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class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" 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<div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Universal subtype in logic and computer science</div> <p>In <a href="/wiki/Type_theory" title="Type theory">type theory</a>, a theory within <a href="/wiki/Mathematical_logic" title="Mathematical logic">mathematical logic</a>, the <b>bottom type</b> of a type system is the type that is a <a href="/wiki/Subtyping" title="Subtyping">subtype</a> of all other types.<sup id="cite_ref-bounded_1-0" class="reference"><a href="#cite_note-bounded-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Where such a type exists, it is often represented with the <a href="/wiki/Up_tack" title="Up tack">up tack</a> (⊥) symbol. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Relation_with_the_empty_type">Relation with the empty type</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bottom_type&action=edit&section=1" title="Edit section: Relation with the empty type"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>When the bottom type is <a href="/wiki/Type_inhabitation" title="Type inhabitation">uninhabited</a>, a function whose return type is bottom cannot return any value, not even the lone value of a <a href="/wiki/Unit_type" title="Unit type">unit type</a>. In such a language, the bottom type may therefore be known as the <b>zero</b>, <b>never</b> or <a href="/wiki/Empty_type" title="Empty type">empty type</a> which, in the <a href="/wiki/Curry%E2%80%93Howard_correspondence" title="Curry–Howard correspondence">Curry–Howard correspondence</a>, corresponds to falsity. </p><p>However, when the bottom type is inhabited, it is then different from the empty type. </p> <div class="mw-heading mw-heading2"><h2 id="Computer_science_applications">Computer science applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bottom_type&action=edit&section=2" title="Edit section: Computer science applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In subtyping systems, the bottom type is a subtype of all types.<sup id="cite_ref-bounded_1-1" class="reference"><a href="#cite_note-bounded-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> It is dual to the <a href="/wiki/Top_type" title="Top type">top type</a>, which spans all possible values in a system. </p><p>If a type system is <a href="/wiki/Type_safety" title="Type safety">sound</a>, the bottom type is uninhabited and a term of bottom type represents a logical contradiction. In such systems, typically no distinction is drawn between the bottom type and the <a href="/wiki/Empty_type" title="Empty type">empty type</a>, and the terms may be used interchangeably. </p><p>If the bottom type is inhabited, its term(s) typically correspond to error conditions such as undefined behavior, infinite recursion, or unrecoverable errors. </p><p>In <i>Bounded Quantification with Bottom</i>,<sup id="cite_ref-bounded_1-2" class="reference"><a href="#cite_note-bounded-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Pierce says that "Bot" has many uses: </p> <ol><li>In a language with <a href="/wiki/Exception_handling" title="Exception handling">exceptions</a>, a natural type for the raise construct is <i>raise ∈ exception -> Bot</i>, and similarly for other control structures. Intuitively, Bot here is the type of computations that do not return an answer.</li> <li>Bot is useful in typing the "leaf nodes" of polymorphic data structures. For example, List(Bot) is a good type for nil.</li> <li>Bot is a natural type for the "<a href="/wiki/Null_pointer" title="Null pointer">null pointer</a>" value (a pointer which does not point to any object) of languages like Java: in <a href="/wiki/Java_(programming_language)" title="Java (programming language)">Java</a>, the <i>null type</i> is the universal subtype of <a href="/wiki/Reference_type" class="mw-redirect" title="Reference type">reference types</a>. <code>null</code> is the only value of the null type; and it can be cast to any reference type.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> However, the null type is not a bottom type as described above, it is not a subtype of <code>int</code> and other primitive types.</li> <li>A type system including both Top and Bot seems to be a natural target for <a href="/wiki/Type_inference" title="Type inference">type inference</a>, allowing the constraints on an omitted type parameter to be captured by a pair of bounds: we write S<:X<:T to mean "the value of X must lie somewhere between S and T." In such a scheme, a completely unconstrained parameter is bounded below by Bot and above by Top.</li></ol> <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=Bottom_type&action=edit&section=3" title="Edit section: In programming languages"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Most commonly used languages don't have a way to denote the bottom type. There are a few notable exceptions. </p><p>In <a href="/wiki/Haskell_(programming_language)" class="mw-redirect" title="Haskell (programming language)">Haskell</a>, the bottom type is called <code>Void</code>.