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<div class="section" id="module-sets">
<span id="sets-unordered-collections-of-unique-elements"></span><h1>8.7. <a class="reference internal" href="#module-sets" title="sets: Implementation of sets of unique elements. (deprecated)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sets</span></code></a> — Unordered collections of unique elements<a class="headerlink" href="#module-sets" title="Permalink to this headline">¶</a></h1>
<div class="versionadded">
<p><span class="versionmodified added">New in version 2.3.</span></p>
</div>
<div class="deprecated">
<p><span class="versionmodified deprecated">Deprecated since version 2.6: </span>The built-in <a class="reference internal" href="stdtypes.html#set" title="set"><code class="xref py py-class docutils literal notranslate"><span class="pre">set</span></code></a>/<a class="reference internal" href="stdtypes.html#frozenset" title="frozenset"><code class="xref py py-class docutils literal notranslate"><span class="pre">frozenset</span></code></a> types replace this module.</p>
</div>
<p>The <a class="reference internal" href="#module-sets" title="sets: Implementation of sets of unique elements. (deprecated)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sets</span></code></a> module provides classes for constructing and manipulating
unordered collections of unique elements. Common uses include membership
testing, removing duplicates from a sequence, and computing standard math
operations on sets such as intersection, union, difference, and symmetric
difference.</p>
<p>Like other collections, sets support <code class="docutils literal notranslate"><span class="pre">x</span> <span class="pre">in</span> <span class="pre">set</span></code>, <code class="docutils literal notranslate"><span class="pre">len(set)</span></code>, and <code class="docutils literal notranslate"><span class="pre">for</span> <span class="pre">x</span> <span class="pre">in</span>
<span class="pre">set</span></code>. Being an unordered collection, sets do not record element position or
order of insertion. Accordingly, sets do not support indexing, slicing, or
other sequence-like behavior.</p>
<p>Most set applications use the <a class="reference internal" href="#sets.Set" title="sets.Set"><code class="xref py py-class docutils literal notranslate"><span class="pre">Set</span></code></a> class which provides every set method
except for <a class="reference internal" href="../reference/datamodel.html#object.__hash__" title="object.__hash__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__hash__()</span></code></a>. For advanced applications requiring a hash method,
the <a class="reference internal" href="#sets.ImmutableSet" title="sets.ImmutableSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImmutableSet</span></code></a> class adds a <a class="reference internal" href="../reference/datamodel.html#object.__hash__" title="object.__hash__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__hash__()</span></code></a> method but omits methods
which alter the contents of the set. Both <a class="reference internal" href="#sets.Set" title="sets.Set"><code class="xref py py-class docutils literal notranslate"><span class="pre">Set</span></code></a> and <a class="reference internal" href="#sets.ImmutableSet" title="sets.ImmutableSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImmutableSet</span></code></a>
derive from <code class="xref py py-class docutils literal notranslate"><span class="pre">BaseSet</span></code>, an abstract class useful for determining whether
something is a set: <code class="docutils literal notranslate"><span class="pre">isinstance(obj,</span> <span class="pre">BaseSet)</span></code>.</p>
<p>The set classes are implemented using dictionaries. Accordingly, the
requirements for set elements are the same as those for dictionary keys; namely,
that the element defines both <a class="reference internal" href="../reference/datamodel.html#object.__eq__" title="object.__eq__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__eq__()</span></code></a> and <a class="reference internal" href="../reference/datamodel.html#object.__hash__" title="object.__hash__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__hash__()</span></code></a>. As a result,
sets cannot contain mutable elements such as lists or dictionaries. However,
they can contain immutable collections such as tuples or instances of
<a class="reference internal" href="#sets.ImmutableSet" title="sets.ImmutableSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImmutableSet</span></code></a>. For convenience in implementing sets of sets, inner sets
are automatically converted to immutable form, for example,
<code class="docutils literal notranslate"><span class="pre">Set([Set(['dog'])])</span></code> is transformed to <code class="docutils literal notranslate"><span class="pre">Set([ImmutableSet(['dog'])])</span></code>.</p>
<dl class="class">
<dt id="sets.Set">
<em class="property">class </em><code class="descclassname">sets.</code><code class="descname">Set</code><span class="sig-paren">(</span><span class="optional">[</span><em>iterable</em><span class="optional">]</span><span class="sig-paren">)</span><a class="headerlink" href="#sets.Set" title="Permalink to this definition">¶</a></dt>
<dd><p>Constructs a new empty <a class="reference internal" href="#sets.Set" title="sets.Set"><code class="xref py py-class docutils literal notranslate"><span class="pre">Set</span></code></a> object. If the optional <em>iterable</em>
parameter is supplied, updates the set with elements obtained from iteration.
