Haskell：为拉链创建类型类

Question

所以我一直在阅读一些关于 Haskell（我想还有其他函数式语言）中的 Zipper 模式来遍历和修改数据结构的内容，我认为这对我来说是一个磨练创建类型技能的好机会Haskell 中的课程，因为 该类可以提供一个通用的遍历接口，供我编写代码，而与所遍历的数据结构无关。

我想我可能需要两个类 - 一个用于根数据结构，一个用于创建的特殊数据结构 遍历第一个：

module Zipper where

class Zipper z where
  go'up :: z -> Maybe z
  go'down :: z -> Maybe z
  go'left :: z -> Maybe z
  go'right :: z -> Maybe z

class Zippable t where
  zipper :: (Zipper z) => t -> z
  get :: (Zipper z) => z -> t
  put :: (Zipper z) => z -> t -> z

但是当我尝试使用一些简单的数据结构（例如列表：

-- store a path through a list, with preceding elements stored in reverse
data ListZipper a = ListZipper { preceding :: [a], following :: [a] }

instance Zipper (ListZipper a) where
  go'up ListZipper { preceding = [] } = Nothing
  go'up ListZipper { preceding = a:ps, following = fs } = 
      Just $ ListZipper { preceding = ps, following = a:fs }
  go'down ListZipper { following = [] } = Nothing
  go'down ListZipper { preceding = ps, following = a:fs } = 
      Just $ ListZipper { preceding = a:ps, following = fs }
  go'left _ = Nothing
  go'right _ = Nothing

instance Zippable ([a]) where
  zipper as = ListZipper { preceding = [], following = as }
  get = following
  put z as = z { following = as }

或二叉树）时：

-- binary tree that only stores values at the leaves
data Tree a = Node { left'child :: Tree a, right'child :: Tree a } | Leaf a
-- store a path down a Tree, with branches not taken stored in reverse
data TreeZipper a = TreeZipper { branches :: [Either (Tree a) (Tree a)], subtree :: Tree a }

instance Zipper (TreeZipper a) where
  go'up TreeZipper { branches = [] } = Nothing
  go'up TreeZipper { branches = (Left l):bs, subtree = r } =  
      Just $ TreeZipper { branches = bs, subtree = Node { left'child = l, right'child = r } }
  go'up TreeZipper { branches = (Right r):bs, subtree = l } =  
      Just $ TreeZipper { branches = bs, subtree = Node { left'child = l, right'child = r } }
  go'down TreeZipper { subtree = Leaf a } = Nothing
  go'down TreeZipper { branches = bs, subtree = Node { left'child = l, right'child = r } } =
      Just $ TreeZipper { branches = (Right r):bs, subtree = l }
  go'left TreeZipper { branches = [] } = Nothing
  go'left TreeZipper { branches = (Right r):bs } = Nothing
  go'left TreeZipper { branches = (Left l):bs, subtree = r } =
      Just $ TreeZipper { branches = (Right r):bs, subtree = l }
  go'right TreeZipper { branches = [] } = Nothing
  go'right TreeZipper { branches = (Left l):bs } = Nothing
  go'right TreeZipper { branches = (Right r):bs, subtree = l } =
      Just $ TreeZipper { branches = (Left l):bs, subtree = r }

instance Zippable (Tree a) where
  zipper t = TreeZipper { branches = [], subtree = t }
  get TreeZipper { subtree = s } = s
  put z s = z { subtree = s }

我无法编译它，我的每个 都会遇到很多这样的错误Zippable 实例定义：

Zipper.hs:28:14:
    Couldn't match expected type `z'
           against inferred type `ListZipper a'
      `z' is a rigid type variable bound by
          the type signature for `zipper' at Zipper.hs:10:20
    In the expression: ListZipper {preceding = [], following = as}
    In the definition of `zipper':
        zipper as = ListZipper {preceding = [], following = as}
    In the definition for method `zipper'

所以我不知道从这里去哪里。 我怀疑我的问题是我试图绑定这两个实例 一起，当 (Zipper z) => 声明只是希望 z 为任何 Zipper 时。

Answer 1

您还可以使用类型同义词族来代替多参数类型类和函数依赖项。 在此类情况下，他们提供了更清晰且更易于理解的解决方案。 在这种情况下，类和实例将变为：

class Zippable t where
  type ZipperType t :: *
  enter :: t -> ZipperType t
  focus :: ZipperType t -> t

instance Zippable [a] where
  type ZipperType [a] = ListZipper a
  enter = ...
  focus = ...

有趣的类型函数对于已经熟悉 Haskell 的人来说是对类型同义词族的一个很好的介绍。 我还写了一篇关于如何输入的文章不久前经常可以使用同义词族来代替函数依赖。

希望这可以帮助！

Answer 2

（旁白：你的 go'up 命名方案很有创意。Haskell 风格通常是驼峰命名法。）

你走在正确的轨道上。 你所写的相当于下面的内容。

{-# LANGUAGE RankNTypes #-}
instance Zippable [a] where
    zipper = ... :: forall z. (Zipper z) => [a] -> z
    get = ... :: forall z. (Zipper z) => z -> [a]
    set = ... :: forall z. (Zipper z) => z -> [a] -> z

，给定 Zipper z，存在一个 zipper :: [a] -> z。）

（对于所有类型 z 定义 zipper = ... :: [a] -> ListZipper a，这显然限制太多。

您的代码将通过以下最小更改进行类型检查：

{-# LANGUAGE MultiParamTypeClasses #-}
class (Zipper z) => Zippable z t where
    zipper :: t -> z
    get :: z -> t
    set :: z -> t -> z
instance Zippable (ListZipper a) [a] where
    ...
instance Zippable (TreeZipper a) (Tree a) where
    ...

请参阅多参数类型类。 它是 Haskell'98 后的扩展，但 Haskell 实现广泛支持它。