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<a href="#var-members">Variables</a> </div>
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<div class="title">Metafunction<div class="ingroups"><a class="el" href="group__group-concepts.html">Concepts</a></div></div> </div>
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<div class="contents">
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<a name="details" id="details"></a><h2 class="groupheader">Description</h2>
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<p>A <code>Metafunction</code> is a function that takes <code><a class="el" href="structboost_1_1hana_1_1type.html" title="C++ type in value-level representation.">hana::type</a></code>s as inputs and returns a <code><a class="el" href="structboost_1_1hana_1_1type.html" title="C++ type in value-level representation.">hana::type</a></code> as output. </p>
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<p>A <code>Metafunction</code> is an object satisfying the <a href="http://en.cppreference.com/w/cpp/named_req/FunctionObject">FunctionObject</a> concept, but with additional requirements. First, it must be possible to apply a <code>Metafunction</code> to arguments whose tag is <code><a class="el" href="structboost_1_1hana_1_1type__tag.html" title="Tag representing hana::type.">type_tag</a></code>, and the result of such an application must be an object whose tag is also <code><a class="el" href="structboost_1_1hana_1_1type__tag.html" title="Tag representing hana::type.">type_tag</a></code>. Note that <code><a class="el" href="structboost_1_1hana_1_1type.html" title="C++ type in value-level representation.">hana::type</a></code> and <code><a class="el" href="structboost_1_1hana_1_1basic__type.html" title="Base class of hana::type; used for pattern-matching.">hana::basic_type</a></code> are the only such types.</p>
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<p>Secondly, a <code>Metafunction</code> must provide a nested <code>::apply</code> template which allows performing the same type-level computation as is done by the call operator. In Boost.MPL parlance, a <code>Metafunction</code> <code>F</code> is hence a <a href="http://www.boost.org/doc/libs/release/libs/mpl/doc/refmanual/metafunction-class.html">MetafunctionClass</a> in addition to being a <code>FunctionObject</code>. Rigorously, the following must be satisfied by any object <code>f</code> of type <code>F</code> which is a <code>Metafunction</code>, and for arbitrary types <code>T...</code>: </p><div class="fragment"><div class="line">f(hana::type_c<T>...) == hana::type_c<<a class="code" href="group__group-functional.html#ga30027c383676084be151ef3c6cf2829f">F::apply</a><T...>::type></div>
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</div><!-- fragment --><p>Thirdly, to ease the inter-operation of values and types, <code>Metafunction</code>s must also allow being called with arguments that are not <code><a class="el" href="structboost_1_1hana_1_1type.html" title="C++ type in value-level representation.">hana::type</a></code>s. In that case, the result is equivalent to calling the metafunction on the types of the arguments. Rigorously, this means that for arbitrary objects <code>x...</code>, </p><div class="fragment"><div class="line">f(x...) == f(hana::type_c<decltype(x)>...)</div>
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</div><!-- fragment --><h2><a class="anchor" id="autotoc_md137"></a>
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Minimal complete definition</h2>
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<p>The <code>Metafunction</code> concept does not have a minimal complete definition in terms of tag-dispatched methods. Instead, the syntactic requirements documented above should be satisfied, and the <code>Metafunction</code> struct should be specialized explicitly in Hana's namespace.</p>
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<h2><a class="anchor" id="autotoc_md138"></a>
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Concrete models</h2>
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<p><code><a class="el" href="group__group-_metafunction.html#gaaa4f85cb8cbce21f5c04ef40ca35cc6a" title="Lift a MPL-style metafunction to a Metafunction.">hana::metafunction</a></code>, <code><a class="el" href="group__group-_metafunction.html#gacec153d7f86aa7cf1efd813b3fd212b4" title="Lift a MPL-style metafunction class to a Metafunction.">hana::metafunction_class</a></code>, <code><a class="el" href="group__group-_metafunction.html#ga246419f6c3263b648412f346106e6543" title="Lift a template to a Metafunction.">hana::template_</a></code></p>
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<h2><a class="anchor" id="autotoc_md139"></a>
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Rationale: Why aren't <tt>Metafunction</tt>s <tt>Comparable</tt>?</h2>
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<p>When seeing <code><a class="el" href="group__group-_metafunction.html#ga246419f6c3263b648412f346106e6543" title="Lift a template to a Metafunction.">hana::template_</a></code>, a question that naturally arises is whether <code>Metafunction</code>s should be made <code>Comparable</code>. Indeed, it would seem to make sense to compare two templates <code>F</code> and <code>G</code> with <code>template_<F> == template_<G></code>. However, in the case where <code>F</code> and/or <code>G</code> are alias templates, it makes sense to talk about two types of comparisons. The first one is <em>shallow</em> comparison, and it determines that two alias templates are equal if they are the same alias template. The second one is <em>deep</em> comparison, and it determines that two template aliases are equal if they alias the same type for any template argument. For example, given <code>F</code> and <code>G</code> defined as </p><div class="fragment"><div class="line"><span class="keyword">template</span> <<span class="keyword">typename</span> T></div>
