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<H2><A NAME="SECTION004370000000000000000"></A><A NAME="types-set"></A>
<BR>
2.3.7 Set Types --
	    <tt class="class">set</tt>, <tt class="class">frozenset</tt>
	    
</H2>
<a id='l2h-226' xml:id='l2h-226'></a>
<P>
A <i class="dfn">set</i> object is an unordered collection of immutable values.
Common uses include membership testing, removing duplicates from a sequence,
and computing mathematical operations such as intersection, union, difference,
and symmetric difference.

<span class="versionnote">New in version 2.4.</span>

<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>
There are currently two builtin set types, <tt class="class">set</tt> and <tt class="class">frozenset</tt>.
The <tt class="class">set</tt> type is mutable -- the contents can be changed using methods
like <tt class="method">add()</tt> and <tt class="method">remove()</tt>.  Since it is mutable, it has no
hash value and cannot be used as either a dictionary key or as an element of
another set.  The <tt class="class">frozenset</tt> type is immutable and hashable -- its
contents cannot be altered after is created; however, it can be used as
a dictionary key or as an element of another set.

<P>
Instances of <tt class="class">set</tt> and <tt class="class">frozenset</tt> provide the following operations:

<P>
<div class="center"><table class="realtable">
  <thead>
    <tr>
      <th class="center">Operation</th>
      <th class="center">Equivalent</th>
      <th class="left"  >Result</th>
      </tr>
    </thead>
  <tbody>
    <tr><td class="center" valign="baseline"><code>len(<var>s</var>)</code></td>
        <td class="center"></td>
        <td class="left"  >cardinality of set <var>s</var></td></tr><P>

    <tr><td class="center" valign="baseline"><code><var>x</var> in <var>s</var></code></td>
        <td class="center"></td>
        <td class="left"  >test <var>x</var> for membership in <var>s</var></td></tr>
    <tr><td class="center" valign="baseline"><code><var>x</var> not in <var>s</var></code></td>
        <td class="center"></td>
        <td class="left"  >test <var>x</var> for non-membership in <var>s</var></td></tr>
    <tr><td class="center" valign="baseline"><code><var>s</var>.issubset(<var>t</var>)</code></td>
        <td class="center"><code><var>s</var> &lt;= <var>t</var></code></td>
        <td class="left"  >test whether every element in <var>s</var> is in <var>t</var></td></tr>
    <tr><td class="center" valign="baseline"><code><var>s</var>.issuperset(<var>t</var>)</code></td>
        <td class="center"><code><var>s</var> &gt;= <var>t</var></code></td>
        <td class="left"  >test whether every element in <var>t</var> is in <var>s</var></td></tr><P>

    <tr><td class="center" valign="baseline"><code><var>s</var>.union(<var>t</var>)</code></td>
        <td class="center"><var>s</var> | <var>t</var></td>
        <td class="left"  >new set with elements from both <var>s</var> and <var>t</var></td></tr>
    <tr><td class="center" valign="baseline"><code><var>s</var>.intersection(<var>t</var>)</code></td>
        <td class="center"><var>s</var> &amp; <var>t</var></td>
        <td class="left"  >new set with elements common to <var>s</var> and <var>t</var></td></tr>
    <tr><td class="center" valign="baseline"><code><var>s</var>.difference(<var>t</var>)</code></td>
        <td class="center"><var>s</var> - <var>t</var></td>
        <td class="left"  >new set with elements in <var>s</var> but not in <var>t</var></td></tr>
    <tr><td class="center" valign="baseline"><code><var>s</var>.symmetric_difference(<var>t</var>)</code></td>
        <td class="center"><var>s</var> ^ <var>t</var></td>
        <td class="left"  >new set with elements in either <var>s</var> or <var>t</var> but not both</td></tr>
    <tr><td class="center" valign="baseline"><code><var>s</var>.copy()</code></td>
        <td class="center"></td>
        <td class="left"  >new set with a shallow copy of <var>s</var></td></tr></tbody>
</table></div>

<P>
Note, the non-operator versions of <tt class="method">union()</tt>, <tt class="method">intersection()</tt>,
<tt class="method">difference()</tt>, and <tt class="method">symmetric_difference()</tt>,
<tt class="method">issubset()</tt>, and <tt class="method">issuperset()</tt> methods 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>set('abc') &amp; 'cbs'</code> in favor of the more readable
<code>set('abc').intersection('cbs')</code>.