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>In <a href="/wiki/Common_Lisp" title="Common Lisp">Common Lisp</a> the type <code>NIL</code>, contains no values and is a subtype of every type.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> The type named <code>NIL</code> is sometimes confused with the type named <code>NULL</code>, which has one value, namely the symbol <code>NIL</code> itself. </p><p>In <a href="/wiki/Scala_(programming_language)" title="Scala (programming language)">Scala</a>, the bottom type is denoted as <code>Nothing</code>. Besides its use for functions that just throw exceptions or otherwise don't return normally, it's also used for <a href="/wiki/Covariance_and_contravariance_(computer_science)" title="Covariance and contravariance (computer science)">covariant</a> <a href="/wiki/Parametric_polymorphism#Parametric_polymorphism" title="Parametric polymorphism">parameterized types</a>. For example, Scala's List is a covariant type constructor, so <code>List[Nothing]</code> is a subtype of <code>List[A]</code> for all types A. So Scala's <code>Nil</code>, the object for marking the end of a list of any type, belongs to the type <code>List[Nothing]</code>. </p><p>In <a href="/wiki/Rust_(programming_language)" title="Rust (programming language)">Rust</a>, the bottom type is called the never type and is denoted by <code>!</code>. It is present in the type signature of functions guaranteed to never return, for example by calling <code>panic!()</code> or looping forever. It is also the type of certain control-flow keywords, such as <code>break</code> and <code>return</code>, which do not produce a value but are nonetheless usable as expressions.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>In <a href="/wiki/Ceylon_(programming_language)" title="Ceylon (programming language)">Ceylon</a>, the bottom type is <code>Nothing</code>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> It is comparable to <code>Nothing</code> in Scala and represents the intersection of all other types as well as an empty set. </p><p>In <a href="/wiki/Julia_(programming_language)" title="Julia (programming language)">Julia</a>, the bottom type is <code>Union{}</code>.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>In <a href="/wiki/TypeScript" title="TypeScript">TypeScript</a>, the bottom type is <code>never</code>.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>In <a href="/wiki/JavaScript" title="JavaScript">JavaScript</a> with <a href="/wiki/Google_Closure_Tools" title="Google Closure Tools">Closure Compiler</a> annotations, the bottom type is <code>!Null</code> (literally, a non-null member of the <code>Null</code> <a href="/wiki/Unit_type" title="Unit type">unit type</a>). </p><p>In <a href="/wiki/PHP" title="PHP">PHP</a>, the bottom type is <code>never</code>. </p><p>In <a href="/wiki/Python_(programming_language)" title="Python (programming language)">Python</a>'s optional static type annotations, the general bottom type is <code>typing.Never</code> (introduced in version 3.11),<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> while <code>typing.NoReturn</code> (introduced in version 3.5) can be used as the return type of non-returning functions specifically (and doubled as the general bottom type prior to the introduction of <code>Never</code>).<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>In <a href="/wiki/Kotlin_(programming_language)" title="Kotlin (programming language)">Kotlin</a>, the bottom type is <code>Nothing</code>.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>In <a href="/wiki/D_(programming_language)" title="D (programming language)">D</a>, the bottom type is <code>noreturn</code>.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>In <a href="/wiki/Dart_(programming_language)" title="Dart (programming language)">Dart</a>, since version 2.12 with the <a rel="nofollow" class="external text" href="https://medium.com/dartlang/announcing-dart-2-12-499a6e689c87">sound null safety update</a>, the <code>Never</code> type was introduced as the bottom type. Before that, the bottom type used to be <code>Null</code>.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </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=Bottom_type&action=edit&section=4" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Contradiction" title="Contradiction">Contradiction</a></li> <li><a href="/wiki/Fail-stop" title="Fail-stop">Fail-stop</a></li> <li><a href="/wiki/NaN" title="NaN">NaN</a></li> <li><a href="/wiki/Top_type" title="Top type">Top type</a></li> <li><a href="/wiki/Unit_type" title="Unit type">Unit type</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bottom_type&action=edit&section=5" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-bounded-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-bounded_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-bounded_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-bounded_1-2"><sup><i><b>c</b></i></sup></a></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="CITEREFPierce1997" class="citation journal cs1">Pierce, Benjamin C. (1997). <a rel="nofollow" class="external text" href="http://www.cis.upenn.edu/~bcpierce/papers/bqb.ps">"Bounded Quantification with Bottom"</a>. <i>Indiana University CSCI Technical Report</i> (492): 1.