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<div class="line"><span class="keyword">using</span> F = void;</div>
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<div class="line"> </div>
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<div class="line"><span class="keyword">template</span> <<span class="keyword">typename</span> T></div>
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<div class="line"><span class="keyword">using</span> G = void;</div>
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</div><!-- fragment --><p>shallow comparison would determine that <code>F</code> and <code>G</code> are different because they are two different template aliases, while deep comparison would determine that <code>F</code> and <code>G</code> are equal because they always expand to the same type, <code>void</code>. Unfortunately, deep comparison is impossible to implement because one would have to check <code>F</code> and <code>G</code> on all possible types. On the other hand, shallow comparison is not satisfactory because <code>Metafunction</code>s are nothing but functions on <code>type</code>s, and the equality of two functions is normally defined with deep comparison. Hence, we adopt a conservative stance and avoid providing comparison for <code>Metafunction</code>s. </p>
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<table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="var-members"></a>
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Variables</h2></td></tr>
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<tr class="memitem:ga246419f6c3263b648412f346106e6543"><td class="memTemplParams" colspan="2">template<template< typename ... > class F> </td></tr>
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<tr class="memitem:ga246419f6c3263b648412f346106e6543"><td class="memTemplItemLeft" align="right" valign="top">constexpr auto </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__group-_metafunction.html#ga246419f6c3263b648412f346106e6543">boost::hana::template_</a></td></tr>
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<tr class="memdesc:ga246419f6c3263b648412f346106e6543"><td class="mdescLeft"> </td><td class="mdescRight">Lift a template to a Metafunction. <a href="group__group-_metafunction.html#ga246419f6c3263b648412f346106e6543">More...</a><br /></td></tr>
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<tr class="separator:ga246419f6c3263b648412f346106e6543"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:gaaa4f85cb8cbce21f5c04ef40ca35cc6a"><td class="memTemplParams" colspan="2">template<template< typename ... > class F> </td></tr>
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<tr class="memitem:gaaa4f85cb8cbce21f5c04ef40ca35cc6a"><td class="memTemplItemLeft" align="right" valign="top">constexpr auto </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__group-_metafunction.html#gaaa4f85cb8cbce21f5c04ef40ca35cc6a">boost::hana::metafunction</a></td></tr>
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<tr class="memdesc:gaaa4f85cb8cbce21f5c04ef40ca35cc6a"><td class="mdescLeft"> </td><td class="mdescRight">Lift a MPL-style metafunction to a Metafunction. <a href="group__group-_metafunction.html#gaaa4f85cb8cbce21f5c04ef40ca35cc6a">More...</a><br /></td></tr>
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<tr class="separator:gaaa4f85cb8cbce21f5c04ef40ca35cc6a"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:gacec153d7f86aa7cf1efd813b3fd212b4"><td class="memTemplParams" colspan="2">template<typename F > </td></tr>
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<tr class="memitem:gacec153d7f86aa7cf1efd813b3fd212b4"><td class="memTemplItemLeft" align="right" valign="top">constexpr auto </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__group-_metafunction.html#gacec153d7f86aa7cf1efd813b3fd212b4">boost::hana::metafunction_class</a></td></tr>
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<tr class="memdesc:gacec153d7f86aa7cf1efd813b3fd212b4"><td class="mdescLeft"> </td><td class="mdescRight">Lift a MPL-style metafunction class to a Metafunction. <a href="group__group-_metafunction.html#gacec153d7f86aa7cf1efd813b3fd212b4">More...</a><br /></td></tr>
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<tr class="separator:gacec153d7f86aa7cf1efd813b3fd212b4"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:gaf7045fe6a627f88f5f646dad22d37aae"><td class="memItemLeft" align="right" valign="top">constexpr auto </td><td class="memItemRight" valign="bottom"><a class="el" href="group__group-_metafunction.html#gaf7045fe6a627f88f5f646dad22d37aae">boost::hana::integral</a></td></tr>
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<tr class="memdesc:gaf7045fe6a627f88f5f646dad22d37aae"><td class="mdescLeft"> </td><td class="mdescRight">Turn a <code>Metafunction</code> into a function taking <code>type</code>s and returning a default-constructed object. <a href="group__group-_metafunction.html#gaf7045fe6a627f88f5f646dad22d37aae">More...</a><br /></td></tr>
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<tr class="separator:gaf7045fe6a627f88f5f646dad22d37aae"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ga6d4093318f46472e62f9539a4dc998a9"><td class="memTemplParams" colspan="2">template<template< typename ... > class F> </td></tr>
