将Scala Type示例转换为Haskell

Question

我在Scala文章中发现了一个非常有趣的例子，我想知道它是如何在Haskell中编码的。

trait Status
trait Open extends Status
trait Closed extends Status

trait Door[S <: Status]
object Door {
  def apply[S <: Status] = new Door[S] {}

  def open[S <: Closed](d: Door[S]) = Door[Open]
  def close[S <: Open](d: Door[S]) = Door[Closed]
}

val closedDoor = Door[Closed]
val openDoor = Door.open(closedDoor)
val closedAgainDoor = Door.close(openDoor)

//val closedClosedDoor = Door.close(closedDoor) // fails to compile
//val openOpenDoor = Door.open(openDoor) // fails to compile

此示例在类型级别进行编码，您只能打开关闭的Door ，并且只关闭打开的Door 。 我的第一次尝试只是使用简单的数据类型，但不能按预期工作：

data Status = Open | Closed deriving (Show)
data Door = Door Status deriving (Show)

open :: Door -> Door
open (Door Closed) = Door Open

close :: Door -> Door
close (Door Open) = Door Closed

main = do
  let closedDoor = (Door Closed)
  let openDoor = open closedDoor
  let closedAgainDoor = close openDoor
  let closeClosedDoor = close closedDoor
  let openOpenedDoor = open openDoor
  print closedAgainDoor

这实际上是编译的（除非我尝试打印closeClosedDoor或openOpenedDoor ，然后在功能打开时抱怨非详尽的模式，这很明显）

所以我试图弄清楚GADT我们的类型家族是否可以完成这项任务，但我还不知道如何。

有任何想法吗？

Answer 1

除了bheklilr的答案，你可以使用一些类型扩展来更接近Scala示例并排除非敏感类型，如

Door String

使用DataKinds ，您可以有效地禁止幻像类型只是一个Status 。

{-# LANGUAGE DataKinds #-}

data Door (status :: Status) = Door
data Status = Open | Closed

open :: Door Closed -> Door Open
open _ = Door

close :: Door Open -> Door Closed
close _ = Door

然后，对于类型系列，我们甚至可以定义“切换”门的含义

{-# LANGUAGE TypeFamilies #-}

type family Toggle (s :: Status) where
  Toggle Open = Closed
  Toggle Closed = Open

toggle :: Door s -> Door (Toggle s)
toggle Door = Door

---

作为一个结束的想法，使用GADT for Door可能更好 - 只是因此你有两个不同的构造函数名称。 我个人认为这看起来更好

{-# LANGUAGE GADTs, DataKinds, TypeFamilies #-}

data Door (status :: Status) where
  OpenDoor :: Door Open
  ClosedDoor :: Door Closed

open :: Door Closed -> Door Open
open _ = OpenDoor

close :: Door Open -> Door Closed
close _ = ClosedDoor

toggle :: Door s -> Door (Toggle s)
toggle OpenDoor = ClosedDoor
toggle ClosedDoor = OpenDoor

Answer 2

我会做点什么的

data Open = Open deriving (Show)
data Closed = Closed deriving (Show)
data Door door_state = Door deriving (Show)

open :: Door Closed -> Door Open
open _ = Door

close :: Door Open -> Door Closed
close _ = Door

现在没有任何情况需要考虑，状态本身是在类型中编码的，就像Scala示例一样。