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  <header>
    <copyright>
      <year>2000</year><year>2022</year>
      <holder>Ericsson AB. All Rights Reserved.</holder>
    </copyright>
    <legalnotice>
      Licensed under the Apache License, Version 2.0 (the "License");
      you may not use this file except in compliance with the License.
      You may obtain a copy of the License at
 
          http://www.apache.org/licenses/LICENSE-2.0

      Unless required by applicable law or agreed to in writing, software
      distributed under the License is distributed on an "AS IS" BASIS,
      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
      See the License for the specific language governing permissions and
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    </legalnotice>

    <title>sets</title>
    <prepared>Robert Virding</prepared>
    <responsible>Bjarne D&auml;cker</responsible>
    <docno>1</docno>
    <approved>Bjarne D&auml;cker</approved>
    <checked></checked>
    <date>1999-07-27</date>
    <rev>A</rev>
    <file>sets.xml</file>
  </header>
  <module since="">sets</module>
  <modulesummary>Functions for set manipulation.</modulesummary>
  <description>
    <p>Sets are collections of elements with no duplicate
    elements.</p>

    <p>The data representing a set as used by this module is to be
    regarded as opaque by other modules.  In abstract terms, the
    representation is a composite type of existing Erlang terms. See
    note on <seeguide
    marker="system/reference_manual:data_types#no_user_types">data
    types</seeguide>. Any code assuming knowledge of the format is
    running on thin ice.</p>


    <p>This module provides the same interface as the
      <seeerl marker="ordsets"><c>ordsets(3)</c></seeerl> module
      but with an undefined representation. One difference is
      that while this module considers two elements as different if they
      do not match (<c>=:=</c>), <c>ordsets</c> considers two elements as
      different if and only if they do not compare equal (<c>==</c>).</p>

    <p>Erlang/OTP 24.0 introduced a new internal representation for sets
      which is more performant. Developers can use this new representation
      by passing the <c>{version, 2}</c> flag to <seemfa marker="#new/1"><c>new/1</c></seemfa>
      and <seemfa marker="#from_list/2"><c>from_list/2</c></seemfa>, such
      as <c>sets:new([{version, 2}])</c>. This new representation will
      become the default in future Erlang/OTP versions. Functions that
      work on two sets, such as <seemfa marker="#union/2"><c>union/2</c></seemfa>
      and similar, will work with sets of different versions. In such cases,
      there is no guarantee about the version of the returned set. Explicit
      conversion from the old version to the new one can be done with
      <c>sets:from_list(sets:to_list(Old), [{version,2}])</c>.
    </p>

  </description>

  <datatypes>
    <datatype>
      <name name="set" n_vars="1"/>
      <desc><p>As returned by
        <seemfa marker="#new/0"><c>new/0</c></seemfa>.</p></desc>
    </datatype>
    <datatype>
      <name name="set" n_vars="0"/>
    </datatype>
  </datatypes>

  <funcs>
    <func>
      <name name="add_element" arity="2" since=""/>
      <fsummary>Add an element to a <c>Set</c>.</fsummary>
      <desc>
        <p>Returns a new set formed from <c><anno>Set1</anno></c> with
          <c><anno>Element</anno></c> inserted.</p>
      </desc>
    </func>

    <func>
      <name name="del_element" arity="2" since=""/>
      <fsummary>Remove an element from a <c>Set</c>.</fsummary>
      <desc>
        <p>Returns <c><anno>Set1</anno></c>, but with
          <c><anno>Element</anno></c> removed.</p>
      </desc>
    </func>

    <func>
      <name name="filter" arity="2" since=""/>
      <fsummary>Filter set elements.</fsummary>
      <desc>
        <p>Filters elements in <c><anno>Set1</anno></c> with boolean function
          <c><anno>Pred</anno></c>.</p>
      </desc>
    </func>

    <func>
      <name name="fold" arity="3" since=""/>
      <fsummary>Fold over set elements.</fsummary>
      <desc>
        <p>Folds <c><anno>Function</anno></c> over every element in
          <c><anno>Set</anno></c> and returns the final value of the
          accumulator. The evaluation order is undefined.</p>
      </desc>
    </func>

    <func>
      <name name="from_list" arity="1" since=""/>
      <fsummary>Convert a list into a <c>Set</c>.</fsummary>
      <desc>
        <p>Returns a set of the elements in <c><anno>List</anno></c>.</p>
      </desc>
    </func>

    <func>
      <name name="from_list" arity="2" since="OTP 24.0"/>
      <fsummary>Convert a list into a <c>Set</c> at the given version.</fsummary>
      <desc>
        <p>Returns a set of the elements in <c><anno>List</anno></c> at the given version.</p>
      </desc>
    </func>

