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  <header>
    <copyright>
      <year>1996</year><year>2018</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,
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      See the License for the specific language governing permissions and
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    <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
      <seealso marker="sets"><c>sets(3)</c></seealso> 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
        <seealso marker="#new/0"><c>new/0</c></seealso>.</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><seealso marker="gb_sets"><c>gb_sets(3)</c></seealso>,
      <seealso marker="sets"><c>sets(3)</c></seealso></p>
  </section>
</erlref>

