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mw-ui-icon-wikimedia-expand"></span> <span>Afficher / masquer la sous-section Définitions</span> </button> <ul id="toc-Définitions-sublist" class="vector-toc-list"> <li id="toc-Type_produit" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Type_produit"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Type produit</span> </div> </a> <ul id="toc-Type_produit-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Type_somme" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Type_somme"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Type somme</span> </div> </a> <ul id="toc-Type_somme-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Type_énuméré" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Type_énuméré"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Type énuméré</span> </div> </a> <ul id="toc-Type_énuméré-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Type_algébrique" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Type_algébrique"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Type algébrique</span> </div> </a> <ul id="toc-Type_algébrique-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Polymorphisme" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Polymorphisme"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Polymorphisme</span> </div> </a> <button aria-controls="toc-Polymorphisme-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Afficher / masquer la sous-section Polymorphisme</span> </button> <ul id="toc-Polymorphisme-sublist" class="vector-toc-list"> <li id="toc-Type_algébrique_généralisé" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Type_algébrique_généralisé"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Type algébrique généralisé</span> </div> </a> <ul id="toc-Type_algébrique_généralisé-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Récursivité" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Récursivité"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Récursivité</span> </div> </a> <button aria-controls="toc-Récursivité-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Afficher / masquer la sous-section Récursivité</span> </button> <ul id="toc-Récursivité-sublist" class="vector-toc-list"> <li id="toc-Listes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Listes"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Listes</span> </div> </a> <ul id="toc-Listes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Arbres" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Arbres"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Arbres</span> </div> </a> <ul id="toc-Arbres-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Abstraction" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Abstraction"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Abstraction</span> </div> </a> <ul id="toc-Abstraction-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Voir_aussi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Voir_aussi"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Voir aussi</span> </div> </a> <ul id="toc-Voir_aussi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes_&_références" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes_&_références"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Notes & références</span> </div> </a> <button aria-controls="toc-Notes_&_références-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Afficher / masquer la sous-section Notes & références</span> </button> <ul id="toc-Notes_&_références-sublist" class="vector-toc-list"> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Références" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Références"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Références</span> </div> </a> <ul id="toc-Références-sublist" class="vector-toc-list"> </ul> </li> </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="Sommaire" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Basculer la table des matières" > <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" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Basculer la table des matières</span> </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"><span class="mw-page-title-main">Type algébrique de données</span></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="Aller à un article dans 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Disponible en 11 langues." > <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-11" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">11 langues</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Tipus_de_dades_algebraic" title="Tipus de dades algebraic – catalan" lang="ca" hreflang="ca" data-title="Tipus de dades algebraic" data-language-autonym="Català" data-language-local-name="catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Algebraischer_Datentyp" title="Algebraischer Datentyp – allemand" lang="de" hreflang="de" data-title="Algebraischer Datentyp" data-language-autonym="Deutsch" data-language-local-name="allemand" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%91%CE%BB%CE%B3%CE%B5%CE%B2%CF%81%CE%B9%CE%BA%CF%8C%CF%82_%CF%84%CF%8D%CF%80%CE%BF%CF%82_%CE%B4%CE%B5%CE%B4%CE%BF%CE%BC%CE%AD%CE%BD%CF%89%CE%BD" title="Αλγεβρικός τύπος δεδομένων – grec" lang="el" hreflang="el" data-title="Αλγεβρικός τύπος δεδομένων" data-language-autonym="Ελληνικά" data-language-local-name="grec" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Algebraic_data_type" title="Algebraic data type – anglais" lang="en" hreflang="en" data-title="Algebraic data type" data-language-autonym="English" data-language-local-name="anglais" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Tipo_de_dato_algebraico" title="Tipo de dato algebraico – espagnol" lang="es" hreflang="es" data-title="Tipo de dato algebraico" data-language-autonym="Español" data-language-local-name="espagnol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E4%BB%A3%E6%95%B0%E7%9A%84%E3%83%87%E3%83%BC%E3%82%BF%E5%9E%8B" title="代数的データ型 – japonais" lang="ja" hreflang="ja" data-title="代数的データ型" data-language-autonym="日本語" data-language-local-name="japonais" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%8C%80%EC%88%98%EC%A0%81_%EC%9E%90%EB%A3%8C%ED%98%95" title="대수적 자료형 – coréen" lang="ko" hreflang="ko" data-title="대수적 자료형" data-language-autonym="한국어" data-language-local-name="coréen" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Algebra%C3%AFsch_datatype" title="Algebraïsch datatype – néerlandais" lang="nl" hreflang="nl" data-title="Algebraïsch datatype" data-language-autonym="Nederlands" data-language-local-name="néerlandais" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B8%D0%B9_%D1%82%D0%B8%D0%BF_%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85" title="Алгебраический тип данных – russe" lang="ru" hreflang="ru" data-title="Алгебраический тип данных" data-language-autonym="Русский" data-language-local-name="russe" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B8%D1%87%D0%BD%D0%B8%D0%B9_%D1%82%D0%B8%D0%BF_%D0%B4%D0%B0%D0%BD%D0%B8%D1%85" title="Алгебричний тип даних – ukrainien" lang="uk" hreflang="uk" data-title="Алгебричний тип даних" data-language-autonym="Українська" data-language-local-name="ukrainien" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%BB%A3%E6%95%B0%E6%95%B0%E6%8D%AE%E7%B1%BB%E5%9E%8B" title="代数数据类型 – chinois" lang="zh" hreflang="zh" data-title="代数数据类型" data-language-autonym="中文" data-language-local-name="chinois" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a 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l'encyclopédie libre.</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="fr" dir="ltr"><div class="bandeau-container metadata homonymie hatnote"><div class="bandeau-cell bandeau-icone" style="display:table-cell;padding-right:0.5em"><span class="noviewer" typeof="mw:File"><a href="/wiki/Aide:Homonymie" title="Aide:Homonymie"><img alt="Page d’aide sur l’homonymie" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Logo_disambig.svg/20px-Logo_disambig.svg.png" decoding="async" width="20" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Logo_disambig.svg/30px-Logo_disambig.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Logo_disambig.svg/40px-Logo_disambig.svg.png 2x" data-file-width="512" data-file-height="375" /></a></span></div><div class="bandeau-cell" style="display:table-cell;padding-right:0.5em"> <p>Pour les articles homonymes, voir <a href="/wiki/Alg%C3%A9brique" class="mw-disambig" title="Algébrique">Algébrique</a>. </p> </div></div> <div class="bandeau-container metadata bandeau-article bandeau-niveau-ebauche"><div class="bandeau-cell bandeau-icone" style="display:table-cell;padding-right:0.5em"><span class="noviewer" typeof="mw:File"><a href="/wiki/Fichier:Circle-icons-computer.