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class="vector-toc-numb">1.1.2</span> <span>Difference in storage</span> </div> </a> <ul id="toc-Difference_in_storage-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-In_Generics" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#In_Generics"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1.3</span> <span>In Generics</span> </div> </a> <ul id="toc-In_Generics-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Null_type" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Null_type"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Null type</span> </div> </a> <ul id="toc-Null_type-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> 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class="mw-page-title-main">Unit type</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="Go to an article in another language. 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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">This article is about the notion used in <a href="/wiki/Computer_programming" title="Computer programming">computer programming</a> and <a href="/wiki/Type_theory" title="Type theory">type theory</a>. For types of measurement units, see <a href="/wiki/Units_of_measurement" class="mw-redirect" title="Units of measurement">Units of measurement</a>. For other uses, see <a href="/wiki/Unit_(disambiguation)" class="mw-redirect mw-disambig" title="Unit (disambiguation)">Unit (disambiguation)</a>.</div> <p>In the area of <a href="/wiki/Mathematical_logic" title="Mathematical logic">mathematical logic</a> and <a href="/wiki/Computer_science" title="Computer science">computer science</a> known as <a href="/wiki/Type_theory" title="Type theory">type theory</a>, a <b>unit type</b> is a <a href="/wiki/Data_type" title="Data type">type</a> that allows only one value (and thus can hold no information). The carrier (underlying set) associated with a unit type can be any <a href="/wiki/Singleton_set" class="mw-redirect" title="Singleton set">singleton set</a>. There is an <a href="/wiki/Isomorphism" title="Isomorphism">isomorphism</a> between any two such sets, so it is customary to talk about <i>the</i> unit type and ignore the details of its value. One may also regard the unit type as the type of 0-<a href="/wiki/Tuple" title="Tuple">tuples</a>, i.e. the <a href="/wiki/Product_(category_theory)" title="Product (category theory)">product</a> of no types. </p><p>The unit type is the <a href="/wiki/Terminal_object" class="mw-redirect" title="Terminal object">terminal object</a> in the <a href="/wiki/Category_theory" title="Category theory">category</a> of types and typed functions. It should not be confused with the <i>zero</i> or <a href="/wiki/Empty_type" title="Empty type">empty type</a>, which allows <i>no</i> values and is the <a href="/wiki/Initial_object" class="mw-redirect" title="Initial object">initial object</a> in this category. Similarly, the <a href="/wiki/Boolean_data_type" title="Boolean data type">Boolean</a> is the type with <i>two</i> values. </p><p>The unit type is implemented in most <a href="/wiki/Functional_programming" title="Functional programming">functional programming</a> languages. The <a href="/wiki/Void_type" title="Void type">void type</a> that is used in some imperative programming languages serves some of its functions, but because its carrier set is empty, it has some limitations (as detailed below). </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="In_programming_languages">In programming languages</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Unit_type&action=edit&section=1" title="Edit section: In programming languages"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Several computer <a href="/wiki/Programming_language" title="Programming language">programming languages</a> provide a unit type to specify the result type of a <a href="/wiki/Function_(computer_science)" class="mw-redirect" title="Function (computer science)">function</a> with the sole purpose of causing a <a href="/wiki/Side_effect_(computer_science)" title="Side effect (computer science)">side effect</a>, and the argument type of a function that does not require arguments. </p> <ul><li>In <a href="/wiki/Haskell_(programming_language)" class="mw-redirect" title="Haskell (programming language)">Haskell</a>, <a href="/wiki/Rust_(programming_language)" title="Rust (programming language)">Rust</a>, and <a href="/wiki/Elm_(programming_language)" title="Elm (programming language)">Elm</a>, the unit type is called <code>()</code> and its only value is also <code>()</code>, reflecting the 0-tuple interpretation.