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Indiana+University+CSCI+Technical+Report&rft.atitle=Bounded+Quantification+with+Bottom&rft.issue=492&rft.pages=1&rft.date=1997&rft.aulast=Pierce&rft.aufirst=Benjamin+C.&rft_id=http%3A%2F%2Fwww.cis.upenn.edu%2F~bcpierce%2Fpapers%2Fbqb.ps&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABottom+type" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation book cs1"><a rel="nofollow" class="external text" href="http://docs.oracle.com/javase/specs/jls/se5.0/html/typesValues.html#4.1">"Section 4.1: The Kinds of Types and Values"</a>. <i>Java Language Specification</i> (3rd ed.).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Section+4.1%3A+The+Kinds+of+Types+and+Values&rft.btitle=Java+Language+Specification&rft.edition=3rd&rft_id=http%3A%2F%2Fdocs.oracle.com%2Fjavase%2Fspecs%2Fjls%2Fse5.0%2Fhtml%2FtypesValues.html%234.1&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABottom+type" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://hackage.haskell.org/package/base-4.18.0.0/docs/Data-Void.html">"Data.Void"</a>. <i>Hackage</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2023-09-20</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Hackage&rft.atitle=Data.Void&rft_id=https%3A%2F%2Fhackage.haskell.org%2Fpackage%2Fbase-4.18.0.0%2Fdocs%2FData-Void.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABottom+type" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.lispworks.com/documentation/HyperSpec/Body/t_nil.htm">"Type NIL"</a>. <i>Common Lisp HyperSpec</i><span class="reference-accessdate">. Retrieved <span class="nowrap">25 October</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Common+Lisp+HyperSpec&rft.atitle=Type+NIL&rft_id=http%3A%2F%2Fwww.lispworks.com%2Fdocumentation%2FHyperSpec%2FBody%2Ft_nil.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABottom+type" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://doc.rust-lang.org/std/primitive.never.html">"Primitive Type never"</a>. <i>The Rust Standard Library Documentation</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2020-09-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+Rust+Standard+Library+Documentation&rft.atitle=Primitive+Type+never&rft_id=https%3A%2F%2Fdoc.rust-lang.org%2Fstd%2Fprimitive.never.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABottom+type" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://ceylon-lang.org/documentation/spec/html/typesystem.html#bottomtype">"Chapter 3. Type system — 3.2.5. The bottom type"</a>. <i>The Ceylon Language</i>. Red Hat, Inc<span class="reference-accessdate">. Retrieved <span class="nowrap">2017-02-19</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+Ceylon+Language&rft.atitle=Chapter+3.+Type+system+%E2%80%94+3.2.5.+The+bottom+type&rft_id=https%3A%2F%2Fceylon-lang.org%2Fdocumentation%2Fspec%2Fhtml%2Ftypesystem.html%23bottomtype&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABottom+type" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://docs.julialang.org/en/v1/base/base/#Union{}">"Essentials - The Julia Language"</a>, <i>The Julia Programming Language Documentation</i><span class="reference-accessdate">, retrieved <span class="nowrap">2021-08-13</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Julia+Programming+Language+Documentation&rft.atitle=Essentials+-+The+Julia+Language&rft_id=https%3A%2F%2Fdocs.julialang.org%2Fen%2Fv1%2Fbase%2Fbase%2F%23Union%7B%7D&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABottom+type" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://www.typescriptlang.org/docs/handbook/release-notes/typescript-2-0.html#the-never-type"><i>The never type, TypeScript 2.0 release notes</i></a>, Microsoft, 2016-10-06<span class="reference-accessdate">, retrieved <span class="nowrap">2019-11-01</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+never+type%2C+TypeScript+2.0+release+notes&rft.pub=Microsoft&rft.date=2016-10-06&rft_id=https%3A%2F%2Fwww.typescriptlang.org%2Fdocs%2Fhandbook%2Frelease-notes%2Ftypescript-2-0.html%23the-never-type&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABottom+type" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://github.com/microsoft/TypeScript-Handbook/blob/bb3564f4f06dd776d430198a137ae9058454d990/pages/release%20notes/TypeScript%202.0.md#the-never-type"><i>The never type, TypeScript 2.0 release notes, source code</i></a>, Microsoft, 2016-10-06<span class="reference-accessdate">, retrieved <span class="nowrap">2019-11-01</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+never+type%2C+TypeScript+2.0+release+notes%2C+source+code&rft.pub=Microsoft&rft.date=2016-10-06&rft_id=https%3A%2F%2Fgithub.com%2Fmicrosoft%2FTypeScript-Handbook%2Fblob%2Fbb3564f4f06dd776d430198a137ae9058454d990%2Fpages%2Frelease%2520notes%2FTypeScript%25202.0.md%23the-never-type&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABottom+type" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://docs.python.org/3.12/library/typing.html#typing.Never">"typing — Support for type hints — Python 3.12.0a0 documentation"</a>. <i>docs.python.