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<H1><A NAME="SECTION0071500000000000000000">
5.15 <tt class="module">sets</tt> --
         Unordered collections of unique elements</A>
</H1>

<P>
<A NAME="module-sets"></A>

<P>

<span class="versionnote">New in version 2.3.</span>

<P>
The <tt class="module">sets</tt> 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>
Like other collections, sets support <code><var>x</var> in <var>set</var></code>,
<code>len(<var>set</var>)</code>, and <code>for <var>x</var> in <var>set</var></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>
Most set applications use the <tt class="class">Set</tt> class which provides every set
method except for <tt class="method">__hash__()</tt>. For advanced applications requiring
a hash method, the <tt class="class">ImmutableSet</tt> class adds a <tt class="method">__hash__()</tt>
method but omits methods which alter the contents of the set. Both
<tt class="class">Set</tt> and <tt class="class">ImmutableSet</tt> derive from <tt class="class">BaseSet</tt>, an
abstract class useful for determining whether something is a set:
<code>isinstance(<var>obj</var>, BaseSet)</code>.

<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 <tt class="method">__eq__</tt> and <tt class="method">__hash__</tt>.
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 <tt class="class">ImmutableSet</tt>.  For convenience in implementing
sets of sets, inner sets are automatically converted to immutable
form, for example, <code>Set([Set(['dog'])])</code> is transformed to
<code>Set([ImmutableSet(['dog'])])</code>.

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><span class="typelabel">class</span>&nbsp;<tt id='l2h-1380' xml:id='l2h-1380' class="class">Set</tt></b>(</nobr></td>
  <td><var></var><big>[</big><var>iterable</var><big>]</big><var></var>)</td></tr></table></dt>
<dd>
Constructs a new empty <tt class="class">Set</tt> object.  If the optional <var>iterable</var>
parameter is supplied, updates the set with elements obtained from iteration.
All of the elements in <var>iterable</var> should be immutable or be transformable
to an immutable using the protocol described in
section&nbsp;<A href="immutable-transforms.html#immutable-transforms">5.15.3</A>.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><span class="typelabel">class</span>&nbsp;<tt id='l2h-1381' xml:id='l2h-1381' class="class">ImmutableSet</tt></b>(</nobr></td>
  <td><var></var><big>[</big><var>iterable</var><big>]</big><var></var>)</td></tr></table></dt>
<dd>
Constructs a new empty <tt class="class">ImmutableSet</tt> object.  If the optional
<var>iterable</var> parameter is supplied, updates the set with elements obtained
from iteration.  All of the elements in <var>iterable</var> should be immutable or
be transformable to an immutable using the protocol described in
section&nbsp;<A href="immutable-transforms.html#immutable-transforms">5.15.3</A>.

<P>
Because <tt class="class">ImmutableSet</tt> objects provide a <tt class="method">__hash__()</tt> method,
they can be used as set elements or as dictionary keys.  <tt class="class">ImmutableSet</tt>
objects do not have methods for adding or removing elements, so all of the
elements must be known when the constructor is called.
</dl>

<P>

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<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></a>

<UL CLASS="ChildLinks">
<LI><A href="set-objects.html">5.15.1 Set Objects</a>
<LI><A href="set-example.html">5.15.2 Example</a>
<LI><A href="immutable-transforms.html">5.15.3 Protocol for automatic conversion to immutable</a>
<LI><A href="comparison-to-builtin-set.html">5.15.4 Comparison to the built-in <tt class="class">set</tt> types</a>
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<span class="release-info">Release 2.4.2, documentation updated on 28 September 2005.</span>
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