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/* __ *\
** ________ ___ / / ___ Scala API **
** / __/ __// _ | / / / _ | (c) 2003-2009, LAMP/EPFL **
** __\ \/ /__/ __ |/ /__/ __ | http://scala-lang.org/ **
** /____/\___/_/ |_/____/_/ | | **
** |/ **
\* */
// $Id$
package scala.math
/** <p>
* A trait for representing equivalence relations. It is important to
* distinguish between a type that can be compared for equality or
* equivalence and a representation of equivalence on some type. This
* trait is for representing the latter.
* </p>
* <p>
* An <a href="http://en.wikipedia.org/wiki/Equivalence_relation">equivalence
* relation</a> is a binary relation on a type. This relation is exposed as
* the <code>equiv</code> method of the <code>Equiv</code> trait. This
* relation must be:
* </p>
* <ul>
* <li>reflexive: <code>equiv(x, x) == true</code>, for any <code>x</code> of
* type <code>T</code>.</li>
* <li>symmetric: <code>equiv(x, y) == equiv(y, x)</code>, for any
* <code>x</code> and <code>y</code> of type <code>T</code>.</li>
* <li>transitive: if <code>equiv(x, y) == true</code> and <code>equiv(y, z) == true</code>
* then <code>equiv(x, z) == true</code>, for any <code>x</code>, <code>y</code>,
* and <code>z</code> of type <code>T</code>.</li>
* </ul>
*
* @author Geoffrey Washburn
* @version 1.0, 2008-04-03
* @since 2.7
*/
trait Equiv[T] {
/** Returns <code>true</code> iff <code>x</code> is equivalent to
* <code>y</code>.
*/
def equiv(x: T, y: T): Boolean
}
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