为类型定义 Monad、Applicative 和 Functor 实例 class

Question

假设我已经为缓存计算定义了一个类型class。

trait Cached[F[_], A] {
  def value: F[A]
}

直观地说，Cached 包装了计算，因此我们可以在运行时对其进行评估，或者改为从数据库加载结果。

我想为此特性定义 Functor、Applicative 和 Monad 实例。使用Kind-projector让我的生活更轻松：

import scalaz._, Scalaz._
object Cached {

  def apply[F[_], A](f: => F[A]): Cached[F, A] = new Cached[F, A] {
    override def value: F[A] = f
  }

  implicit def functor[F[_] : Functor]: Functor[Cached[F, ?]] = new Functor[Cached[F, ?]] {
    override def map[A, B](fa: Cached[F, A])(f: A => B): Cached[F, B] =
      Cached(fa.value map f)
  }

  implicit def applicative[F[_] : Applicative]: Applicative[Cached[F, ?]] = new Applicative[Cached[F, ?]] {
    override def point[A](a: => A): Cached[F, A] = Cached(a.point[F])

    override def ap[A, B](fa: => Cached[F, A])(f: => Cached[F, A => B]): Cached[F, B] =
      Cached(fa.value <*> f.value)
  }

  implicit def monad[F[_] : Monad](implicit app: Applicative[Cached[F, ?]], func: Functor[Cached[F, ?]]): Monad[Cached[F, ?]] =
    new Monad[Cached[F, ?]] {
      override def point[A](a: => A): Cached[F, A] = app.point(a)

      override def bind[A, B](fa: Cached[F, A])(f: A => Cached[F, B]): Cached[F, B] =
        Cached(func.map(fa)(f).value >>= (_.value))
    }
}

到目前为止，还不错。现在，让我们在一个简单的例子中使用 monad：

import Cached._
val y = Cached(2.point[Id])
val z = for {
  a <- Cached(1.point[Id])
  b <- y
} yield a + b

运行代码，我在运行时得到以下错误：

[error] diverging implicit expansion for type scalaz.Applicative[[β$]Cached[scalaz.Scalaz.Id,β$]]
[error] starting with method monad in object Cached
[error]       a <- Cached(1.point[Id])
[error]                  ^
[error] diverging implicit expansion for type scalaz.Applicative[[β$]Cached[scalaz.Scalaz.Id,β$]]
[error] starting with method monad in object Cached
[error]       b <- y
[error]            ^
[error] two errors found
[error] (Test / compileIncremental) Compilation failed

我知道当编译器在扩展隐式定义时陷入循环时会发生发散式隐式扩展，但我不明白为什么我的代码会出现这种情况。

如果有人能指出正确的方向，我将不胜感激。我对函数式编程概念还很陌生，所以我在这里所做的可能毫无意义！

Answer 1

编译器不知道您的方法 point 是指 applicative 还是 monad。

Monad 类型类通常用于扩展 Applicatives，因为每个 monad 实际上都是一个应用函子（加上 "join"，在 Scala 中称为 "flatten"）。如果您想避免层次结构并希望您的 monad 和应用程序都定义自己的 point，那么您需要以不同的方式命名它们，或者以某种方式告诉编译器您指的是哪一个（例如，通过类型参数） .

Answer 2

我最终定义了这样的实例：

implicit def instance[F[_] : Monad]: Functor[Cached[F, ?]] with Applicative[Cached[F, ?]] with Monad[Cached[F, ?]] =
    new Functor[Cached[F, ?]] with Applicative[Cached[F, ?]] with Monad[Cached[F, ?]] {
      def eval[A](fa: => Cached[F, A]): F[A] = {
        println("loading stuff from the database...")
        fa.value
      }

      override def point[A](a: => A): Cached[F, A] =
        Cached(a.point[F])

      override def map[A, B](fa: Cached[F, A])(f: A => B): Cached[F, B] = {
        Cached(eval(fa) map f)
      }

      override def bind[A, B](fa: Cached[F, A])(f: A => Cached[F, B]): Cached[F, B] = {
        Cached(eval(fa) >>= (a => f(a).value))
      }

      override def ap[A, B](fa: => Cached[F, A])(f: => Cached[F, A => B]): Cached[F, B] =
        Cached(eval(fa) <*> f.value)
    }

为类型定义 Monad、Applicative 和 Functor 实例 class

Defining Monad, Applicative, and Functor instances for a type class

functional-programming

scala

scalaz