元组 #

-- 二元组（对）
pair :: (Int, String)
pair = (1, "hello")

-- 三元组
triple :: (Int, String, Bool)
triple = (1, "hello", True)

-- 单元类型（零元组）
unit :: ()
unit = ()

-- 元组可以包含不同类型
mixed :: (Int, String, Bool, Double)
mixed = (1, "hello", True, 3.14)

-- 元组长度固定
-- 不能动态添加或删除元素

-- 元组类型由长度和元素类型共同决定
-- (Int, String) 和 (String, Int) 是不同类型
-- (Int, String) 和 (Int, String, Bool) 是不同类型

-- 类型语法
(类型1, 类型2, ...) 

-- 示例
(Int, String)           -- 二元组
(Int, String, Bool)     -- 三元组
(Int, Int, Int, Int)    -- 四元组
()                      -- 单元类型

-- 二元组
point2D :: (Double, Double)
point2D = (1.0, 2.0)

-- 三元组
point3D :: (Double, Double, Double)
point3D = (1.0, 2.0, 3.0)

-- 嵌套元组
nested :: ((Int, Int), String)
nested = ((1, 2), "hello")

-- 二元组构造器
(,) :: a -> b -> (a, b)

-- 使用
pair = (,) 1 "hello"  -- (1, "hello")

-- 三元组构造器
(,,) :: a -> b -> c -> (a, b, c)

triple = (,,) 1 "hello" True  -- (1, "hello", True)

-- 四元组构造器
(,,,) :: a -> b -> c -> d -> (a, b, c, d)

-- 创建特定类型的元组构造器
makePair :: Int -> (Int, String)
makePair = (, "default")

-- 使用
result = makePair 5  -- (5, "default")

-- 另一个例子
withTimestamp :: String -> (String, Int)
withTimestamp s = (s, getCurrentTime)
  where getCurrentTime = 12345

-- fst：获取二元组第一个元素
fst (1, "hello")  -- 1

-- snd：获取二元组第二个元素
snd (1, "hello")  -- "hello"

-- 注意：只适用于二元组
-- fst (1, 2, 3)  -- 错误！

-- 函数参数中模式匹配
first :: (a, b) -> a
first (x, _) = x

second :: (a, b) -> b
second (_, y) = y

-- 三元组
third :: (a, b, c) -> c
third (_, _, z) = z

-- 解构元组
sumPair :: (Int, Int) -> Int
sumPair (x, y) = x + y

-- let中解构
result = let (x, y) = (1, 2) in x + y  -- 3

-- where中解构
distance :: (Double, Double) -> (Double, Double) -> Double
distance p1 p2 = sqrt (dx * dx + dy * dy)
  where
    (x1, y1) = p1
    (x2, y2) = p2
    dx = x2 - x1
    dy = y2 - y1

-- swap：交换二元组
swap :: (a, b) -> (b, a)
swap (x, y) = (y, x)

-- 示例
swap (1, "hello")  -- ("hello", 1)

-- curry：将元组参数转为柯里化
curry :: ((a, b) -> c) -> a -> b -> c
curry f x y = f (x, y)

-- uncurry：将柯里化转为元组参数
uncurry :: (a -> b -> c) -> (a, b) -> c
uncurry f (x, y) = f x y

-- 使用curry
addPair :: (Int, Int) -> Int
addPair (x, y) = x + y

addCurried :: Int -> Int -> Int
addCurried = curry addPair

-- 使用
addCurried 1 2  -- 3

-- 使用uncurry
add :: Int -> Int -> Int
add x y = x + y

addUncurried :: (Int, Int) -> Int
addUncurried = uncurry add

-- 使用
addUncurried (1, 2)  -- 3

-- 对二元组两个元素应用函数
both :: (a -> b) -> (a, a) -> (b, b)
both f (x, y) = (f x, f y)

-- 示例
both (*2) (3, 4)  -- (6, 8)

-- 对第一个元素应用函数
first :: (a -> a') -> (a, b) -> (a', b)
first f (x, y) = (f x, y)

-- 对第二个元素应用函数
second :: (b -> b') -> (a, b) -> (a, b')
second f (x, y) = (x, f y)

-- 示例
first (*2) (3, 4)   -- (6, 4)
second (*2) (3, 4)  -- (3, 8)

-- zip：将两个列表配对成元组列表
zip :: [a] -> [b] -> [(a, b)]

-- 示例
zip [1, 2, 3] ['a', 'b', 'c']  -- [(1, 'a'), (2, 'b'), (3, 'c')]

-- unzip：将元组列表解成两个列表
unzip :: [(a, b)] -> ([a], [b])

-- 示例
unzip [(1, 'a'), (2, 'b'), (3, 'c')]  -- ([1, 2, 3], "abc")

-- zip3：三个列表配对
zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]

