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vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-Language" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Language"> <div class="vector-toc-text"> 1 Language </div> </a> <button aria-controls="toc-Language-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Language subsection </button> <ul id="toc-Language-sublist" class="vector-toc-list"> <li id="toc-Functions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Functions"> <div class="vector-toc-text"> 1.1 Functions </div> </a> <ul id="toc-Functions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Type_inference" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Type_inference"> <div class="vector-toc-text"> 1.2 Type inference </div> </a> <ul id="toc-Type_inference-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Declarative_definitions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Declarative_definitions"> <div class="vector-toc-text"> 1.3 Declarative definitions </div> </a> <ul id="toc-Declarative_definitions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Imperative_definitions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Imperative_definitions"> <div class="vector-toc-text"> 1.4 Imperative definitions </div> </a> <ul id="toc-Imperative_definitions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lambda_functions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lambda_functions"> <div class="vector-toc-text"> 1.5 Lambda functions </div> </a> <ul id="toc-Lambda_functions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Local_definitions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Local_definitions"> <div class="vector-toc-text"> 1.6 Local definitions </div> </a> <ul id="toc-Local_definitions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Type_synonyms" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Type_synonyms"> <div class="vector-toc-text"> 1.7 Type synonyms </div> </a> <ul id="toc-Type_synonyms-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Algebraic_datatypes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Algebraic_datatypes"> <div class="vector-toc-text"> 1.8 Algebraic datatypes </div> </a> <ul id="toc-Algebraic_datatypes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pattern_matching" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Pattern_matching"> <div class="vector-toc-text"> 1.9 Pattern matching </div> </a> <ul id="toc-Pattern_matching-sublist" class="vector-toc-list"> <li id="toc-Exhaustiveness_checking" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Exhaustiveness_checking"> <div class="vector-toc-text"> 1.9.1 Exhaustiveness checking </div> </a> <ul id="toc-Exhaustiveness_checking-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Redundancy_checking" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Redundancy_checking"> <div class="vector-toc-text"> 1.9.2 Redundancy checking </div> </a> <ul id="toc-Redundancy_checking-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Higher-order_functions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Higher-order_functions"> <div class="vector-toc-text"> 1.10 Higher-order functions </div> </a> <ul id="toc-Higher-order_functions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Exceptions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Exceptions"> <div class="vector-toc-text"> 1.11 Exceptions </div> </a> <ul id="toc-Exceptions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Module_system" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Module_system"> <div class="vector-toc-text"> 1.12 Module system </div> </a> <ul id="toc-Module_system-sublist" class="vector-toc-list"> <li id="toc-Signatures" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Signatures"> <div class="vector-toc-text"> 1.12.1 Signatures </div> </a> <ul id="toc-Signatures-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Structures" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Structures"> <div class="vector-toc-text"> 1.12.2 Structures </div> </a> <ul id="toc-Structures-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Functors" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Functors"> <div class="vector-toc-text"> 1.12.3 Functors </div> </a> <ul id="toc-Functors-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Code_examples" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Code_examples"> <div class="vector-toc-text"> 2 Code examples </div> </a> <button aria-controls="toc-Code_examples-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Code examples subsection </button> <ul id="toc-Code_examples-sublist" class="vector-toc-list"> <li id="toc-Hello,_world!" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Hello,_world!"> <div class="vector-toc-text"> 2.1 Hello, world! </div> </a> <ul id="toc-Hello,_world!-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Algorithms" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Algorithms"> <div class="vector-toc-text"> 2.2 Algorithms </div> </a> <ul id="toc-Algorithms-sublist" class="vector-toc-list"> <li id="toc-Insertion_sort" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Insertion_sort"> <div class="vector-toc-text"> 2.2.1 Insertion sort </div> </a> <ul id="toc-Insertion_sort-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mergesort" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Mergesort"> <div class="vector-toc-text"> 2.2.2 Mergesort </div> </a> <ul id="toc-Mergesort-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quicksort" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Quicksort"> <div class="vector-toc-text"> 2.2.3 Quicksort </div> </a> <ul id="toc-Quicksort-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Expression_interpreter" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Expression_interpreter"> <div class="vector-toc-text"> 2.3 Expression interpreter </div> </a> <ul id="toc-Expression_interpreter-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Arbitrary-precision_integers" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Arbitrary-precision_integers"> <div class="vector-toc-text"> 2.4 Arbitrary-precision integers </div> </a> <ul id="toc-Arbitrary-precision_integers-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Partial_application" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Partial_application"> <div class="vector-toc-text"> 2.5 Partial application </div> </a> <ul id="toc-Partial_application-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Libraries" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Libraries"> <div class="vector-toc-text"> 3 Libraries </div> </a> <button aria-controls="toc-Libraries-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Libraries subsection </button> <ul id="toc-Libraries-sublist" class="vector-toc-list"> <li id="toc-Standard" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Standard"> <div class="vector-toc-text"> 3.1 Standard </div> </a> <ul id="toc-Standard-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Third_party" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Third_party"> <div class="vector-toc-text"> 3.2 Third party </div> </a> <ul id="toc-Third_party-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Implementations" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Implementations"> <div class="vector-toc-text"> 4 Implementations </div> </a> <ul id="toc-Implementations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Major_projects_using_SML" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Major_projects_using_SML"> <div class="vector-toc-text"> 5 Major projects using SML </div> </a> <ul id="toc-Major_projects_using_SML-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <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-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> 7 References </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> 8 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" title="Table of Contents" > <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">Standard ML</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 23 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-23" aria-hidden="true" > 23 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%A3%D9%85_%D8%A3%D9%84_%D8%A7%D9%84%D9%85%D8%B9%D9%8A%D8%A7%D8%B1%D9%8A%D8%A9" title="أم أل المعيارية – Arabic" lang="ar" hreflang="ar" data-title="أم أل المعيارية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/ML_Est%C3%A0ndard" title="ML Estàndard – Catalan" lang="ca" hreflang="ca" data-title="ML Estàndard" 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/Standard_ML" title="Standard ML – Czech" lang="cs" hreflang="cs" data-title="Standard ML" 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/Standard_ML" title="Standard ML – Danish" lang="da" hreflang="da" data-title="Standard ML" 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/Standard_ML" title="Standard ML – German" lang="de" hreflang="de" data-title="Standard ML" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target">Deutsch</a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Standard_ML" title="Standard ML – Spanish" lang="es" hreflang="es" data-title="Standard ML" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Standard_ML" title="Standard ML – Esperanto" lang="eo" hreflang="eo" data-title="Standard ML" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target">Esperanto</a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D8%B3%D8%AA%D8%A7%D9%86%D8%AF%D8%A7%D8%B1%D8%AF_%D8%A7%D9%85%E2%80%8C%D8%A7%D9%84" title="استاندارد ام‌ال – Persian" lang="fa" hreflang="fa" data-title="استاندارد ام‌ال" 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/Standard_ML" title="Standard