haskell - 了解不同的文件夹语句

Question

我理解简单的 foldr 语句，例如

foldr (+) 0 [1,2,3]

但是，我在处理更复杂的 foldr 语句时遇到了麻烦，即在函数中采用 2 个参数以及/和 - 计算的语句。谁能解释为获得这些答案而发生的步骤？

foldr (\x y -> (x+y)*2) 2 [1,3] = 22

foldr (/) 2 [8,12,24,4] = 8.0

谢谢。

Answer 1

foldr函数定义如下:

foldr :: (a -> b -> b) -> b -> [a] -> b
foldr _ a []     = a
foldr f a (x:xs) = f x (foldr f a xs)

现在考虑以下表达式:

foldr (\x y -> (x + y) * 2) 2 [1,3]

我们将为 lambda 命名:

f x y = (x + y) * 2

因此:

foldr f 2 [1,3]
-- is
f 1 (foldr f 2 [3])
-- is
f 1 (f 3 (foldr f 2 []))
-- is
f 1 (f 3 2)
-- is
f 1 10
-- is
22

同样:

foldr (/) 2 [8,12,24,4]
-- is
8 / (foldr (/) 2 [12,24,4])
-- is
8 / (12 / (foldr (/) 2 [24,4]))
-- is
8 / (12 / (24 / (foldr (/) 2 [4])))
-- is
8 / (12 / (24 / (4 / (foldr (/) 2 []))))
-- is
8 / (12 / (24 / (4 / 2)))
-- is
8 / (12 / (24 / 2.0))
-- is
8 / (12 / 12.0)
-- is
8 / 1.0
-- is
8.0

希望有所帮助。