Haskell Catamorphic

-- 函数签名
map :: (a -> b) -> [a] -> [b]

filter :: (a -> Bool) -> [a] -> [a]

1 + 2
-- 等价于……
(+) 1 2

-- 函数签名
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]

-- 使用例
zipWith (+) [0,2,5] [1,4,7]
-- Result = [1, 6, 12]

-- 反斜杠，用空格隔开的参数，->，函数体
\x y z -> x + y + z
\x -> x > 7

-- 使用例
filter (\x -> x > 7) [1, 10, 100]

(.) :: (b -> c) -> (a -> b) -> a -> c

-- 考虑……
(f . g) x
-- 等价于
f (g x)

-- 使用例
third = head . tail . tail
    -- fetches the third element of a list

($) :: (a -> b) -> a -> b

-- 即
f $ x
-- 等价于
f x

f1 (f2 (f3 ...... (fn x)))
-- 用 $ 符号化简
f1 $ f2 $ f3 ...... $ fn x

-- 或者同时用 . 和 $ 化简
f1 . f2 . f3 ...... fn $ x

takeWhile :: (a -> Bool) -> [a] -> [a]
    -- take elements from a list as long as they satisfy a predicate
dropWhile :: (a -> Bool) -> [a] -> [a]
    -- drop elements from a list as long as they satisfy a predicate

-- 使用例
takeWhile even [2,4,1,2,3]  -- ==> [2,4]
dropWhile even [2,4,1,2,3]  -- ==> [1,2,3]

const :: a -> b -> a

(:) :: a -> [a] -> [a]

-- 使用例
1:[2,3]

[x:_] -- 提取列表第一个元素
f (_:x:_) = x -- 提取第二个元素
[x:y:_] -- 前两个元素
[x:y:z:_] -- 前三个元素

[f x | x <- lis] -- <=> map f lis

[x | x <- lis, pred x] -- <=> filter pred lis

[f x | x <- lis, p x]
-- 等价于
map f (filter p lis)

-- 多个列表
[ first ++ " " ++ last | first <- ["John", "Mary"], last <- ["Smith","Cooper"] ]
  ==> ["John Smith","John Cooper","Mary Smith","Mary Cooper"]

-- Local Definition
[ reversed | word <- ["this","is","a","string"], let reversed = reverse word ]
  ==> ["siht","si","a","gnirts"]

-- Pattern Matching
firstLetters string = [ char | (char:_) <- words string ]
firstLetters "Hello World!"
  ==> "HW"

-- For example
(<+>) :: [Int] -> [Int] -> [Int]
xs <+> ys = zipWith (+) xs ys

keepElements :: [a] -> [Bool] -> [a]
keepElements xs bs = _doIt (zip xs bs)

-- <interactive>: error:
--    • Found hole: _doIt :: [(a, Bool)] -> [a]