ML – French" lang="fr" hreflang="fr" data-title="Standard ML" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%91%9C%EC%A4%80_ML" title="표준 ML – Korean" lang="ko" hreflang="ko" data-title="표준 ML" 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/Standard_ML" title="Standard ML – Armenian" lang="hy" hreflang="hy" data-title="Standard ML" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target">Հայերեն</a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Standard_ML" title="Standard ML – Italian" lang="it" hreflang="it" data-title="Standard ML" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target">Italiano</a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/Standard_ML" title="Standard ML – Georgian" lang="ka" hreflang="ka" data-title="Standard ML" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target">ქართული</a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/SML" title="SML – Hungarian" lang="hu" hreflang="hu" data-title="SML" 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%B8%E0%B5%8D%E0%B4%B1%E0%B5%8D%E0%B4%B1%E0%B4%BE%E0%B5%BB%E0%B4%A1%E0%B5%87%E0%B5%BC%E0%B4%A1%E0%B5%8D_%E0%B4%8E%E0%B4%82%E0%B4%8E%E0%B5%BD" title="സ്റ്റാൻഡേർഡ് എംഎൽ – Malayalam" lang="ml" hreflang="ml" data-title="സ്റ്റാൻഡേർഡ് എംഎൽ" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target">മലയാളം</a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/Standard_ML" title="Standard ML – Japanese" lang="ja" hreflang="ja" data-title="Standard ML" 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Standard_ML" title="Standard ML – Polish" lang="pl" hreflang="pl" data-title="Standard ML" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target">Polski</a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Standard_ML" title="Standard ML – Portuguese" lang="pt" hreflang="pt" data-title="Standard ML" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target">Português</a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/Standard_ML" title="Standard ML – Russian" lang="ru" hreflang="ru" data-title="Standard ML" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target">Русский</a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Standard_ML" title="Standard ML – Simple English" lang="en-simple" hreflang="en-simple" data-title="Standard ML" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target">Simple English</a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Standart_ML" title="Standart ML – Turkish" lang="tr" hreflang="tr" data-title="Standart ML" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target">Türkçe</a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/Standard_ML" title="Standard ML – Ukrainian" lang="uk" hreflang="uk" data-title="Standard ML" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target">Українська</a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/Standard_ML" title="Standard ML – Chinese" lang="zh" hreflang="zh" data-title="Standard ML" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target">中文</a></li> </ul> <div class="after-portlet after-portlet-lang"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q597330#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></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 id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Standard_ML" title="View the content page [c]" accesskey="c">Article</a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:Standard_ML" rel="discussion" title="Discuss improvements to the content page [t]" accesskey="t">Talk</a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" 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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">General-purpose functional programming language</div> <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">Standard 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/Programming_paradigm" title="Programming paradigm">Multi-paradigm</a>: <a href="/wiki/Functional_programming" title="Functional programming">functional</a>, <a href="/wiki/Imperative_programming" title="Imperative programming">imperative</a>, <a href="/wiki/Modular_programming" title="Modular programming">modular</a><a href="#cite_note-intro-1">[1]</a></td></tr><tr><th scope="row" class="infobox-label">Family</th><td class="infobox-data"><a href="/wiki/ML_(programming_language)" title="ML (programming language)">ML</a></td></tr><tr><th scope="row" class="infobox-label">First appeared</th><td class="infobox-data">1983; 42 years ago (1983)<a href="#cite_note-smlnj-2">[2]</a></td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546" /></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="/wiki/Software_release_life_cycle" title="Software release life cycle">Stable release</a></th><td class="infobox-data"><div style="margin:0px;">Standard ML '97<a href="#cite_note-smlnj-2">[2]</a> / 1997; 28 years ago (1997)</div></td></tr><tr style="display:none"><td colspan="2"> </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/Type_system#static_type_checking" title="Type system">static</a>, <a href="/wiki/Strong_and_weak_typing" title="Strong and weak typing">strong</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Filename_extension" title="Filename extension">Filename extensions</a></th><td class="infobox-data">.sml</td></tr><tr><th scope="row" class="infobox-label">Website</th><td class="infobox-data"><a rel="nofollow" class="external text" href="https://smlfamily.github.io/">smlfamily.github.io</a></td></tr><tr><th colspan="2" class="infobox-header" style="background-color: #eee;">Major <a href="/wiki/Programming_language_implementation" title="Programming language implementation">implementations</a></th></tr><tr><td colspan="2" class="infobox-full-data"><a href="/wiki/Standard_ML_of_New_Jersey" title="Standard ML of New Jersey">SML/NJ</a>, <a href="/wiki/MLton" title="MLton">MLton</a>, <a href="/wiki/Poly/ML" class="mw-redirect" title="Poly/ML">Poly/ML</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/Alice_(programming_language)" title="Alice (programming language)">Alice</a>, <a href="/wiki/Concurrent_ML" title="Concurrent ML">Concurrent ML</a>, <a href="/wiki/Dependent_ML" title="Dependent ML">Dependent ML</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/ML_(programming_language)" title="ML (programming language)">ML</a>, <a href="/wiki/Hope_(programming_language)" title="Hope (programming language)">Hope</a>, <a href="/wiki/Pascal_(programming_language)" title="Pascal (programming language)">Pascal</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/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/OCaml" title="OCaml">OCaml</a>, <a href="/wiki/Python_(programming_language)" title="Python (programming language)">Python</a>,<a href="#cite_note-itertools-3">[3]</a> <a href="/wiki/Rust_(programming_language)" title="Rust (programming language)">Rust</a>,<a href="#cite_note-4">[4]</a> <a href="/wiki/Scala_(programming_language)" title="Scala (programming language)">Scala</a></td></tr></tbody></table> Standard ML (SML) 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/Modular_programming" title="Modular programming">modular</a>, <a href="/wiki/Functional_programming" title="Functional programming">functional</a> <a href="/wiki/Programming_language" title="Programming language">programming language</a> with compile-time <a href="/wiki/Type_checking" class="mw-redirect" title="Type checking">type checking</a> and <a href="/wiki/Type_inference" title="Type inference">type inference</a>. It is popular for writing <a href="/wiki/Compiler" title="Compiler">compilers</a>, for <a href="/wiki/Programming_language_research" class="mw-redirect" title="Programming language research">programming language research</a>, and for developing <a href="/wiki/Automated_theorem_proving" title="Automated theorem proving">theorem provers</a>. Standard ML is a modern dialect of <a href="/wiki/ML_(programming_language)" title="ML (programming language)">ML</a>, the language used in the <a href="/wiki/Logic_for_Computable_Functions" title="Logic for Computable Functions">Logic for Computable Functions</a> (LCF) theorem-proving project. It is distinctive among widely used languages in that it has a <a href="/wiki/Formal_specification" title="Formal specification">formal specification</a>, given as <a href="/wiki/Typing_rule" title="Typing rule">typing rules</a> and <a href="/wiki/Operational_semantics" title="Operational semantics">operational semantics</a> in The Definition of Standard ML.<a href="#cite_note-revision-5">[5]</a> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Language">Language</h2>[<a href="/w/index.php?title=Standard_ML&action=edit&section=1" title="Edit section: Language">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><style data-mw-deduplicate="TemplateStyles:r1248332772">.mw-parser-output .multiple-issues-text{width:95%;margin:0.2em 0}.mw-parser-output .multiple-issues-text>.mw-collapsible-content{margin-top:0.3em}.mw-parser-output .compact-ambox .ambox{border:none;border-collapse:collapse;background-color:transparent;margin:0 0 0 1.6em!important;padding:0!important;width:auto;display:block}body.mediawiki .mw-parser-output .compact-ambox .ambox.mbox-small-left{font-size:100%;width:auto;margin:0}.mw-parser-output .compact-ambox .ambox .mbox-text{padding:0!important;margin:0!important}.mw-parser-output .compact-ambox .ambox .mbox-text-span{display:list-item;line-height:1.5em;list-style-type:disc}body.skin-minerva .mw-parser-output .multiple-issues-text>.mw-collapsible-toggle,.mw-parser-output .compact-ambox .ambox .mbox-image,.mw-parser-output .compact-ambox .ambox .mbox-imageright,.mw-parser-output .compact-ambox .ambox .mbox-empty-cell,.mw-parser-output .compact-ambox .hide-when-compact{display:none}</style><table class="box-Multiple_issues plainlinks metadata ambox ambox-content ambox-multiple_issues compact-ambox" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/40px-Ambox_important.