如何定义 <*>对于 Option[List[_]] n Scala [英] How to define <*> for Option[List[_]] n Scala

问题描述

这是我之前的问题的后续，示例见于互联网.

This is a followup to my previous question with an example found on the Internet.

假设我定义了一个类型类 Applicative 如下:

Suppose I define a typeclass Applicative as follows:

trait Functor[T[_]]{
  def map[A,B](f:A=>B, ta:T[A]):T[B]
}

trait Applicative[T[_]] extends Functor[T] {
  def unit[A](a:A):T[A]
  def ap[A,B](tf:T[A=>B], ta:T[A]):T[B]
}

我可以为List

object AppList extends Applicative[List] {
  def map[A,B](f:A=>B, as:List[A]) = as.map(f)
  def unit[A](a: A) = List(a)
  def ap[A,B](fs:List[A=>B], as:List[A]) = for(f <- fs; a <- as) yield f(a)
}

为了方便，我可以定义一个隐式转换来添加一个方法<*>到List[A=>B]

For convenience I can define an implicit conversion to add a method <*> to List[A=>B]

implicit def toApplicative[A, B](fs: List[A=>B]) = new {
  def <*>(as: List[A]) = AppList.ap(fs, as)
}

现在我可以做一件很酷的事情了！
压缩两个列表 List[String] 并将 f2 应用到 applicative 风格的每一对

Now I can do a cool thing !
zip two lists List[String] and apply f2 to every pair in applicative style

val f2: (String, String) => String = {(first, last) => s"$first $last"}
val firsts = List("a", "b", "c")
val lasts  = List("x", "y", "z")

scala> AppList.unit(f2.curried) <*> firsts <*> lasts
res31: List[String] = List(a x, a y, a z, b x, b y, b z, c x, c y, c z)

到目前为止，很好，但现在我有:

So far, so good but now I have:

val firstsOpt = Some(firsts)
val lastsOpt  = Some(lasts) 

我想压缩 firsts 和 lasts，应用 f2，然后得到 Option[List[String]] applicative 风格.换句话说，我需要 <*> 用于 Option[List[_]].我该怎么做?

I would like to zip firsts and lasts, apply f2, and get Option[List[String]] in applicative style. In other words I need <*> for Option[List[_]]. How can I do it ?

推荐答案

首先，你需要一个Option的applicative实例:

Firstly, you need an instance of applicative for Option:

implicit object AppOption extends Applicative[Option] {
  def map[A, B](f: A => B, o: Option[A]) = o.map(f)
  def unit[A](a: A): Option[A] = Some(a)
  def ap[A, B](of: Option[A => B], oa: Option[A]) = of match {
    case Some(f) => oa.map(f)
    case None => None
  }
}

然后你也可以为两个应用程序的组合创建一个应用程序实例(注意，基于 Haskell 版本):

Then you can also create an applicative instance for the composition of two applicatives (note, based on the Haskell version):

class AppComp[F[_], G[_]](fa: Applicative[F], ga: Applicative[G]) extends Applicative[({ type f[A] = F[G[A]]})#f] {
  def map[A, B](f: A => B, a: F[G[A]]): F[G[B]] = fa.map((g: G[A]) => ga.map(f, g), a)
  def unit[A](a: A) = fa.unit(ga.unit(a))
  def ap[A, B](f: F[G[A => B]], a: F[G[A]]): F[G[B]] = {
    val liftg: G[A => B] => (G[A] => G[B]) = gf => (gx => ga.ap(gf, gx))
    val ffg: F[G[A] => G[B]] = fa.map(liftg, f)
    fa.ap(ffg, a)
  }
}

implicit def toComp[F[_], G[_]](implicit fa: Applicative[F], ga: Applicative[G]) = new AppComp[F, G](fa, ga)

现在你终于可以这样做了:

Finally you can now do:

val ola = toComp[Option, List]
ola.ap(ola.ap(ola.unit(f2.curried), firstsOpt), lastsOpt)

您也可以通过将 <*> 概括为适用于任何应用程序来消除一些噪音.

You could probably also remove some of the noise by generalising <*> to work for any applicative.

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