Scalaz（19）－ Monad： \/ - Monad 版本的 Either

scala标准库提供了一个Either类型，它可以说是Option的升级版。与Option相同，Either也有两种状态：Left和Right，分别对应Option的None和Some，不同的是Left可以返回一个值。我们通常用这个值来表述异常信息。scalaz也提供了自己版本的Either，并用\/来分辨表示，以及两种状态-\/和\/-。我想scalaz特别提供\/是有原因的：\/不单是一种类型，它是一种type class。更重要的是\/是一种Monad，具备了函数组合能力（composibility）。如此能够方便把Either功能整合到FP编程中去。我们先看看\/的定义：scalaz/Either.scala

sealed abstract class \/[+A, +B] extends Product with Serializable {
...
  def isLeft: Boolean =
    this match {
      case -\/(_) => true
      case \/-(_) => false
    }

  /** Return `true` if this disjunction is right. */
  def isRight: Boolean =
    this match {
      case -\/(_) => false
      case \/-(_) => true
    }
...
 /** Return the right value of this disjunction or the given default if left. Alias for `|` */
  def getOrElse[BB >: B](x: => BB): BB =
    this match {
      case -\/(_) => x
      case \/-(b) => b
    }

  /** Return the right value of this disjunction or the given default if left. Alias for `getOrElse` */
  def |[BB >: B](x: => BB): BB =
    getOrElse(x)

  /** Return the right value of this disjunction or run the given function on the left. */
  def valueOr[BB >: B](x: A => BB): BB =
    this match {
      case -\/(a) => x(a)
      case \/-(b) => b
    }

  /** Return this if it is a right, otherwise, return the given value. Alias for `|||` */
  def orElse[AA >: A, BB >: B](x: => AA \/ BB): AA \/ BB =
    this match {
      case -\/(_) => x
      case \/-(_) => this
    }

  /** Return this if it is a right, otherwise, return the given value. Alias for `orElse` */
  def |||[AA >: A, BB >: B](x: => AA \/ BB): AA \/ BB =
    orElse(x)
...

与Option相同：\/也提供了函数来获取运算值（Right[A]）,如getOrElse。那么如何获取异常信息呢？可以用swap后再用getOrElse:

  /** Flip the left/right values in this disjunction. Alias for `unary_~` */
  def swap: (B \/ A) =
    this match {
      case -\/(a) => \/-(a)
      case \/-(b) => -\/(b)
    }

  /** Flip the left/right values in this disjunction. Alias for `swap` */
  def unary_~ : (B \/ A) =
    swap

"ah, error!".left[Int].getOrElse("no error")      //> res2: Any = no error
"ah, error!".left[Int].swap.getOrElse("no error") //> res3: String = ah, error!
(~"ah, error!".left[Int]).getOrElse("no error")   //> res4: String = ah, error!

与Option一样，\/也有两种状态：

/** A left disjunction
 *
 * Often used to represent the failure case of a result
 */
final case class -\/[+A](a: A) extends (A \/ Nothing)

/** A right disjunction
 *
 * Often used to represent the success case of a result
 */
final case class \/-[+B](b: B) extends (Nothing \/ B)

\/实现了map和flatMap：

  /** Map on the right of this disjunction. */
  def map[D](g: B => D): (A \/ D) =
    this match {
      case \/-(a)     => \/-(g(a))
      case b @ -\/(_) => b
    }
 /** Bind through the right of this disjunction. */
  def flatMap[AA >: A, D](g: B => (AA \/ D)): (AA \/ D) =
    this match {
      case a @ -\/(_) => a
      case \/-(b) => g(b)
    }

注意flatMap：如果状态为\/- 则连续运算g(b)，如果状态为-\/ 则立即停止运算返回-\/状态。这与Option功能相当。我们用for-comprehension来证明：

 val epok = for {
     a <- \/-()
     b <- \/-()
 } yield a + b                                     //> epok  : scalaz.\/[Nothing,Int] = \/-(5)
 val epno = for {
     a <- \/-()
     c <- -\/("breaking out...")
     b <- \/-()
 } yield a + b                                     //> epno  : scalaz.\/[String,Int] = -\/(breaking out...)
 if (epno.isLeft) (~epno).getOrElse("no error")    //> res5: Any = breaking out...

\/在for-comprehension里的运算行为与Option一致。不过这个\/写法比较别扭。\/type class为任何类型提供了注入方法left和right: scalaz.syntax/EitherOps.scala

  final def left[B]: (A \/ B) =
    -\/(self)

  final def right[B]: (B \/ A) =
    \/-(self)
}

trait ToEitherOps { //可以为任何类型A注入方法
  implicit def ToEitherOps[A](a: A) = new EitherOps(a)
}

现在这个for-comprehension可以这样写：

 val epok1 = for {
     a <- .right
     b <- .right
 } yield a + b                                     //> epok1  : scalaz.\/[Nothing,Int] = \/-(5)
 val epno1 = for {
     a <- .right
     c <- "breaking out...".left[Int]
     b <- .right
 } yield a + b                                     //> epno1  : scalaz.\/[String,Int] = -\/(breaking out...)
 if (epno1.isLeft) (~epno1).getOrElse("no error")  //> res6: Any = breaking out...

这样表述是不是清晰直白多了。