All of the elements in <em>iterable</em> should be immutable or be transformable to an
immutable using the protocol described in section <a class="reference internal" href="#immutable-transforms"><span class="std std-ref">Protocol for automatic conversion to immutable</span></a>.</p>
</dd></dl>
<dl class="class">
<dt id="sets.ImmutableSet">
<em class="property">class </em><code class="descclassname">sets.</code><code class="descname">ImmutableSet</code><span class="sig-paren">(</span><span class="optional">[</span><em>iterable</em><span class="optional">]</span><span class="sig-paren">)</span><a class="headerlink" href="#sets.ImmutableSet" title="Permalink to this definition">¶</a></dt>
<dd><p>Constructs a new empty <a class="reference internal" href="#sets.ImmutableSet" title="sets.ImmutableSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImmutableSet</span></code></a> object. If the optional <em>iterable</em>
parameter is supplied, updates the set with elements obtained from iteration.
All of the elements in <em>iterable</em> should be immutable or be transformable to an
immutable using the protocol described in section <a class="reference internal" href="#immutable-transforms"><span class="std std-ref">Protocol for automatic conversion to immutable</span></a>.</p>
<p>Because <a class="reference internal" href="#sets.ImmutableSet" title="sets.ImmutableSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImmutableSet</span></code></a> objects provide a <a class="reference internal" href="../reference/datamodel.html#object.__hash__" title="object.__hash__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__hash__()</span></code></a> method, they
can be used as set elements or as dictionary keys. <a class="reference internal" href="#sets.ImmutableSet" title="sets.ImmutableSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImmutableSet</span></code></a>
objects do not have methods for adding or removing elements, so all of the
elements must be known when the constructor is called.</p>
</dd></dl>
<div class="section" id="set-objects">
<span id="id1"></span><h2>8.7.1. Set Objects<a class="headerlink" href="#set-objects" title="Permalink to this headline">¶</a></h2>
<p>Instances of <a class="reference internal" href="#sets.Set" title="sets.Set"><code class="xref py py-class docutils literal notranslate"><span class="pre">Set</span></code></a> and <a class="reference internal" href="#sets.ImmutableSet" title="sets.ImmutableSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImmutableSet</span></code></a> both provide the following
operations:</p>
<table class="docutils align-center">
<colgroup>
<col style="width: 41%" />
<col style="width: 16%" />
<col style="width: 43%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head"><p>Operation</p></th>
<th class="head"><p>Equivalent</p></th>
<th class="head"><p>Result</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">len(s)</span></code></p></td>
<td></td>
<td><p>number of elements in set <em>s</em>
(cardinality)</p></td>
</tr>
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">x</span> <span class="pre">in</span> <span class="pre">s</span></code></p></td>
<td></td>
<td><p>test <em>x</em> for membership in <em>s</em></p></td>
</tr>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">x</span> <span class="pre">not</span> <span class="pre">in</span> <span class="pre">s</span></code></p></td>
<td></td>
<td><p>test <em>x</em> for non-membership in
<em>s</em></p></td>
</tr>
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">s.issubset(t)</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">s</span> <span class="pre"><=</span> <span class="pre">t</span></code></p></td>
<td><p>test whether every element in
<em>s</em> is in <em>t</em></p></td>
</tr>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">s.issuperset(t)</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">s</span> <span class="pre">>=</span> <span class="pre">t</span></code></p></td>
<td><p>test whether every element in
<em>t</em> is in <em>s</em></p></td>
</tr>
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">s.union(t)</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">s</span> <span class="pre">|</span> <span class="pre">t</span></code></p></td>
<td><p>new set with elements from both
