Scala中的Comonad示例

Question

什么是Comonad，如果可以用Scala语法描述的话。我找到了scalaz库实现，但不清楚它在哪里有用。

Answer 1

monad允许您向它们添加值，基于从非monad到monad的计算来更改它们。comonad允许您从它们中提取值，并基于从comonad到非comonad的计算来更改它们。

自然的直觉是，它们通常会出现在你有一个CMA并想要提取A的地方。

请参阅this非常有趣的帖子，其中稍微提到了comonads，但至少对我来说，让它们变得非常清晰。

Answer 2

下面是this博客文章中代码的直译。

case class U[X](left: Stream[X], center: X, right: Stream[X]) {
  def shiftRight = this match {
    case U(a, b, c #:: cs) => U(b #:: a, c, cs)
  }

  def shiftLeft = this match {
    case U(a #:: as, b, c) => U(as, a, b #:: c)
  }
}

// Not necessary, as Comonad also has fmap.
/*
implicit object uFunctor extends Functor[U] {
  def fmap[A, B](x: U[A], f: A => B): U[B] = U(x.left.map(f), f(x.center), x.right.map(f))
}
*/

implicit object uComonad extends Comonad[U] {
  def copure[A](u: U[A]): A = u.center
  def cojoin[A](a: U[A]): U[U[A]] = U(Stream.iterate(a)(_.shiftLeft).tail, a, Stream.iterate(a)(_.shiftRight).tail)
  def fmap[A, B](x: U[A], f: A => B): U[B] = U(x.left.map(f), x.center |> f, x.right.map(f))
}

def rule(u: U[Boolean]) = u match {
  case U(a #:: _, b, c #:: _) => !(a && b && !c || (a == b))
}

def shift[A](i: Int, u: U[A]) = {
  Stream.iterate(u)(x => if (i < 0) x.shiftLeft else x.shiftRight).apply(i.abs)
}

def half[A](u: U[A]) = u match {
  case U(_, b, c) => Stream(b) ++ c
}

def toList[A](i: Int, j: Int, u: U[A]) = half(shift(i, u)).take(j - i)

val u = U(Stream continually false, true, Stream continually false)

val s = Stream.iterate(u)(_ =>> rule)

val s0 = s.map(r => toList(-20, 20, r).map(x => if(x) '#' else ' '))

val s1 = s.map(r => toList(-20, 20, r).map(x => if(x) '#' else ' ').mkString("|")).take(20).force.mkString("\n")

println(s1)

输出：

 | | | | | | | | | | | | | | | | | | | |#| | | | | | | | | | | | | | | | | | |
 | | | | | | | | | | | | | | | | | | | |#|#| | | | | | | | | | | | | | | | | |
 | | | | | | | | | | | | | | | | | | | |#| |#| | | | | | | | | | | | | | | | |
 | | | | | | | | | | | | | | | | | | | |#|#|#|#| | | | | | | | | | | | | | | |
 | | | | | | | | | | | | | | | | | | | |#| | | |#| | | | | | | | | | | | | | |
 | | | | | | | | | | | | | | | | | | | |#|#| | |#|#| | | | | | | | | | | | | |
 | | | | | | | | | | | | | | | | | | | |#| |#| |#| |#| | | | | | | | | | | | |
 | | | | | | | | | | | | | | | | | | | |#|#|#|#|#|#|#|#| | | | | | | | | | | |
 | | | | | | | | | | | | | | | | | | | |#| | | | | | | |#| | | | | | | | | | |
 | | | | | | | | | | | | | | | | | | | |#|#| | | | | | |#|#| | | | | | | | | |
 | | | | | | | | | | | | | | | | | | | |#| |#| | | | | |#| |#| | | | | | | | |
 | | | | | | | | | | | | | | | | | | | |#|#|#|#| | | | |#|#|#|#| | | | | | | |
 | | | | | | | | | | | | | | | | | | | |#| | | |#| | | |#| | | |#| | | | | | |
 | | | | | | | | | | | | | | | | | | | |#|#| | |#|#| | |#|#| | |#|#| | | | | |
 | | | | | | | | | | | | | | | | | | | |#| |#| |#| |#| |#| |#| |#| |#| | | | |
 | | | | | | | | | | | | | | | | | | | |#|#|#|#|#|#|#|#|#|#|#|#|#|#|#|#| | | |
 | | | | | | | | | | | | | | | | | | | |#| | | | | | | | | | | | | | | |#| | |
 | | | | | | | | | | | | | | | | | | | |#|#| | | | | | | | | | | | | | |#|#| |
 | | | | | | | | | | | | | | | | | | | |#| |#| | | | | | | | | | | | | |#| |#|
 | | | | | | | | | | | | | | | | | | | |#|#|#|#| | | | | | | | | | | | |#|#|#|#

Answer 3

scalaz library提供了一个扩展Comonad属性的ComonadStore。它的定义如下：

trait ComonadStore[F[_], S] extends Comonad[F] { self =>

  def pos[A](w: F[A]): S
  def peek[A](s: S, w: F[A]): A

  def peeks[A](s: S => S, w: F[A]): A =
    peek(s(pos(w)), w)

  def seek[A](s: S, w: F[A]): F[A] =
    peek(s, cojoin(w))

  def seeks[A](s: S => S, w: F[A]): F[A] =
    peeks(s, cojoin(w))

  def experiment[G[_], A](s: S => G[S], w: F[A])(implicit FG: Functor[G]): G[A] =
    FG.map(s(pos(w)))(peek(_, w))

}

Store(类似于(S => A, S))有一个Comonad实例。您可以查看此question，它更具体地解释了它是什么。

你还有Coreader和Cowriter Comonads，它们是Reader和Writer Monads的对偶，这里有一篇用Scala写的很棒的blog文章。