违反了斯卡拉兹未来单子的左身份法 [英] Violation of the left identity law for Future monads in scalaz

问题描述

假设我为Future定义了Monad类型类的实例:

Suppose I define an instance of the Monad typeclass for Future:

val futureMonad = new Monad[Future] {
  override def point[A](a: ⇒ A): Future[A] =
    Future(a)

  override def bind[A, B](fa: Future[A])(f: A => Future[B]): Future[B] =
    fa flatMap f
}

严格来讲，这不是单子，因为它违反了左派身份定律:

Strictly speaking, this is not a monad, since it violates the law of left identity:

futureMonad.point(a) bind f == f(a)

如果f引发异常，则左侧的表达式结果将是失败的Future，而右侧的表达式当然会引发异常.

If f throws an exception, the result of the expression on the left hand side will be a failed Future, whereas the right hand side will, of course, throw the exception.

但是这种违反行为的实际含义是什么?系统会因这种不当行为"而以何种方式发生故障?

But what are the practical implications of this violation? In which ways can a system fail as a result of this "misbehavior"?

推荐答案

就理解而言，它仅意味着以下重构不保留语义:

It just means, in terms of for comprehensions, that the following refactoring is not semantics-preserving:

for (fut <- Future(a); x <- f(fut)) yield x  ==>  f(a)

但这确实是写左身份法则的另一种方式.

But that's just another way of writing the left identity law, really.

要说明无效进一步重构，请执行以下操作:

To explain that invalid refactoring further:

for (fut <- Future(a); x <- f(fut)) yield x
==>  for (x <- f(a)) yield x  // by left identity law: WRONG, because left identity law does not hold
==>  f(a)                     // by 1st functor law:   WRONG, because previous line was wrong

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