<em>s</em> and <em>t</em></p></td>
</tr>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">s.intersection(t)</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">s</span> <span class="pre">&</span> <span class="pre">t</span></code></p></td>
<td><p>new set with elements common to
<em>s</em> and <em>t</em></p></td>
</tr>
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">s.difference(t)</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">s</span> <span class="pre">-</span> <span class="pre">t</span></code></p></td>
<td><p>new set with elements in <em>s</em>
but not in <em>t</em></p></td>
</tr>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">s.symmetric_difference(t)</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">s</span> <span class="pre">^</span> <span class="pre">t</span></code></p></td>
<td><p>new set with elements in either
<em>s</em> or <em>t</em> but not both</p></td>
</tr>
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">s.copy()</span></code></p></td>
<td></td>
<td><p>new set with a shallow copy of
<em>s</em></p></td>
</tr>
</tbody>
</table>
<p>Note, the non-operator versions of <code class="xref py py-meth docutils literal notranslate"><span class="pre">union()</span></code>, <code class="xref py py-meth docutils literal notranslate"><span class="pre">intersection()</span></code>,
<code class="xref py py-meth docutils literal notranslate"><span class="pre">difference()</span></code>, and <code class="xref py py-meth docutils literal notranslate"><span class="pre">symmetric_difference()</span></code> will accept any iterable as
an argument. In contrast, their operator based counterparts require their
arguments to be sets. This precludes error-prone constructions like
<code class="docutils literal notranslate"><span class="pre">Set('abc')</span> <span class="pre">&</span> <span class="pre">'cbs'</span></code> in favor of the more readable
<code class="docutils literal notranslate"><span class="pre">Set('abc').intersection('cbs')</span></code>.</p>
<div class="versionchanged">
<p><span class="versionmodified changed">Changed in version 2.3.1: </span>Formerly all arguments were required to be sets.</p>
</div>
<p>In addition, both <a class="reference internal" href="#sets.Set" title="sets.Set"><code class="xref py py-class docutils literal notranslate"><span class="pre">Set</span></code></a> and <a class="reference internal" href="#sets.ImmutableSet" title="sets.ImmutableSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImmutableSet</span></code></a> support set to set
comparisons. Two sets are equal if and only if every element of each set is
contained in the other (each is a subset of the other). A set is less than
another set if and only if the first set is a proper subset of the second set
(is a subset, but is not equal). A set is greater than another set if and only
if the first set is a proper superset of the second set (is a superset, but is
not equal).</p>
<p>The subset and equality comparisons do not generalize to a complete ordering
function. For example, any two disjoint sets are not equal and are not subsets
of each other, so <em>all</em> of the following return <code class="docutils literal notranslate"><span class="pre">False</span></code>: <code class="docutils literal notranslate"><span class="pre">a<b</span></code>, <code class="docutils literal notranslate"><span class="pre">a==b</span></code>,
or <code class="docutils literal notranslate"><span class="pre">a>b</span></code>. Accordingly, sets do not implement the <a class="reference internal" href="../reference/datamodel.html#object.__cmp__" title="object.__cmp__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__cmp__()</span></code></a> method.</p>
<p>Since sets only define partial ordering (subset relationships), the output of
the <code class="xref py py-meth docutils literal notranslate"><span class="pre">list.sort()</span></code> method is undefined for lists of sets.</p>
<p>The following table lists operations available in <a class="reference internal" href="#sets.ImmutableSet" title="sets.ImmutableSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImmutableSet</span></code></a> but not
found in <a class="reference internal" href="#sets.Set" title="sets.Set"><code class="xref py py-class docutils literal notranslate"><span class="pre">Set</span></code></a>:</p>
