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   &#160;<span id="projectnumber">1.6.0</span>
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<div class="header">
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<a href="#var-members">Variables</a>  </div>
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<div class="title">Hashable<div class="ingroups"><a class="el" href="group__group-concepts.html">Concepts</a></div></div>  </div>
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<a name="details" id="details"></a><h2 class="groupheader">Description</h2>
<p>The <code>Hashable</code> concept represents objects that can be normalized to a type-level hash. </p>
<p>In day to day programming, hashes are very important as a way to efficiently lookup objects in maps. While the implementation of maps is very different, the same idea of using hashes for efficient lookup applies in metaprogramming. The <code>Hashable</code> concept represents objects that can be summarized (possibly with loss of information) to a type, in a way suitable for use in hash-based data structures. Of course, in order for a hash to be well-behaved, it must obey some laws that are explained below.</p>
<h2>Minimal complete definition </h2>
<p><code>hash</code>, satisfying the laws below</p>
<h2>Laws </h2>
<p>First, <code><a class="el" href="group__group-Hashable.html#ga6e906f44f47b210615491385e5c8a7b5" title="Returns a hana::type representing the compile-time hash of an object.Given an arbitrary object x,...">hana::hash</a></code> must return a <code><a class="el" href="structboost_1_1hana_1_1type.html" title="C++ type in value-level representation.">hana::type</a></code>. Furthermore, for any two <code>Hashable</code> objects <code>x</code> and <code>y</code>, it must be the case that </p><div class="fragment"><div class="line">x == y   implies   <a class="code" href="group__group-Hashable.html#ga6e906f44f47b210615491385e5c8a7b5">hash</a>(x) == <a class="code" href="group__group-Hashable.html#ga6e906f44f47b210615491385e5c8a7b5">hash</a>(y)</div></div><!-- fragment --><p>where <code>==</code> denotes <code><a class="el" href="group__group-Comparable.html#gacaf1ebea6b3ab96ac9dcb82f0e64e547" title="Returns a Logical representing whether x is equal to y.The equal function can be called in two differ...">hana::equal</a></code>. In other words, any two objects that compare equal (with <code><a class="el" href="group__group-Comparable.html#gacaf1ebea6b3ab96ac9dcb82f0e64e547" title="Returns a Logical representing whether x is equal to y.The equal function can be called in two differ...">hana::equal</a></code>) must also have the same hash. However, the reverse is not true, and two different objects may have the same hash. This situation of two different objects having the same hash is called a <em>collision</em>.</p>
<h2>Concrete models </h2>
<p><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>, <code><a class="el" href="structboost_1_1hana_1_1type.html" title="C++ type in value-level representation.">hana::type</a></code>, <code><a class="el" href="structboost_1_1hana_1_1string.html" title="Compile-time string.">hana::string</a></code></p>
<h2>Free model for <code><a class="el" href="structboost_1_1hana_1_1IntegralConstant.html" title="The IntegralConstant concept represents compile-time integral values.">IntegralConstant</a></code>s </h2>
<p>Any <code><a class="el" href="structboost_1_1hana_1_1IntegralConstant.html" title="The IntegralConstant concept represents compile-time integral values.">IntegralConstant</a></code> is <code>Hashable</code>, by normalizing its value to 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>. The type of the value held in the normalized <code><a class="el" href="structboost_1_1hana_1_1integral__constant.html" title="Compile-time value of an integral type.">integral_constant</a></code> is <code>unsigned long long</code> for unsigned integral types, and <code>signed long long</code> for signed integral types. </p>
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Variables</h2></td></tr>
<tr class="memitem:ga6e906f44f47b210615491385e5c8a7b5"><td class="memItemLeft" align="right" valign="top">constexpr auto&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__group-Hashable.html#ga6e906f44f47b210615491385e5c8a7b5">boost::hana::hash</a></td></tr>