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<tr class="memitem:ga6d4093318f46472e62f9539a4dc998a9"><td class="memTemplItemLeft" align="right" valign="top">constexpr auto </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__group-_metafunction.html#ga6d4093318f46472e62f9539a4dc998a9">boost::hana::trait</a> = <a class="el" href="group__group-_metafunction.html#gaf7045fe6a627f88f5f646dad22d37aae">hana::integral</a>(<a class="el" href="group__group-_metafunction.html#gaaa4f85cb8cbce21f5c04ef40ca35cc6a">hana::metafunction</a><F>)</td></tr>
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<tr class="memdesc:ga6d4093318f46472e62f9539a4dc998a9"><td class="mdescLeft"> </td><td class="mdescRight">Alias to <code>integral(metafunction<F>)</code>, provided for convenience. <a href="group__group-_metafunction.html#ga6d4093318f46472e62f9539a4dc998a9">More...</a><br /></td></tr>
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<tr class="separator:ga6d4093318f46472e62f9539a4dc998a9"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
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<h2 class="groupheader">Variable Documentation</h2>
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<a id="ga246419f6c3263b648412f346106e6543"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ga246419f6c3263b648412f346106e6543">◆ </a></span>template_</h2>
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template<template< typename ... > class F> </div>
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<td class="memname">constexpr auto boost::hana::template_</td>
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<span class="mlabels"><span class="mlabel">constexpr</span></span> </td>
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<p><code>#include <<a class="el" href="fwd_2type_8hpp.html">boost/hana/fwd/type.hpp</a>></code></p>
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<b>Initial value:</b><div class="fragment"><div class="line">= [](basic_type<T>...) {</div>
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<div class="line"> <span class="keywordflow">return</span> hana::type_c<F<T...>>;</div>
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<div class="line"> }</div>
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</div><!-- fragment -->
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<p>Lift a template to a Metafunction. </p>
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<p>Given a template class or template alias <code>f</code>, <code>template_<f></code> is a <code>Metafunction</code> satisfying </p><div class="fragment"><div class="line">template_<f>(type_c<x>...) == type_c<f<x...>></div>
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<div class="line">decltype(template_<f>)::<a class="code" href="group__group-functional.html#ga30027c383676084be151ef3c6cf2829f">apply</a><x...>::type == f<x...></div>
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</div><!-- fragment --><dl class="section note"><dt>Note</dt><dd>In a SFINAE context, the expression <code>template_<f>(type_c<x>...)</code> is valid whenever the expression <code>f<x...></code> is valid.</dd></dl>
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<h2><a class="anchor" id="autotoc_md405"></a>
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Example</h2>
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<div class="fragment"><div class="line"><span class="comment">// Copyright Louis Dionne 2013-2017</span></div>
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<div class="line"><span class="comment">// Distributed under the Boost Software License, Version 1.0.</span></div>
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<div class="line"><span class="comment">// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)</span></div>
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<div class="line"> </div>
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<div class="line"><span class="preprocessor">#include <<a class="code" href="assert_8hpp.html">boost/hana/assert.hpp</a>></span></div>
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<div class="line"><span class="preprocessor">#include <<a class="code" href="equal_8hpp.html">boost/hana/equal.hpp</a>></span></div>
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<div class="line"><span class="preprocessor">#include <<a class="code" href="type_8hpp.html">boost/hana/type.hpp</a>></span></div>
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<div class="line"> </div>
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<div class="line"><span class="preprocessor">#include <type_traits></span></div>
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<div class="line"><span class="keyword">namespace </span>hana = <a class="code" href="namespaceboost_1_1hana.html">boost::hana</a>;</div>
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<div class="line"> </div>
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<div class="line"> </div>
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<div class="line"><span class="keyword">template</span> <<span class="keyword">typename</span> ...> <span class="keyword">struct </span>f;</div>
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<div class="line"><span class="keyword">struct </span>x;</div>
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<div class="line"><span class="keyword">struct </span>y;</div>