<table class="docutils align-center">
<colgroup>
<col style="width: 30%" />
<col style="width: 70%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head"><p>Operation</p></th>
<th class="head"><p>Result</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">hash(s)</span></code></p></td>
<td><p>returns a hash value for <em>s</em></p></td>
</tr>
</tbody>
</table>
<p>The following table lists operations available in <a class="reference internal" href="#sets.Set" title="sets.Set"><code class="xref py py-class docutils literal notranslate"><span class="pre">Set</span></code></a> but not found in
<a class="reference internal" href="#sets.ImmutableSet" title="sets.ImmutableSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImmutableSet</span></code></a>:</p>
<table class="docutils align-center">
<colgroup>
<col style="width: 45%" />
<col style="width: 15%" />
<col style="width: 39%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head"><p>Operation</p></th>
<th class="head"><p>Equivalent</p></th>
<th class="head"><p>Result</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">s.update(t)</span></code></p></td>
<td><p><em>s</em> |= <em>t</em></p></td>
<td><p>return set <em>s</em> with elements
added from <em>t</em></p></td>
</tr>
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">s.intersection_update(t)</span></code></p></td>
<td><p><em>s</em> &= <em>t</em></p></td>
<td><p>return set <em>s</em> keeping only
elements also found in <em>t</em></p></td>
</tr>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">s.difference_update(t)</span></code></p></td>
<td><p><em>s</em> -= <em>t</em></p></td>
<td><p>return set <em>s</em> after removing
elements found in <em>t</em></p></td>
</tr>
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">s.symmetric_difference_update(t)</span></code></p></td>
<td><p><em>s</em> ^= <em>t</em></p></td>
<td><p>return set <em>s</em> with elements
from <em>s</em> or <em>t</em> but not both</p></td>
</tr>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">s.add(x)</span></code></p></td>
<td></td>
<td><p>add element <em>x</em> to set <em>s</em></p></td>
</tr>
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">s.remove(x)</span></code></p></td>
<td></td>
<td><p>remove <em>x</em> from set <em>s</em>; raises
<a class="reference internal" href="exceptions.html#exceptions.KeyError" title="exceptions.KeyError"><code class="xref py py-exc docutils literal notranslate"><span class="pre">KeyError</span></code></a> if not present</p></td>
</tr>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">s.discard(x)</span></code></p></td>
<td></td>
<td><p>removes <em>x</em> from set <em>s</em> if
present</p></td>
</tr>
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">s.pop()</span></code></p></td>
<td></td>
<td><p>remove and return an arbitrary
element from <em>s</em>; raises
<a class="reference internal" href="exceptions.html#exceptions.KeyError" title="exceptions.KeyError"><code class="xref py py-exc docutils literal notranslate"><span class="pre">KeyError</span></code></a> if empty</p></td>
</tr>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">s.clear()</span></code></p></td>
<td></td>
<td><p>remove all elements from set
<em>s</em></p></td>
</tr>
</tbody>
</table>
<p>Note, the non-operator versions of <code class="xref py py-meth docutils literal notranslate"><span class="pre">update()</span></code>, <code class="xref py py-meth docutils literal notranslate"><span class="pre">intersection_update()</span></code>,
<code class="xref py py-meth docutils literal notranslate"><span class="pre">difference_update()</span></code>, and <code class="xref py py-meth docutils literal notranslate"><span class="pre">symmetric_difference_update()</span></code> will accept
any iterable as an argument.</p>
<div class="versionchanged">
<p><span class="versionmodified changed">Changed in version 2.3.1: </span>Formerly all arguments were required to be sets.</p>
</div>
<p>Also note, the module also includes a <code class="xref py py-meth docutils literal notranslate"><span class="pre">union_update()</span></code> method which is an
alias for <code class="xref py py-meth docutils literal notranslate"><span class="pre">update()</span></code>. The method is included for backwards compatibility.