<tr class="memdesc:ga6e906f44f47b210615491385e5c8a7b5"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns a <code><a class="el" href="structboost_1_1hana_1_1type.html" title="C++ type in value-level representation.">hana::type</a></code> representing the compile-time hash of an object.Given an arbitrary object <code>x</code>, <code><a class="el" href="group__group-Hashable.html#ga6e906f44f47b210615491385e5c8a7b5" title="Returns a hana::type representing the compile-time hash of an object.Given an arbitrary object x,...">hana::hash</a></code> returns a <code><a class="el" href="structboost_1_1hana_1_1type.html" title="C++ type in value-level representation.">hana::type</a></code> representing the hash of <code>x</code>. In normal programming, hashes are usually numerical values that can be used e.g. as indices in an array as part of the implementation of a hash table. In the context of metaprogramming, we are interested in type-level hashes instead. Thus, <code><a class="el" href="group__group-Hashable.html#ga6e906f44f47b210615491385e5c8a7b5" title="Returns a hana::type representing the compile-time hash of an object.Given an arbitrary object x,...">hana::hash</a></code> must return a <code><a class="el" href="structboost_1_1hana_1_1type.html" title="C++ type in value-level representation.">hana::type</a></code> object instead of an integer. This <code><a class="el" href="structboost_1_1hana_1_1type.html" title="C++ type in value-level representation.">hana::type</a></code> must somehow summarize the object being hashed, but that summary may of course lose some information.  <a href="group__group-Hashable.html#ga6e906f44f47b210615491385e5c8a7b5">More...</a><br /></td></tr>
<tr class="separator:ga6e906f44f47b210615491385e5c8a7b5"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<h2 class="groupheader">Variable Documentation</h2>
<a id="ga6e906f44f47b210615491385e5c8a7b5"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ga6e906f44f47b210615491385e5c8a7b5">&#9670;&nbsp;</a></span>hash</h2>

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          <td class="memname">constexpr auto boost::hana::hash</td>
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<p><code>#include &lt;<a class="el" href="fwd_2hash_8hpp.html">boost/hana/fwd/hash.hpp</a>&gt;</code></p>
<b>Initial value:</b><div class="fragment"><div class="line">= [](<span class="keyword">auto</span> <span class="keyword">const</span>&amp; x) {</div><div class="line">        <span class="keywordflow">return</span> tag-dispatched;</div><div class="line">    }</div></div><!-- fragment -->
<p>Returns a <code><a class="el" href="structboost_1_1hana_1_1type.html" title="C++ type in value-level representation.">hana::type</a></code> representing the compile-time hash of an object.Given an arbitrary object <code>x</code>, <code><a class="el" href="group__group-Hashable.html#ga6e906f44f47b210615491385e5c8a7b5" title="Returns a hana::type representing the compile-time hash of an object.Given an arbitrary object x,...">hana::hash</a></code> returns a <code><a class="el" href="structboost_1_1hana_1_1type.html" title="C++ type in value-level representation.">hana::type</a></code> representing the hash of <code>x</code>. In normal programming, hashes are usually numerical values that can be used e.g. as indices in an array as part of the implementation of a hash table. In the context of metaprogramming, we are interested in type-level hashes instead. Thus, <code><a class="el" href="group__group-Hashable.html#ga6e906f44f47b210615491385e5c8a7b5" title="Returns a hana::type representing the compile-time hash of an object.Given an arbitrary object x,...">hana::hash</a></code> must return a <code><a class="el" href="structboost_1_1hana_1_1type.html" title="C++ type in value-level representation.">hana::type</a></code> object instead of an integer. This <code><a class="el" href="structboost_1_1hana_1_1type.html" title="C++ type in value-level representation.">hana::type</a></code> must somehow summarize the object being hashed, but that summary may of course lose some information. </p>
<p>In order for the <code>hash</code> function to be defined properly, it must be the case that whenever <code>x</code> is equal to <code>y</code>, then <code>hash(x)</code> is equal to <code>hash(y)</code>. This ensures that <code><a class="el" href="group__group-Hashable.html#ga6e906f44f47b210615491385e5c8a7b5" title="Returns a hana::type representing the compile-time hash of an object.Given an arbitrary object x,...">hana::hash</a></code> is a function in the mathematical sense of the term.</p>
<h2>Signature </h2>