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<div class="line"> </div>
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<div class="line"><a class="code" href="group__group-assertions.html#ga2c5006540936d9f8880e3a39f4fcc035">BOOST_HANA_CONSTANT_CHECK</a>(hana::template_<f>() == hana::type_c<f<>>);</div>
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<div class="line"><a class="code" href="group__group-assertions.html#ga2c5006540936d9f8880e3a39f4fcc035">BOOST_HANA_CONSTANT_CHECK</a>(hana::template_<f>(hana::type_c<x>) == hana::type_c<f<x>>);</div>
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<div class="line"><a class="code" href="group__group-assertions.html#ga2c5006540936d9f8880e3a39f4fcc035">BOOST_HANA_CONSTANT_CHECK</a>(hana::template_<f>(hana::type_c<x>, hana::type_c<y>) == hana::type_c<f<x, y>>);</div>
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<div class="line"> </div>
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<div class="line">static_assert(std::is_same<</div>
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<div class="line"> decltype(hana::template_<f>)::apply<x, y>::type,</div>
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<div class="line"> f<x, y></div>
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<div class="line">>::<a class="code" href="group__group-_constant.html#ga1687520692a6b0c49e3a69de2980f388">value</a>, <span class="stringliteral">""</span>);</div>
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<div class="line"> </div>
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<div class="line"><span class="keywordtype">int</span> main() { }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#gaaa4f85cb8cbce21f5c04ef40ca35cc6a">◆ </a></span>metafunction</h2>
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<td class="memname">constexpr auto boost::hana::metafunction</td>
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<span class="mlabels"><span class="mlabel">constexpr</span></span> </td>
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<p><code>#include <<a class="el" href="fwd_2type_8hpp.html">boost/hana/fwd/type.hpp</a>></code></p>
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<b>Initial value:</b><div class="fragment"><div class="line">= [](basic_type<T>...) {</div>
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<div class="line"> <span class="keywordflow">return</span> hana::type_c<<span class="keyword">typename</span> F<T...>::type>;</div>
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<div class="line"> }</div>
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</div><!-- fragment -->
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<p>Lift a MPL-style metafunction to a Metafunction. </p>
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<p>Given a MPL-style metafunction, <code>metafunction<f></code> is a <code>Metafunction</code> satisfying </p><div class="fragment"><div class="line">metafunction<f>(type_c<x>...) == type_c<f<x...>::type></div>
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<div class="line">decltype(metafunction<f>)::<a class="code" href="group__group-functional.html#ga30027c383676084be151ef3c6cf2829f">apply</a><x...>::type == f<x...>::type</div>
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</div><!-- fragment --><dl class="section note"><dt>Note</dt><dd>In a SFINAE context, the expression <code>metafunction<f>(type_c<x>...)</code> is valid whenever the expression <code>f<x...>::type</code> is valid.</dd></dl>
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<h2><a class="anchor" id="autotoc_md406"></a>
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Example</h2>
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<div class="fragment"><div class="line"><span class="comment">// Copyright Louis Dionne 2013-2017</span></div>
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<div class="line"><span class="comment">// Distributed under the Boost Software License, Version 1.0.</span></div>
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<div class="line"><span class="comment">// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)</span></div>
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<div class="line"> </div>
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<div class="line"><span class="preprocessor">#include <<a class="code" href="assert_8hpp.html">boost/hana/assert.hpp</a>></span></div>
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<div class="line"><span class="preprocessor">#include <<a class="code" href="equal_8hpp.html">boost/hana/equal.hpp</a>></span></div>
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<div class="line"><span class="preprocessor">#include <<a class="code" href="type_8hpp.html">boost/hana/type.hpp</a>></span></div>
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<div class="line"> </div>
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<div class="line"><span class="preprocessor">#include <type_traits></span></div>
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<div class="line"><span class="keyword">namespace </span>hana = <a class="code" href="namespaceboost_1_1hana.html">boost::hana</a>;</div>
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<div class="line"> </div>
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<div class="line"> </div>
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<div class="line"><span class="keyword">template</span> <<span class="keyword">typename</span> ...> <span class="keyword">struct </span>f { <span class="keyword">struct </span>type; };</div>