Programmers should prefer the <code class="xref py py-meth docutils literal notranslate"><span class="pre">update()</span></code> method because it is supported by
the built-in <a class="reference internal" href="stdtypes.html#set" title="set"><code class="xref py py-class docutils literal notranslate"><span class="pre">set()</span></code></a> and <a class="reference internal" href="stdtypes.html#frozenset" title="frozenset"><code class="xref py py-class docutils literal notranslate"><span class="pre">frozenset()</span></code></a> types.</p>
</div>
<div class="section" id="example">
<span id="set-example"></span><h2>8.7.2. Example<a class="headerlink" href="#example" title="Permalink to this headline">¶</a></h2>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sets</span> <span class="k">import</span> <span class="n">Set</span>
<span class="gp">>>> </span><span class="n">engineers</span> <span class="o">=</span> <span class="n">Set</span><span class="p">([</span><span class="s1">'John'</span><span class="p">,</span> <span class="s1">'Jane'</span><span class="p">,</span> <span class="s1">'Jack'</span><span class="p">,</span> <span class="s1">'Janice'</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">programmers</span> <span class="o">=</span> <span class="n">Set</span><span class="p">([</span><span class="s1">'Jack'</span><span class="p">,</span> <span class="s1">'Sam'</span><span class="p">,</span> <span class="s1">'Susan'</span><span class="p">,</span> <span class="s1">'Janice'</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">managers</span> <span class="o">=</span> <span class="n">Set</span><span class="p">([</span><span class="s1">'Jane'</span><span class="p">,</span> <span class="s1">'Jack'</span><span class="p">,</span> <span class="s1">'Susan'</span><span class="p">,</span> <span class="s1">'Zack'</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">employees</span> <span class="o">=</span> <span class="n">engineers</span> <span class="o">|</span> <span class="n">programmers</span> <span class="o">|</span> <span class="n">managers</span> <span class="c1"># union</span>
<span class="gp">>>> </span><span class="n">engineering_management</span> <span class="o">=</span> <span class="n">engineers</span> <span class="o">&</span> <span class="n">managers</span> <span class="c1"># intersection</span>
<span class="gp">>>> </span><span class="n">fulltime_management</span> <span class="o">=</span> <span class="n">managers</span> <span class="o">-</span> <span class="n">engineers</span> <span class="o">-</span> <span class="n">programmers</span> <span class="c1"># difference</span>
<span class="gp">>>> </span><span class="n">engineers</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="s1">'Marvin'</span><span class="p">)</span> <span class="c1"># add element</span>
<span class="gp">>>> </span><span class="nb">print</span> <span class="n">engineers</span> <span class="c1"># doctest: +SKIP</span>
<span class="go">Set(['Jane', 'Marvin', 'Janice', 'John', 'Jack'])</span>
<span class="gp">>>> </span><span class="n">employees</span><span class="o">.</span><span class="n">issuperset</span><span class="p">(</span><span class="n">engineers</span><span class="p">)</span> <span class="c1"># superset test</span>
<span class="go">False</span>
<span class="gp">>>> </span><span class="n">employees</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">engineers</span><span class="p">)</span> <span class="c1"># update from another set</span>
<span class="gp">>>> </span><span class="n">employees</span><span class="o">.</span><span class="n">issuperset</span><span class="p">(</span><span class="n">engineers</span><span class="p">)</span>
<span class="go">True</span>
<span class="gp">>>> </span><span class="k">for</span> <span class="n">group</span> <span class="ow">in</span> <span class="p">[</span><span class="n">engineers</span><span class="p">,</span> <span class="n">programmers</span><span class="p">,</span> <span class="n">managers</span><span class="p">,</span> <span class="n">employees</span><span class="p">]:</span> <span class="c1"># doctest: +SKIP</span>
<span class="gp">... </span> <span class="n">group</span><span class="o">.</span><span class="n">discard</span><span class="p">(</span><span class="s1">'Susan'</span><span class="p">)</span> <span class="c1"># unconditionally remove element</span>
<span class="gp">... </span> <span class="nb">print</span> <span class="n">group</span>
