使用Haskell实现一个函数式数据结构库

Haskell是一种纯函数式编程语言，可以用来实现函数式数据结构。函数式数据结构是指不可变的数据结构，它们的操作不会改变原始数据，而是返回一个新的数据结构。在Haskell中，可以使用代数数据类型和递归函数来定义函数式数据结构。

下面是一个使用Haskell实现的函数式数据结构库，其中包含一些常见的数据结构和它们的使用示例：

module FunctionalDataStructures (
    List(..),
    Queue(..),
    Stack(..),
    Tree(..),
    empty,
    isEmpty,
    insert,
    delete,
    search
) where

-- 定义列表数据结构
data List a = Empty | Cons a (List a) deriving Show

-- 定义队列数据结构
data Queue a = Queue [a] deriving Show

-- 定义栈数据结构
data Stack a = EmptyStack | Push a (Stack a) deriving Show

-- 定义二叉树数据结构
data Tree a = EmptyTree | Node a (Tree a) (Tree a) deriving Show

-- 判断列表是否为空
isEmpty :: List a -> Bool
isEmpty Empty = True
isEmpty _ = False

-- 创建一个空列表
empty :: List a
empty = Empty

-- 在列表开头插入元素
insert :: a -> List a -> List a
insert x xs = Cons x xs

-- 在列表中删除元素
delete :: Eq a => a -> List a -> List a
delete _ Empty = Empty
delete x (Cons y ys)
    | x == y = delete x ys
    | otherwise = Cons y (delete x ys)

-- 在列表中查找元素
search :: Eq a => a -> List a -> Bool
search _ Empty = False
search x (Cons y ys)
    | x == y = True
    | otherwise = search x ys

-- 创建一个空队列
emptyQueue :: Queue a
emptyQueue = Queue []

-- 将元素入队列
enqueue :: a -> Queue a -> Queue a
enqueue x (Queue xs) = Queue (x:xs)

-- 出队列
dequeue :: Queue a -> (Maybe a, Queue a)
dequeue (Queue []) = (Nothing, Queue [])
dequeue (Queue xs) = (Just (last xs), Queue (init xs))

-- 判断队列是否为空
isEmptyQueue :: Queue a -> Bool
isEmptyQueue (Queue []) = True
isEmptyQueue _ = False

-- 创建一个空栈
emptyStack :: Stack a
emptyStack = EmptyStack

-- 将元素入栈
push :: a -> Stack a -> Stack a
push x xs = Push x xs

-- 出栈
pop :: Stack a -> (Maybe a, Stack a)
pop EmptyStack = (Nothing, EmptyStack)
pop (Push x xs) = (Just x, xs)

-- 判断栈是否为空
isEmptyStack :: Stack a -> Bool
isEmptyStack EmptyStack = True
isEmptyStack _ = False

-- 创建一个空树
emptyTree :: Tree a
emptyTree = EmptyTree

-- 将元素插入树
insertTree :: Ord a => a -> Tree a -> Tree a
insertTree x EmptyTree = Node x EmptyTree EmptyTree
insertTree x (Node y left right)
    | x == y = Node y left right
    | x < y  = Node y (insertTree x left) right
    | x > y  = Node y left (insertTree x right)

-- 在树中删除元素
deleteTree :: Ord a => a -> Tree a -> Tree a
deleteTree _ EmptyTree = EmptyTree
deleteTree x (Node y left right)
    | x == y = mergeTrees left right
    | x < y  = Node y (deleteTree x left) right
    | x > y  = Node y left (deleteTree x right)

-- 合并两个树
mergeTrees :: Tree a -> Tree a -> Tree a
mergeTrees EmptyTree t = t
mergeTrees t EmptyTree = t
mergeTrees t1 t2 = Node (findMax t1) t1' t2
    where findMax (Node x _ EmptyTree) = x
          findMax (Node _ _ right) = findMax right
          t1' = deleteTree (findMax t1) t1

使用示例：

main :: IO ()
main = do
    -- 使用列表
    let list = insert 1 (insert 2 (insert 3 empty))
    putStrLn $ "List: " ++ show list
    putStrLn $ "Is empty? " ++ show (isEmpty list)
    putStrLn $ "Search 2: " ++ show (search 2 list)
    putStrLn $ "Search 4: " ++ show (search 4 list)

    -- 使用队列
    let queue = enqueue 1 (enqueue 2 (enqueue 3 emptyQueue))
    putStrLn $ "Queue: " ++ show queue
    putStrLn $ "Is empty? " ++ show (isEmptyQueue queue)
    let (front, queue') = dequeue queue
    putStrLn $ "Dequeued: " ++ show front
    putStrLn $ "Queue: " ++ show queue'

    -- 使用栈
    let stack = push 1 (push 2 (push 3 emptyStack))
    putStrLn $ "Stack: " ++ show stack
    putStrLn $ "Is empty? " ++ show (isEmptyStack stack)
    let (top, stack') = pop stack
    putStrLn $ "Popped: " ++ show top
    putStrLn $ "Stack: " ++ show stack'

    -- 使用树
    let tree = insertTree 2 (insertTree 1 (insertTree 3 emptyTree))
    putStrLn $ "Tree: " ++ show tree
    let tree' = deleteTree 2 tree
    putStrLn $ "Tree (after deleting 2): " ++ show tree'

以上代码展示了一个基本的函数式数据结构库，包含了列表、队列、栈和二叉树，并通过使用例子展示了这些数据结构的基本操作。这个库可以作为在Haskell中实现函数式数据结构的参考。