-- 示例
zip3 [1, 2, 3] ['a', 'b', 'c'] [True, False, True]
-- [(1, 'a', True), (2, 'b', False), (3, 'c', True)]

-- unzip3：三元组列表解成三个列表
unzip3 :: [(a, b, c)] -> ([a], [b], [c])

-- 示例
unzip3 [(1, 'a', True), (2, 'b', False)]
-- ([1, 2], "ab", [True, False])

-- 提取元组列表的第一个元素
firsts :: [(a, b)] -> [a]
firsts = map fst

-- 提取元组列表的第二个元素
seconds :: [(a, b)] -> [b]
seconds = map snd

-- 示例
firsts [(1, 'a'), (2, 'b'), (3, 'c')]  -- [1, 2, 3]
seconds [(1, 'a'), (2, 'b'), (3, 'c')] -- "abc"

-- 关联列表
phoneBook :: [(String, String)]
phoneBook = 
    [ ("Alice", "123-4567")
    , ("Bob", "234-5678")
    , ("Charlie", "345-6789")
    ]

-- lookup：在关联列表中查找
lookup :: Eq a => a -> [(a, b)] -> Maybe b

-- 示例
lookup "Alice" phoneBook   -- Just "123-4567"
lookup "David" phoneBook   -- Nothing

-- 更新关联列表
update :: Eq a => a -> b -> [(a, b)] -> [(a, b)]
update key value assoc = (key, value) : filter ((/= key) . fst) assoc

-- 删除键
deleteKey :: Eq a => a -> [(a, b)] -> [(a, b)]
deleteKey key = filter ((/= key) . fst)

-- 获取所有键
keys :: [(a, b)] -> [a]
keys = map fst

-- 获取所有值
values :: [(a, b)] -> [b]
values = map snd

-- 二维点
type Point = (Double, Double)

-- 距离
distance :: Point -> Point -> Double
distance (x1, y1) (x2, y2) = sqrt ((x2 - x1)^2 + (y2 - y1)^2)

-- 中点
midpoint :: Point -> Point -> Point
midpoint (x1, y1) (x2, y2) = ((x1 + x2) / 2, (y1 + y2) / 2)

-- 移动
translate :: Double -> Double -> Point -> Point
translate dx dy (x, y) = (x + dx, y + dy)

-- 学生数据
type Student = (String, Int, Int)  -- (姓名, 数学, 英语)

-- 计算总分
totalScore :: Student -> Int
totalScore (_, math, eng) = math + eng

-- 计算平均分
averageScore :: Student -> Double
averageScore s = fromIntegral (totalScore s) / 2

-- 判断是否及格
isPassing :: Student -> Bool
isPassing (_, math, eng) = math >= 60 && eng >= 60

-- 获取学生姓名
getName :: Student -> String
getName (name, _, _) = name

-- 复数表示
type Complex = (Double, Double)  -- (实部, 虚部)

-- 加法
addComplex :: Complex -> Complex -> Complex
addComplex (a, b) (c, d) = (a + c, b + d)

-- 乘法
mulComplex :: Complex -> Complex -> Complex
mulComplex (a, b) (c, d) = (a * c - b * d, a * d + b * c)

-- 模
magnitude :: Complex -> Double
magnitude (a, b) = sqrt (a * a + b * b)

-- 共轭
conjugate :: Complex -> Complex
conjugate (a, b) = (a, -b)

-- 统计数据
type Stats = (Int, Int, Int, Int)  -- (最小值, 最大值, 总和, 数量)

-- 计算统计
stats :: [Int] -> Stats
stats [] = error "empty list"
stats xs = (minimum xs, maximum xs, sum xs, length xs)

-- 计算平均值
average :: Stats -> Double
average (_, _, total, count) = fromIntegral total / fromIntegral count

-- 格式化输出
showStats :: Stats -> String
showStats (minVal, maxVal, total, count) =
    "Min: " ++ show minVal ++ 
    ", Max: " ++ show maxVal ++ 
    ", Sum: " ++ show total ++ 
    ", Count: " ++ show count

-- 好：临时组合少量数据
getMinMax :: [Int] -> (Int, Int)
getMinMax xs = (minimum xs, maximum xs)

-- 好：返回多个值
divideWithRemainder :: Int -> Int -> (Int, Int)
divideWithRemainder x y = (x `div` y, x `mod` y)

-- 不好：大量元素或需要命名字段
-- 使用data或record代替
data Person = Person 
    { name :: String
    , age :: Int
    , email :: String
    }

-- 使用类型别名提高可读性
type Point = (Double, Double)
type Name = String
type Age = Int

-- 但不创建新类型
-- type只是别名

-- 好：使用模式匹配解构
process :: (Int, String) -> String
process (n, s) = s ++ ": " ++ show n

-- 不好：使用fst和snd链式调用
processBad pair = snd pair ++ ": " ++ show (fst pair)