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  <header>
    <copyright>
      <year>1996</year><year>2021</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>ordsets</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>ordsets.xml</file>
  </header>
  <module since="">ordsets</module>
  <modulesummary>Functions for manipulating sets as ordered lists.
  </modulesummary>
  <description>
    <p>Sets are collections of elements with no duplicate elements.
      An <c>ordset</c> is a representation of a set, where an ordered
      list is used to store the elements of the set. An ordered list
      is more efficient than an unordered list. Elements are ordered
      according to the <em>Erlang term order</em>.</p>

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

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

  <funcs>
    <func>
      <name name="add_element" arity="2" since=""/>
      <fsummary>Add an element to an <c>Ordset</c>.</fsummary>
      <desc>
        <p>Returns a new ordered set formed from <c><anno>Ordset1</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 an <c>Ordset</c>.</fsummary>
      <desc>
        <p>Returns <c><anno>Ordset1</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>Ordset1</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>Ordset</anno></c> and returns the final value of the
          accumulator.</p>
      </desc>
    </func>

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

    <func>
      <name name="intersection" arity="1" since=""/>
      <fsummary>Return the intersection of a list of <c>Ordsets</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>Ordsets</c>.</fsummary>
      <desc>
        <p>Returns the intersection of <c><anno>Ordset1</anno></c> and
          <c><anno>Ordset2</anno></c>.</p>
      </desc>
    </func>

    <func>
      <name name="is_disjoint" arity="2" since=""/>
      <fsummary>Check whether two <c>Ordsets</c> are disjoint.</fsummary>
      <desc>
        <p>Returns <c>true</c> if <c><anno>Ordset1</anno></c> and
          <c><anno>Ordset2</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 an <c>Ordset</c>.</fsummary>
      <desc>
        <p>Returns <c>true</c> if <c><anno>Element</anno></c> is an element of
          <c><anno>Ordset</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>Ordset</anno></c> is an empty set,
          otherwise <c>false</c>.</p>
      </desc>
    </func>

    <func>
      <name name="is_set" arity="1" since=""/>
      <fsummary>Test for an <c>Ordset</c>.</fsummary>
      <desc>
        <p>Returns <c>true</c> if <c><anno>Ordset</anno></c> is an ordered set
          of elements, otherwise <c>false</c>.</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>Ordset1</anno></c>
          is also a member of <c><anno>Ordset2</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 ordered set.</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>Ordset</anno></c>.</p>
      </desc>
    </func>

    <func>
      <name name="subtract" arity="2" since=""/>
      <fsummary>Return the difference of two <c>Ordsets</c>.</fsummary>
      <desc>
        <p>Returns only the elements of <c><anno>Ordset1</anno></c> that are not
          also elements of <c><anno>Ordset2</anno></c>.</p>
      </desc>
    </func>

    <func>
      <name name="to_list" arity="1" since=""/>
      <fsummary>Convert an <c>Ordset</c> into a list.</fsummary>
      <desc>
        <p>Returns the elements of <c><anno>Ordset</anno></c> as a list.</p>
      </desc>
    </func>

    <func>
      <name name="union" arity="1" since=""/>
      <fsummary>Return the union of a list of <c>Ordsets</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>Ordsets</c>.</fsummary>
      <desc>
        <p>Returns the merged (union) set of <c><anno>Ordset1</anno></c> and
          <c><anno>Ordset2</anno></c>.</p>
      </desc>
    </func>
  </funcs>

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