<p>Given a <code>Hashable</code> <code>H</code>, the signature is \( \mathtt{hash} : H \to \mathtt{type\_tag} \)</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">x</td><td>An object whose hash is to be computed.</td></tr>
  </table>
  </dd>
</dl>
<h2>Example </h2>
<div class="fragment"><div class="line"><span class="comment">// Copyright Louis Dionne 2013-2017</span></div><div class="line"><span class="comment">// Distributed under the Boost Software License, Version 1.0.</span></div><div class="line"><span class="comment">// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)</span></div><div class="line"></div><div class="line"><span class="preprocessor">#include &lt;<a class="code" href="assert_8hpp.html">boost/hana/assert.hpp</a>&gt;</span></div><div class="line"><span class="preprocessor">#include &lt;<a class="code" href="equal_8hpp.html">boost/hana/equal.hpp</a>&gt;</span></div><div class="line"><span class="preprocessor">#include &lt;<a class="code" href="hash_8hpp.html">boost/hana/hash.hpp</a>&gt;</span></div><div class="line"><span class="preprocessor">#include &lt;<a class="code" href="integral__constant_8hpp.html">boost/hana/integral_constant.hpp</a>&gt;</span></div><div class="line"><span class="preprocessor">#include &lt;<a class="code" href="type_8hpp.html">boost/hana/type.hpp</a>&gt;</span></div><div class="line"></div><div class="line"><span class="preprocessor">#include &lt;type_traits&gt;</span></div><div class="line"><span class="preprocessor">#include &lt;utility&gt;</span></div><div class="line"><span class="keyword">namespace </span>hana = <a class="code" href="namespaceboost_1_1hana.html">boost::hana</a>;</div><div class="line"></div><div class="line"></div><div class="line"><span class="comment">// Sample implementation of a compile-time set data structure. Of course,</span></div><div class="line"><span class="comment">// this naive implementation only works when no two elements of the same</span></div><div class="line"><span class="comment">// set have the same hash.</span></div><div class="line"><span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div><div class="line"><span class="keyword">struct </span>bucket { };</div><div class="line"></div><div class="line"><span class="keyword">template</span> &lt;<span class="keyword">typename</span> ...T&gt;</div><div class="line"><span class="keyword">struct </span>set</div><div class="line">    : bucket&lt;typename decltype(hana::hash(std::declval&lt;T&gt;()))::type&gt;...</div><div class="line">{ };</div><div class="line"></div><div class="line"><span class="keyword">template</span> &lt;<span class="keyword">typename</span> Set, <span class="keyword">typename</span> T&gt;</div><div class="line"><span class="keyword">struct </span><a class="code" href="group__group-Searchable.html#ga38e7748956cbc9f3d9bb035ac8577906">contains</a></div><div class="line">    : std::is_base_of&lt;</div><div class="line">        bucket&lt;typename decltype(hana::hash(std::declval&lt;T&gt;()))::type&gt;,</div><div class="line">        Set</div><div class="line">    &gt;</div><div class="line">{ };</div><div class="line"></div><div class="line"><span class="keyword">using</span> Set = set&lt;hana::int_&lt;1&gt;, hana::ulong&lt;2&gt;, hana::type&lt;char&gt;&gt;;</div><div class="line"></div><div class="line">static_assert(<a class="code" href="group__group-Searchable.html#ga38e7748956cbc9f3d9bb035ac8577906">contains</a>&lt;Set, hana::int_&lt;1&gt;&gt;{}, <span class="stringliteral">&quot;&quot;</span>);</div><div class="line">static_assert(<a class="code" href="group__group-Searchable.html#ga38e7748956cbc9f3d9bb035ac8577906">contains</a>&lt;Set, hana::ulong&lt;2&gt;&gt;{}, <span class="stringliteral">&quot;&quot;</span>);</div><div class="line">static_assert(<a class="code" href="group__group-Searchable.html#ga38e7748956cbc9f3d9bb035ac8577906">contains</a>&lt;Set, hana::type&lt;char&gt;&gt;{}, <span class="stringliteral">&quot;&quot;</span>);</div><div class="line"></div><div class="line">static_assert(!<a class="code" href="group__group-Searchable.html#ga38e7748956cbc9f3d9bb035ac8577906">contains</a>&lt;Set, hana::int_&lt;3&gt;&gt;{}, <span class="stringliteral">&quot;&quot;</span>);</div><div class="line">static_assert(!<a class="code" href="group__group-Searchable.html#ga38e7748956cbc9f3d9bb035ac8577906">contains</a>&lt;Set, hana::type&lt;float&gt;&gt;{}, <span class="stringliteral">&quot;&quot;</span>);</div><div class="line"></div><div class="line"><span class="keywordtype">int</span> main() { }</div></div><!-- fragment --> 
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