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/60px-Ambox_important.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/80px-Ambox_important.svg.png 2x" data-file-width="40" data-file-height="40" /></div></td><td class="mbox-text"><div class="mbox-text-span"><div class="multiple-issues-text mw-collapsible">This section has multiple issues. Please help <a href="/wiki/Special:EditPage/Standard_ML" title="Special:EditPage/Standard ML">improve it</a> or discuss these issues on the <a href="/wiki/Talk:Standard_ML" title="Talk:Standard ML">talk page</a>. (<a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove these messages</a>) <div class="mw-collapsible-content"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444" /><table class="box-Howto plainlinks metadata ambox ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/40px-Ambox_important.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/60px-Ambox_important.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/80px-Ambox_important.svg.png 2x" data-file-width="40" data-file-height="40" /></div></td><td class="mbox-text"><div class="mbox-text-span">This section contains <a href="/wiki/Wikipedia:What_Wikipedia_is_not#NOTHOWTO" title="Wikipedia:What Wikipedia is not">instructions, advice, or how-to content</a>. Please help <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Standard_ML&action=edit">rewrite the content</a> so that it is more encyclopedic or <a href="https://meta.wikimedia.org/wiki/Help:Transwiki" class="extiw" title="m:Help:Transwiki">move</a> it to <a href="https://en.wikiversity.org/wiki/" class="extiw" title="v:">Wikiversity</a>, <a href="https://en.wikibooks.org/wiki/" class="extiw" title="b:">Wikibooks</a>, or <a href="https://en.wikivoyage.org/wiki/" class="extiw" title="voy:">Wikivoyage</a>. (November 2021)</div></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444" /><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><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></div></td><td class="mbox-text"><div class="mbox-text-span">This section does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a>. Please help <a href="/wiki/Special:EditPage/Standard_ML" title="Special:EditPage/Standard ML">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>. (November 2021) (<a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a>)</div></td></tr></tbody></table> </div> </div> (<a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a>)</div></td></tr></tbody></table> Standard ML is a functional <a href="/wiki/Programming_language" title="Programming language">programming language</a> with some impure features. Programs written in Standard ML consist of <a href="/wiki/Expression_(computer_science)" title="Expression (computer science)">expressions</a> in contrast to statements or commands, although some expressions of type <a href="/wiki/Unit_type" title="Unit type">unit</a> are only evaluated for their <a href="/wiki/Side_effect_(computer_science)" title="Side effect (computer science)">side-effects</a>. <div class="mw-heading mw-heading3"><h3 id="Functions">Functions</h3>[<a href="/w/index.php?title=Standard_ML&action=edit&section=2" title="Edit section: Functions">edit</a>]</div> Like all functional languages, a key feature of Standard ML is the <a href="/wiki/Function_(programming)" class="mw-redirect" title="Function (programming)">function</a>, which is used for abstraction. The factorial function can be expressed as follows: <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>fun factorial n = if n = 0 then 1 else n * factorial (n - 1) </pre></div> <div class="mw-heading mw-heading3"><h3 id="Type_inference">Type inference</h3>[<a href="/w/index.php?title=Standard_ML&action=edit&section=3" title="Edit section: Type inference">edit</a>]</div> An SML compiler must infer the static type <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">val factorial : int -> int</code> without user-supplied type annotations. It has to deduce that <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">n</code> is only used with integer expressions, and must therefore itself be an integer, and that all terminal expressions are integer expressions. <div class="mw-heading mw-heading3"><h3 id="Declarative_definitions">Declarative definitions</h3>[<a href="/w/index.php?title=Standard_ML&action=edit&section=4" title="Edit section: Declarative definitions">edit</a>]</div> The same function can be expressed with <a href="/w/index.php?title=Clausal_function_definition&action=edit&redlink=1" class="new" title="Clausal function definition (page does not exist)">clausal function definitions</a> where the if-then-else conditional is replaced with templates of the factorial function evaluated for specific values: <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>fun factorial 0 = 1 | factorial n = n * factorial (n - 1) </pre></div> <div class="mw-heading mw-heading3"><h3 id="Imperative_definitions">Imperative definitions</h3>[<a href="/w/index.php?title=Standard_ML&action=edit&section=5" title="Edit section: Imperative definitions">edit</a>]</div> or iteratively: <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>fun factorial n = let val i = ref n and acc = ref 1 in while !i > 0 do (acc := !acc * !i; i := !i - 1); !acc end </pre></div> <div class="mw-heading mw-heading3"><h3 id="Lambda_functions">Lambda functions</h3>[<a href="/w/index.php?title=Standard_ML&action=edit&section=6" title="Edit section: Lambda functions">edit</a>]</div> or as a lambda function: <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>val rec factorial = fn 0 => 1 | n => n * factorial (n - 1) </pre></div> Here, the keyword <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">val</code> introduces a binding of an identifier to a value, <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">fn</code> introduces an <a href="/wiki/Anonymous_function" title="Anonymous function">anonymous function</a>, and <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">rec</code> allows the definition to be self-referential. <div class="mw-heading mw-heading3"><h3 id="Local_definitions">Local definitions</h3>[<a href="/w/index.php?title=Standard_ML&action=edit&section=7" title="Edit section: Local definitions">edit</a>]</div> The encapsulation of an invariant-preserving tail-recursive tight loop with one or more accumulator parameters within an invariant-free outer function, as seen here, is a common idiom in Standard ML. Using a local function, it can be rewritten in a more efficient tail-recursive style: <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>local fun loop (0, acc) = acc | loop (m, acc) = loop (m - 1, m * acc) in fun factorial n = loop (n, 1) end </pre></div> <div class="mw-heading mw-heading3"><h3 id="Type_synonyms">Type synonyms</h3>[<a href="/w/index.php?title=Standard_ML&action=edit&section=8" title="Edit section: Type synonyms">edit</a>]</div> A type synonym is defined with the keyword <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">type</code>. Here is a type synonym for points on a <a href="/wiki/Plane_(geometry)" class="mw-redirect" title="Plane (geometry)">plane</a>, and functions computing the distances between two points, and the area of a triangle with the given corners as per <a href="/wiki/Heron%27s_formula" title="Heron's formula">Heron's formula</a>. (These definitions will be used in subsequent examples). <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>type loc = real * real fun square (x : real) = x * x fun dist (x, y) (x', y') = Math.sqrt (square (x' - x) + square (y' - y)) fun heron (a, b, c) = let val x = dist a b val y = dist b c val z = dist a c val s = (x + y + z) / 2.0 in Math.sqrt (s * (s - x) * (s - y) * (s - z)) end </pre></div> <div class="mw-heading mw-heading3"><h3 id="Algebraic_datatypes">Algebraic datatypes</h3>[<a href="/w/index.php?title=Standard_ML&action=edit&section=9" title="Edit section: Algebraic datatypes">edit</a>]</div> Standard ML provides strong support for <a href="/wiki/Algebraic_datatype" class="mw-redirect" title="Algebraic datatype">algebraic datatypes</a> (ADT). A <a href="/wiki/Data_type" title="Data type">data type</a> can be thought of as a <a href="/wiki/Disjoint_union" title="Disjoint union">disjoint union</a> of tuples (or a "sum of products"). They are easy to define and easy to use, largely because of <a href="/wiki/Pattern_matching" title="Pattern matching">pattern matching</a>, and most Standard ML implementations' <a href="/wiki/Partial_function" title="Partial function">pattern-exhaustiveness</a> checking and pattern redundancy checking. In <a href="/wiki/Object-oriented_programming" title="Object-oriented programming">object-oriented programming</a> languages, a disjoint union can be expressed as <a href="/wiki/Class_(computer_programming)" title="Class (computer programming)">class</a> hierarchies. However, in contrast to <a href="/wiki/Class_hierarchy" title="Class hierarchy">class hierarchies</a>, ADTs are <a href="/wiki/Closed-world_assumption" title="Closed-world assumption">closed</a>. Thus, the extensibility of ADTs is orthogonal to the extensibility of class hierarchies. Class hierarchies can be extended with new subclasses which implement the same interface, while the functions of ADTs can be extended for the fixed set of constructors. See <a href="/wiki/Expression_problem" title="Expression problem">expression problem</a>. A