Scala 中的 Comonad 示例

Question

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

Answer 1

嗯，monad 允许您向它们添加值，根据计算将它们从非 monad 更改为 monad。 Comonad 允许您从中提取值，并根据计算将它们从 Comonad 更改为 non-comonad。

自然的直觉是，它们通常会出现在您有 CM[A] 并想要提取 A 的地方。

请参阅this 非常有趣的帖子，它有点随意地触及了共胞，但至少对我来说，让它们非常清楚。

Answer 2

以下是来自this 博客文章的代码的字面翻译。

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ComonadStore，它扩展了Comonad 的属性。它是这样定义的：

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 的实例。你可以看看这个question，它更具体地解释了它的含义。

您还拥有Coreader 和Cowriter Comonads，它们是Reader 和Writer Monads 的对偶，这里有一篇很棒的blog 帖子，在Scala 中讨论了它。