“功能箭头与右边相关”的用处？ [英] Usefulness of "function arrows associate to the right"?

问题描述

阅读 http：//www.seas。 upenn.edu/~cis194/spring13/lectures/04-higher-order.html 它声明

特别注意那个函数箭头与右边相关，
是，W - > X - > Y - > Z相当于W - >（X - >（Y - > Z））。我们可以
总是在一个类型的最右边的顶级箭头
的周围添加或删除括号。

函数箭头与右侧相关，但作为函数应用关联到左侧，那么这些信息的用处是什么？我觉得我不了解某些事情，对于我来说，这是一个无意义的点，箭头指向右边。由于函数应用程序总是与左边关联，那么这是我应该关注的唯一关联性？

解决方案

功能箭头与右侧相关，但此信息的用处？

如果您看到类型签名，例如 f：String - > Int - > Bool 您需要知道函数箭头的关联性，以了解 f 的类型真的是：

$如果箭头关联到左侧，则类型表示（String - > Int） - > Bool ，也就是 f 接受一个函数作为参数并返回一个布尔值。

关联到右侧，那么类型意味着字符串 - > （int - > Bool），也就是 f 将一个字符串作为参数并返回一个函数。

这是一个很大的区别，如果你想使用 f ，你需要知道它是哪一个。由于函数箭头与右边相关，所以您知道它必须是第二个选项： f 接受一个字符串并返回一个函数。

与右侧功能应用关联的功能箭头与左侧关联

这两个选择很好地结合在一起。例如，我们可以从上面调用 f 作为 fanswer42 ，这实际上意味着（f答案）42 。所以我们将字符串answer传递给 f ，它返回一个函数。然后我们将数字 42 传递给该函数，该函数返回一个布尔值。实际上，我们几乎使用 f 作为带有两个参数的函数。

这是标准方法用Haskell中的两个（或更多）参数编写函数，所以这是一个非常常见的用例。由于函数应用程序和函数箭头的关联性，我们可以在不使用括号的情况下编写此常见用例。

Reading http://www.seas.upenn.edu/~cis194/spring13/lectures/04-higher-order.html it states

In particular, note that function arrows associate to the right, that is, W -> X -> Y -> Z is equivalent to W -> (X -> (Y -> Z)). We can always add or remove parentheses around the rightmost top-level arrow in a type.

Function arrows associate to the right but as function application associates to the left then what is usefulness of this information ? I feel I'm not understanding something as to me it is a meaningless point that function arrows associate to the right. As function application always associates to the left then this the only associativity I should be concerned with ?

解决方案

Function arrows associate to the right but [...] what is usefulness of this information?

If you see a type signature like, for example, f : String -> Int -> Bool you need to know the associativity of the function arrow to understand what the type of f really is:

1. if the arrow associates to the left, then the type means (String -> Int) -> Bool, that is, f takes a function as argument and returns a boolean.
2. if the arrow associates to the right, then the type means String -> (Int -> Bool), that is, f takes a string as argument and returns a function.

That's a big difference, and if you want to use f, you need to know which one it is. Since the function arrow associates to the right, you know that it has to be the second option: f takes a string and returns a function.

Function arrows associate to the right [...] function application associates to the left

These two choices work well together. For example, we can call the f from above as f "answer" 42 which really means (f "answer") 42. So we are passing the string "answer" to f which returns a function. And then we're passing the number 42 to that function, which returns a boolean. In effect, we're almost using f as a function with two arguments.

This is the standard way of writing functions with two (or more) arguments in Haskell, so it is a very common use case. Because of the associativity of function application and of the function arrow, we can write this common use case without parentheses.

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