equiv.scala

来自「JAVA 语言的函数式编程扩展」· SCALA 代码 · 共 42 行

/*                     __                                               *\
**     ________ ___   / /  ___     Scala API                            **
**    / __/ __// _ | / /  / _ |    (c) 2003-2008, LAMP/EPFL             **
**  __\ \/ /__/ __ |/ /__/ __ |                                         **
** /____/\___/_/ |_/____/_/ | |                                         **
**                          |/                                          **
\*                                                                      */

// $Id: Equiv.scala 14488 2008-04-03 14:16:41Z washburn $

package scala

/** 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.  
 *
 * 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:
 * <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
 */

trait Equiv[T] {
  /** Returns <code>true</code> iff <code>x</code> is equivalent to
   *  <code>y</code>.  
   */
  def equiv(x: T, y: T): Boolean 
}