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/* __ *\
** ________ ___ / / ___ Scala API **
** / __/ __// _ | / / / _ | (c) 2003-2011, LAMP/EPFL **
** __\ \/ /__/ __ |/ /__/ __ | http://scala-lang.org/ **
** /____/\___/_/ |_/____/_/ | | **
** |/ **
\* */
package scala.math
import java.util.Comparator
/** 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 [[http://en.wikipedia.org/wiki/Equivalence_relation equivalence relation]]
* is a binary relation on a type. This relation is exposed as
* the `equiv` method of the `Equiv` trait. The relation must be:
*
* 1. reflexive: `equiv(x, x) == true` for any x of type `T`.
* 1. symmetric: `equiv(x, y) == equiv(y, x)` for any `x` and `y` of type `T`.
* 1. transitive: if `equiv(x, y) == true` and `equiv(y, z) == true`, then
* `equiv(x, z) == true` for any `x`, `y`, and `z` of type `T`.
*
* @author Geoffrey Washburn, Paul Phillips
* @version 1.0, 2008-04-03
* @since 2.7
*/
trait Equiv[T] extends Any {
/** Returns `true` iff `x` is equivalent to `y`.
*/
def equiv(x: T, y: T): Boolean
}
trait LowPriorityEquiv {
self: Equiv.type =>
implicit def universalEquiv[T] : Equiv[T] = universal[T]
}
object Equiv extends LowPriorityEquiv {
def reference[T <: AnyRef] : Equiv[T] = new Equiv[T] {
def equiv(x: T, y: T) = x eq y
}
def universal[T] : Equiv[T] = new Equiv[T] {
def equiv(x: T, y: T) = x == y
}
def fromComparator[T](cmp: Comparator[T]): Equiv[T] = new Equiv[T] {
def equiv(x: T, y: T) = cmp.compare(x, y) == 0
}
def fromFunction[T](cmp: (T, T) => Boolean): Equiv[T] = new Equiv[T] {
def equiv(x: T, y: T) = cmp(x, y)
}
def by[T, S: Equiv](f: T => S): Equiv[T] =
fromFunction((x, y) => implicitly[Equiv[S]].equiv(f(x), f(y)))
def apply[T: Equiv] : Equiv[T] = implicitly[Equiv[T]]
}
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