haskell - (flip .) 的类型是什么？

Question

我试图理解为什么类型：

(flip .) is: (a -> a1 -> b -> c) -> a -> b -> a1 -> c

首先，类型：

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

我将重命名变量以在我的解释中更清楚，所以类型：

flip: is (ax -> bx -> cx) -> bx -> ax -> cx (.): is (by -> cy) -> (ay -> by) -> ay -> cy

然后我尝试像这样替换：

ax = (by -> cy) bx = (ay -> by) cx = ay -> cy

所以得到的类型是：(ay -> by) (by -> cy) -> ay -> cy，与正确的结果不同。

有什么帮助吗？

谢谢，塞巴斯蒂安。

Answer 1

(flip .)是(.) flip，所以：

• (.) :: (bx -> cx) -> (ax -> bx) -> ax -> cx
• flip :: (ay -> by -> cy) -> by -> ay -> cy
• 在(.) flip,
  • bx是ay -> by -> cy
  • cx是by -> ay -> cy
  • 所以 it's all (ax -> (ay -> by -> cy)) -> ax -> (by -> ay -> cy),
    which is just (ax -> ay -> by -> cy) -> ax -> by -> ay -> cy,
    匹配(flip .) :: (a -> a1 -> b -> c) -> a -> b -> a1 -> c.