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<div class="line"><span class="keyword">struct </span>x;</div>
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<div class="line"><span class="keyword">struct </span>y;</div>
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<div class="line"> </div>
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<div class="line"><a class="code" href="group__group-assertions.html#ga2c5006540936d9f8880e3a39f4fcc035">BOOST_HANA_CONSTANT_CHECK</a>(hana::metafunction<f>() == hana::type_c<f<>::type>);</div>
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<div class="line"><a class="code" href="group__group-assertions.html#ga2c5006540936d9f8880e3a39f4fcc035">BOOST_HANA_CONSTANT_CHECK</a>(hana::metafunction<f>(hana::type_c<x>) == hana::type_c<f<x>::type>);</div>
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<div class="line"><a class="code" href="group__group-assertions.html#ga2c5006540936d9f8880e3a39f4fcc035">BOOST_HANA_CONSTANT_CHECK</a>(hana::metafunction<f>(hana::type_c<x>, hana::type_c<y>) == hana::type_c<f<x, y>::type>);</div>
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<div class="line"> </div>
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<div class="line">static_assert(std::is_same<</div>
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<div class="line"> decltype(hana::metafunction<f>)::apply<x, y>::type,</div>
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<div class="line"> f<x, y>::type</div>
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<div class="line">>::<a class="code" href="group__group-_constant.html#ga1687520692a6b0c49e3a69de2980f388">value</a>, <span class="stringliteral">""</span>);</div>
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<div class="line"> </div>
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<div class="line"><span class="keywordtype">int</span> main() { }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#gacec153d7f86aa7cf1efd813b3fd212b4">◆ </a></span>metafunction_class</h2>
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<td class="memname">constexpr auto boost::hana::metafunction_class</td>
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<span class="mlabels"><span class="mlabel">constexpr</span></span> </td>
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<p><code>#include <<a class="el" href="fwd_2type_8hpp.html">boost/hana/fwd/type.hpp</a>></code></p>
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<b>Initial value:</b><div class="fragment"><div class="line">= [](basic_type<T>...) {</div>
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<div class="line"> <span class="keywordflow">return</span> hana::type_c<<span class="keyword">typename</span> F::template <a class="code" href="group__group-functional.html#ga30027c383676084be151ef3c6cf2829f">apply</a><T...>::type>;</div>
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<div class="line"> }</div>
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</div><!-- fragment -->
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<p>Lift a MPL-style metafunction class to a Metafunction. </p>
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<p>Given a MPL-style metafunction class, <code>metafunction_class<f></code> is a <code>Metafunction</code> satisfying </p><div class="fragment"><div class="line">metafunction_class<f>(type_c<x>...) == type_c<<a class="code" href="group__group-functional.html#ga30027c383676084be151ef3c6cf2829f">f::apply</a><x...>::type></div>
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<div class="line">decltype(metafunction_class<f>)::<a class="code" href="group__group-functional.html#ga30027c383676084be151ef3c6cf2829f">apply</a><x...>::type == f::<a class="code" href="group__group-functional.html#ga30027c383676084be151ef3c6cf2829f">apply</a><x...>::type</div>
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</div><!-- fragment --><dl class="section note"><dt>Note</dt><dd>In a SFINAE context, the expression <code>metafunction_class<f>(type_c<x>...)</code> is valid whenever the expression <code>f::apply<x...>::type</code> is valid.</dd></dl>
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<h2><a class="anchor" id="autotoc_md407"></a>
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Example</h2>
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<div class="fragment"><div class="line"><span class="comment">// Copyright Louis Dionne 2013-2017</span></div>
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<div class="line"><span class="comment">// Distributed under the Boost Software License, Version 1.0.</span></div>
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<div class="line"><span class="comment">// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)</span></div>
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<div class="line"> </div>
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<div class="line"><span class="preprocessor">#include <<a class="code" href="assert_8hpp.html">boost/hana/assert.hpp</a>></span></div>
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<div class="line"><span class="preprocessor">#include <<a class="code" href="equal_8hpp.html">boost/hana/equal.hpp</a>></span></div>
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<div class="line"><span class="preprocessor">#include <<a class="code" href="type_8hpp.html">boost/hana/type.hpp</a>></span></div>
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<div class="line"> </div>