<P>
Both <tt class="class">set</tt> and <tt class="class">frozenset</tt> 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>
Instances of <tt class="class">set</tt> are compared to instances of <tt class="class">frozenset</tt> based
on their members.  For example, "<tt class="samp">set('abc') == frozenset('abc')</tt>" returns
<code>True</code>.     

<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>False</code>:  <code><var>a</var>&lt;<var>b</var></code>, <code><var>a</var>==<var>b</var></code>, or
<code><var>a</var>&gt;<var>b</var></code>.
Accordingly, sets do not implement the <tt class="method">__cmp__</tt> method.

<P>
Since sets only define partial ordering (subset relationships), the output
of the <tt class="method">list.sort()</tt> method is undefined for lists of sets.

<P>
Set elements are like dictionary keys; they need to define both
<tt class="method">__hash__</tt> and <tt class="method">__eq__</tt> methods.

<P>
Binary operations that mix <tt class="class">set</tt> instances with <tt class="class">frozenset</tt>
return the type of the first operand.  For example:
"<tt class="samp">frozenset('ab') | set('bc')</tt>" returns an instance of <tt class="class">frozenset</tt>.

<P>
The following table lists operations available for <tt class="class">set</tt>
that do not apply to immutable instances of <tt class="class">frozenset</tt>:

<P>
<div class="center"><table class="realtable">
  <thead>
    <tr>
      <th class="center">Operation</th>
      <th class="center">Equivalent</th>
      <th class="left"  >Result</th>
      </tr>
    </thead>
  <tbody>
    <tr><td class="center" valign="baseline"><code><var>s</var>.update(<var>t</var>)</code></td>
        <td class="center"><var>s</var> |= <var>t</var></td>
        <td class="left"  >return set <var>s</var> with elements added from <var>t</var></td></tr>
    <tr><td class="center" valign="baseline"><code><var>s</var>.intersection_update(<var>t</var>)</code></td>
        <td class="center"><var>s</var> &amp;= <var>t</var></td>
        <td class="left"  >return set <var>s</var> keeping only elements also found in <var>t</var></td></tr>
    <tr><td class="center" valign="baseline"><code><var>s</var>.difference_update(<var>t</var>)</code></td>
        <td class="center"><var>s</var> -= <var>t</var></td>
        <td class="left"  >return set <var>s</var> after removing elements found in <var>t</var></td></tr>
    <tr><td class="center" valign="baseline"><code><var>s</var>.symmetric_difference_update(<var>t</var>)</code></td>
        <td class="center"><var>s</var> ^= <var>t</var></td>
        <td class="left"  >return set <var>s</var> with elements from <var>s</var> or <var>t</var>
          but not both</td></tr><P>

    <tr><td class="center" valign="baseline"><code><var>s</var>.add(<var>x</var>)</code></td>
        <td class="center"></td>
        <td class="left"  >add element <var>x</var> to set <var>s</var></td></tr>
    <tr><td class="center" valign="baseline"><code><var>s</var>.remove(<var>x</var>)</code></td>
        <td class="center"></td>
        <td class="left"  >remove <var>x</var> from set <var>s</var>; raises KeyError if not present</td></tr>
    <tr><td class="center" valign="baseline"><code><var>s</var>.discard(<var>x</var>)</code></td>
        <td class="center"></td>
        <td class="left"  >removes <var>x</var> from set <var>s</var> if present</td></tr>
    <tr><td class="center" valign="baseline"><code><var>s</var>.pop()</code></td>
        <td class="center"></td>
        <td class="left"  >remove and return an arbitrary element from <var>s</var>; raises
	  <tt class="exception">KeyError</tt> if empty</td></tr>
    <tr><td class="center" valign="baseline"><code><var>s</var>.clear()</code></td>
        <td class="center"></td>
        <td class="left"  >remove all elements from set <var>s</var></td></tr></tbody>
</table></div>

