice">Community</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Designers" scope="row" class="navbox-group" style="width:1%">Designers</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <li><a href="/wiki/Lennart_Augustsson" title="Lennart Augustsson">Lennart Augustsson</a> (Lazy ML)</li> <li><a href="/wiki/Damien_Doligez" title="Damien Doligez">Damien Doligez</a> (OCaml)</li> <li><a href="/wiki/G%C3%A9rard_Huet" title="Gérard Huet">Gérard Huet</a> (Caml)</li> <li><a href="/wiki/Xavier_Leroy" title="Xavier Leroy">Xavier Leroy</a> (Caml, OCaml)</li> <li><a href="/wiki/Robin_Milner" title="Robin Milner">Robin Milner</a> (ML)</li> <li><a href="/wiki/Don_Sannella" title="Don Sannella">Don Sannella</a> (Extended ML)</li> <li><a href="/wiki/Don_Syme" title="Don Syme">Don Syme</a> (F#)</li> </div></td></tr></tbody></table><div> <ul><li><a href="/wiki/Thierry_Coquand" title="Thierry Coquand">Thierry Coquand</a></li> <li><a href="/wiki/Steven_G._Johnson" title="Steven G. Johnson">Steven G. Johnson</a></li> <li><a href="/wiki/Christine_Paulin-Mohring" title="Christine Paulin-Mohring">Christine Paulin-Mohring</a></li> <li><a href="/wiki/Frank_Pfenning" title="Frank Pfenning">Frank Pfenning</a></li> <li><a href="/wiki/Simon_Thompson_(professor)" title="Simon Thompson (professor)">Simon Thompson</a></li></ul></div></td></tr><tr><td class="navbox-abovebelow" colspan="3"><div> <li><i>Italics</i> <b>= discontinued</b></li> <li><b>° = <a href="/wiki/Open-source_software" title="Open-source software">Open-source software</a></b><br /><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Symbol_book_class2.svg" class="mw-file-description" title="Wikipedia book"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/89/Symbol_book_class2.svg/16px-Symbol_book_class2.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/89/Symbol_book_class2.svg/23px-Symbol_book_class2.svg.png 1.5x, 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