为什么可以找到树的`Functor` 实例，但不能找到分支或叶子的实例？

Question

我有以下 Functor 定义：

import cats.Functor
import cats.syntax.functor._

object Theory {

  implicit val treeFunctor: Functor[Tree] =
    new Functor[Tree] {
      def map[A, B](fa: Tree[A])(f: A => B): Tree[B] =
        fa match {
          case Branch(left, right) =>
            Branch(map(left)(f), map(right)(f))
          case Leaf(value) =>
            Leaf(f(value))
        }
    }

  def main(args: Array[String]): Unit = {
    Branch(Leaf(10), Leaf(20)).map(_ * 2)
  }


}

对于：

sealed trait Tree[+A]

final case class Branch[A](left: Tree[A], right: Tree[A]) extends Tree[A]

final case class Leaf[A](value: A) extends Tree[A]

为什么编译器会报错：

// <console>:42: error: value map is not a member of wrapper.Branch[
Int]
//
Branch(Leaf(10), Leaf(20)).map(_ * 2)
//

所以我必须创建一个智能构造函数：

object Tree {
  def branch[A](left: Tree[A], right: Tree[A]): Tree[A] =
    Branch(left, right)
  def leaf[A](value: A): Tree[A] =
    Leaf(value)
}

在这种情况下什么是智能构造函数？

Answer 1

Functor[F[_]]在cats中的声明在F中是不变的。因此，Functor[Tree] 既不是 Functor[Branch] 的概括，也不是其特化。这些类型不相关。

您的代码存在以下问题。表达式

Branch(Leaf(10), Leaf(20))

属于 Branch[Int] 类型。当您尝试直接将 .map[X] 应用于它时，您表示您希望获得 Branch[X] 作为结果。但是范围内没有 Functor[Branch]（并不是说你不能写一个，但就目前而言，有 none）。

为了使用 Functor[Tree]，您必须向编译器明确表示您希望将此实例视为 Tree[Int]。铸造会起作用。或者使用隐藏 Branch 并公开 Tree 的自定义工厂方法也可以工作：这就是 "smart" 构造函数正在做的事情。

Answer 2

您可以使用kittens并实现Branch和Leaf的实例，然后可以派生Tree的实例。

libraryDependencies += "org.typelevel" %% "kittens" % "1.0.0-RC2"

  import cats.Functor
  import cats.syntax.functor._

  sealed trait Tree[+A]
  final case class Branch[A](left: Tree[A], right: Tree[A]) extends Tree[A]
  final case class Leaf[A](value: A) extends Tree[A]

  implicit val treeFunctor: Functor[Tree] = cats.derive.functor[Tree]

  implicit val branchFunctor: Functor[Branch] =
    new Functor[Branch] {
      def map[A, B](fa: Branch[A])(f: A => B): Branch[B] =
        fa match {
          case Branch(left, right) =>
            Branch(left.map(f), right.map(f))
        }
    }

    // or without extension method
//  implicit def branchFunctor(implicit treeFunctor: Functor[Tree]): Functor[Branch] =
//    new Functor[Branch] {
//      def map[A, B](fa: Branch[A])(f: A => B): Branch[B] =
//        fa match {
//          case Branch(left, right) =>
//            Branch(treeFunctor.map(left)(f), treeFunctor.map(right)(f))
//        }
//    }

  implicit val leafFunctor: Functor[Leaf] =
    new Functor[Leaf] {
      def map[A, B](fa: Leaf[A])(f: A => B): Leaf[B] =
        fa match {
          case Leaf(value) =>
            Leaf(f(value))
        }
    }

  def main(args: Array[String]): Unit = {
    (Branch(Leaf(10), Leaf(20)): Tree[Int]).map(_ * 2)
    Branch(Leaf(10), Leaf(20)).map(_ * 2)
    Leaf(10).map(_ * 2)
  }

实际上你可以导出所有三个实例：

  implicit val treeFunctor: Functor[Tree] = cats.derive.functor[Tree]
  implicit val leafFunctor: Functor[Leaf] = cats.derive.functor[Leaf]
  implicit val branchFunctor: Functor[Branch] = cats.derive.functor[Branch]

  def main(args: Array[String]): Unit = {
    (Branch(Leaf(10), Leaf(20)): Tree[Int]).map(_ * 2)
    Branch(Leaf(10), Leaf(20)).map(_ * 2)
    Leaf(10).map(_ * 2)
  }

为什么可以找到树的`Functor` 实例，但不能找到分支或叶子的实例？

Why can find `Functor` instance for Tree but not for Branch or Leaf?

scala

scala-cats

invariance