</li> <li>In <a href="/wiki/ML_(programming_language)" title="ML (programming language)">ML</a> descendants (including <a href="/wiki/OCaml" title="OCaml">OCaml</a>, <a href="/wiki/Standard_ML" title="Standard ML">Standard ML</a>, and <a href="/wiki/F_Sharp_(programming_language)" title="F Sharp (programming language)">F#</a>), the type is called <code>unit</code> but the value is written as <code>()</code>.</li> <li>In <a href="/wiki/Scala_(programming_language)" title="Scala (programming language)">Scala</a>, the unit type is called <code>Unit</code> and its only value is written as <code>()</code>.</li> <li>In <a href="/wiki/Common_Lisp" title="Common Lisp">Common Lisp</a> the type named <style data-mw-deduplicate="TemplateStyles:r886049734">.mw-parser-output .monospaced{font-family:monospace,monospace}</style><span class="monospaced">NULL</span> is a unit type which has one value, namely the symbol <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734" /><span class="monospaced">NIL</span>. This should not be confused with the <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734" /><span class="monospaced">NIL</span> <i>type</i>, which is the <a href="/wiki/Bottom_type" title="Bottom type">bottom type</a>.</li> <li>In <a href="/wiki/Python_(programming_language)" title="Python (programming language)">Python</a>, there is a type called <code>NoneType</code> which allows the single value of <code>None</code>. In Python's optional static type annotations, this type is represented as <code>None</code>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></li> <li>In <a href="/wiki/Swift_(programming_language)" title="Swift (programming language)">Swift</a>, the unit type is called <code>Void</code> or <code>()</code> and its only value is also <code>()</code>, reflecting the 0-tuple interpretation.</li> <li>In <a href="/wiki/Java_(programming_language)" title="Java (programming language)">Java</a>, the unit type is called <code>Void</code> and its only value is <code>null</code>.</li> <li>In <a href="/wiki/Go_(programming_language)" title="Go (programming language)">Go</a>, the unit type is written <code>struct{}</code> and its value is <code>struct{}{}</code>.</li> <li>In <a href="/wiki/PHP" title="PHP">PHP</a>, the unit type is called null, which only value is NULL itself.</li> <li>In <a href="/wiki/JavaScript" title="JavaScript">JavaScript</a>, both <code>Null</code> (its only value is <code>null</code>) and <code>Undefined</code> (its only value is <code>undefined</code>) are built-in unit types.</li> <li>in <a href="/wiki/Kotlin_(programming_language)" title="Kotlin (programming language)">Kotlin</a>, <code>Unit</code> is a singleton with only one value: the <code>Unit</code> object.</li> <li>In <a href="/wiki/Ruby_(programming_language)" title="Ruby (programming language)">Ruby</a>, <code>nil</code> is the only instance of the <code>NilClass</code> class.</li> <li>In <a href="/wiki/C%2B%2B" title="C++">C++</a>, the <code>std::monostate</code> unit type was added in C++17. Before that, it is possible to define a custom unit type using an empty struct such as <code>struct empty{}</code>.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Void_type_as_unit_type">Void type as unit type</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Unit_type&action=edit&section=2" title="Edit section: Void type as unit type"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/wiki/C_(programming_language)" title="C (programming language)">C</a>, <a href="/wiki/C%2B%2B" title="C++">C++</a>, <a href="/wiki/C_Sharp_(programming_language)" title="C Sharp (programming language)">C#</a>, <a href="/wiki/D_(programming_language)" title="D (programming language)">D</a>, and <a href="/wiki/PHP" title="PHP">PHP</a>, <code><a href="/wiki/Void_return_type" class="mw-redirect" title="Void return type">void</a></code> is used to designate a function that does not return anything useful, or a function that accepts no arguments. The unit type in C is conceptually similar to an empty <code>struct</code>, but a struct without members is not allowed in the C language specification (this is allowed in C++). Instead, '<code>void</code>' is used in a manner that simulates some, but not all, of the properties of the unit type, as detailed below. Like