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Circle-icons-computer.svg/35px-Circle-icons-computer.svg.png" decoding="async" width="35" height="35" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Circle-icons-computer.svg/53px-Circle-icons-computer.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/02/Circle-icons-computer.svg/70px-Circle-icons-computer.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span></div><div class="bandeau-cell" style="display:table-cell;padding-right:0.5em"> <p><strong class="bandeau-titre">Cet article est une <a href="/wiki/Aide:%C3%89bauche" title="Aide:Ébauche">ébauche</a> concernant l’<a href="/wiki/Informatique" title="Informatique">informatique</a>.</strong> </p><p>Vous pouvez partager vos connaissances en l’améliorant (<b><a href="/wiki/Aide:Comment_modifier_une_page" title="Aide:Comment modifier une page">comment ?</a></b>) selon les recommandations des <a href="/wiki/Projet:Accueil" title="Projet:Accueil">projets correspondants</a>. </p> </div></div> <p>Un <b>type algébrique</b> est une forme de <a href="/wiki/Type_(informatique)" title="Type (informatique)">type de données</a> composite<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite_crochet">[</span>note 1<span class="cite_crochet">]</span></a></sup>, qui combine les fonctionnalités des <b>types produits</b> (<a href="/wiki/Uplet" title="Uplet"><span class="texhtml"><i>n</i></span>‐uplets</a> ou <a href="/wiki/Enregistrement_(structure_de_donn%C3%A9es)" title="Enregistrement (structure de données)">enregistrements</a>) et des <b>types sommes</b> (<a href="/wiki/Union_disjointe" class="mw-redirect" title="Union disjointe">union disjointe</a>). Combinée à la <a href="/wiki/Type_r%C3%A9cursif" title="Type récursif">récursivité</a>, elle permet d’exprimer les données structurées telles que les <a href="/wiki/Liste_(informatique)" title="Liste (informatique)">listes</a> et les <a href="/wiki/Arbre_enracin%C3%A9" title="Arbre enraciné">arbres</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Définitions"><span id="D.C3.A9finitions"></span>Définitions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&veaction=edit&section=1" title="Modifier la section : Définitions" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&action=edit&section=1" title="Modifier le code source de la section : Définitions"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Type_produit">Type produit</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&veaction=edit&section=2" title="Modifier la section : Type produit" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&action=edit&section=2" title="Modifier le code source de la section : Type produit"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Le <b>type produit</b> de deux types <span class="texhtml mvar" style="font-style:italic;">A</span> et <span class="texhtml mvar" style="font-style:italic;">B</span> est l’analogue en <a href="/wiki/Th%C3%A9orie_des_types" title="Théorie des types">théorie des types</a> du <a href="/wiki/Produit_cart%C3%A9sien" title="Produit cartésien">produit cartésien</a> <a href="/wiki/Th%C3%A9orie_des_ensembles" title="Théorie des ensembles">ensembliste</a> et est noté <span class="texhtml"><span class="texhtml mvar" style="font-style:italic;">A</span> × <span class="texhtml mvar" style="font-style:italic;">B</span></span>. C’est le type des couples dont la première composante est de type <span class="texhtml mvar" style="font-style:italic;">A</span> et la seconde de type <span class="texhtml mvar" style="font-style:italic;">B</span>. Deux <a href="/wiki/Fonction_(informatique)" class="mw-redirect" title="Fonction (informatique)">fonctions</a> canoniques lui sont associées, appelées <i>projections</i>, donnant la valeur de chaque composante. </p> <div style="margin:0.5em 2em;"><strong>Exemple : type produit en <a href="/wiki/OCaml" title="OCaml">OCaml</a> :</strong> <div style="padding-left:2em; border-left:1px dotted #999;"> <p>On peut définir en langage OCaml le type d’une entrée de <a href="/wiki/Tableau_associatif" title="Tableau associatif">dictionnaire</a> : </p> <div class="mw-highlight mw-highlight-lang-ocaml mw-content-ltr" dir="ltr"><pre><span></span><span class="k">type</span> <span class="n">dict_entry</span> <span class="o">=</span> <span class="kt">string</span> <span class="o">*</span> <span class="kt">int</span> <span class="k">let</span> <span class="n">entry</span> <span class="o">=</span> <span class="o">(</span><span class="s2">"clé"</span><span class="o">,</span> <span class="mi">37</span><span class="o">)</span> <span class="c">(* get_value : dict_entry -> int *)</span> <span class="k">let</span> <span class="n">get_value</span> <span class="o">(</span><span class="n">key</span><span class="o">,</span> <span class="n">value</span><span class="o">)</span> <span class="o">=</span> <span class="n">value</span> </pre></div> </div></div> <p>Le produit se généralise naturellement à un nombre quelconque d’opérandes, pour donner des types de <span class="texhtml mvar" style="font-style:italic;">n</span>‐uplets. Dans le cas particulier du <a href="/wiki/Produit_vide" title="Produit vide">produit vide</a>, le type des 0‐uplets est nommé <b><a href="/wiki/Type_unit%C3%A9" title="Type unité">type unité</a></b> et noté <span class="texhtml"><b>1</b></span> : c’est l’<a href="/wiki/%C3%89l%C3%A9ment_neutre" title="Élément neutre">élément neutre</a> du produit et il contient une unique valeur, souvent notée <span class="texhtml">()</span>. </p><p>Des considérations pratiques amènent souvent à nommer les composantes<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite_crochet">[</span>note 2<span class="cite_crochet">]</span></a></sup>. Dans ce contexte, le type est souvent appelé <i>structure</i> et ses valeurs des <i>enregistrements</i> ; les composantes sont appelées <i>membres</i>, et la projection selon le membre <code>m</code> s’écrit avec une notation suffixe <code>.m</code>. </p> <div style="margin:0.5em 2em;"><strong>Exemple : structure en OCaml :</strong> <div style="padding-left:2em; border-left:1px dotted #999;"> <p>Toujours en OCaml, l’exemple précédent s’adapte ainsi : </p> <div class="mw-highlight mw-highlight-lang-ocaml mw-content-ltr" dir="ltr"><pre><span></span><span class="k">type</span> <span class="n">dict_entry</span> <span class="o">=</span> <span class="o">{</span> <span class="n">key</span> <span class="o">:</span> <span class="kt">string</span> <span class="o">;</span> <span class="n">value</span> <span class="o">:</span> <span class="kt">int</span> <span class="o">;</span> <span class="o">}</span> <span class="k">let</span> <span class="n">entry</span> <span class="o">=</span> <span class="o">{</span> <span class="n">key</span> <span class="o">=</span> <span class="s2">"clé"</span> <span class="o">;</span> <span class="n">value</span> <span class="o">=</span> <span class="mi">37</span> <span class="o">}</span> <span class="c">(* get_value : dict_entry -> int *)</span> <span class="k">let</span> <span class="n">get_value</span> <span class="n">entry</span> <span class="o">=</span> <span class="n">entry</span><span class="o">.</span><span class="n">value</span> </pre></div> </div></div> <div style="margin:0.5em 2em;"><strong>Exemple : structure en <a href="/wiki/Langage_C" class="mw-redirect" title="Langage C">langage C</a> :</strong> <div style="padding-left:2em; border-left:1px dotted #999;"> <p>Cette fonctionnalité se traduit en langage C par <a href="/w/index.php?title=Struct_(langage_C)&action=edit&redlink=1" class="new" title="Struct (langage C) (page inexistante)">le mot‐clé <code>struct</code></a> <a href="https://en.wikipedia.org/wiki/struct_(C_programming_language)" class="extiw" title="en:struct (C programming language)"><span class="indicateur-langue" title="Article en anglais : « struct (C programming language) »">(en)</span></a> : </p> <div class="mw-highlight mw-highlight-lang-c mw-content-ltr" dir="ltr"><pre><span></span><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="p">{</span> <span class="w"> </span><span class="kt">char</span><span class="o">*</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="p">;</span> <span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">value</span><span class="w"> </span><span class="p">;</span> <span class="p">}</span><span class="w"> </span><span class="n">dict_entry</span><span class="w"> </span><span class="p">;</span> <span class="n">dict_entry</span><span class="w"> </span><span class="n">entry</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="p">.