<P>
Note, the non-operator versions of the <tt class="method">update()</tt>,
<tt class="method">intersection_update()</tt>, <tt class="method">difference_update()</tt>, and
<tt class="method">symmetric_difference_update()</tt> methods will accept any iterable
as an argument.

<P>
The design of the set types was based on lessons learned from the
<tt class="module">sets</tt> module.

<P>
<div class="seealso">
  <p class="heading">See Also:</p>
     
  <dl compact="compact" class="seemodule">
    <dt>Module <b><tt class="module"><a href="module-comparison-to-builtin-set.html">sets</a></tt>:</b>
    <dd>Differences between
     the <tt class="module">sets</tt> module and the built-in set types.
  </dl>					      
</div>

<P>

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<span class="release-info">Release 2.4.2, documentation updated on 28 September 2005.</span>
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	54
	55	<H2><A NAME="SECTION004370000000000000000"></A><A NAME="types-set"></A>
	56	<BR>
	57	2.3.7 Set Types --
	58	<tt class="class">set</tt>, <tt class="class">frozenset</tt>
	59
	60	</H2>
	61	<a id='l2h-226' xml:id='l2h-226'></a>
	62	<P>
	63	A <i class="dfn">set</i> object is an unordered collection of immutable values.
	64	Common uses include membership testing, removing duplicates from a sequence,
65	and computing mathematical operations such as intersection, union, difference,
66	and symmetric difference.
67
68	<span class="versionnote">New in version 2.4.</span>
69
70	<P>
71	Like other collections, sets support <code><var>x</var> in <var>set</var></code>,
72	<code>len(<var>set</var>)</code>, and <code>for <var>x</var> in <var>set</var></code>. Being an
73	unordered collection, sets do not record element position or order of
74	insertion. Accordingly, sets do not support indexing, slicing, or
75	other sequence-like behavior.
76
77	<P>
78	There are currently two builtin set types, <tt class="class">set</tt> and <tt class="class">frozenset</tt>.
79	The <tt class="class">set</tt> type is mutable -- the contents can be changed using methods
80	like <tt class="method">add()</tt> and <tt class="method">remove()</tt>. Since it is mutable, it has no
81	hash value and cannot be used as either a dictionary key or as an element of
82	another set. The <tt class="class">frozenset</tt> type is immutable and hashable -- its
83	contents cannot be altered after is created; however, it can be used as
84	a dictionary key or as an element of another set.
85
86	<P>
87	Instances of <tt class="class">set</tt> and <tt class="class">frozenset</tt> provide the following operations:
88
89	<P>
90	<div class="center"><table class="realtable">
91	<thead>
92	<tr>
93	<th class="center">Operation</th>
94	<th class="center">Equivalent</th>
95	<th class="left" >Result</th>
96	</tr>
97	</thead>
98	<tbody>
99	<tr><td class="center" valign="baseline"><code>len(<var>s</var>)</code></td>
100	<td class="center"></td>
101	<td class="left" >cardinality of set <var>s</var></td></tr><P>
102
103	<tr><td class="center" valign="baseline"><code><var>x</var> in <var>s</var></code></td>
104	<td class="center"></td>
105	<td class="left" >test <var>x</var> for membership in <var>s</var></td></tr>
106	<tr><td class="center" valign="baseline"><code><var>x</var> not in <var>s</var></code></td>
107	<td class="center"></td>
108	<td class="left" >test <var>x</var> for non-membership in <var>s</var></td></tr>
109	<tr><td class="center" valign="baseline"><code><var>s</var>.issubset(<var>t</var>)</code></td>
110	<td class="center"><code><var>s</var> <= <var>t</var></code></td>
111	<td class="left" >test whether every element in <var>s</var> is in <var>t</var></td></tr>
