Question

我试图找到一个comonad的实际应用程序，我想我会试着看看我是否可以代表经典的Wumpus世界作为一个comonad。

我想使用此代码让Wumpus左右移动穿过世界并清理脏瓷砖并避免凹坑。似乎唯一有用的comonad功能是提取（获取当前的磁贴），并且移动和清理磁贴将无法使用扩展或复制。

我不确定comonad是否合适，但我已经看过一个谈话（Dominic Orchard: A Notation for Comonads），其中comonads用于在二维矩阵中建模光标。

如果comonad是代表Wumpus世界的好方法，请问您能说明我的代码错误吗？如果它错了，你能否建议一个简单的comonads应用程序？

module Wumpus where

-- Incomplete model of a world inhabited by a Wumpus who likes a nice
-- tidy world but does not like falling in pits.

import Control.Comonad

-- The Wumpus world is made up of tiles that can be in one of three
-- states.
data Tile = Clean | Dirty | Pit
  deriving (Show, Eq)

-- The Wumpus world is a one dimensional array partitioned into three
-- values: the tiles to the left of the Wumpus, the tile occupied by
-- the Wumpus, and the tiles to the right of the Wumpus.
data World a = World [a] a [a]
  deriving (Show, Eq)

-- Applies a function to every tile in the world
instance Functor World where
  fmap f (World as b cs) = World (fmap f as) (f b) (fmap f cs)

-- The Wumpus world is a Comonad
instance Comonad World where
  -- get the part of the world the Wumpus currently occupies
  extract (World _ b _) = b
  -- not sure what this means in the Wumpus world.  This type checks
  -- but does not make sense to me.
  extend f w@(World as b cs) = World (map world as) (f w) (map world cs)
      where world v = f (World [] v [])

-- returns a world in which the Wumpus has either 1) moved one tile to
-- the left or 2) stayed in the same place if the Wumpus could not move
-- to the left.
moveLeft :: World a -> World a
moveLeft w@(World [] _ _) = w
moveLeft (World as b cs) = World (init as) (last as) (b:cs)

-- returns a world in which the Wumpus has either 1) moved one tile to
-- the right or 2) stayed in the same place if the Wumpus could not move
-- to the right.
moveRight :: World a -> World a
moveRight w@(World _ _ []) = w
moveRight (World as b cs) = World (as ++ [b]) (head cs) (tail cs)

initWorld = World [Dirty, Clean, Dirty] Dirty [Clean, Dirty, Pit]

-- cleans the current tile
cleanTile :: Tile -> Tile
cleanTile Dirty = Clean
cleanTile t = t

谢谢！

Answer 1

我会将我的一系列评论移到一个更连贯的答案中。

你所拥有的实际上是一个“拉链”，特别是列表的拉链

data ListZip a = ListZip {lefts   :: [a]
                         ,focus   ::  a
                         ,rights  :: [a]}

我们可以将非空列表转换为ListZip

toZip :: [a] -> Maybe (ListZip a)
toZip (x:xs) = Just $ ListZip [] x xs
toZip  _     = Nothing

与所有拉链一样，ListZip有重点，我们可以在这个重点领域开展工作

modifyFocus :: (a -> a) -> ListZip a -> ListZip a
modifyFocus f z = z{focus = f $ focus z}

我们可以将焦点转移到您所谓的moveLeft和moveRight

moveLeft, moveRight :: ListZip a -> ListZip a

moveLeft  (ListZip (x:xs) y ys) = ListZip xs x (y : ys)
moveRight (ListZip xs x (y:ys)) = ListZip (x : xs) y ys

现在像所有拉链一样，ListZip是一个comonad！

extract提取焦点或当前占用的方块

instance Comonad ListZip where
  extract = focus

和extend会返回一个新世界，我们根据“规则”修改了每个有针对性的广场。

  extend f w = ListZip (moving moveLeft) (f w) (moving moveRight)
    where moving i = map f $ iterate i w

本案例中的规则是函数

ZipList a -> a

如果这让你想起细胞自动机，你就是对的！这与Conway的生命游戏之类的游戏非常相似：简单的上下文相关规则。

我们还定义了duplicate，它会返回Listzip ListZip个ListZip的{{1}}，其中焦点已在每个{{1}}上朝着可能的方向移动。

现在我不知道在Wumpus的背景下究竟有什么用处，你可以对你板上的每个方块进行任何统一的转换吗？能否将Wumpus世界变为Wumpus世界所有可能的Wumpus世界，您能从中获益吗？

这就是comonads在这种情况下给你的东西。

comonads是否适合对Wumpus世界进行建模？

1 个答案: