
Scala example source code file (PartialOrdering.scala)
The PartialOrdering.scala Scala example source code/* __ *\ ** ________ ___ / / ___ Scala API ** ** / __/ __// _  / / / _  (c) 20032013, LAMP/EPFL ** ** __\ \/ /__/ __ / /__/ __  http://scalalang.org/ ** ** /____/\___/_/ _/____/_/   ** ** / ** \* */ package scala package math /** A trait for representing partial orderings. It is important to * distinguish between a type that has a partial order and a representation * of partial ordering on some type. This trait is for representing the * latter. * * A [[http://en.wikipedia.org/wiki/Partial_order partial ordering]] is a * binary relation on a type `T` that is also an equivalence relation on * values of type `T`. This relation is exposed as the `lteq` method of * the `PartialOrdering` trait. This relation must be: * *  reflexive: `lteq(x, x) == '''true'''`, for any `x` of type `T`. *  antisymmetric: `lteq(x, y) == '''true'''` and `lteq(y, x) == true` * then `equiv(x, y)`, for any `x` and `y` of type `T`. *  transitive: if `lteq(x, y) == '''true'''` and * `lteq(y, z) == '''true'''` then `lteq(x, z) == '''true'''`, * for any `x`, `y`, and `z` of type `T`. * * @author Geoffrey Washburn * @version 1.0, 20080403 * @since 2.7 */ trait PartialOrdering[T] extends Equiv[T] { outer => /** Result of comparing `x` with operand `y`. * Returns `None` if operands are not comparable. * If operands are comparable, returns `Some(r)` where *  `r < 0` iff `x < y` *  `r == 0` iff `x == y` *  `r > 0` iff `x > y` */ def tryCompare(x: T, y: T): Option[Int] /** Returns `'''true'''` iff `x` comes before `y` in the ordering. */ def lteq(x: T, y: T): Boolean /** Returns `'''true'''` iff `y` comes before `x` in the ordering. */ def gteq(x: T, y: T): Boolean = lteq(y, x) /** Returns `'''true'''` iff `x` comes before `y` in the ordering * and is not the same as `y`. */ def lt(x: T, y: T): Boolean = lteq(x, y) && !equiv(x, y) /** Returns `'''true'''` iff `y` comes before `x` in the ordering * and is not the same as `x`. */ def gt(x: T, y: T): Boolean = gteq(x, y) && !equiv(x, y) /** Returns `'''true'''` iff `x` is equivalent to `y` in the ordering. */ def equiv(x: T, y: T): Boolean = lteq(x,y) && lteq(y,x) def reverse : PartialOrdering[T] = new PartialOrdering[T] { override def reverse = outer def lteq(x: T, y: T) = outer.lteq(y, x) def tryCompare(x: T, y: T) = outer.tryCompare(y, x) } } Other Scala source code examplesHere is a short list of links related to this Scala PartialOrdering.scala source code file: 
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