</span><span class="n">key</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">"clé"</span><span class="p">,</span><span class="w"> </span><span class="p">.</span><span class="n">value</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">37</span><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="p">;</span> <span class="kt">int</span><span class="w"> </span><span class="nf">get_value</span><span class="w"> </span><span class="p">(</span><span class="n">dict_entry</span><span class="w"> </span><span class="n">entry</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> <span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">entry</span><span class="p">.</span><span class="n">value</span><span class="w"> </span><span class="p">;</span> <span class="p">}</span> </pre></div> </div></div> <div class="bandeau-container bandeau-section metadata bandeau-niveau-information"><div class="bandeau-cell bandeau-icone-css loupe">Article détaillé : <a href="/wiki/Enregistrement_(structure_de_donn%C3%A9es)" title="Enregistrement (structure de données)">enregistrement (structure de données)</a>.</div></div> <div class="mw-heading mw-heading3"><h3 id="Type_somme">Type somme</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&veaction=edit&section=3" title="Modifier la section : Type somme" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&action=edit&section=3" title="Modifier le code source de la section : Type somme"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Le <b>type somme</b> de deux types <span class="texhtml mvar" style="font-style:italic;">A</span> et <span class="texhtml mvar" style="font-style:italic;">B</span> est l’analogue en théorie des types de l’<a href="/wiki/Union_disjointe" class="mw-redirect" title="Union disjointe">union disjointe</a> ensembliste et est noté <span class="texhtml"><span class="texhtml mvar" style="font-style:italic;">A</span> + <span class="texhtml mvar" style="font-style:italic;">B</span></span>. Il représente un type contenant toutes les valeurs de chacun des deux types <span class="texhtml mvar" style="font-style:italic;">A</span> et <span class="texhtml mvar" style="font-style:italic;">B</span>, de telle sorte qu’une valeur issue de <span class="texhtml mvar" style="font-style:italic;">A</span> ne puisse pas être confondue avec une valeur issue de <span class="texhtml mvar" style="font-style:italic;">B</span> (même si <span class="texhtml"><span class="texhtml mvar" style="font-style:italic;">A</span> = <span class="texhtml mvar" style="font-style:italic;">B</span></span>). </p><p>En théorie des ensembles, on représenterait la somme par l’ensemble <span class="texhtml">{1}×<span class="texhtml mvar" style="font-style:italic;">A</span> ∪ {2}×<span class="texhtml mvar" style="font-style:italic;">B</span></span> ; la première composante (1 ou 2) d’un tel objet est une étiquette qui indique si cet objet se trouve dans le bras de gauche (<span class="texhtml mvar" style="font-style:italic;">A</span>) ou dans le bras de droite (<span class="texhtml mvar" style="font-style:italic;">B</span>) de la somme. Les analogues en théorie des types des expressions <span class="texhtml">(1, <span class="texhtml mvar" style="font-style:italic;">a</span>)</span> et <span class="texhtml">(2, <span class="texhtml mvar" style="font-style:italic;">b</span>)</span> sont souvent notés <span class="texhtml">ι<sub>1</sub> <span class="texhtml mvar" style="font-style:italic;">a</span></span> et <span class="texhtml">ι<sub>2</sub> <span class="texhtml mvar" style="font-style:italic;">b</span></span> (<span class="texhtml">ι</span> est la lettre grecque <i>iota</i>). Ces notations <span class="texhtml">ι<sub>1</sub></span> et <span class="texhtml">ι<sub>2</sub></span> peuvent être vues comme des fonctions <a href="/wiki/Fonction_injective" class="mw-redirect" title="Fonction injective">injectives</a>, respectivement de <span class="texhtml mvar" style="font-style:italic;">A</span> dans <span class="texhtml"><span class="texhtml mvar" style="font-style:italic;">A</span> + <span class="texhtml mvar" style="font-style:italic;">B</span></span> et de <span class="texhtml mvar" style="font-style:italic;">B</span> dans <span class="texhtml"><span class="texhtml mvar" style="font-style:italic;">A</span> + <span class="texhtml mvar" style="font-style:italic;">B</span></span>, qui permettent de construire les valeurs de la somme, d’où leur nom de <i>constructeurs</i>. Dans <span class="texhtml">ι<sub>1</sub> <span class="texhtml mvar" style="font-style:italic;">a</span></span>, la valeur <span class="texhtml mvar" style="font-style:italic;">a</span> est appelée l’<i>argument</i> du constructeur <span class="texhtml">ι<sub>1</sub></span>. </p><p>Traiter des valeurs d’un type somme requiert un raisonnement par cas, nommé dans ce contexte <i><a href="/wiki/Filtrage_par_motif" title="Filtrage par motif">filtrage par motif</a></i>. Chaque bras — qu’on reconnaît par son constructeur et dont on peut récupérer la valeur puisque ce constructeur est injectif — fait l’objet d’un cas séparé. </p> <div style="margin:0.5em 2em;"><strong>Exemple : type somme en OCaml :</strong> <div style="padding-left:2em; border-left:1px dotted #999;"> <p>On peut définir on OCaml l’union disjointe des nombres entiers et des nombres flottants et définir par filtrage une fonction sur cette union : </p> <div class="mw-highlight mw-highlight-lang-ocaml mw-content-ltr" dir="ltr"><pre><span></span><span class="k">type</span> <span class="n">sum</span> <span class="o">=</span> <span class="nc">Int</span> <span class="k">of</span> <span class="kt">int</span> <span class="o">|</span> <span class="nc">Float</span> <span class="k">of</span> <span class="kt">float</span> <span class="c">(* print : sum -> unit *)</span> <span class="k">let</span> <span class="n">print</span> <span class="o">=</span> <span class="k">function</span> <span class="o">|</span> <span class="nc">Int</span> <span class="n">i</span> <span class="o">-></span> <span class="nn">Printf</span><span class="p">.</span><span class="n">printf</span> <span class="s2">"%i"</span> <span class="n">i</span> <span class="o">|</span> <span class="nc">Float</span> <span class="n">f</span> <span class="o">-></span> <span class="nn">Printf</span><span class="p">.</span><span class="n">printf</span> <span class="s2">"%f"</span> <span class="n">f</span> </pre></div> <p>Ici, les constructeurs sont nommés <code>Int</code> et <code>Float</code>. </p> </div></div> <div style="margin:0.5em 2em;"><strong>Exemple : type « union » en langage C :</strong> <div style="padding-left:2em; border-left:1px dotted #999;"> <p>Cette fonctionnalité s’approxime en langage C avec <a href="/w/index.php?title=Union_(langage_C)&action=edit&redlink=1" class="new" title="Union (langage C) (page inexistante)">le mot clé <code>union</code></a> <a href="https://en.wikipedia.org/wiki/Union_type#C/C++" class="extiw" title="en:Union type"><span class="indicateur-langue" title="Article en anglais : « Union type#C/C++ »">(en)</span></a> à condition d’y adjoindre une étiquette, mais cela n’offre pas les mêmes garanties (on peut lire et modifier un objet du type somme en faisant fi de son étiquette — quitte à provoquer des <a href="/wiki/Bug_informatique" class="mw-redirect" title="Bug informatique">bugs</a>) : </p> <div class="mw-highlight mw-highlight-lang-c mw-content-ltr" dir="ltr"><pre><span></span><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="p">{</span> <span class="w"> </span><span class="k">enum</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">INT</span><span class="p">,</span><span class="w"> </span><span class="n">FLOAT</span><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="n">tag</span><span class="w"> </span><span class="p">;</span> <span class="w"> </span><span class="k">union</span><span class="w"> </span><span class="p">{</span> <span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">;</span> <span class="w"> </span><span class="kt">float</span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="p">;</span> <span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="p">;</span> <span class="p">}</span><span class="w"> </span><span class="n">sum_t</span><span class="w"> </span><span class="p">;</span> <span class="kt">void</span><span class="w"> </span><span class="nf">print</span><span class="w"> </span><span class="p">(</span><span class="n">sum_t</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> <span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">x</span><span class="p">.</span><span class="n">tag</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">INT</span><span class="p">)</span> <span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">"%i"</span><span class="p">,</span><span class="w"> </span><span class="n">x</span><span class="p">.</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">;</span> <span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">x</span><span class="p">.</span><span class="n">tag</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">FLOAT</span><span class="p">)</span> <span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">"%f"</span><span class="p">,</span><span class="w"> </span><span class="n">x</span><span class="p">.</span><span class="n">f</span><span class="p">)</span><span class="w"> </span><span class="p">;</span> <span class="p">}</span> </pre></div> </div></div> <p>La somme se généralise naturellement à un nombre quelconque d’opérandes. Dans le cas particulier de la <a href="/wiki/Somme_vide" title="Somme vide">somme vide</a>, le type est nommé <b><a href="/wiki/Type_vide" title="Type vide">type vide</a></b> et noté <span class="texhtml"><b>0</b></span> : c’est l’élément neutre de la somme (et <a href="/wiki/%C3%89l%C3%A9ment_absorbant" title="Élément absorbant">élément absorbant</a> du produit) et il ne contient aucune valeur. </p> <div class="mw-heading mw-heading3"><h3 id="Type_énuméré"><span id="Type_.C3.A9num.C3.A9r.C3.A9"></span>Type énuméré</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&veaction=edit&section=4" title="Modifier la section : Type énuméré" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&action=edit&section=4" title="Modifier le code source de la section : Type énuméré"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Un <b>type énuméré</b> représente un <a href="/wiki/Ensemble_fini" title="Ensemble fini">ensemble fini</a>, dont les éléments sont les différents constructeurs. Définir une fonction dessus revient à définir l’image de chaque élément, individuellement. </p> <div style="margin:0.5em 2em;"><strong>Exemple : type énuméré en OCaml :</strong> <div style="padding-left:2em; border-left:1px dotted #999;"> <p>On peut par exemple coder l’ensemble des quatre <a href="/wiki/Enseigne_(carte_%C3%A0_jouer)" title="Enseigne (carte à jouer)">couleurs d’un jeu de cartes classique</a> : </p> <div class="mw-highlight mw-highlight-lang-ocaml mw-content-ltr" dir="ltr"><pre><span></span><span class="k">type</span> <span class="n">couleur</span> <span class="o">=</span> <span class="nc">Coeur</span> <span class="o">|</span> <span class="nc">Carreau</span> <span class="o">|</span> <span class="nc">Trefle</span> <span class="o">|</span> <span class="nc">Pique</span> <span class="c">(* nom_de_la_couleur : couleur -> string *)</span> <span class="k">let</span> <span class="n">nom_de_la_couleur</span> <span class="o">=</span> <span class="k">function</span> <span class="o">|</span> <span class="nc">Coeur</span> <span class="o">-></span> <span class="s2">"♥ cœur"</span> <span class="o">|</span> <span class="nc">Carreau</span> <span class="o">-></span> <span class="s2">"♦ carreau"</span> <span class="o">|</span> <span class="nc">Trefle</span> <span class="o">-></span> <span class="s2">"♣ trèfle"</span> <span class="o">|</span> <span class="nc">Pique</span> <span class="o">-></span> <span class="s2">"♠ pique"</span> </pre></div> </div></div> <div style="margin:0.5em 2em;"><strong>Exemple : type énuméré en langage C :</strong> <div style="padding-left:2em; border-left:1px dotted #999;"> <p>Cette fonctionnalité se traduit en langage C par le mot‐clé <code>enum</code> : </p> <div class="mw-highlight mw-highlight-lang-c mw-content-ltr" dir="ltr"><pre><span></span><span class="k">typedef</span><span class="w"> </span><span class="k">enum</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">COEUR</span><span class="p">,</span><span class="w"> </span><span class="n">CARREAU</span><span class="p">,</span><span class="w"> </span><span class="n">TREFLE</span><span class="p">,</span><span class="w"> </span><span class="n">PIQUE</span><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="n">couleur</span><span class="w"> </span><span class="p">;</span> <span class="kt">char</span><span class="o">*</span><span class="w"> </span><span class="nf">nom_de_la_couleur</span><span class="w"> </span><span class="p">(</span><span class="n">couleur</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> <span class="w"> </span><span class="k">switch</span><span class="w"> </span><span class="p">(</span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> <span class="w"> </span><span class="k">case</span><span class="w"> </span><span class="no">COEUR</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="s">"♥ cœur"</span><span class="w"> </span><span class="p">;</span> <span class="w"> </span><span class="k">case</span><span class="w"> </span><span class="no">CARREAU</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="s">"♦ carreau"</span><span class="w"> </span><span class="p">;</span> <span class="w"> </span><span class="k">case</span><span class="w"> </span><span class="no">TREFLE</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="s">"♣ trèfle"</span><span class="w"> </span><span class="p">;</span> <span class="w"> </span><span class="k">case</span><span class="w"> </span><span class="no">PIQUE</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="s">"♠ pique"</span><span class="w"> </span><span class="p">;</span> <span class="w"> </span><span class="p">}</span> <span class="p">}</span> </pre></div> </div></div> <div class="bandeau-container bandeau-section metadata bandeau-niveau-information"><div class="bandeau-cell bandeau-icone-css loupe">Article détaillé : <a href="/wiki/Type_%C3%A9num%C3%A9r%C3%A9" title="Type énuméré">type énuméré</a>.</div></div> <div class="mw-heading mw-heading3"><h3 id="Type_algébrique"><span id="Type_alg.C3.A9brique"></span>Type algébrique</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&veaction=edit&section=5" title="Modifier la section : Type algébrique" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&action=edit&section=5" title="Modifier le code source de la section : Type algébrique"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Un <b>type algébrique</b> est une somme de produits, et généralise donc ces deux notions. </p><p>Ainsi, des cas spéciaux de types algébriques sont les types produits (un seul constructeur), les types sommes (un seul argument pour chaque constructeur) et les types énumérations (plusieurs constructeurs sans argument). </p> <div style="margin:0.5em 2em;"><strong>Exemple : type option et type résultat :</strong> <div style="padding-left:2em; border-left:1px dotted #999;"> <p>Les <a href="/w/index.php?title=Type_option&action=edit&redlink=1" class="new" title="Type option (page inexistante)">types options</a> <a href="https://en.wikipedia.org/wiki/option_type" class="extiw" title="en:option type"><span class="indicateur-langue" title="Article en anglais : « option type »">(en)</span></a> sont des applications courantes de types algébriques. Ils permettent d’ajouter à un type donné une valeur spéciale, considérée comme « indéfinie » ou comme valeur d’erreur (l’équivalent de <code>null</code> dans certains langages de programmation), ce qui permet de définir des fonctions partielles de façon contrôlée. </p><p>La valeur spéciale est représentée par un constructeur <code>None</code> qui ne prend aucun argument, tandis que les valeurs du type à compléter sont enveloppées dans un constructeur <code>Some</code> (qui prend donc un argument de ce type). </p> <div class="mw-highlight mw-highlight-lang-ocaml mw-content-ltr" dir="ltr"><pre><span></span><span class="k">type</span> <span class="n">int_option</span> <span class="o">=</span> <span class="nc">None</span> <span class="o">|</span> <span class="nc">Some</span> <span class="k">of</span> <span class="kt">int</span> <span class="c">(* division : int -> int -> int_option *)</span> <span class="k">let</span> <span class="n">division</span> <span class="n">x</span> <span class="n">y</span> <span class="o">=</span> <span class="k">if</span> <span class="n">y</span> <span class="o">=</span> <span class="mi">0</span> <span class="k">then</span> <span class="nc">None</span> <span class="k">else</span> <span class="nc">Some</span> <span class="o">(</span><span class="n">x</span> <span class="o">/</span> <span class="n">y</span><span class="o">)</span> </pre></div> <p>On peut perfectionner le mécanisme en