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<div class="line"><span class="preprocessor">#include <type_traits></span></div>
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<div class="line"><span class="keyword">namespace </span>hana = <a class="code" href="namespaceboost_1_1hana.html">boost::hana</a>;</div>
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<div class="line"> </div>
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<div class="line"> </div>
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<div class="line"><span class="keyword">struct </span>f { <span class="keyword">template</span> <<span class="keyword">typename</span> ...> <span class="keyword">struct </span><a class="code" href="group__group-functional.html#ga30027c383676084be151ef3c6cf2829f">apply</a> { <span class="keyword">struct </span>type; }; };</div>
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<div class="line"><span class="keyword">struct </span>x;</div>
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<div class="line"><span class="keyword">struct </span>y;</div>
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<div class="line"> </div>
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<div class="line"><a class="code" href="group__group-assertions.html#ga2c5006540936d9f8880e3a39f4fcc035">BOOST_HANA_CONSTANT_CHECK</a>(hana::metafunction_class<f>() == hana::type_c<f::apply<>::type>);</div>
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<div class="line"><a class="code" href="group__group-assertions.html#ga2c5006540936d9f8880e3a39f4fcc035">BOOST_HANA_CONSTANT_CHECK</a>(hana::metafunction_class<f>(hana::type_c<x>) == hana::type_c<f::apply<x>::type>);</div>
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<div class="line"><a class="code" href="group__group-assertions.html#ga2c5006540936d9f8880e3a39f4fcc035">BOOST_HANA_CONSTANT_CHECK</a>(hana::metafunction_class<f>(hana::type_c<x>, hana::type_c<y>) == hana::type_c<f::apply<x, y>::type>);</div>
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<div class="line"> </div>
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<div class="line">static_assert(std::is_same<</div>
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<div class="line"> decltype(hana::metafunction_class<f>)::apply<x, y>::type,</div>
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<div class="line"> f::apply<x, y>::type</div>
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<div class="line">>::<a class="code" href="group__group-_constant.html#ga1687520692a6b0c49e3a69de2980f388">value</a>, <span class="stringliteral">""</span>);</div>
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<div class="line"> </div>
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<div class="line"><span class="keywordtype">int</span> main() { }</div>
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<a id="gaf7045fe6a627f88f5f646dad22d37aae"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#gaf7045fe6a627f88f5f646dad22d37aae">◆ </a></span>integral</h2>
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<td class="memname">constexpr auto boost::hana::integral</td>
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<p><code>#include <<a class="el" href="fwd_2type_8hpp.html">boost/hana/fwd/type.hpp</a>></code></p>
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<b>Initial value:</b><div class="fragment"><div class="line">= [](<span class="keyword">auto</span> f) {</div>
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<div class="line"> <span class="keywordflow">return</span> [](basic_type<T>...) {</div>
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<div class="line"> <span class="keywordflow">return</span> decltype(f)::<a class="code" href="group__group-functional.html#ga30027c383676084be151ef3c6cf2829f">apply</a><T...>::type{};</div>
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<div class="line"> };</div>
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<div class="line"> }</div>
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<p>Turn a <code>Metafunction</code> into a function taking <code>type</code>s and returning a default-constructed object. </p>
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<p>Given a <code>Metafunction</code> <code>f</code>, <code>integral</code> returns a new <code>Metafunction</code> that default-constructs an object of the type returned by <code>f</code>. More specifically, the following holds: </p><div class="fragment"><div class="line"><a class="code" href="group__group-_metafunction.html#gaf7045fe6a627f88f5f646dad22d37aae">integral</a>(f)(t...) == decltype(f(t...))::type{}</div>
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</div><!-- fragment --><p>The principal use case for <code>integral</code> is to transform <code>Metafunction</code>s returning a type that inherits from a meaningful base like <code><a class="el" href="structstd_1_1integral__constant.html" title="Adapter for std::integral_constants.">std::integral_constant</a></code> into functions returning e.g. a <code><a class="el" href="structboost_1_1hana_1_1integral__constant.html" title="Compile-time value of an integral type.">hana::integral_constant</a></code>.</p>
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<dl class="section note"><dt>Note</dt><dd><ul>
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<li>This is not a <code>Metafunction</code> because it does not return a <code>type</code>. As such, it would not make sense to make <code>decltype(integral(f))</code> a MPL metafunction class like the usual <code>Metafunction</code>s are.</li>