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2024-03-02</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=docs.python.org&rft.atitle=typing+%E2%80%94+Support+for+type+hints+%E2%80%94+Python+3.12.0a0+documentation&rft_id=https%3A%2F%2Fdocs.python.org%2F3.12%2Flibrary%2Ftyping.html%23typing.Never&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABottom+type" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://docs.python.org/3/library/typing.html#typing.NoReturn"><i>typing.NoReturn, typing — Support for type hints, Python documentation</i></a>, Python Software Foundation<span class="reference-accessdate">, retrieved <span class="nowrap">2024-03-02</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=typing.NoReturn%2C+typing+%E2%80%94+Support+for+type+hints%2C+Python+documentation&rft.pub=Python+Software+Foundation&rft_id=https%3A%2F%2Fdocs.python.org%2F3%2Flibrary%2Ftyping.html%23typing.NoReturn&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABottom+type" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://kotlinlang.org/api/latest/jvm/stdlib/kotlin/-nothing.html"><i>Nothing</i></a><span class="reference-accessdate">, retrieved <span class="nowrap">2020-05-15</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Nothing&rft_id=https%3A%2F%2Fkotlinlang.org%2Fapi%2Flatest%2Fjvm%2Fstdlib%2Fkotlin%2F-nothing.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABottom+type" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://dlang.org/spec/type.html#noreturn">"Types - D Programming Language"</a>. <i>dlang.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2022-10-20</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=dlang.org&rft.atitle=Types+-+D+Programming+Language&rft_id=https%3A%2F%2Fdlang.org%2Fspec%2Ftype.html%23noreturn&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABottom+type" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://dart.dev/null-safety/understanding-null-safety#top-and-bottom"><i>Understanding null safety - top and bottom</i></a><span class="reference-accessdate">, retrieved <span class="nowrap">2022-04-13</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Understanding+null+safety+-+top+and+bottom&rft_id=https%3A%2F%2Fdart.dev%2Fnull-safety%2Funderstanding-null-safety%23top-and-bottom&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABottom+type" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://dart.dev/null-safety/understanding-null-safety#never-for-unreachable-code"><i>Understanding null safety - never for unreachable code</i></a><span class="reference-accessdate">, retrieved <span class="nowrap">2022-04-13</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Understanding+null+safety+-+never+for+unreachable+code&rft_id=https%3A%2F%2Fdart.dev%2Fnull-safety%2Funderstanding-null-safety%23never-for-unreachable-code&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABottom+type" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bottom_type&action=edit&section=6" title="Edit section: Further reading"><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>. <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.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%3ABottom+type" class="Z3988"></span></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output 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numeral system">Trit</a></li> <li><a href="/wiki/Ternary_numeral_system#Tryte" title="Ternary numeral system">Tryte</a></li> <li><a href="/wiki/Word_(computer_architecture)" title="Word (computer architecture)">Word</a></li> <li><a href="/wiki/Bit_array" title="Bit array">Bit array</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Numeric</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/Arbitrary-precision_arithmetic" title="Arbitrary-precision arithmetic">Arbitrary-precision or bignum</a></li> <li><a href="/wiki/Complex_data_type" 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 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class">Type class</a></li> <li><a href="/wiki/Empty_type" title="Empty type">Empty type</a></li> <li><a href="/wiki/Unit_type" title="Unit type">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 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