most imperative languages, C allows functions that do not return a value; these are specified as having the void return type. Such functions are called procedures in other imperative languages like <a href="/wiki/Pascal_(programming_language)" title="Pascal (programming language)">Pascal</a>, where a syntactic distinction, instead of type-system distinction, is made between functions and procedures. </p> <div class="mw-heading mw-heading4"><h4 id="Difference_in_calling_convention">Difference in calling convention</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Unit_type&action=edit&section=3" title="Edit section: Difference in calling convention"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The first notable difference between a true unit type and the void type is that the unit type may always be the type of the argument to a function, but the void type cannot be the type of an argument in C, despite the fact that it may appear as the sole argument in the list. This problem is best illustrated by the following program, which is a compile-time error in C: </p> <div class="mw-highlight mw-highlight-lang-c mw-content-ltr" dir="ltr"><pre><span></span><span class="kt">void</span><span class="w"> </span><span class="nf">f</span><span class="p">(</span><span class="kt">void</span><span class="p">)</span><span class="w"> </span><span class="p">{}</span> <span class="kt">void</span><span class="w"> </span><span class="nf">g</span><span class="p">(</span><span class="kt">void</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">main</span><span class="p">(</span><span class="kt">void</span><span class="p">)</span> <span class="p">{</span> <span class="w"> </span><span class="n">f</span><span class="p">(</span><span class="n">g</span><span class="p">());</span><span class="w"> </span><span class="c1">// compile-time error here</span> <span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span> <span class="p">}</span> </pre></div> <p>This issue does not arise in most programming practice in C, because since the <code>void</code> type carries no information, it is useless to pass it anyway; but it may arise in <a href="/wiki/Generic_programming" title="Generic programming">generic programming</a>, such as C++ <a href="/wiki/Template_(programming)" class="mw-redirect" title="Template (programming)">templates</a>, where <code><a href="/wiki/Void_return_type" class="mw-redirect" title="Void return type">void</a></code> must be treated differently from other types. In C++ however, empty classes are allowed, so it is possible to implement a real unit type; the above example becomes compilable as: </p> <div class="mw-highlight mw-highlight-lang-cpp mw-content-ltr" dir="ltr"><pre><span></span><span class="k">class</span><span class="w"> </span><span class="nc">unit_type</span><span class="w"> </span><span class="p">{};</span> <span class="k">const</span><span class="w"> </span><span class="n">unit_type</span><span class="w"> </span><span class="n">the_unit</span><span class="p">;</span> <span class="n">unit_type</span><span class="w"> </span><span class="nf">f</span><span class="p">(</span><span class="n">unit_type</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">the_unit</span><span class="p">;</span><span class="w"> </span><span class="p">}</span> <span class="n">unit_type</span><span class="w"> </span><span class="nf">g</span><span class="p">(</span><span class="n">unit_type</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">the_unit</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">main</span><span class="p">()</span> <span class="p">{</span> <span class="w"> </span><span class="n">f</span><span class="p">(</span><span class="n">g</span><span class="p">(</span><span class="n">the_unit</span><span class="p">));</span> <span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span> <span class="p">}</span> </pre></div> <p>(For brevity, we're not worried in the above example whether <code>the_unit</code> is really a <a href="/wiki/Singleton_pattern" title="Singleton pattern">singleton</a>; see <a href="/wiki/Singleton_pattern" title="Singleton pattern">singleton pattern</a> for details on that issue.) </p> <div class="mw-heading mw-heading4"><h4 id="Difference_in_storage">Difference in storage</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Unit_type&action=edit&section=4" title="Edit section: Difference in storage"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The second