L型在A型中处于逆变位置=>要么[L, B] [英] Type L is in contravariant position in type A => Either[L, B]

问题描述

我尝试为任何一个编写 flatMap 的简单实现

I tried to write simple implementation of flatMap for Either

sealed trait Either[+L, +R] {
  def flatMap[B](f: R => Either[L, B]): Either[L, B] = this match {
    case Left(e) => Left(e)
    case Right(e) => f(e)
  }
}

final case class Right[+A, +B](right: B) extends Either[A, B]
final case class Left[+A, +B](left: A) extends Either[A, B]

并面临以下问题:协变类型 L 在类型 f 中处于逆变位置:R => 值 f 的任一 [L，B]，但为什么会这样?当我们将变体类型作为函数的参数时，我认为我们的类型处于逆变位置，它与类型声明无关

and faced following problem: covariant type L is in contravariant position in type f: R => Either[L, B] of value f, but why is it so? I thought that our type is in contravariant position when we take variant type as an argument for function and it has nothing to do with a type declaration

推荐答案

你可以想到 R =>[L, B] 作为L 类型的广义值" - 它与 L 不完全相同，但给定了 R它可能产生一个L.因此，您的 flatMap 使用 L 类型的广义值".同时，您的方差声明声称 Either[+L, +R] 在 L 中是协变的，因此，Either[VerySpecial, R] 必须是 Either[RatherGeneral, R] 的特例.但这是不可能的，因为只能使用 VerySpecial 值的 flatMap 会阻塞 RatherGeneral 输入.

You can think of R => Either[L, B] as a "generalized value of type L" - it's not exactly the same thing as an L, but given an R it might produce an L. So, your flatMap "consumes generalized values of type L". At the same time, your variance declaration claims that Either[+L, +R] is covariant in L, therefore, an Either[VerySpecial, R] would have to be a special case of Either[RatherGeneral, R]. But this is impossible, because the flatMap that can consume only VerySpecial values would choke on a RatherGeneral input.

• 在 Either[+L, +R] 中，L 处于协变位置(它 产生" Ls，在至少有时)
• 在R =>[L, B], L 仍然处于协变位置(因为函数产生Either[L, B]，而Either[L, B] 依次产生 Ls，所以整个事情产生 Ls)
• 在(R =>Either[L, B]) =>要么[L, B]，第一个L出现在contra变体位置，因为参数部分被方法消耗flatMap.

• In Either[+L, +R], L is in covariant position (it "produces" Ls, at least sometimes)
• In R => Either[L, B], L is still in covariant position (because the function produces Either[L, B], and Either[L, B] in turn produces Ls, so the whole thing produces Ls)
• In (R => Either[L, B]) => Either[L, B], the first L appears in contravariant position, because the argument part is consumed by the method flatMap.

使用标准的下限技巧很容易解决这个问题:

This is easily fixed with the standard lower-type-bounds trick:

sealed trait Either[+L, +R] {
  def flatMap[B, M >: L](f: R => Either[M, B]): Either[M, B] = this match {
    case Left(e) => Left(e)
    case Right(e) => f(e)
  }
}

final case class Right[+A, +B](right: B) extends Either[A, B]
final case class Left[+A, +B](left: A) extends Either[A, B]

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