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<li>When using <code>integral</code> with metafunctions returning <code><a class="el" href="structstd_1_1integral__constant.html" title="Adapter for std::integral_constants.">std::integral_constant</a></code>s, don't forget to include the <a class="el" href="ext_2std_2integral__constant_8hpp.html" title="Adapts std::integral_constant for use with Hana.">boost/hana/ext/std/integral_constant.hpp</a> header to ensure Hana can interoperate with the result.</li>
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<li>In a SFINAE context, the expression <code>integral(f)(t...)</code> is valid whenever the expression <code>decltype(f(t...))::type</code> is valid.</li>
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<h2><a class="anchor" id="autotoc_md408"></a>
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Example</h2>
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<div class="fragment"><div class="line"><span class="comment">// Copyright Louis Dionne 2013-2017</span></div>
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<div class="line"><span class="comment">// Distributed under the Boost Software License, Version 1.0.</span></div>
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<div class="line"><span class="comment">// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)</span></div>
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<div class="line"> </div>
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<div class="line"><span class="preprocessor">#include <<a class="code" href="assert_8hpp.html">boost/hana/assert.hpp</a>></span></div>
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<div class="line"><span class="preprocessor">#include <<a class="code" href="ext_2std_2integral__constant_8hpp.html">boost/hana/ext/std/integral_constant.hpp</a>></span></div>
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<div class="line"><span class="preprocessor">#include <<a class="code" href="not_8hpp.html">boost/hana/not.hpp</a>></span></div>
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<div class="line"><span class="preprocessor">#include <<a class="code" href="type_8hpp.html">boost/hana/type.hpp</a>></span></div>
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<div class="line"> </div>
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<div class="line"><span class="preprocessor">#include <type_traits></span></div>
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<div class="line"><span class="keyword">namespace </span>hana = <a class="code" href="namespaceboost_1_1hana.html">boost::hana</a>;</div>
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<div class="line"> </div>
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<div class="line"> </div>
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<div class="line">constexpr <span class="keyword">auto</span> is_void = <a class="code" href="group__group-_metafunction.html#gaf7045fe6a627f88f5f646dad22d37aae">hana::integral</a>(hana::metafunction<std::is_void>);</div>
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<div class="line"><a class="code" href="group__group-assertions.html#ga2c5006540936d9f8880e3a39f4fcc035">BOOST_HANA_CONSTANT_CHECK</a>(is_void(hana::type_c<void>));</div>
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<div class="line"><a class="code" href="group__group-assertions.html#ga2c5006540936d9f8880e3a39f4fcc035">BOOST_HANA_CONSTANT_CHECK</a>(<a class="code" href="group__group-_logical.html#ga4a7c9d7037601d5e553fd20777958980">hana::not_</a>(is_void(hana::type_c<int>)));</div>
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<div class="line"> </div>
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<div class="line"><span class="keywordtype">int</span> main() { }</div>
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<td class="memname">constexpr auto boost::hana::trait = <a class="el" href="group__group-_metafunction.html#gaf7045fe6a627f88f5f646dad22d37aae">hana::integral</a>(<a class="el" href="group__group-_metafunction.html#gaaa4f85cb8cbce21f5c04ef40ca35cc6a">hana::metafunction</a><F>)</td>
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<p><code>#include <<a class="el" href="fwd_2type_8hpp.html">boost/hana/fwd/type.hpp</a>></code></p>
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<p>Alias to <code>integral(metafunction<F>)</code>, provided for convenience. </p>
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<h2><a class="anchor" id="autotoc_md409"></a>
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Example</h2>
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<div class="fragment"><div class="line"><span class="comment">// Copyright Louis Dionne 2013-2017</span></div>
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<div class="line"><span class="comment">// Distributed under the Boost Software License, Version 1.0.</span></div>
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<div class="line"><span class="comment">// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)</span></div>
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<div class="line"> </div>
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<div class="line"><span class="preprocessor">#include <<a class="code" href="assert_8hpp.html">boost/hana/assert.hpp</a>></span></div>
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<div class="line"><span class="preprocessor">#include <<a class="code" href="ext_2std_2integral__constant_8hpp.html">boost/hana/ext/std/integral_constant.hpp</a>></span></div>
