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<Head>
<Title>Equality Comparable</Title>
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<H1>Equality Comparable</H1>

<Table CellPadding=0 CellSpacing=0 width=100%>
<TR>
<TD Align=left><Img src = "utilities.gif" Alt=""   WIDTH = "194"  HEIGHT = "38" ></TD>
<TD Align=right><Img src = "concept.gif" Alt=""   WIDTH = "194"  HEIGHT = "38" ></TD>
</TR>
<TR>
<TD Align=left VAlign=top><b>Category</b>: utilities</TD>
<TD Align=right VAlign=top><b>Component type</b>: concept</TD>
</TR>
</Table>

<h3>Description</h3>
A type is EqualityComparable if objects of that type can be compared for
equality using <tt>operator==</tt>, and if <tt>operator==</tt> is an equivalence relation.
<h3>Refinement of</h3>
<h3>Associated types</h3>
<h3>Notation</h3>
<Table>
<TR>
<TD VAlign=top>
<tt>X</tt>
</TD>
<TD VAlign=top>
A type that is a model of EqualityComparable
</TD>
</TR>
<TR>
<TD VAlign=top>
<tt>x</tt>, <tt>y</tt>, <tt>z</tt>
</TD>
<TD VAlign=top>
Object of type <tt>X</tt>
</TD>
</tr>
</table>
<h3>Definitions</h3>
<h3>Valid expressions</h3>
<Table border>
<TR>
<TH>
Name
</TH>
<TH>
Expression
</TH>
<TH>
Type requirements
</TH>
<TH>
Return type
</TH>
</TR>
<TR>
<TD VAlign=top>
Equality
</TD>
<TD VAlign=top>
<tt>x == y</tt>
</TD>
<TD VAlign=top>
&nbsp;
</TD>
<TD VAlign=top>
Convertible to <tt>bool</tt>
</TD>
</TR>
<TR>
<TD VAlign=top>
Inequality
</TD>
<TD VAlign=top>
<tt>x != y</tt>
</TD>
<TD VAlign=top>
&nbsp;
</TD>
<TD VAlign=top>
Convertible to <tt>bool</tt>
</TD>
</tr>
</table>
<h3>Expression semantics</h3>
<Table border>
<TR>
<TH>
Name
</TH>
<TH>
Expression
</TH>
<TH>
Precondition
</TH>
<TH>
Semantics
</TH>
<TH>
Postcondition
</TH>
</TR>
<TR>
<TD VAlign=top>
Equality
</TD>
<TD VAlign=top>
<tt>x == y</tt>
</TD>
<TD VAlign=top>
<tt>x</tt> and <tt>y</tt> are in the domain of <tt>==</tt>
</TD>
<TD VAlign=top>
&nbsp;
</TD>
<TD VAlign=top>
&nbsp;
</TD>
</TR>
<TR>
<TD VAlign=top>
Inequality
</TD>
<TD VAlign=top>
<tt>x != y</tt>
</TD>
<TD VAlign=top>
<tt>x</tt> and <tt>y</tt> are in the domain of <tt>==</tt>
</TD>
<TD VAlign=top>
Equivalent to <tt>!(x == y)</tt>
</TD>
<TD VAlign=top>
&nbsp;
</TD>
</tr>
</table>
<h3>Complexity guarantees</h3>
<h3>Invariants</h3>
<Table border>
<TR>
<TD VAlign=top>
Identity
</TD>
<TD VAlign=top>
<tt>&amp;x == &amp;y</tt> implies <tt>x</tt> == <tt>y</tt>
</TD>
</TR>
<TR>
<TD VAlign=top>
Reflexivity
</TD>
<TD VAlign=top>
<tt>x == x</tt>
</TD>
</TR>
<TR>
<TD VAlign=top>
Symmetry
</TD>
<TD VAlign=top>
<tt>x == y</tt> implies <tt>y == x</tt>
</TD>
</TR>
<TR>
<TD VAlign=top>
Transitivity
</TD>
<TD VAlign=top>
<tt>x == y</tt> and <tt>y == z</tt> implies <tt>x == z</tt>
</TD>
</tr>
</table>
<h3>Models</h3>
<UL>
<LI>
int
<LI>
<tt><A href="Vector.html">vector</A>&lt;int&gt;</tt>
</UL>
<h3>Notes</h3>
<h3>See also</h3>
<A href="LessThanComparable.html">LessThanComparable</A>.

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