agrémentant le cas d’erreur d’un message de description (donnée de type <code>string</code>). </p> <div class="mw-highlight mw-highlight-lang-ocaml mw-content-ltr" dir="ltr"><pre><span></span><span class="k">type</span> <span class="n">int_result</span> <span class="o">=</span> <span class="nc">Result</span> <span class="k">of</span> <span class="kt">int</span> <span class="o">|</span> <span class="nc">Error</span> <span class="k">of</span> <span class="kt">string</span> <span class="c">(* division : int -> int -> int_result *)</span> <span class="k">let</span> <span class="n">division</span> <span class="n">x</span> <span class="n">y</span> <span class="o">=</span> <span class="k">if</span> <span class="n">y</span> <span class="o">=</span> <span class="mi">0</span> <span class="k">then</span> <span class="nc">Error</span> <span class="s2">"division by zero"</span> <span class="k">else</span> <span class="nc">Result</span> <span class="o">(</span><span class="n">x</span> <span class="o">/</span> <span class="n">y</span><span class="o">)</span> </pre></div> </div></div> <div class="mw-heading mw-heading2"><h2 id="Polymorphisme">Polymorphisme</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&veaction=edit&section=6" title="Modifier la section : Polymorphisme" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&action=edit&section=6" title="Modifier le code source de la section : Polymorphisme"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="bandeau-container bandeau-section metadata bandeau-niveau-information"><div class="bandeau-cell bandeau-icone"><span class="mw-valign-text-top noviewer" typeof="mw:File"><a href="/wiki/Fichier:Fairytale_warning.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Fairytale_warning.png/17px-Fairytale_warning.png" decoding="async" width="17" height="17" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Fairytale_warning.png/26px-Fairytale_warning.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/Fairytale_warning.png/34px-Fairytale_warning.png 2x" data-file-width="64" data-file-height="64" /></a></span></div><div class="bandeau-cell">Cette section est vide, insuffisamment détaillée ou incomplète. <a href="/wiki/Sp%C3%A9cial:EditPage/Type_alg%C3%A9brique_de_donn%C3%A9es" title="Spécial:EditPage/Type algébrique de données">Votre aide</a> est la bienvenue ! <a href="/wiki/Aide:Comment_modifier_une_page" title="Aide:Comment modifier une page">Comment faire ?</a></div></div> <p>Dans les <a href="/wiki/Langage_de_programmation" title="Langage de programmation">langages</a> qui les supportent, les types algébriques peuvent être <a href="/wiki/Polymorphisme_(informatique)" title="Polymorphisme (informatique)">(paramétriquement) polymorphes</a>, ce qui permet la <a href="/wiki/Programmation_g%C3%A9n%C3%A9rique" class="mw-redirect" title="Programmation générique">programmation générique</a>. Ainsi, la définition d’un type algébrique peut être paramétrée par des variables de types. </p><p>On peut alors définir des fonctions génériques agissant sur de tels types polymorphes. </p> <div style="margin:0.5em 2em;"><strong>Exemple : type option polymorphe :</strong> <div style="padding-left:2em; border-left:1px dotted #999;"> <p>On peut rendre polymorphe la définition du type option vue précédemment. Ça s’écrit ainsi en langage OCaml (où <code>'a</code> dénote une variable de type) : </p> <div class="mw-highlight mw-highlight-lang-ocaml mw-content-ltr" dir="ltr"><pre><span></span><span class="k">type</span> <span class="k">'</span><span class="n">a</span> <span class="n">option</span> <span class="o">=</span> <span class="nc">None</span> <span class="o">|</span> <span class="nc">Some</span> <span class="k">of</span> <span class="k">'</span><span class="n">a</span> <span class="c">(** Utilisation d’instances du type polymorphe : **)</span> <span class="c">(* int_division : int -> int -> int option *)</span> <span class="k">let</span> <span class="n">int_division</span> <span class="n">x</span> <span class="n">y</span> <span class="o">=</span> <span class="k">if</span> <span class="n">y</span> <span class="o">=</span> <span class="mi">0</span> <span class="k">then</span> <span class="nc">None</span> <span class="k">else</span> <span class="nc">Some</span> <span class="o">(</span><span class="n">x</span> <span class="o">/</span> <span class="n">y</span><span class="o">)</span> <span class="c">(* float_division : float -> float -> float option *)</span> <span class="k">let</span> <span class="n">float_division</span> <span class="n">x</span> <span class="n">y</span> <span class="o">=</span> <span class="k">if</span> <span class="n">y</span> <span class="o">=</span> <span class="mi">0</span><span class="o">.</span><span class="mi">0</span> <span class="k">then</span> <span class="nc">None</span> <span class="k">else</span> <span class="nc">Some</span> <span class="o">(</span><span class="n">x</span> <span class="o">/.</span> <span class="n">y</span><span class="o">)</span> <span class="c">(** Définition d’une fonction générique : **)</span> <span class="c">(* get_value : 'a -> 'a option -> 'a *)</span> <span class="k">let</span> <span class="n">get_value</span> <span class="n">default_value</span> <span class="n">optional_value</span> <span class="o">=</span> <span class="k">match</span> <span class="n">optional_value</span> <span class="k">with</span> <span class="o">|</span> <span class="nc">None</span> <span class="o">-></span> <span class="n">default_value</span> <span class="o">|</span> <span class="nc">Some</span> <span class="n">value</span> <span class="o">-></span> <span class="n">value</span> </pre></div> </div></div> <div class="mw-heading mw-heading3"><h3 id="Type_algébrique_généralisé"><span id="Type_alg.C3.A9brique_g.C3.A9n.C3.A9ralis.C3.A9"></span>Type algébrique généralisé <span id="GADT"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&veaction=edit&section=7" title="Modifier la section : Type algébrique généralisé" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&action=edit&section=7" title="Modifier le code source de la section : Type algébrique généralisé"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="bandeau-container bandeau-section metadata bandeau-niveau-information"><div class="bandeau-cell bandeau-icone"><span class="mw-valign-text-top noviewer" typeof="mw:File"><a href="/wiki/Fichier:Fairytale_warning.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Fairytale_warning.png/17px-Fairytale_warning.png" decoding="async" width="17" height="17" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Fairytale_warning.png/26px-Fairytale_warning.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/Fairytale_warning.png/34px-Fairytale_warning.png 2x" data-file-width="64" data-file-height="64" /></a></span></div><div class="bandeau-cell">Cette section est vide, insuffisamment détaillée ou incomplète. <a href="/wiki/Sp%C3%A9cial:EditPage/Type_alg%C3%A9brique_de_donn%C3%A9es" title="Spécial:EditPage/Type algébrique de données">Votre aide</a> est la bienvenue ! <a href="/wiki/Aide:Comment_modifier_une_page" title="Aide:Comment modifier une page">Comment faire ?</a></div></div> <div class="mw-heading mw-heading2"><h2 id="Récursivité"><span id="R.C3.A9cursivit.C3.A9"></span>Récursivité</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&veaction=edit&section=8" title="Modifier la section : Récursivité" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&action=edit&section=8" title="Modifier le code source de la section : Récursivité"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="bandeau-container bandeau-section metadata bandeau-niveau-information"><div class="bandeau-cell bandeau-icone-css loupe">Article détaillé : <a href="/wiki/Type_r%C3%A9cursif" title="Type récursif">type récursif</a>.</div></div> <div class="bandeau-container bandeau-section metadata bandeau-niveau-information"><div class="bandeau-cell bandeau-icone"><span class="mw-valign-text-top noviewer" typeof="mw:File"><a href="/wiki/Fichier:Fairytale_warning.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Fairytale_warning.png/17px-Fairytale_warning.png" decoding="async" width="17" height="17" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Fairytale_warning.png/26px-Fairytale_warning.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/Fairytale_warning.png/34px-Fairytale_warning.png 2x" data-file-width="64" data-file-height="64" /></a></span></div><div class="bandeau-cell">Cette section est vide, insuffisamment détaillée ou incomplète. <a href="/wiki/Sp%C3%A9cial:EditPage/Type_alg%C3%A9brique_de_donn%C3%A9es" title="Spécial:EditPage/Type algébrique de données">Votre aide</a> est la bienvenue ! <a href="/wiki/Aide:Comment_modifier_une_page" title="Aide:Comment modifier une page">Comment faire ?