notable difference is that the void type is special and can never be stored in a <a href="/wiki/Record_(computer_science)" title="Record (computer science)">record type</a>, i.e. in a struct or a class in C/C++. In contrast, the unit type can be stored in records in functional programming languages, i.e. it can appear as the type of a field; the above implementation of the unit type in C++ can also be stored. While this may seem a useless feature, it does allow one for instance to elegantly implement a <a href="/wiki/Set_(computer_science)" class="mw-redirect" title="Set (computer science)">set</a> as a <a href="/wiki/Associative_array" title="Associative array">map</a> to the unit type; in the absence of a unit type, one can still implement a set this way by storing some dummy value of another type for each key. </p> <div class="mw-heading mw-heading4"><h4 id="In_Generics">In Generics</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Unit_type&action=edit&section=5" title="Edit section: In Generics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In Java Generics, type parameters must be reference types. The wrapper type <code>Void</code> is often used when a unit type parameter is needed. Although the <code>Void</code> type can never have any instances, it does have one value, <code>null</code> (like all other reference types), so it acts as a unit type. In practice, any other non-instantiable type, e.g. <code>Math</code>, can also be used for this purpose, since they also have exactly one value, <code>null</code>. </p> <div class="mw-highlight mw-highlight-lang-java mw-content-ltr" dir="ltr"><pre><span></span><span class="kd">public</span><span class="w"> </span><span class="kd">static</span><span class="w"> </span><span class="n">Void</span><span class="w"> </span><span class="nf">f</span><span class="p">(</span><span class="n">Void</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">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span><span class="w"> </span><span class="p">}</span> <span class="kd">public</span><span class="w"> </span><span class="kd">static</span><span class="w"> </span><span class="n">Void</span><span class="w"> </span><span class="nf">g</span><span class="p">(</span><span class="n">Void</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">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span><span class="w"> </span><span class="p">}</span> <span class="kd">public</span><span class="w"> </span><span class="kd">static</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">main</span><span class="p">(</span><span class="n">String</span><span class="o">[]</span><span class="w"> </span><span class="n">args</span><span class="p">)</span> <span class="p">{</span> <span class="w"> </span><span class="n">f</span><span class="p">(</span><span class="n">g</span><span class="p">(</span><span class="kc">null</span><span class="p">));</span> <span class="p">}</span> </pre></div> <div class="mw-heading mw-heading3"><h3 id="Null_type">Null type</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Unit_type&action=edit&section=6" title="Edit section: Null type"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Statically typed languages give a type to every possible expression. They need to associate a type to the <b>null</b> expression. A type will be defined for <b>null</b> and it will only have this value. </p><p>For example in D, it's possible to declare functions that may only return <b>null</b>: </p> <div class="mw-highlight mw-highlight-lang-d mw-content-ltr" dir="ltr"><pre><span></span><span class="k">typeof</span><span class="p">(</span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="n">returnThatSpecialThing</span><span class="p">(){</span> <span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span> <span class="p">}</span> </pre></div> <p><b>null</b> is the only value that <b>typeof(null)</b>, a unit type, can have. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Unit_type&action=edit&section=7" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Singleton_pattern" title="Singleton pattern">Singleton pattern</a> (where a particular class has only one instance, but narrowly-typed non-nullable references to it are usually not held by other classes)</li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Unit_type&action=edit&section=8" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFvan_RossumLevkivskyi" class="citation web cs1">van Rossum, Guido; Levkivskyi, Ivan. <a rel="nofollow" class="external text" href="https://peps.python.org/pep-0484/#using-none">"PEP 483 - Using None"</a>. <i>Python Enhancement Proposals</i>. Python Software Foundation<span class="reference-accessdate">. Retrieved <span class="nowrap">2 March</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Python+Enhancement+Proposals&rft.atitle=PEP+483+-+Using+None&rft.aulast=van+Rossum&rft.aufirst=Guido&rft.au=Levkivskyi%2C+Ivan&rft_id=https%3A%2F%2Fpeps.python.org%2Fpep-0484%2F%23using-none&rfr_id=info%3Asid%2Fen.wikipedia.org%3AUnit+type" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Unit_type&action=edit&section=9" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFPierce2002" class="citation book cs1"><a href="/wiki/Benjamin_C._Pierce" title="Benjamin C. Pierce">Pierce, Benjamin C.</a> (2002). <i><a href="/wiki/Types_and_Programming_Languages" title="Types and Programming Languages">Types and Programming Languages</a></i>. <a href="/wiki/MIT_Press" title="MIT Press">MIT Press</a>. pp. <span class="nowrap">118–</span>119. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-262-16209-1" title="Special:BookSources/0-262-16209-1"><bdi>0-262-16209-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Types+and+Programming+Languages&rft.pages=%3Cspan+class%3D%22nowrap%22%3E118-%3C%2Fspan%3E119&rft.pub=MIT+Press&rft.date=2002&rft.isbn=0-262-16209-1&rft.aulast=Pierce&rft.aufirst=Benjamin+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AUnit+type" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="https://ncatlab.org/nlab/show/unit+type">unit type</a> at the <a href="/wiki/NLab" 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title="Complex data type">Complex</a></li> <li><a href="/wiki/Decimal_data_type" title="Decimal data type">Decimal</a></li> <li><a href="/wiki/Fixed-point_arithmetic" title="Fixed-point arithmetic">Fixed point</a></li> <li><a href="/wiki/Floating-point_arithmetic" title="Floating-point arithmetic">Floating point</a> <ul><li>Reduced precision <ul><li><a href="/wiki/Minifloat" title="Minifloat">Minifloat</a></li> <li><a href="/wiki/Half-precision_floating-point_format" title="Half-precision floating-point format">Half precision</a></li> <li><a href="/wiki/Bfloat16_floating-point_format" title="Bfloat16 floating-point format">bfloat16</a></li></ul></li> <li><a href="/wiki/Single-precision_floating-point_format" title="Single-precision floating-point format">Single precision</a></li> <li><a href="/wiki/Double-precision_floating-point_format" title="Double-precision floating-point format">Double precision</a></li> <li><a href="/wiki/Quadruple-precision_floating-point_format" title="Quadruple-precision floating-point format">Quadruple precision</a></li> <li><a href="/wiki/Octuple-precision_floating-point_format" title="Octuple-precision floating-point format">Octuple precision</a></li> <li><a href="/wiki/Extended_precision" title="Extended precision">Extended precision</a> <ul><li><a href="/wiki/Long_double" title="Long double">Long double</a></li></ul></li></ul></li> <li><a href="/wiki/Integer_(computer_science)" title="Integer (computer science)">Integer</a> <ul><li><a href="/wiki/Signedness" title="Signedness">signedness</a></li></ul></li> <li><a href="/wiki/Interval_arithmetic#Implementations" title="Interval arithmetic">Interval</a></li> <li><a href="/wiki/Rational_data_type" title="Rational data type">Rational</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Pointer_(computer_programming)" title="Pointer (computer programming)">Pointer</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/Memory_address" title="Memory address">Address</a> <ul><li><a href="/wiki/Physical_address" title="Physical address">physical</a></li> <li><a href="/wiki/Virtual_address_space" title="Virtual address space">virtual</a></li></ul></li> <li><a href="/wiki/Reference_(computer_science)" title="Reference (computer science)">Reference</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Plain_text" title="Plain text">Text</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/Character_(computing)" title="Character (computing)">Character</a></li> <li><a href="/wiki/String_(computer_science)" title="String (computer science)">String</a> <ul><li><a href="/wiki/Null-terminated_string" title="Null-terminated string">null-terminated</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Composite_data_type" title="Composite data