112	<tr><td class="center" valign="baseline"><code><var>s</var>.issuperset(<var>t</var>)</code></td>
113	<td class="center"><code><var>s</var> >= <var>t</var></code></td>
114	<td class="left" >test whether every element in <var>t</var> is in <var>s</var></td></tr><P>
115
116	<tr><td class="center" valign="baseline"><code><var>s</var>.union(<var>t</var>)</code></td>
117	<td class="center"><var>s</var> \| <var>t</var></td>
118	<td class="left" >new set with elements from both <var>s</var> and <var>t</var></td></tr>
119	<tr><td class="center" valign="baseline"><code><var>s</var>.intersection(<var>t</var>)</code></td>
120	<td class="center"><var>s</var> & <var>t</var></td>
121	<td class="left" >new set with elements common to <var>s</var> and <var>t</var></td></tr>
122	<tr><td class="center" valign="baseline"><code><var>s</var>.difference(<var>t</var>)</code></td>
123	<td class="center"><var>s</var> - <var>t</var></td>
124	<td class="left" >new set with elements in <var>s</var> but not in <var>t</var></td></tr>
125	<tr><td class="center" valign="baseline"><code><var>s</var>.symmetric_difference(<var>t</var>)</code></td>
126	<td class="center"><var>s</var> ^ <var>t</var></td>
127	<td class="left" >new set with elements in either <var>s</var> or <var>t</var> but not both</td></tr>
128	<tr><td class="center" valign="baseline"><code><var>s</var>.copy()</code></td>
129	<td class="center"></td>
130	<td class="left" >new set with a shallow copy of <var>s</var></td></tr></tbody>
131	</table></div>
132
133	<P>
134	Note, the non-operator versions of <tt class="method">union()</tt>, <tt class="method">intersection()</tt>,
135	<tt class="method">difference()</tt>, and <tt class="method">symmetric_difference()</tt>,
136	<tt class="method">issubset()</tt>, and <tt class="method">issuperset()</tt> methods will accept any
137	iterable as an argument. In contrast, their operator based counterparts
138	require their arguments to be sets. This precludes error-prone constructions
139	like <code>set('abc') & 'cbs'</code> in favor of the more readable
140	<code>set('abc').intersection('cbs')</code>.
141
142	<P>
143	Both <tt class="class">set</tt> and <tt class="class">frozenset</tt> support set to set comparisons.
144	Two sets are equal if and only if every element of each set is contained in
145	the other (each is a subset of the other).
146	A set is less than another set if and only if the first set is a proper
147	subset of the second set (is a subset, but is not equal).
148	A set is greater than another set if and only if the first set is a proper
149	superset of the second set (is a superset, but is not equal).
150
151	<P>
152	Instances of <tt class="class">set</tt> are compared to instances of <tt class="class">frozenset</tt> based
153	on their members. For example, "<tt class="samp">set('abc') == frozenset('abc')</tt>" returns
154	<code>True</code>.
155
156	<P>
157	The subset and equality comparisons do not generalize to a complete
158	ordering function. For example, any two disjoint sets are not equal and
159	are not subsets of each other, so <em>all</em> of the following return
160	<code>False</code>: <code><var>a</var><<var>b</var></code>, <code><var>a</var>==<var>b</var></code>, or
161	<code><var>a</var>><var>b</var></code>.
162	Accordingly, sets do not implement the <tt class="method">__cmp__</tt> method.
163
164	<P>
165	Since sets only define partial ordering (subset relationships), the output
166	of the <tt class="method">list.sort()</tt> method is undefined for lists of sets.
167
168	<P>
169	Set elements are like dictionary keys; they need to define both
170	<tt class="method">__hash__</tt> and <tt class="method">__eq__</tt> methods.
171
172	<P>