datatype is defined with the keyword <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">datatype</code>, as in: <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>datatype shape = Circle of loc * real (* center and radius *) | Square of loc * real (* upper-left corner and side length; axis-aligned *) | Triangle of loc * loc * loc (* corners *) </pre></div> Note that a type synonym cannot be recursive; datatypes are necessary to define recursive constructors. (This is not at issue in this example.) <div class="mw-heading mw-heading3"><h3 id="Pattern_matching">Pattern matching</h3>[<a href="/w/index.php?title=Standard_ML&action=edit&section=10" title="Edit section: Pattern matching">edit</a>]</div> Patterns are matched in the order in which they are defined. <a href="/wiki/C_(programming_language)" title="C (programming language)">C</a> programmers can use <a href="/wiki/Tagged_union" title="Tagged union">tagged unions</a>, dispatching on tag values, to do what ML does with datatypes and pattern matching. Nevertheless, while a C program decorated with appropriate checks will, in a sense, be as robust as the corresponding ML program, those checks will of necessity be dynamic; ML's <a href="/wiki/Static_program_analysis" title="Static program analysis">static checks</a> provide strong guarantees about the correctness of the program at compile time. Function arguments can be defined as patterns as follows: <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>fun area (Circle (_, r)) = Math.pi * square r | area (Square (_, s)) = square s | area (Triangle p) = heron p (* see above *) </pre></div> The so-called "clausal form" of function definition, where arguments are defined as patterns, is merely <a href="/wiki/Syntactic_sugar" title="Syntactic sugar">syntactic sugar</a> for a case expression: <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>fun area shape = case shape of Circle (_, r) => Math.pi * square r | Square (_, s) => square s | Triangle p => heron p </pre></div> <div class="mw-heading mw-heading4"><h4 id="Exhaustiveness_checking">Exhaustiveness checking</h4>[<a href="/w/index.php?title=Standard_ML&action=edit&section=11" title="Edit section: Exhaustiveness checking">edit</a>]</div> Pattern-exhaustiveness checking will make sure that each constructor of the datatype is matched by at least one pattern. The following pattern is not exhaustive: <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>fun center (Circle (c, _)) = c | center (Square ((x, y), s)) = (x + s / 2.0, y + s / 2.0) </pre></div> There is no pattern for the <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">Triangle</code> case in the <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">center</code> function. The compiler will issue a warning that the case expression is not exhaustive, and if a <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">Triangle</code> is passed to this function at runtime, <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">exception Match</code> will be raised. <div class="mw-heading mw-heading4"><h4 id="Redundancy_checking">Redundancy checking</h4>[<a href="/w/index.php?title=Standard_ML&action=edit&section=12" title="Edit section: Redundancy checking">edit</a>]</div> The pattern in the second clause of the following (meaningless) function is redundant: <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>fun f (Circle ((x, y), r)) = x + y | f (Circle _) = 1.0 | f _ = 0.0 </pre></div> Any value that would match the pattern in the second clause would also match the pattern in the first clause, so the second clause is unreachable. Therefore, this definition as a whole exhibits redundancy, and causes a compile-time warning. The following function definition is exhaustive and not redundant: <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>val hasCorners = fn (Circle _) => false | _ => true </pre></div> If control gets past the first pattern (<code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">Circle</code>), we know the shape must be either a <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">Square</code> or a <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">Triangle</code>. In either of those cases, we know the shape has corners, so we can return <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">true</code> without discerning the actual shape. <div class="mw-heading mw-heading3"><h3 id="Higher-order_functions">Higher-order functions</h3>[<a href="/w/index.php?title=Standard_ML&action=edit&section=13" title="Edit section: Higher-order functions">edit</a>]</div> Functions can consume functions as arguments: <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>fun map f (x, y) = (f x, f y) </pre></div> Functions can produce functions as return values: <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>fun constant k = (fn _ => k) </pre></div> Functions can also both consume and produce functions: <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>fun compose (f, g) = (fn x => f (g x)) </pre></div> The function <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">List.map</code> from the basis <a href="/wiki/Library_(computing)" title="Library (computing)">library</a> is one of the most commonly used higher-order functions in Standard ML: <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>fun map _ [] = [] | map f (x :: xs) = f x :: map f xs </pre></div> A more efficient implementation with tail-recursive <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">List.foldl</code>: <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>fun map f = List.rev o List.foldl (fn (x, acc) => f x :: acc) [] </pre></div> <div class="mw-heading mw-heading3"><h3 id="Exceptions">Exceptions</h3>[<a href="/w/index.php?title=Standard_ML&action=edit&section=14" title="Edit section: Exceptions">edit</a>]</div> Exceptions are raised with the keyword <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">raise</code> and handled with the pattern matching <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">handle</code> construct. The exception system can implement <a href="/w/index.php?title=Non-local_exit&action=edit&redlink=1" class="new" title="Non-local exit (page does not exist)">non-local exit</a>; this optimization technique is suitable for functions like the following. <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>local exception Zero; val p = fn (0, _) => raise Zero | (a, b) => a * b in fun prod xs = List.foldl p 1 xs handle Zero => 0 end </pre></div> When <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">exception Zero</code> is raised, control leaves the function <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">List.foldl</code> altogether. Consider the alternative: the value 0 would be returned, it would be multiplied by the next integer in the list, the resulting value (inevitably 0) would be returned, and so on. The raising of the exception allows control to skip over the entire chain of frames and avoid the associated computation. Note the use of the underscore (<code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">_</code>) as a wildcard pattern. The same optimization can be obtained with a <a href="/wiki/Tail_call" title="Tail call">tail call</a>. <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>local fun p a (0 :: _) = 0 | p a (x :: xs) = p (a * x) xs | p a [] = a in val prod = p 1 end </pre></div> <div class="mw-heading mw-heading3"><h3 id="Module_system">Module system</h3>[<a href="/w/index.php?title=Standard_ML&action=edit&section=15" title="Edit section: Module system">edit</a>]</div> Standard ML's advanced module system allows programs to be decomposed into hierarchically organized structures of logically related type and value definitions. Modules provide not only <a href="/wiki/Namespace" title="Namespace">namespace</a> control but also abstraction, in the sense that they allow the definition of <a href="/wiki/Abstract_data_type" title="Abstract data type">abstract data types</a>. Three main syntactic constructs comprise the module system: signatures, structures and functors. <div class="mw-heading mw-heading4"><h4 id="Signatures">Signatures</h4>[<a href="/w/index.php?title=Standard_ML&action=edit&section=16" title="Edit section: Signatures">edit</a>]</div> A signature is an <a href="/wiki/Interface_(computing)" title="Interface (computing)">interface</a>, usually thought of as a type for a structure; it specifies the names of all entities provided by the structure, the <a href="/wiki/Arity" title="Arity">arity</a> of each type component, the type of each value component, and the signature of each substructure. The definitions of type components are optional; type components whose definitions are hidden are abstract types. For example, the signature for a <a href="/wiki/Queue_(data_structure)" class="mw-redirect" title="Queue (data structure)">queue</a> may be: <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>signature QUEUE = sig type 'a queue exception QueueError; val empty : 'a queue val isEmpty : 'a queue -> bool val singleton : 'a -> 'a queue val fromList : 'a list -> 'a queue val insert : 'a * 'a queue -> 'a queue val peek : 'a queue -> 'a val remove : 'a queue -> 'a * 'a queue end </pre></div> This signature describes a module that provides a polymorphic type <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">'a queue</code>, <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">exception QueueError</code>, and values that define basic operations on queues. <div class="mw-heading mw-heading4"><h4 id="Structures">Structures</h4>[<a href="/w/index.php?title=Standard_ML&action=edit&section=17" title="Edit section: Structures">edit</a>]</div> A structure is a module; it consists of a collection of types, exceptions, values and structures (called substructures) packaged together into a logical unit. A queue structure can be implemented as follows: <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>structure TwoListQueue :> QUEUE = struct type 'a queue = 'a list * 'a list exception QueueError; val empty = ([], []) fun isEmpty ([], []) = true | isEmpty _ = false fun singleton a = ([], [a]) fun fromList a = ([], a) fun insert (a, ([], [])) = singleton a | insert (a, (ins, outs)) = (a :: ins, outs) fun peek (_, []) = raise QueueError | peek (ins, outs) = List.hd outs fun remove (_, []) = raise QueueError | remove (ins, [a]) = (a, ([], List.rev ins)) | remove (ins, a :: outs) = (a, (ins, outs)) end </pre></div> This definition declares that <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">structure TwoListQueue</code> implements <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">signature QUEUE</code>. Furthermore, the opaque ascription denoted by <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">:></code> states that any types which are not defined in the signature (i.e. <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">type 'a queue</code>) should be abstract, meaning that the definition of a queue as a pair of lists is not visible outside the module. The structure implements all of the definitions in the signature. The types and values in a structure can be accessed with "dot notation": <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>val q : string TwoListQueue.queue = TwoListQueue.empty val q' = TwoListQueue.insert (Real.toString Math.pi, q) </pre></div> <div class="mw-heading mw-heading4"><h4 id="Functors">Functors</h4>[<a href="/w/index.php?title=Standard_ML&action=edit&section=18" title="Edit section: Functors">edit</a>]</div> A functor is a function from structures to structures; that is, a functor accepts one or more arguments, which are usually structures of a given signature, and produces a structure as its result. Functors are used to implement <a href="/wiki/Generic_programming" title="Generic programming">generic</a> data structures and algorithms. One popular algorithm<a href="#cite_note-bfs-6">[6]</a> for <a href="/wiki/Breadth-first_search" title="Breadth-first search">breadth-first search</a> of trees makes use of queues. Here is a version of that algorithm parameterized over an abstract queue structure: <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>(* after Okasaki, ICFP, 2000 *) functor BFS (Q: QUEUE) = struct datatype 'a tree = E | T of 'a * 'a tree * 'a tree local fun bfsQ q = if Q.isEmpty q then [] else search (Q.remove q) and search (E, q) = bfsQ q | search (T (x, l, r), q) = x :: bfsQ (insert (insert q l) r) and insert q a = Q.insert (a, q) in fun bfs t = bfsQ (Q.singleton t) end end structure QueueBFS = BFS (TwoListQueue) </pre></div> Within <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">functor BFS</code>, the representation of the queue is not visible. More concretely, there is no way to select the first list in the two-list queue, if that is indeed the representation being used. This <a href="/wiki/Data_abstraction" class="mw-redirect" title="Data abstraction">data abstraction</a> mechanism makes the breadth-first search truly agnostic to the queue's implementation. This is in general desirable; in this case, the queue structure can safely maintain any logical invariants on which its correctness depends behind the bulletproof wall of abstraction. <div class="mw-heading mw-heading2"><h2 id="Code_examples">Code examples</h2>[<a href="/w/index.php?title=Standard_ML&action=edit&section=19" title="Edit section: Code examples">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><a href="/wiki/File:Wikibooks-logo-en-noslogan.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/40px-Wikibooks-logo-en-noslogan.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/60px-Wikibooks-logo-en-noslogan.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/120px-Wikibooks-logo-en-noslogan.svg.png 2x" data-file-width="400" data-file-height="400" /></a></div> <div class="side-box-text plainlist">Wikibooks has a book on the topic of: <a href="https://en.wikibooks.org/wiki/Standard_ML_Programming" class="extiw" title="wikibooks:Standard ML Programming">Standard ML Programming</a></div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444" /><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><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></div></td><td class="mbox-text"><div class="mbox-text-span">This section does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a>. Please help <a href="/wiki/Special:EditPage/Standard_ML" title="Special:EditPage/Standard ML">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>. (June 2013) (<a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a>)</div></td></tr></tbody></table> Snippets of SML code are most easily studied by entering them into an <a href="/wiki/Read%E2%80%93eval%E2%80%93print_loop" title="Read–eval–print loop">interactive top-level</a>. <div class="mw-heading mw-heading3"><h3 id="Hello,_world!">Hello, world!</h3>[<a href="/w/index.php?title=Standard_ML&action=edit&section=20" title="Edit section: Hello, world!">edit</a>]</div> The following is a <a href="/wiki/%22Hello,_World!%22_program" title=""Hello, World!" program">"Hello, World!" program</a>: <table class="wikitable"> <tbody><tr> <th>hello.sml </th></tr> <tr> <td> <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr mw-highlight-lines" dir="ltr"><pre>print "Hello, world!\n"; </pre></div> </td></tr> <tr> <th>sh </th></tr> <tr> <td> <div class="mw-highlight mw-highlight-lang-console mw-content-ltr" dir="ltr"><pre>$ mlton hello.sml $ ./hello Hello, world! </pre></div> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Algorithms">Algorithms</h3>[<a href="/w/index.php?title=Standard_ML&action=edit&section=21" title="Edit section: Algorithms">edit</a>]</div> <div class="mw-heading mw-heading4"><h4 id="Insertion_sort">Insertion sort</h4>[<a href="/w/index.php?title=Standard_ML&action=edit&section=22" title="Edit section: Insertion sort">edit</a>]</div> Insertion sort for <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">int list</code> (ascending) can be expressed concisely as follows: <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>fun insert (x, []) = [x] | insert (x, h :: t) = sort x (h, t) and sort x (h, t) = if x < h then [x, h] @ t else h :: insert (x, t) val insertionsort = List.foldl insert [] </pre></div> <div class="mw-heading mw-heading4"><h4 id="Mergesort">Mergesort</h4>[<a href="/w/index.php?title=Standard_ML&action=edit&section=23" title="Edit section: Mergesort">edit</a>]</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">Main article: <a href="/wiki/Merge_sort" title="Merge sort">Merge sort</a></div> Here, the classic mergesort algorithm is implemented in three functions: split, merge and mergesort. Also note the absence of types, with the exception of the syntax <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">op ::</code> and <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">[]</code> which signify lists. This code will sort lists of any type, so long as a consistent ordering function <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">cmp</code> is defined. Using <a href="/wiki/Hindley%E2%80%93Milner_type_inference" class="mw-redirect" title="Hindley–Milner type inference">Hindley–Milner type inference</a>, the types of all variables can be inferred, even complicated types such as that of the function <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">cmp</code>. Split <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">fun split</code> is implemented with a <a href="/wiki/State_(computer_science)" title="State (computer science)">stateful</a> closure which alternates between <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">true</code> and <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">false</code>, ignoring the input: <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>fun alternator {} = let val state = ref true in fn a => !state before state := not (!state) end (* Split a list into near-halves which will either be the same length, * or the first will have one more element than the other. * Runs in O(n) time, where n = |xs|. *) fun split xs = List.partition (alternator {}) xs </pre></div> Merge Merge uses a local function loop for efficiency. The inner <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">loop</code> is defined in terms of cases: when both lists are non-empty (<code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">x :: xs</code>) and when one list is empty (<code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">[]</code>). This function merges two sorted lists into one sorted list. Note how the accumulator <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">acc</code> is built backwards, then reversed before being returned. This is a common technique, since <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">'a list</code> is represented as a <a href="/wiki/Linked_list#Linked_lists_vs._dynamic_arrays" title="Linked list">linked list</a>; this technique requires more clock time, but the <a href="/wiki/Asymptotic_analysis#Applications" title="Asymptotic analysis">asymptotics</a> are not worse. <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>(* Merge two ordered lists using the order cmp. * Pre: each list must already be ordered per cmp. * Runs in O(n) time, where n = |xs| + |ys|. *) fun merge cmp (xs, []) = xs | merge cmp (xs, y :: ys) = let fun loop (a, acc) (xs, []) = List.revAppend (a :: acc, xs) | loop (a, acc) (xs, y :: ys) = if cmp (a, y) then loop (y, a :: acc) (ys, xs) else loop (a, y :: acc) (xs, ys) in loop (y, []) (ys, xs) end </pre></div> Mergesort The main function: <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>fun ap f (x, y) = (f x, f y) (* Sort a list in according to the given ordering operation cmp. * Runs in O(n log n) time, where n = |xs|. *) fun mergesort cmp [] = [] | mergesort cmp [x] = [x] | mergesort cmp xs = (merge cmp o ap (mergesort cmp) o split) xs </pre></div> <div class="mw-heading mw-heading4"><h4 id="Quicksort">Quicksort</h4>[<a href="/w/index.php?title=Standard_ML&action=edit&section=24" title="Edit section: Quicksort">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/Quicksort" title="Quicksort">Quicksort</a></div> Quicksort can be expressed as follows. <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">fun part</code> is a <a href="/wiki/Closure_(computer_programming)" title="Closure (computer programming)">closure</a> that consumes an order operator <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">op <<</code>. <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>infix << fun quicksort (op <<) = let fun part p = List.partition (fn x => x << p) fun sort [] = [] | sort (p :: xs) = join p (part p xs) and join p (l, r) = sort l @ p :: sort r in sort end </pre></div> <div class="mw-heading mw-heading3"><h3 id="Expression_interpreter">Expression interpreter</h3>[<a href="/w/index.php?title=Standard_ML&action=edit&section=25" title="Edit section: Expression interpreter">edit</a>]</div> Note the relative ease with which a small expression language can be defined and processed: <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>exception TyErr; datatype ty = IntTy | BoolTy fun unify (IntTy, IntTy) = IntTy | unify (BoolTy, BoolTy) = BoolTy | unify (_, _) = raise TyErr datatype exp = True | False | Int of int | Not of exp | Add of exp * exp | If of exp * exp * exp fun infer True = BoolTy | infer False = BoolTy | infer (Int _) = IntTy | infer (Not e) = (assert e BoolTy; BoolTy) | infer (Add (a, b)) = (assert a IntTy; assert b IntTy; IntTy) | infer (If (e, t, f)) = (assert e BoolTy; unify (infer t, infer f)) and assert e t = unify (infer e, t) fun eval True = True | eval False = False | eval (Int n) = Int n | eval (Not e) = if eval e = True then False else True | eval (Add (a, b)) = (case (eval a, eval b) of (Int x, Int y) => Int (x + y)) | eval (If (e, t, f)) = eval (if eval e = True then t else f) fun run e = (infer e; SOME (eval e)) handle TyErr => NONE </pre></div> Example usage on well-typed and ill-typed expressions: <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>val SOME (Int 3) = run (Add (Int 1, Int 2)) (* well-typed *) val NONE = run (If (Not (Int 1), True, False)) (* ill-typed *) </pre></div> <div class="mw-heading mw-heading3"><h3 id="Arbitrary-precision_integers">Arbitrary-precision integers</h3>[<a href="/w/index.php?title=Standard_ML&action=edit&section=26" title="Edit section: Arbitrary-precision integers">edit</a>]</div> The <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">IntInf</code> module provides arbitrary-precision integer arithmetic. Moreover, integer literals may be used as arbitrary-precision integers without the programmer having to do anything. The following program implements an arbitrary-precision factorial function: <table class="wikitable"> <tbody><tr> <th>fact.sml </th></tr> <tr> <td> <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr mw-highlight-lines" dir="ltr"><pre>fun fact n : IntInf.int = if n = 0 then 1 else n * fact (n - 1); fun printLine str = TextIO.output (TextIO.stdOut, str ^ "\n"); val () = printLine (IntInf.toString (fact 120)); </pre></div> </td></tr> <tr> <th>bash </th></tr> <tr> <td> <div class="mw-highlight mw-highlight-lang-console mw-content-ltr" dir="ltr"><pre>$ mlton fact.sml $ ./fact 6689502913449127057588118054090372586752746333138029810295671352301 6335572449629893668741652719849813081576378932140905525344085894081 21859898481114389650005964960521256960000000000000000000000000000 </pre></div> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Partial_application">Partial application</h3>[<a href="/w/index.php?title=Standard_ML&action=edit&section=27" title="Edit section: Partial application">edit</a>]</div> Curried functions have many applications, such as eliminating redundant code. For example, a module may require functions of type <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">a -> b</code>, but it is more convenient to write functions of type <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">a * c -> b</code> where there is a fixed relationship between the objects of type <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">a</code> and <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">c</code>. A function of type <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">c -> (a * c -> b) -> a -> b</code> can factor out this commonality. This is an example of the <a href="/wiki/Adapter_pattern" title="Adapter pattern">adapter pattern</a>.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] In this example, <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">fun d</code> computes the numerical derivative of a given function <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">f</code> at point <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">x</code>: <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>- fun d delta f x = (f (x + delta) - f (x - delta)) / (2.0 * delta) val d = fn : real -> (real -> real) -> real -> real </pre></div> The type of <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">fun d</code> indicates that it maps a "float" onto a function with the type <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">(real -> real) -> real -> real</code>. This allows us to partially apply arguments, known as <a href="/wiki/Currying" title="Currying">currying</a>. In this case, function <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">d</code> can be specialised by partially applying it with the argument <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">delta</code>. A good choice for <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">delta</code> when using this algorithm is the cube root of the <a href="/wiki/Machine_epsilon" title="Machine epsilon">machine epsilon</a>.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>- val d' = d 1E~8; val d' = fn : (real -> real) -> real -> real </pre></div> The inferred type indicates that <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">d'</code> expects a function with the type <code class="mw-highlight mw-highlight-lang-sml mw-content-ltr" style="" dir="ltr">real -> real</code> as its first argument. We can compute an approximation to the derivative of <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)=x^{3}-x-1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>−</mo> <mi>x</mi> <mo>−</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)=x^{3}-x-1}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1168fe8be3d478e75505c2a35c865e48e112c4b5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.073ex; height:3.176ex;" alt="{\displaystyle f(x)=x^{3}-x-1}" /> at <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x=3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x=3}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/871a5063af170fa536b144fbcc5745146a42cc13" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.591ex; height:2.176ex;" alt="{\displaystyle x=3}" />. The correct answer is <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f'(3)=27-1=26}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mn>27</mn> <mo>−</mo> <mn>1</mn> <mo>=</mo> <mn>26</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f'(3)=27-1=26}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ab36e829bece8e8b70171f894c867efc74005d5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.827ex; height:3.009ex;" alt="{\displaystyle f'(3)=27-1=26}" />. <div class="mw-highlight mw-highlight-lang-sml mw-content-ltr" dir="ltr"><pre>- d' (fn x => x * x * x - x - 1.0) 3.0; val it = 25.9999996644 : real </pre></div> <div class="mw-heading mw-heading2"><h2 id="Libraries">Libraries</h2>[<a href="/w/index.php?title=Standard_ML&action=edit&section=28" title="Edit section: Libraries">edit</a>]</div> <div class="mw-heading mw-heading3"><h3 id="Standard">Standard</h3>[<a href="/w/index.php?title=Standard_ML&action=edit&section=29" title="Edit section: Standard">edit</a>]</div> The Basis Library<a href="#cite_note-7">[7]</a> has been standardized and ships with most implementations. It provides modules for trees, arrays, and other data structures, and <a href="/wiki/Input/output" title="Input/output">input/output</a> and system interfaces. <div class="mw-heading mw-heading3"><h3 id="Third_party">Third party</h3>[<a href="/w/index.php?title=Standard_ML&action=edit&section=30" title="Edit section: Third party">edit</a>]</div> For <a href="/wiki/Numerical_analysis" title="Numerical analysis">numerical computing</a>, a Matrix module exists (but is currently broken), <a rel="nofollow" class="external free" href="https://www.cs.cmu.edu/afs/cs/project/pscico/pscico/src/matrix/README.html">https://www.cs.cmu.edu/afs/cs/project/pscico/pscico/src/matrix/README.html</a>. For graphics, cairo-sml is an open source interface to the <a href="/wiki/Cairo_(graphics)" title="Cairo (graphics)">Cairo</a> graphics library. For machine learning, a library for graphical models exists. <div class="mw-heading mw-heading2"><h2 id="Implementations">Implementations</h2>[<a href="/w/index.php?title=Standard_ML&action=edit&section=31" title="Edit