    <func>
      <name name="intersection" arity="1" since=""/>
      <fsummary>Return the intersection of a list of <c>Sets</c>.</fsummary>
      <desc>
        <p>Returns the intersection of the non-empty list of sets.</p>
      </desc>
    </func>

    <func>
      <name name="intersection" arity="2" since=""/>
      <fsummary>Return the intersection of two <c>Sets</c>.</fsummary>
      <desc>
        <p>Returns the intersection of <c><anno>Set1</anno></c> and
          <c><anno>Set2</anno></c>.</p>
      </desc>
    </func>

    <func>
      <name name="is_disjoint" arity="2" since=""/>
      <fsummary>Check whether two <c>Sets</c> are disjoint.</fsummary>
      <desc>
        <p>Returns <c>true</c> if <c><anno>Set1</anno></c> and
          <c><anno>Set2</anno></c> are disjoint (have no elements in common),
	  otherwise <c>false</c>.</p>
      </desc>
    </func>

    <func>
      <name name="is_element" arity="2" since=""/>
      <fsummary>Test for membership of a <c>Set</c>.</fsummary>
      <desc>
        <p>Returns <c>true</c> if <c><anno>Element</anno></c> is an element of
          <c><anno>Set</anno></c>, otherwise <c>false</c>.</p>
      </desc>
    </func>

    <func>
      <name name="is_empty" arity="1" since="OTP 21.0"/>
      <fsummary>Test for empty set.</fsummary>
      <desc>
        <p>Returns <c>true</c> if <c><anno>Set</anno></c> is an empty set,
          otherwise <c>false</c>.</p>
      </desc>
    </func>

    <func>
      <name name="is_set" arity="1" since=""/>
      <fsummary>Test for a <c>Set</c>.</fsummary>
      <desc>
        <p>Returns <c>true</c> if <c><anno>Set</anno></c> appears to
        be a set of elements, otherwise <c>false</c>.  Note that the
        test is shallow and will return <c>true</c> for any term that
        coincides with the possible representations of a set.  See
        also note on <seeguide
        marker="system/reference_manual:data_types#no_user_types">data
        types</seeguide>.</p>
      </desc>
    </func>

    <func>
      <name name="is_subset" arity="2" since=""/>
      <fsummary>Test for subset.</fsummary>
      <desc>
        <p>Returns <c>true</c> when every element of <c><anno>Set1</anno></c> is
          also a member of <c><anno>Set2</anno></c>, otherwise <c>false</c>.</p>
      </desc>
    </func>

    <func>
      <name name="new" arity="0" since=""/>
      <fsummary>Return an empty set.</fsummary>
      <desc>
        <p>Returns a new empty set.</p>
      </desc>
    </func>

    <func>
      <name name="new" arity="1" since="OTP 24.0"/>
      <fsummary>Return an empty set at the given version.</fsummary>
      <desc>
        <p>Returns a new empty set at the given version.</p>
      </desc>
    </func>

    <func>
      <name name="size" arity="1" since=""/>
      <fsummary>Return the number of elements in a set.</fsummary>
      <desc>
        <p>Returns the number of elements in <c><anno>Set</anno></c>.</p>
      </desc>
    </func>

    <func>
      <name name="subtract" arity="2" since=""/>
      <fsummary>Return the difference of two <c>Sets</c>.</fsummary>
      <desc>
        <p>Returns only the elements of <c><anno>Set1</anno></c> that are not
          also elements of <c><anno>Set2</anno></c>.</p>
      </desc>
    </func>

    <func>
      <name name="to_list" arity="1" since=""/>
      <fsummary>Convert a <c>Set</c>into a list.</fsummary>
      <desc>
        <p>Returns the elements of <c><anno>Set</anno></c> as a list.
          The order of the returned elements is undefined.</p>
      </desc>
    </func>

    <func>
      <name name="union" arity="1" since=""/>
      <fsummary>Return the union of a list of <c>Sets</c>.</fsummary>
      <desc>
        <p>Returns the merged (union) set of the list of sets.</p>
      </desc>
    </func>

    <func>
      <name name="union" arity="2" since=""/>
      <fsummary>Return the union of two <c>Sets</c>.</fsummary>
      <desc>
        <p>Returns the merged (union) set of <c><anno>Set1</anno></c> and
          <c><anno>Set2</anno></c>.</p>
      </desc>
    </func>
  </funcs>

  <section>
    <title>See Also</title>
    <p><seeerl marker="gb_sets"><c>gb_sets(3)</c></seeerl>,
      <seeerl marker="ordsets"><c>ordsets(3)</c></seeerl></p>
  </section>
</erlref>