173	Binary operations that mix <tt class="class">set</tt> instances with <tt class="class">frozenset</tt>
174	return the type of the first operand. For example:
175	"<tt class="samp">frozenset('ab') \| set('bc')</tt>" returns an instance of <tt class="class">frozenset</tt>.
176
177	<P>
178	The following table lists operations available for <tt class="class">set</tt>
179	that do not apply to immutable instances of <tt class="class">frozenset</tt>:
180
181	<P>
182	<div class="center"><table class="realtable">
183	<thead>
184	<tr>
185	<th class="center">Operation</th>
186	<th class="center">Equivalent</th>
187	<th class="left" >Result</th>
188	</tr>
189	</thead>
190	<tbody>
191	<tr><td class="center" valign="baseline"><code><var>s</var>.update(<var>t</var>)</code></td>
192	<td class="center"><var>s</var> \|= <var>t</var></td>
193	<td class="left" >return set <var>s</var> with elements added from <var>t</var></td></tr>
194	<tr><td class="center" valign="baseline"><code><var>s</var>.intersection_update(<var>t</var>)</code></td>
195	<td class="center"><var>s</var> &= <var>t</var></td>
196	<td class="left" >return set <var>s</var> keeping only elements also found in <var>t</var></td></tr>
197	<tr><td class="center" valign="baseline"><code><var>s</var>.difference_update(<var>t</var>)</code></td>
198	<td class="center"><var>s</var> -= <var>t</var></td>
199	<td class="left" >return set <var>s</var> after removing elements found in <var>t</var></td></tr>
200	<tr><td class="center" valign="baseline"><code><var>s</var>.symmetric_difference_update(<var>t</var>)</code></td>
201	<td class="center"><var>s</var> ^= <var>t</var></td>
202	<td class="left" >return set <var>s</var> with elements from <var>s</var> or <var>t</var>
203	but not both</td></tr><P>
204
205	<tr><td class="center" valign="baseline"><code><var>s</var>.add(<var>x</var>)</code></td>
206	<td class="center"></td>
207	<td class="left" >add element <var>x</var> to set <var>s</var></td></tr>
208	<tr><td class="center" valign="baseline"><code><var>s</var>.remove(<var>x</var>)</code></td>
209	<td class="center"></td>
210	<td class="left" >remove <var>x</var> from set <var>s</var>; raises KeyError if not present</td></tr>
211	<tr><td class="center" valign="baseline"><code><var>s</var>.discard(<var>x</var>)</code></td>
212	<td class="center"></td>
213	<td class="left" >removes <var>x</var> from set <var>s</var> if present</td></tr>
214	<tr><td class="center" valign="baseline"><code><var>s</var>.pop()</code></td>
215	<td class="center"></td>
216	<td class="left" >remove and return an arbitrary element from <var>s</var>; raises
217	<tt class="exception">KeyError</tt> if empty</td></tr>
218	<tr><td class="center" valign="baseline"><code><var>s</var>.clear()</code></td>
219	<td class="center"></td>
220	<td class="left" >remove all elements from set <var>s</var></td></tr></tbody>
221	</table></div>
222
223	<P>
224	Note, the non-operator versions of the <tt class="method">update()</tt>,
225	<tt class="method">intersection_update()</tt>, <tt class="method">difference_update()</tt>, and
226	<tt class="method">symmetric_difference_update()</tt> methods will accept any iterable
227	as an argument.
228
229	<P>
230	The design of the set types was based on lessons learned from the
231	<tt class="module">sets</tt> module.
232
233	<P>
234	<div class="seealso">
235	<p class="heading">See Also:</p>
236
237	<dl compact="compact" class="seemodule">
238	<dt>Module <b><tt class="module"><a href="module-comparison-to-builtin-set.html">sets</a></tt>:</b>
239	<dd>Differences between
240	the <tt class="module">sets</tt> module and the built-in set types.
241	</dl>
242	</div>
243
244	<P>
245
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