section: Implementations">edit</a>]</div> Implementations of Standard ML include the following: Standard <ul><li><a rel="nofollow" class="external text" href="https://www.mpi-sws.org/~rossberg/hamlet/">HaMLet</a>: a Standard ML interpreter that aims to be an accurate and accessible reference implementation of the standard</li> <li><a href="/wiki/MLton" title="MLton">MLton</a> (<a rel="nofollow" class="external text" href="http://www.mlton.org">mlton.org</a>): a <a href="/wiki/Interprocedural_optimization" title="Interprocedural optimization">whole-program optimizing</a> compiler which strictly conforms to the Definition and produces very fast code compared to other ML implementations, including <a href="/wiki/Compiler#Back_end" title="Compiler">backends</a> for <a href="/wiki/LLVM" title="LLVM">LLVM</a> and C</li> <li><a rel="nofollow" class="external text" href="http://www.itu.dk/people/sestoft/mosml.html">Moscow ML</a>: a light-weight implementation, based on the <a href="/wiki/Caml" title="Caml">Caml</a> Light runtime engine which implements the full Standard ML language, including modules and much of the basis library</li> <li><a rel="nofollow" class="external text" href="http://www.polyml.org/">Poly/ML</a>: a full implementation of Standard ML that produces fast code and supports multicore hardware (via Portable Operating System Interface (<a href="/wiki/POSIX" title="POSIX">POSIX</a>) threads); its runtime system performs parallel <a href="/wiki/Garbage_collection_(computer_science)" title="Garbage collection (computer science)">garbage collection</a> and online sharing of immutable substructures.</li> <li><a href="/wiki/Standard_ML_of_New_Jersey" title="Standard ML of New Jersey">Standard ML of New Jersey</a> (<a rel="nofollow" class="external text" href="http://www.smlnj.org/">smlnj.org</a>): a full compiler, with associated libraries, tools, an interactive shell, and documentation with support for <a href="/wiki/Concurrent_ML" title="Concurrent ML">Concurrent ML</a></li> <li><a rel="nofollow" class="external text" href="http://www.cl.cam.ac.uk/Research/TSG/SMLNET/">SML.NET</a>: a Standard ML compiler for the <a href="/wiki/Common_Language_Runtime" title="Common Language Runtime">Common Language Runtime</a> with extensions for linking with other <a href="/wiki/.NET" title=".NET">.NET</a> framework code</li> <li><a rel="nofollow" class="external text" href="http://www.elsman.com/mlkit/">ML Kit</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160107005413/http://www.elsman.com/mlkit/">Archived</a> 2016-01-07 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>: an implementation based very closely on the Definition, integrating a garbage collector (which can be disabled) and <a href="/wiki/Region-based_memory_management" title="Region-based memory management">region-based memory management</a> with automatic inference of regions, aiming to support real-time applications</li></ul> Derivative <ul><li><a href="/wiki/Alice_(programming_language)" title="Alice (programming language)">Alice</a>: an interpreter for Standard ML by Saarland University with support for parallel programming using <a href="/wiki/Futures_and_promises" title="Futures and promises">futures</a>, <a href="/wiki/Lazy_evaluation" title="Lazy evaluation">lazy evaluation</a>, <a href="/wiki/Distributed_computing" title="Distributed computing">distributed computing</a> via <a href="/wiki/Remote_procedure_call" title="Remote procedure call">remote procedure calls</a> and <a href="/wiki/Constraint_programming" title="Constraint programming">constraint programming</a></li> <li><a rel="nofollow" class="external text" href="http://www.pllab.riec.tohoku.ac.jp/smlsharp/">SML#</a>: an extension of SML providing record polymorphism and C language interoperability. It is a conventional native compiler and its name is not an allusion to running on the .NET framework</li> <li><a rel="nofollow" class="external text" href="https://github.com/SOSML/SOSML">SOSML</a>: an implementation written in <a href="/wiki/TypeScript" title="TypeScript">TypeScript</a>, supporting most of the SML language and select parts of the basis library</li></ul> Research <ul><li><a rel="nofollow" class="external text" href="https://cakeml.org/">CakeML</a> is a REPL version of ML with formally verified runtime and translation to assembler.</li> <li><a href="/wiki/Isabelle_(proof_assistant)" title="Isabelle (proof assistant)">Isabelle</a> (<a rel="nofollow" class="external text" href="https://isabelle.in.tum.de">Isabelle/ML</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200830080049/http://isabelle.in.tum.de/">Archived</a> 2020-08-30 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>) integrates parallel Poly/ML into an interactive theorem prover, with a sophisticated IDE (based on <a href="/wiki/JEdit" title="JEdit">jEdit</a>) for official Standard ML (SML'97), the Isabelle/ML dialect, and the proof language. Starting with Isabelle2016, there is also a source-level debugger for ML.</li> <li><a href="/wiki/Poplog" title="Poplog">Poplog</a> implements a version of Standard ML, along with <a href="/wiki/Common_Lisp" title="Common Lisp">Common Lisp</a> and <a href="/wiki/Prolog" title="Prolog">Prolog</a>, allowing mixed language programming; all are implemented in <a href="/wiki/POP-11" title="POP-11">POP-11</a>, which is <a href="/wiki/Incremental_compiler" title="Incremental compiler">compiled incrementally</a>.</li> <li><a rel="nofollow" class="external text" href="http://www.cs.cornell.edu/home/jgm/tilt.html">TILT</a> is a full certifying compiler for Standard ML which uses typed <a href="/wiki/Intermediate_representation" title="Intermediate representation">intermediate languages</a> to <a href="/wiki/Program_optimization" title="Program optimization">optimize</a> code and ensure correctness, and can compile to <a href="/wiki/Typed_assembly_language" title="Typed assembly language">typed assembly language</a>.</li></ul> All of these implementations are <a href="/wiki/Open-source_license" title="Open-source license">open-source</a> and freely available. Most are implemented themselves in Standard ML. There are no longer any commercial implementations; <a href="/wiki/Harlequin_(software_company)" title="Harlequin (software company)">Harlequin</a>, now defunct, once produced a commercial IDE and compiler called MLWorks which passed on to <a href="/wiki/Xanalys" title="Xanalys">Xanalys</a> and was later open-sourced after it was acquired by Ravenbrook Limited on April 26, 2013. <div class="mw-heading mw-heading2"><h2 id="Major_projects_using_SML">Major projects using SML</h2>[<a href="/w/index.php?title=Standard_ML&action=edit&section=32" title="Edit section: Major projects using SML">edit</a>]</div> The <a href="/wiki/IT_University_of_Copenhagen" title="IT University of Copenhagen">IT University of Copenhagen</a>'s entire <a href="/wiki/Enterprise_architecture" title="Enterprise architecture">enterprise architecture</a> is implemented in around 100,000 lines of SML, including staff records, payroll, course administration and feedback, student project management, and web-based self-service interfaces.<a href="#cite_note-sml-8">[8]</a> The <a href="/wiki/Proof_assistant" title="Proof assistant">proof assistants</a> <a href="/wiki/HOL_(proof_assistant)" title="HOL (proof assistant)">HOL4</a>, <a href="/wiki/Isabelle_(proof_assistant)" title="Isabelle (proof assistant)">Isabelle</a>, <a href="/wiki/LEGO_(proof_assistant)" title="LEGO (proof assistant)">LEGO</a>, and <a href="/wiki/Twelf" title="Twelf">Twelf</a> are written in Standard ML. It is also used by <a href="/wiki/Compiler#Compiler_construction" title="Compiler">compiler writers</a> and <a href="/wiki/Integrated_circuit_design" title="Integrated circuit design">integrated circuit designers</a> such as <a href="/wiki/ARM_architecture" class="mw-redirect" title="ARM architecture">ARM</a>.<a href="#cite_note-machine_code_verification-9">[9]</a> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2>[<a href="/w/index.php?title=Standard_ML&action=edit&section=33" title="Edit section: See also">edit</a>]</div> <ul><li><a href="/wiki/Declarative_programming" title="Declarative programming">Declarative programming</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2>[<a href="/w/index.php?title=Standard_ML&action=edit&section=34" title="Edit section: 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="cite-bracket" style="column-width: <ol class="references"> <li id="cite_note-intro-1">^ <a href="#cite_ref-intro_1-0">a</a> <a href="#cite_ref-intro_1-1">b</a> <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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.cs.cmu.edu/~rwh/introsml/modules/subfun.htm">"Programming in Standard ML: Hierarchies and Parameterization"</a>. 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International Conference on Functional Programming 2000. ACM.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.atitle=Breadth-First+Numbering%3A+Lessons+from+a+Small+Exercise+in+Algorithm+Design&rft.btitle=International+Conference+on+Functional+Programming+2000&rft.pub=ACM&rft.date=2000&rft.aulast=Okasaki&rft.aufirst=Chris&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStandard+ML" class="Z3988"> </li> <li id="cite_note-7"><a href="#cite_ref-7">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://smlfamily.github.io/Basis/index.html">"Standard ML Basis Library"</a>. smlfamily.github.io. Retrieved 2022-01-10.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=smlfamily.github.io&rft.atitle=Standard+ML+Basis+Library&rft_id=https%3A%2F%2Fsmlfamily.github.io%2FBasis%2Findex.