为类型类定义 Monad、Applicative 和 Functor 实例

Question

假设我已经为缓存计算定义了一个类型类。

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，也可以从数据库加载结果。

我想为这个特征定义 Functor、Applicative 和 Monad 实例。使用Kind投影仪让我的生活更轻松：

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))
    }
}

目前为止，一切都好。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，我在运行时收到以下错误：

[error] diverging implicit expansion for type scalaz.Applicative[[β$4$]Cached[scalaz.Scalaz.Id,β$4$]]
[error] starting with method monad in object Cached
[error]       a <- Cached(1.point[Id])
[error]                  ^
[error] diverging implicit expansion for type scalaz.Applicative[[β$4$]Cached[scalaz.Scalaz.Id,β$4$]]
[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隐式扩展，但我不明白为什么我的代码会这样。

如果有人能指出我正确的方向，我将不胜感激。我对函数式编程概念很陌生，所以我在这里所做的甚至可能没有意义！

Answer 1

编译器

不知道你的方法point是指applicative方法还是monad方法。

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"(。如果你想避免层次结构，并希望你的monads和应用程序定义自己的point，那么你需要以不同的方式命名它们，或者以某种方式告诉编译器你指的是哪一个(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)
    }