type">Composite</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/Algebraic_data_type" title="Algebraic data type">Algebraic data type</a> <ul><li><a href="/wiki/Generalized_algebraic_data_type" title="Generalized algebraic data type">generalized</a></li></ul></li> <li><a href="/wiki/Array_data_type" class="mw-redirect" title="Array data type">Array</a></li> <li><a href="/wiki/Associative_array" title="Associative array">Associative array</a></li> <li><a href="/wiki/Class_(computer_programming)" title="Class (computer programming)">Class</a></li> <li><a href="/wiki/Dependent_type" title="Dependent type">Dependent</a></li> <li><a href="/wiki/Intuitionistic_type_theory#Equality_type" title="Intuitionistic type theory">Equality</a></li> <li><a href="/wiki/Inductive_type" title="Inductive type">Inductive</a></li> <li><a href="/wiki/Intersection_type" title="Intersection type">Intersection</a></li> <li><a href="/wiki/List_(abstract_data_type)" title="List (abstract data type)">List</a></li> <li><a href="/wiki/Object_(computer_science)" title="Object (computer science)">Object</a> <ul><li><a href="/wiki/Metaobject" title="Metaobject">metaobject</a></li></ul></li> <li><a href="/wiki/Option_type" title="Option type">Option type</a></li> <li><a href="/wiki/Product_type" title="Product type">Product</a></li> <li><a href="/wiki/Record_(computer_science)" title="Record (computer science)">Record or Struct</a></li> <li><a href="/wiki/Refinement_type" title="Refinement type">Refinement</a></li> <li><a href="/wiki/Set_(abstract_data_type)" title="Set (abstract data type)">Set</a></li> <li><a href="/wiki/Union_type" title="Union type">Union</a> <ul><li><a href="/wiki/Tagged_union" title="Tagged union">tagged</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</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/Boolean_data_type" title="Boolean data type">Boolean</a></li> <li><a href="/wiki/Bottom_type" title="Bottom type">Bottom type</a></li> <li><a href="/wiki/Container_(abstract_data_type)" title="Container (abstract data type)">Collection</a></li> <li><a href="/wiki/Enumerated_type" title="Enumerated type">Enumerated type</a></li> <li><a href="/wiki/Exception_handling" title="Exception handling">Exception</a></li> <li><a href="/wiki/Function_type" title="Function type">Function type</a></li> <li><a href="/wiki/Opaque_data_type" title="Opaque data type">Opaque data type</a></li> <li><a href="/wiki/Recursive_data_type" title="Recursive data type">Recursive data type</a></li> <li><a href="/wiki/Semaphore_(programming)" title="Semaphore (programming)">Semaphore</a></li> <li><a href="/wiki/Stream_(computing)" title="Stream (computing)">Stream</a></li> <li><a href="/wiki/Strongly_typed_identifier" title="Strongly typed identifier">Strongly typed identifier</a></li> <li><a href="/wiki/Top_type" title="Top type">Top type</a></li> <li><a href="/wiki/Type_class" title="Type class">Type class</a></li> <li><a href="/wiki/Empty_type" title="Empty type">Empty type</a></li> <li><a class="mw-selflink selflink">Unit type</a></li> <li><a href="/wiki/Void_type" title="Void type">Void</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related<br />topics</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/Abstract_data_type" title="Abstract data type">Abstract data type</a></li> <li><a href="/wiki/Boxing_(computer_science)" class="mw-redirect" title="Boxing (computer science)">Boxing</a></li> <li><a href="/wiki/Data_structure" title="Data structure">Data structure</a></li> <li><a href="/wiki/Generic_programming" title="Generic programming">Generic</a></li> <li><a href="/wiki/Kind_(type_theory)" title="Kind (type theory)">Kind</a> <ul><li><a href="/wiki/Metaclass" title="Metaclass">metaclass</a></li></ul></li> <li><a href="/wiki/Parametric_polymorphism" title="Parametric polymorphism">Parametric polymorphism</a></li> <li><a href="/wiki/Primitive_data_type" title="Primitive data type">Primitive data type</a></li> <li><a href="/wiki/Interface_(object-oriented_programming)" title="Interface (object-oriented programming)">Interface</a></li> <li><a href="/wiki/Subtyping" title="Subtyping">Subtyping</a></li> <li><a href="/wiki/Type_constructor" title="Type constructor">Type constructor</a></li> <li><a href="/wiki/Type_conversion" title="Type conversion">Type conversion</a></li> <li><a href="/wiki/Type_system" title="Type system">Type system</a></li> <li><a href="/wiki/Type_theory" title="Type theory">Type theory</a></li> 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