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStandard+ML" class="Z3988"> </li> <li id="cite_note-sml-8">^ <a href="#cite_ref-sml_8-0">a</a> <a href="#cite_ref-sml_8-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFTofte2009" class="citation journal cs1">Tofte, Mads (2009). <a rel="nofollow" class="external text" href="https://doi.org/10.4249%2Fscholarpedia.7515">"Standard ML language"</a>. 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section: External links">edit</a>]</div> About Standard ML <ul><li><a rel="nofollow" class="external text" href="https://smlfamily.github.io/sml97-defn.pdf">Revised definition</a></li> <li><a rel="nofollow" class="external text" href="http://sml-family.org">Standard ML Family GitHub Project</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200220023435/http://sml-family.org/">Archived</a> 2020-02-20 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a rel="nofollow" class="external text" href="http://www.smlnj.org/sml.html">What is SML?</a></li> <li><a rel="nofollow" class="external text" href="http://www.smlnj.org/sml97.html">What is SML '97?</a></li></ul> About successor ML <ul><li><a rel="nofollow" class="external text" href="https://github.com/SMLFamily/Successor-ML">successor ML (sML)</a>: evolution of ML using Standard ML as a starting point</li> <li><a rel="nofollow" class="external text" href="https://github.com/rossberg/hamlet/tree/succ">HaMLet on GitHub</a>: reference implementation for successor ML</li></ul> Practical <ul><li><a rel="nofollow" class="external text" href="https://learnxinyminutes.com/docs/standard-ml/">Basic introductory tutorial</a></li> <li><a rel="nofollow" class="external text" href="http://www.rosettacode.org/wiki/Category:Standard_ML">Examples in Rosetta Code</a></li></ul> Academic <ul><li><a rel="nofollow" class="external text" href="https://www.cs.cmu.edu/~rwh/isml/book.pdf">Programming in Standard ML</a></li> <li><a rel="nofollow" class="external text" href="http://www.dcs.ed.ac.uk/home/stg/NOTES/notes.html">Programming in Standard ML '97: An Online Tutorial</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 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style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Programming_language_implementation" title="Programming language implementation">Implementations</a>, <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 class="mw-selflink selflink">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><a href="/wiki/Alice_(programming_language)" title="Alice (programming language)">Alice</a>°</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%"><a href="/wiki/Dependent_ML" title="Dependent ML">Dependent ML</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/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>, <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/Rocq" title="Rocq">Rocq</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><a href="/wiki/Logic_for_Computable_Functions" title="Logic for Computable Functions">Logic for Computable Functions</a></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><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></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="Designers9" 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>Italics = discontinued</li> <li>° = <a href="/wiki/Open-source_software" title="Open-source software">Open-source software</a> <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/20px-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/40px-Symbol_book_class2.svg.png 1.5x" data-file-width="180" data-file-height="185" /></a> <a href="https://en.wikibooks.org/wiki/OCaml" class="extiw" title="wikibooks:OCaml">Book</a> <img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /> <a href="/wiki/Category:ML_programming_language_family" title="Category:ML programming language family">Category:Family:ML</a> <img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /> <a href="/wiki/Category:OCaml_programming_language_family" title="Category:OCaml programming language family">Category:Family:OCaml</a> <img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /> <a href="/wiki/Category:OCaml_software" title="Category:OCaml software">Category:Software:OCaml</a></li> </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="Programming_languages625" style="padding:3px"><table class="nowraplinks hlist mw-collapsible expanded 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:Programming_languages" title="Template:Programming languages"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Programming_languages" title="Template talk:Programming languages"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Programming_languages" title="Special:EditPage/Template:Programming languages"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Programming_languages625" style="font-size:114%;margin:0 4em"><a href="/wiki/Programming_language" title="Programming language">Programming languages</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/Comparison_of_programming_languages" title="Comparison of programming languages">Comparison</a></li> <li><a href="/wiki/Timeline_of_programming_languages" title="Timeline of programming languages">Timeline</a></li> <li><a href="/wiki/History_of_programming_languages" title="History of programming languages">History</a></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ada_(programming_language)" title="Ada (programming language)">Ada</a></li> <li><a href="/wiki/ALGOL" title="ALGOL">ALGOL</a> <ul><li><a href="/wiki/Simula" title="Simula">Simula</a></li></ul></li> <li><a href="/wiki/APL_(programming_language)" title="APL (programming language)">APL</a></li> <li><a href="/wiki/Assembly_language" title="Assembly language">Assembly</a></li> <li><a href="/wiki/BASIC" title="BASIC">BASIC</a> <ul><li><a href="/wiki/Visual_Basic" title="Visual Basic">Visual Basic</a> <ul><li><a href="/wiki/Visual_Basic_(classic)" title="Visual Basic (classic)">classic</a></li> <li><a href="/wiki/Visual_Basic_(.NET)" title="Visual Basic (.NET)">.NET</a></li></ul></li></ul></li> <li><a href="/wiki/C_(programming_language)" title="C (programming language)">C</a></li> <li><a href="/wiki/C%2B%2B" title="C++">C++</a></li> <li><a href="/wiki/C_Sharp_(programming_language)" title="C Sharp (programming language)">C#</a></li> <li><a href="/wiki/COBOL" title="COBOL">COBOL</a></li> <li><a href="/wiki/Erlang_(programming_language)" title="Erlang (programming language)">Erlang</a> <ul><li><a href="/wiki/Elixir_(programming_language)" title="Elixir (programming language)">Elixir</a></li></ul></li> <li><a href="/wiki/Forth_(programming_language)" title="Forth (programming language)">Forth</a></li> <li><a href="/wiki/Fortran" title="Fortran">Fortran</a></li> <li><a href="/wiki/Go_(programming_language)" title="Go (programming language)">Go</a></li> <li><a href="/wiki/Haskell" title="Haskell">Haskell</a></li> <li><a href="/wiki/Java_(programming_language)" title="Java (programming language)">Java</a></li> <li><a href="/wiki/JavaScript" title="JavaScript">JavaScript</a> <ul><li><a href="/wiki/TypeScript" title="TypeScript">TypeScript</a></li></ul></li> <li><a href="/wiki/Julia_(programming_language)" title="Julia (programming language)">Julia</a></li> <li><a href="/wiki/Kotlin_(programming_language)" title="Kotlin (programming language)">Kotlin</a></li> <li><a href="/wiki/Lisp_(programming_language)" title="Lisp (programming language)">Lisp</a></li> <li><a href="/wiki/Lua_(programming_language)" title="Lua (programming language)">Lua</a></li> <li><a href="/wiki/MATLAB" title="MATLAB">MATLAB</a></li> <li><a href="/wiki/ML_(programming_language)" title="ML (programming language)">ML</a> <ul><li><a href="/wiki/Caml" title="Caml">Caml </a> <ul><li><a href="/wiki/OCaml" title="OCaml">OCaml</a></li></ul></li></ul></li> <li><a href="/wiki/Pascal_(programming_language)" title="Pascal (programming language)">Pascal</a> <ul><li><a href="/wiki/Object_Pascal" title="Object Pascal">Object Pascal</a></li></ul></li> <li><a href="/wiki/Perl" title="Perl">Perl </a> <ul><li><a href="/wiki/Raku_(programming_language)" title="Raku (programming language)">Raku</a></li></ul></li> <li><a href="/wiki/PHP" title="PHP">PHP</a></li> <li><a href="/wiki/Prolog" title="Prolog">Prolog</a></li> <li><a href="/wiki/Python_(programming_language)" title="Python (programming language)">Python</a></li> <li><a href="/wiki/R_(programming_language)" title="R (programming language)">R</a></li> <li><a href="/wiki/Ruby_(programming_language)" title="Ruby (programming language)">Ruby</a></li> <li><a href="/wiki/Rust_(programming_language)" title="Rust (programming language)">Rust</a></li> <li><a href="/wiki/SQL" title="SQL">SQL</a></li> <li><a href="/wiki/Scratch_(programming_language)" title="Scratch (programming language)">Scratch</a></li> <li><a href="/wiki/Shell_script" title="Shell script">Shell</a></li> <li><a href="/wiki/Smalltalk" title="Smalltalk">Smalltalk</a></li> <li><a href="/wiki/Swift_(programming_language)" title="Swift (programming language)">Swift</a></li> <li><a href="/wiki/List_of_programming_languages" title="List of programming languages">more...</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/d/db/Symbol_list_class.svg/16px-Symbol_list_class.svg.png" decoding="async" 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class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /> <a href="/wiki/Category:Programming_languages" title="Category:Programming languages">Category</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 authority-control" aria-label="Navbox390" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Help:Authority_control" title="Help:Authority 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