<span class="gp">...</span>
<span class="go">Set(['Jane', 'Marvin', 'Janice', 'John', 'Jack'])</span>
<span class="go">Set(['Janice', 'Jack', 'Sam'])</span>
<span class="go">Set(['Jane', 'Zack', 'Jack'])</span>
<span class="go">Set(['Jack', 'Sam', 'Jane', 'Marvin', 'Janice', 'John', 'Zack'])</span>
</pre></div>
</div>
</div>
<div class="section" id="protocol-for-automatic-conversion-to-immutable">
<span id="immutable-transforms"></span><h2>8.7.3. Protocol for automatic conversion to immutable<a class="headerlink" href="#protocol-for-automatic-conversion-to-immutable" title="Permalink to this headline">¶</a></h2>
<p>Sets can only contain immutable elements. For convenience, mutable <a class="reference internal" href="#sets.Set" title="sets.Set"><code class="xref py py-class docutils literal notranslate"><span class="pre">Set</span></code></a>
objects are automatically copied to an <a class="reference internal" href="#sets.ImmutableSet" title="sets.ImmutableSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImmutableSet</span></code></a> before being added
as a set element.</p>
<p>The mechanism is to always add a <a class="reference internal" href="../glossary.html#term-hashable"><span class="xref std std-term">hashable</span></a> element, or if it is not
hashable, the element is checked to see if it has an <code class="xref py py-meth docutils literal notranslate"><span class="pre">__as_immutable__()</span></code>
method which returns an immutable equivalent.</p>
<p>Since <a class="reference internal" href="#sets.Set" title="sets.Set"><code class="xref py py-class docutils literal notranslate"><span class="pre">Set</span></code></a> objects have a <code class="xref py py-meth docutils literal notranslate"><span class="pre">__as_immutable__()</span></code> method returning an
instance of <a class="reference internal" href="#sets.ImmutableSet" title="sets.ImmutableSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImmutableSet</span></code></a>, it is possible to construct sets of sets.</p>
<p>A similar mechanism is needed by the <a class="reference internal" href="../reference/datamodel.html#object.__contains__" title="object.__contains__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__contains__()</span></code></a> and <code class="xref py py-meth docutils literal notranslate"><span class="pre">remove()</span></code>
methods which need to hash an element to check for membership in a set. Those
methods check an element for hashability and, if not, check for a
<code class="xref py py-meth docutils literal notranslate"><span class="pre">__as_temporarily_immutable__()</span></code> method which returns the element wrapped by
a class that provides temporary methods for <a class="reference internal" href="../reference/datamodel.html#object.__hash__" title="object.__hash__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__hash__()</span></code></a>, <a class="reference internal" href="../reference/datamodel.html#object.__eq__" title="object.__eq__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__eq__()</span></code></a>,
and <a class="reference internal" href="../reference/datamodel.html#object.__ne__" title="object.__ne__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__ne__()</span></code></a>.</p>
<p>The alternate mechanism spares the need to build a separate copy of the original
mutable object.</p>
<p><a class="reference internal" href="#sets.Set" title="sets.Set"><code class="xref py py-class docutils literal notranslate"><span class="pre">Set</span></code></a> objects implement the <code class="xref py py-meth docutils literal notranslate"><span class="pre">__as_temporarily_immutable__()</span></code> method
which returns the <a class="reference internal" href="#sets.Set" title="sets.Set"><code class="xref py py-class docutils literal notranslate"><span class="pre">Set</span></code></a> object wrapped by a new class
<code class="xref py py-class docutils literal notranslate"><span class="pre">_TemporarilyImmutableSet</span></code>.</p>
<p>The two mechanisms for adding hashability are normally invisible to the user;
however, a conflict can arise in a multi-threaded environment where one thread
is updating a set while another has temporarily wrapped it in
<code class="xref py py-class docutils literal notranslate"><span class="pre">_TemporarilyImmutableSet</span></code>. In other words, sets of mutable sets are not
thread-safe.</p>
</div>