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<div class="line"><span class="preprocessor">#include <<a class="code" href="not_8hpp.html">boost/hana/not.hpp</a>></span></div>
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<div class="line"><span class="preprocessor">#include <<a class="code" href="type_8hpp.html">boost/hana/type.hpp</a>></span></div>
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<div class="line"> </div>
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<div class="line"><span class="preprocessor">#include <type_traits></span></div>
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<div class="line"><span class="keyword">namespace </span>hana = <a class="code" href="namespaceboost_1_1hana.html">boost::hana</a>;</div>
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<div class="line"> </div>
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<div class="line"> </div>
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<div class="line"><a class="code" href="group__group-assertions.html#ga2c5006540936d9f8880e3a39f4fcc035">BOOST_HANA_CONSTANT_CHECK</a>(hana::trait<std::is_integral>(hana::type_c<int>));</div>
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<div class="line"><a class="code" href="group__group-assertions.html#ga2c5006540936d9f8880e3a39f4fcc035">BOOST_HANA_CONSTANT_CHECK</a>(<a class="code" href="group__group-_logical.html#ga4a7c9d7037601d5e553fd20777958980">hana::not_</a>(hana::trait<std::is_integral>(hana::type_c<float>)));</div>
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<div class="line"> </div>
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<div class="line"><span class="keywordtype">int</span> main() { }</div>
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<div class="ttc" id="aequal_8hpp_html"><div class="ttname"><a href="equal_8hpp.html">equal.hpp</a></div><div class="ttdoc">Defines boost::hana::equal.</div></div>
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<div class="ttc" id="agroup__group-assertions_html_ga2c5006540936d9f8880e3a39f4fcc035"><div class="ttname"><a href="group__group-assertions.html#ga2c5006540936d9f8880e3a39f4fcc035">BOOST_HANA_CONSTANT_CHECK</a></div><div class="ttdeci">#define BOOST_HANA_CONSTANT_CHECK(...)</div><div class="ttdoc">Equivalent to BOOST_HANA_CONSTANT_ASSERT, but not influenced by the BOOST_HANA_CONFIG_DISABLE_ASSERTI...</div><div class="ttdef"><b>Definition:</b> assert.hpp:239</div></div>
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<div class="ttc" id="agroup__group-_metafunction_html_gaf7045fe6a627f88f5f646dad22d37aae"><div class="ttname"><a href="group__group-_metafunction.html#gaf7045fe6a627f88f5f646dad22d37aae">boost::hana::integral</a></div><div class="ttdeci">constexpr auto integral</div><div class="ttdoc">Turn a Metafunction into a function taking types and returning a default-constructed object.</div><div class="ttdef"><b>Definition:</b> type.hpp:513</div></div>
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<div class="ttc" id="agroup__group-_logical_html_ga4a7c9d7037601d5e553fd20777958980"><div class="ttname"><a href="group__group-_logical.html#ga4a7c9d7037601d5e553fd20777958980">boost::hana::not_</a></div><div class="ttdeci">constexpr auto not_</div><div class="ttdoc">Negates a Logical.</div><div class="ttdef"><b>Definition:</b> not.hpp:31</div></div>
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<div class="ttc" id="agroup__group-_constant_html_ga1687520692a6b0c49e3a69de2980f388"><div class="ttname"><a href="group__group-_constant.html#ga1687520692a6b0c49e3a69de2980f388">boost::hana::value</a></div><div class="ttdeci">constexpr auto value</div><div class="ttdoc">Return the compile-time value associated to a constant.</div><div class="ttdef"><b>Definition:</b> value.hpp:54</div></div>
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<div class="ttc" id="atype_8hpp_html"><div class="ttname"><a href="type_8hpp.html">type.hpp</a></div><div class="ttdoc">Defines boost::hana::type and related utilities.</div></div>
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<div class="ttc" id="anamespaceboost_1_1hana_html"><div class="ttname"><a href="namespaceboost_1_1hana.html">boost::hana</a></div><div class="ttdoc">Namespace containing everything in the library.</div><div class="ttdef"><b>Definition:</b> accessors.hpp:20</div></div>
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<div class="ttc" id="aassert_8hpp_html"><div class="ttname"><a href="assert_8hpp.html">assert.hpp</a></div><div class="ttdoc">Defines macros to perform different kinds of assertions.</div></div>
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<div class="ttc" id="aext_2std_2integral__constant_8hpp_html"><div class="ttname"><a href="ext_2std_2integral__constant_8hpp.html">integral_constant.hpp</a></div><div class="ttdoc">Adapts std::integral_constant for use with Hana.</div></div>
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<div class="ttc" id="anot_8hpp_html"><div class="ttname"><a href="not_8hpp.html">not.hpp</a></div><div class="ttdoc">Defines boost::hana::not_.</div></div>
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<div class="ttc" id="agroup__group-functional_html_ga30027c383676084be151ef3c6cf2829f"><div class="ttname"><a href="group__group-functional.html#ga30027c383676084be151ef3c6cf2829f">boost::hana::apply</a></div><div class="ttdeci">constexpr auto apply</div><div class="ttdoc">Invokes a Callable with the given arguments.</div><div class="ttdef"><b>Definition:</b> apply.hpp:40</div></div>
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