</a></div></div> <div class="mw-heading mw-heading3"><h3 id="Listes">Listes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&veaction=edit&section=9" title="Modifier la section : Listes" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&action=edit&section=9" title="Modifier le code source de la section : Listes"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Un des exemples les plus importants de type algébrique est le type <a href="/wiki/Liste_(informatique)" title="Liste (informatique)">liste</a>, défini de façon récursive par deux constructeurs : </p> <ul><li><span class="texhtml">Nil</span>, aussi noté <code>[]</code>, qui désigne la liste vide,</li> <li>et <span class="texhtml">Cons</span> (abréviation de « constructeur »), aussi noté <code>::</code> ou <code>:</code>, qui désigne la combinaison d’un élément et d’une liste plus courte.</li></ul> <p>Par exemple, <span class="texhtml">Cons 1 (Cons 2 (Cons 3 (Cons 4 Nil)))</span>, aussi noté <code>1 :: 2 :: 3 :: 4 :: []</code>, est la liste constituée des quatre éléments 1, 2, 3, 4, dans cet ordre. </p><p>Toutes les opérations sur les listes se définissent alors par récurrence, en utilisant le filtrage par motif. Par exemple, pour calculer la longueur d’une liste : </p> <ul><li>la longueur de la liste vide (<span class="texhtml">Nil</span>) est zéro,</li> <li>et la longueur d’une liste de la forme <span class="texhtml">Cons <span class="texhtml mvar" style="font-style:italic;">x</span> <span class="texhtml mvar" style="font-style:italic;">suite</span></span> est un plus la longueur de la liste <span class="texhtml mvar" style="font-style:italic;">suite</span>.</li></ul> <div style="margin:0.5em 2em;"><strong>Exemple : type liste en OCaml :</strong> <div style="padding-left:2em; border-left:1px dotted #999;"> <p>Cette définition se traduit ainsi en langage OCaml : </p> <div class="mw-highlight mw-highlight-lang-ocaml mw-content-ltr" dir="ltr"><pre><span></span><span class="k">type</span> <span class="k">'</span><span class="n">a</span> <span class="kt">list</span> <span class="o">=</span> <span class="o">|</span> <span class="nc">Nil</span> <span class="o">|</span> <span class="nc">Cons</span> <span class="k">of</span> <span class="k">'</span><span class="n">a</span> <span class="o">*</span> <span class="k">'</span><span class="n">a</span> <span class="kt">list</span> <span class="k">let</span> <span class="n">list1234</span> <span class="o">=</span> <span class="nc">Cons</span> <span class="mi">1</span> <span class="o">(</span><span class="nc">Cons</span> <span class="mi">2</span> <span class="o">(</span><span class="nc">Cons</span> <span class="mi">3</span> <span class="o">(</span><span class="nc">Cons</span> <span class="mi">4</span> <span class="nc">Nil</span><span class="o">)))</span> <span class="k">let</span> <span class="k">rec</span> <span class="n">length</span> <span class="o">=</span> <span class="k">function</span> <span class="o">|</span> <span class="nc">Nil</span> <span class="o">-></span> <span class="mi">0</span> <span class="o">|</span> <span class="nc">Cons</span> <span class="n">x</span> <span class="n">s</span> <span class="o">-></span> <span class="mi">1</span> <span class="o">+</span> <span class="n">length</span> <span class="n">s</span> </pre></div> </div></div> <div class="mw-heading mw-heading3"><h3 id="Arbres">Arbres</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&veaction=edit&section=10" title="Modifier la section : Arbres" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&action=edit&section=10" title="Modifier le code source de la section : Arbres"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Les types algébriques permettent également de définir des structures d’<a href="/wiki/Arbre_(informatique)" class="mw-redirect" title="Arbre (informatique)">arbres</a>. Un <a href="/wiki/Arbre_binaire" title="Arbre binaire">arbre binaire</a> peut se construire au moyen de deux constructeurs : </p> <ul><li><span class="texhtml">Leaf <span class="texhtml mvar" style="font-style:italic;">e</span></span> qui désigne une feuille d’étiquette <span class="texhtml mvar" style="font-style:italic;">e</span>,</li> <li>et <span class="texhtml">Node <span class="texhtml mvar" style="font-style:italic;">e</span> <span class="texhtml mvar" style="font-style:italic;">g</span> <span class="texhtml mvar" style="font-style:italic;">d</span></span> qui désigne un nœud interne d’étiquette <span class="texhtml mvar" style="font-style:italic;">e</span>, de fils gauche <span class="texhtml mvar" style="font-style:italic;">g</span> et de fils droit <span class="texhtml mvar" style="font-style:italic;">d</span>.</li></ul> <p>Par exemple, </p> <pre>Node 1 (Node 2 (Leaf 4) (Node 5 (Leaf 6) (Leaf 7) ) ) (Leaf 3) </pre> <p>est l’arbre suivant : </p> <pre> 1 / \ 2 3 / \ 4 5 / \ 6 7 </pre> <p>Comme pour les listes, les opérations sur les arbres se définissent par récurrence. Par exemple, pour calculer la hauteur d’un arbre : </p> <ul><li>la hauteur d’une feuille est un,</li> <li>et la hauteur d’un nœud interne est un plus le maximum de la hauteur de ses deux fils.</li></ul> <div style="margin:0.5em 2em;"><strong>Exemple : type arbre binaire en OCaml :</strong> <div style="padding-left:2em; border-left:1px dotted #999;"> <p>Cette définition se traduit ainsi en langage OCaml : </p> <div class="mw-highlight mw-highlight-lang-ocaml mw-content-ltr" dir="ltr"><pre><span></span><span class="k">type</span> <span class="n">tree</span> <span class="o">=</span> <span class="o">|</span> <span class="nc">Leaf</span> <span class="k">of</span> <span class="kt">int</span> <span class="o">|</span> <span class="nc">Node</span> <span class="k">of</span> <span class="n">tree</span> <span class="o">*</span> <span class="kt">int</span> <span class="o">*</span> <span class="n">tree</span> <span class="k">let</span> <span class="n">my_tree</span> <span class="o">=</span> <span class="nc">Node</span> <span class="mi">1</span> <span class="o">(</span><span class="nc">Node</span> <span class="mi">2</span> <span class="o">(</span><span class="nc">Leaf</span> <span class="mi">4</span><span class="o">)</span> <span class="o">(</span><span class="nc">Node</span> <span class="mi">5</span> <span class="o">(</span><span class="nc">Leaf</span> <span class="mi">6</span><span class="o">)</span> <span class="o">(</span><span class="nc">Leaf</span> <span class="mi">7</span><span class="o">)))</span> <span class="o">(</span><span class="nc">Leaf</span> <span class="mi">3</span><span class="o">)</span> <span class="k">let</span> <span class="k">rec</span> <span class="n">height</span> <span class="o">=</span> <span class="k">function</span> <span class="o">|</span> <span class="nc">Leaf</span> <span class="n">e</span> <span class="o">-></span> <span class="mi">1</span> <span class="o">|</span> <span class="nc">Node</span> <span class="n">e</span> <span class="n">l</span> <span class="n">r</span> <span class="o">-></span> <span class="mi">1</span> <span class="o">+</span> <span class="n">max</span> <span class="o">(</span><span class="n">height</span> <span class="n">l</span><span class="o">)</span> <span class="o">(</span><span class="n">height</span> <span class="n">r</span><span class="o">)</span> </pre></div> </div></div> <div class="mw-heading mw-heading2"><h2 id="Abstraction">Abstraction</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&veaction=edit&section=11" title="Modifier la section : Abstraction" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&action=edit&section=11" title="Modifier le code source de la section : Abstraction"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Un type algébrique peut être <a href="/wiki/Type_abstrait" title="Type abstrait">abstrait</a> : il suffit pour ça de ne pas exposer sa structure interne (ses constructeurs et leurs divers champs). Ainsi, il ne peut être manipulé que par les fonctions prévues à cet effet, et son implémentation peut être changée. </p><p>C’est une technique fréquente car les types algébriques permettent de réaliser des structures de données complexes. </p> <div class="mw-heading mw-heading2"><h2 id="Voir_aussi">Voir aussi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&veaction=edit&section=12" title="Modifier la section : Voir aussi" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&action=edit&section=12" title="Modifier le code source de la section : Voir aussi"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Type_(informatique)" title="Type (informatique)">Type</a></li> <li><a href="/wiki/Type_r%C3%A9cursif" title="Type récursif">Type récursif</a></li> <li><a href="/wiki/Filtrage_par_motif" title="Filtrage par motif">Filtrage par motif</a></li> <li><a href="/wiki/Enregistrement_(structure_de_donn%C3%A9es)" title="Enregistrement (structure de données)">Enregistrement</a></li> <li><a href="/wiki/Type_%C3%A9num%C3%A9r%C3%A9" title="Type énuméré">Énumération</a></li> <li><a href="/w/index.php?title=Type_option&action=edit&redlink=1" class="new" title="Type option (page inexistante)">Type option</a> <a href="https://en.wikipedia.org/wiki/Option_type" class="extiw" title="en:Option type"><span class="indicateur-langue" title="Article en anglais : « Option type »">(en)</span></a></li> <li><a href="/wiki/Liste_(informatique)" title="Liste (informatique)">Liste</a></li> <li><a href="/wiki/Arbre_(informatique)" class="mw-redirect" title="Arbre (informatique)">Arbre</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes_&_références"><span id="Notes_.26_r.C3.A9f.C3.A9rences"></span>Notes & références</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&veaction=edit&section=13" title="Modifier la section : Notes & références" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&action=edit&section=13" title="Modifier le code source de la section : Notes & références"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Notes">Notes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&veaction=edit&section=14" title="Modifier la section : Notes" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&action=edit&section=14" title="Modifier le code source de la section : Notes"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="references-small decimal" style=""><div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink noprint"><a href="#cite_ref-1">↑</a> </span><span class="reference-text">C’est‐à‐dire un type formé en combinant d’autres types plus simples.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink noprint"><a href="#cite_ref-2">↑</a> </span><span class="reference-text">De <i><a href="/wiki/Typage_structurel" class="mw-redirect" title="Typage structurel">structurel</a></i>, le typage devient alors <i><a href="/wiki/Typage_nominatif" class="mw-redirect" title="Typage nominatif">nominal</a></i>. Dans le premier cas, l’expression d’un <span class="texhtml mvar" style="font-style:italic;">n</span>‐uplet permet de déduire entièrement sa structure (par exemple, <code>("clé", 37)</code> est de type <code>string * int</code>) et déclarer le type est donc superflu. Dans le second cas, au contraire, l’expression ne suffit pas (<code>{ key = "clé" ; value = 37 }</code> peut suivre la structure <code>{ key : string ; value : int }</code> mais aussi <code>{ value : int ; key : string }</code> — qui est différente —, et l’expression <code>entry.value</code> permet seulement de déduire que la structure de <code>entry</code> contient un champ nommé <code>value</code>), et il faut donc déclarer les structures utilisées afin d’associer chaque nom de membre à une structure.</span> </li> </ol></div> </div> <div class="mw-heading mw-heading3"><h3 id="Références"><span id="R.C3.A9f.C3.A9rences"></span>Références</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&veaction=edit&section=15" title="Modifier la section : Références" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Type_alg%C3%A9brique_de_donn%C3%A9es&action=edit&section=15" title="Modifier le code source de la section : Références"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="references-small decimal" style=""> </div> <ul><li><abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> <a rel="nofollow" class="external text" href="http://foldoc.doc.ic.ac.uk/foldoc/foldoc.cgi?algebraic+data+type"><i><span class="lang-en" lang="en">Algebraic data type</span></i></a> dans <i><span class="lang-en" lang="en">The Free On-line Dictionary of Computing</span></i>, rédacteur en chef Denis Howe.</li></ul> <div class="navbox-container" style="clear:both;"> <table class="navbox collapsible noprint autocollapse" style=""> <tbody><tr><th class="navbox-title" colspan="2" style=""><div style="float:left; width:6em; text-align:left"><div class="noprint plainlinks nowrap tnavbar" style="padding:0; font-size:xx-small; color:var(--color-emphasized, #000000);"><a href="/wiki/Mod%C3%A8le:Palette_Types_de_donn%C3%A9es" title="Modèle:Palette Types de données"><abbr class="abbr" title="Voir ce modèle.">v</abbr></a> · <a class="external text" href="https://fr.wikipedia.org/w/index.php?title=Mod%C3%A8le:Palette_Types_de_donn%C3%A9es&action=edit"><abbr class="abbr" title="Modifier ce modèle. Merci de prévisualiser avant de sauvegarder.">m</abbr></a></div></div><div style="font-size:110%"><a href="/wiki/Type_(informatique)" title="Type (informatique)">Types de données</a></div></th> </tr> <tr> <th class="navbox-group" style="">Non interprétée</th> <td class="navbox-list" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Bit" title="Bit">Bit</a></li> <li><a href="/wiki/Byte" title="Byte">Byte</a></li> <li><a href="/wiki/Syst%C3%A8me_ternaire" title="Système ternaire">Trit</a></li> <li><a href="/wiki/Syst%C3%A8me_ternaire#Représentation_ternaire_compacte" title="Système ternaire">Tryte</a></li> <li><a href="/wiki/Mot_(architecture_informatique)" title="Mot (architecture informatique)">Mot</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="">Numérique</th> <td class="navbox-list navbox-even" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Arithm%C3%A9tique_multipr%C3%A9cision" title="Arithmétique multiprécision">Bignum</a></li> <li><a href="/w/index.php?title=Complex_data_type&action=edit&redlink=1" class="new" title="Complex data type (page inexistante)">Complexe</a> <a href="https://en.wikipedia.org/wiki/complex_data_type" class="extiw" title="en:complex data type"><span class="indicateur-langue" title="Article en anglais : « complex data type »">(en)</span></a></li> <li><a href="/w/index.php?title=Decimal_data_type&action=edit&redlink=1" class="new" title="Decimal data type (page inexistante)">Décimal</a> <a href="https://en.wikipedia.org/wiki/Decimal_data_type" class="extiw" title="en:Decimal data type"><span class="indicateur-langue" title="Article en anglais : « Decimal data type »">(en)</span></a></li> <li><a href="/wiki/Virgule_fixe" title="Virgule fixe">Virgule fixe</a></li> <li><a href="/wiki/Virgule_flottante" title="Virgule flottante">Virgule flottante</a></li> <li><a href="/wiki/Entier_(informatique)" title="Entier (informatique)">Entier</a> <ul><li><a href="/w/index.php?title=Signedness&action=edit&redlink=1" class="new" title="Signedness (page inexistante)">Non signé</a> <a href="https://en.wikipedia.org/wiki/Signedness" class="extiw" title="en:Signedness"><span class="indicateur-langue" title="Article en anglais : « Signedness »">(en)</span></a></li></ul></li> <li><a href="/wiki/Arithm%C3%A9tique_d%27intervalles" title="Arithmétique d'intervalles">Intervalle</a></li> <li><a href="/w/index.php?title=Rational_data_type&action=edit&redlink=1" class="new" title="Rational data type (page inexistante)">Rationnel</a> <a href="https://en.wikipedia.org/wiki/Rational_data_type" class="extiw" title="en:Rational data type"><span class="indicateur-langue" title="Article en anglais : « Rational data type »">(en)</span></a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style=""><a href="/wiki/Texte_brut" title="Texte brut">Texte brut</a></th> <td class="navbox-list" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Caract%C3%A8re_(informatique)" title="Caractère (informatique)">Caractère</a></li> <li><a href="/wiki/Cha%C3%AEne_de_caract%C3%A8res" title="Chaîne de caractères">Chaîne de caractères</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style=""><a href="/wiki/Pointeur_(programmation)" title="Pointeur (programmation)">Pointeur</a></th> <td class="navbox-list navbox-even" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Adressage_m%C3%A9moire" title="Adressage mémoire">Adressage mémoire</a> <ul><li><a href="/wiki/Adresse_physique" title="Adresse physique">Physique</a></li> <li><a href="/wiki/Adresse_virtuelle" title="Adresse virtuelle">Virtuelle</a></li></ul></li> <li><a href="/wiki/R%C3%A9f%C3%A9rence_(programmation)" title="Référence (programmation)">Référence</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style=""><a href="/w/index.php?title=Composite_data_type&action=edit&redlink=1" class="new" title="Composite data type (page inexistante)">Composite</a> <a href="https://en.wikipedia.org/wiki/Composite_data_type" class="extiw" title="en:Composite