<div class="section" id="comparison-to-the-built-in-set-types">
<span id="comparison-to-builtin-set"></span><h2>8.7.4. Comparison to the built-in <a class="reference internal" href="stdtypes.html#set" title="set"><code class="xref py py-class docutils literal notranslate"><span class="pre">set</span></code></a> types<a class="headerlink" href="#comparison-to-the-built-in-set-types" title="Permalink to this headline">¶</a></h2>
<p>The built-in <a class="reference internal" href="stdtypes.html#set" title="set"><code class="xref py py-class docutils literal notranslate"><span class="pre">set</span></code></a> and <a class="reference internal" href="stdtypes.html#frozenset" title="frozenset"><code class="xref py py-class docutils literal notranslate"><span class="pre">frozenset</span></code></a> types were designed based on
lessons learned from the <a class="reference internal" href="#module-sets" title="sets: Implementation of sets of unique elements. (deprecated)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sets</span></code></a> module. The key differences are:</p>
<ul class="simple">
<li><p><a class="reference internal" href="#sets.Set" title="sets.Set"><code class="xref py py-class docutils literal notranslate"><span class="pre">Set</span></code></a> and <a class="reference internal" href="#sets.ImmutableSet" title="sets.ImmutableSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImmutableSet</span></code></a> were renamed to <a class="reference internal" href="stdtypes.html#set" title="set"><code class="xref py py-class docutils literal notranslate"><span class="pre">set</span></code></a> and
<a class="reference internal" href="stdtypes.html#frozenset" title="frozenset"><code class="xref py py-class docutils literal notranslate"><span class="pre">frozenset</span></code></a>.</p></li>
<li><p>There is no equivalent to <code class="xref py py-class docutils literal notranslate"><span class="pre">BaseSet</span></code>. Instead, use <code class="docutils literal notranslate"><span class="pre">isinstance(x,</span>
<span class="pre">(set,</span> <span class="pre">frozenset))</span></code>.</p></li>
<li><p>The hash algorithm for the built-ins performs significantly better (fewer
collisions) for most datasets.</p></li>
<li><p>The built-in versions have more space efficient pickles.</p></li>
<li><p>The built-in versions do not have a <code class="xref py py-meth docutils literal notranslate"><span class="pre">union_update()</span></code> method. Instead, use
the <code class="xref py py-meth docutils literal notranslate"><span class="pre">update()</span></code> method which is equivalent.</p></li>
<li><p>The built-in versions do not have a <code class="docutils literal notranslate"><span class="pre">_repr(sorted=True)</span></code> method.
Instead, use the built-in <a class="reference internal" href="functions.html#repr" title="repr"><code class="xref py py-func docutils literal notranslate"><span class="pre">repr()</span></code></a> and <a class="reference internal" href="functions.html#sorted" title="sorted"><code class="xref py py-func docutils literal notranslate"><span class="pre">sorted()</span></code></a> functions:
<code class="docutils literal notranslate"><span class="pre">repr(sorted(s))</span></code>.</p></li>
<li><p>The built-in version does not have a protocol for automatic conversion to
immutable. Many found this feature to be confusing and no one in the community
reported having found real uses for it.</p></li>
</ul>
</div>
</div>
</div>
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<h3><a href="../contents.html">Table of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">8.7. <code class="xref py py-mod docutils literal notranslate"><span class="pre">sets</span></code> — Unordered collections of unique elements</a><ul>
<li><a class="reference internal" href="#set-objects">8.7.1. Set Objects</a></li>
<li><a class="reference internal" href="#example">8.7.2. Example</a></li>
<li><a class="reference internal" href="#protocol-for-automatic-conversion-to-immutable">8.7.3. Protocol for automatic conversion to immutable</a></li>
<li><a class="reference internal" href="#comparison-to-the-built-in-set-types">8.7.4. Comparison to the built-in <code class="xref py py-class docutils literal notranslate"><span class="pre">set</span></code> types</a></li>
</ul>
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<h4>Previous topic</h4>
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