data type"><span class="indicateur-langue" title="Article en anglais : « Composite data type »">(en)</span></a></th> <td class="navbox-list" style=""><div class="liste-horizontale"> <ul><li><a class="mw-selflink selflink">Type algébrique de données</a> <ul><li><a class="mw-selflink-fragment" href="#GADT">Généralisé</a></li></ul></li> <li><a href="/wiki/Tableau_(structure_de_donn%C3%A9es)" title="Tableau (structure de données)">Tableau</a></li> <li><a href="/wiki/Tableau_associatif" title="Tableau associatif">Tableau associatif</a></li> <li><a href="/wiki/Classe_(informatique)" title="Classe (informatique)">Classe</a></li> <li><a href="/wiki/Type_d%C3%A9pendant" title="Type dépendant">Dépendant</a></li> <li><a href="/w/index.php?title=Intuitionistic_type_theory&action=edit&redlink=1" class="new" title="Intuitionistic type theory (page inexistante)">Égalité</a> <a href="https://en.wikipedia.org/wiki/Intuitionistic_type_theory#Equality_type" class="extiw" title="en:Intuitionistic type theory"><span class="indicateur-langue" title="Article en anglais : « Intuitionistic type theory#Equality type »">(en)</span></a></li> <li><a href="/w/index.php?title=Inductive_type&action=edit&redlink=1" class="new" title="Inductive type (page inexistante)">Inductive</a> <a href="https://en.wikipedia.org/wiki/Inductive_type" class="extiw" title="en:Inductive type"><span class="indicateur-langue" title="Article en anglais : « Inductive type »">(en)</span></a></li> <li><a href="/wiki/Liste_(informatique)" title="Liste (informatique)">Liste</a></li> <li><a href="/wiki/Objet_(informatique)" title="Objet (informatique)">Objet</a> <ul><li><a href="/wiki/M%C3%A9taobjet" title="Métaobjet">Métaobjet</a></li></ul></li> <li><a href="/w/index.php?title=Option_type&action=edit&redlink=1" class="new" title="Option type (page inexistante)">Option</a> <a href="https://en.wikipedia.org/wiki/Option_type" class="extiw" title="en:Option type"><span class="indicateur-langue" title="Article en anglais : « Option type »">(en)</span></a></li> <li><a class="mw-selflink-fragment" href="#Type_produit">Produit</a> <ul><li><a href="/wiki/Enregistrement_(structure_de_donn%C3%A9es)" title="Enregistrement (structure de données)">Enregistrement</a></li></ul></li> <li><a href="/wiki/Ensemble_(informatique)" title="Ensemble (informatique)">Ensemble (set)</a></li> <li><a href="/wiki/Vecteur_(structure_de_donn%C3%A9es)" title="Vecteur (structure de données)">Vecteur</a></li> <li><a href="/w/index.php?title=Union_type&action=edit&redlink=1" class="new" title="Union type (page inexistante)">Union</a> <a href="https://en.wikipedia.org/wiki/Union_type" class="extiw" title="en:Union type"><span class="indicateur-langue" title="Article en anglais : « Union type »">(en)</span></a> <ul><li><a class="mw-selflink-fragment" href="#Type_somme">Disjointe</a></li></ul></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="">Autres</th> <td class="navbox-list navbox-even" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Bool%C3%A9en" title="Booléen">Booléen</a></li> <li><a href="/wiki/Type_vide" title="Type vide">Type vide</a></li> <li><a href="/wiki/Collection_(type_de_donn%C3%A9es)" title="Collection (type de données)">Collection</a></li> <li><a href="/wiki/Conteneur_(informatique)" title="Conteneur (informatique)">Conteneur</a></li> <li><a href="/wiki/Type_%C3%A9num%C3%A9r%C3%A9" title="Type énuméré">Type énuméré</a></li> <li><a href="/wiki/Syst%C3%A8me_de_gestion_d%27exceptions" title="Système de gestion d'exceptions">Exception</a></li> <li><a href="/wiki/Routine_(informatique)" title="Routine (informatique)">Fonction</a></li> <li><a href="/w/index.php?title=Opaque_data_type&action=edit&redlink=1" class="new" title="Opaque data type (page inexistante)">Opaque</a> <a href="https://en.wikipedia.org/wiki/Opaque_data_type" class="extiw" title="en:Opaque data type"><span class="indicateur-langue" title="Article en anglais : « Opaque data type »">(en)</span></a></li> <li><a href="/wiki/Type_r%C3%A9cursif" title="Type récursif">Type récursif</a></li> <li><a href="/wiki/S%C3%A9maphore_(informatique)" title="Sémaphore (informatique)">Sémaphore</a></li> <li><a href="/wiki/Flux_(informatique)" title="Flux (informatique)">Flux</a></li> <li><a href="/w/index.php?title=Top_type&action=edit&redlink=1" class="new" title="Top type (page inexistante)">Top</a> <a href="https://en.wikipedia.org/wiki/Top_type" class="extiw" title="en:Top type"><span class="indicateur-langue" title="Article en anglais : « Top type »">(en)</span></a></li> <li><a href="/w/index.php?title=Type_class&action=edit&redlink=1" class="new" title="Type class (page inexistante)">Type class</a> <a href="https://en.wikipedia.org/wiki/Type_class" class="extiw" title="en:Type class"><span class="indicateur-langue" title="Article en anglais : « Type class »">(en)</span></a></li> <li><a href="/wiki/Type_unit%C3%A9" title="Type unité">Type unité</a></li> <li><a href="/wiki/Void" title="Void">Void</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="">Articles liés</th> <td class="navbox-list" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Type_abstrait" title="Type abstrait">Type abstrait</a></li> <li><a href="/wiki/Structure_de_donn%C3%A9es" title="Structure de données">Structure de données</a></li> <li><a href="/wiki/G%C3%A9n%C3%A9ricit%C3%A9" title="Généricité">Généricité</a></li> <li><a href="/w/index.php?title=Kind_(type_theory)&action=edit&redlink=1" class="new" title="Kind (type theory) (page inexistante)">Kind</a> <a href="https://en.wikipedia.org/wiki/Kind_(type_theory)" class="extiw" title="en:Kind (type theory)"><span class="indicateur-langue" title="Article en anglais : « Kind (type theory) »">(en)</span></a> <ul><li><a href="/wiki/M%C3%A9taclasse" title="Métaclasse">Métaclasse</a></li></ul></li> <li><a href="/w/index.php?title=Parametric_polymorphism&action=edit&redlink=1" class="new" title="Parametric polymorphism (page inexistante)">Parametric polymorphism</a> <a href="https://en.wikipedia.org/wiki/Parametric_polymorphism" class="extiw" title="en:Parametric polymorphism"><span class="indicateur-langue" title="Article en anglais : « Parametric polymorphism »">(en)</span></a></li> <li><a href="/w/index.php?title=Primitive_data_type&action=edit&redlink=1" class="new" title="Primitive data type (page inexistante)">Primitive data type</a> <a href="https://en.wikipedia.org/wiki/Primitive_data_type" class="extiw" title="en:Primitive data type"><span class="indicateur-langue" title="Article en anglais : « Primitive data type »">(en)</span></a></li> <li><a href="/wiki/Interface_(programmation_orient%C3%A9e_objet)" title="Interface (programmation orientée objet)">Interface</a></li> <li><a href="/w/index.php?title=Subtyping&action=edit&redlink=1" class="new" title="Subtyping (page inexistante)">Subtyping</a> <a href="https://en.wikipedia.org/wiki/Subtyping" class="extiw" title="en:Subtyping"><span class="indicateur-langue" title="Article en anglais : « Subtyping »">(en)</span></a></li> <li><a href="/w/index.php?title=Type_constructor&action=edit&redlink=1" class="new" title="Type constructor (page inexistante)">Type constructor</a> <a href="https://en.wikipedia.org/wiki/Type_constructor" class="extiw" title="en:Type constructor"><span class="indicateur-langue" title="Article en anglais : « Type constructor »">(en)</span></a></li> <li><a href="/wiki/Conversion_de_type" title="Conversion de type">Conversion de type</a></li> <li><a href="/w/index.php?title=Type_system&action=edit&redlink=1" class="new" title="Type system (page inexistante)">Type system</a> <a href="https://en.wikipedia.org/wiki/Type_system" class="extiw" title="en:Type system"><span class="indicateur-langue" title="Article en anglais : « Type system »">(en)</span></a></li></ul> </div></td> </tr> </tbody></table> </div> <ul id="bandeau-portail" class="bandeau-portail"><li><span class="bandeau-portail-element"><span class="bandeau-portail-icone"><span class="noviewer" typeof="mw:File"><a href="/wiki/Portail:Programmation_informatique" title="Portail de la programmation informatique"><img alt="icône décorative" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Circle-icons-dev.svg/24px-Circle-icons-dev.svg.png" decoding="async" width="24" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Circle-icons-dev.svg/36px-Circle-icons-dev.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Circle-icons-dev.svg/48px-Circle-icons-dev.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span></span> <span class="bandeau-portail-texte"><a href="/wiki/Portail:Programmation_informatique" 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