带有中点符号的自由点样式 [英] Point free style with infix notation

问题描述

您好，有没有一种在使用中缀表示法时编写无点样式的方法?

Hello is there a way to write point free style when using infix notation?

f::Int->Int->Int->Int
f a b=(+) (a+b)

为什么您不能做这样的事情?

Why you cannot do something like this ?

 f::Int->Int->Int->Int
 f a b=(a+b) +

      or

 f a b= (a+b) `+`

您是否不能将诸如点之类的运算符组合在一起?

Can you not combine operators in point free style like e.g?

ptfree::Int->Int->Int->Int
ptfree=(+) (+)

我的意思是您可以砍碎像fold这样的函数的参数，但是为什么不算运算符参数呢?

I mean you can chop arguments of functions like fold but why not for operator arguments?

推荐答案

好了，因为您需要传递两个参数，所以我们可以使用所谓的"惊讶的猫头鹰运算符 em>".这基本上是参数的组合.所以我们可以使用:

Well since you need to pass two parameters, we can use what is known as the "surprised owl operator". This is basically a composition of parameters. So we can use:

f = ((.).(.)) (+) (+)

或者我们可以像这样进一步内联运算符:

Or we can more inline the operator like:

f = ((+) .) . (+)

猫头鹰运算符((.).(.)) f g基本上是\x y -> f (g x y)

The owl operator ((.).(.)) f g basically is short for \x y -> f (g x y)

这是如何工作的?

"惊讶的猫头鹰算子"的规范形式为:

= ((.) . (.))
------------- (canonical form)
  (.) (.) (.)

因此，我们现在可以将(.)替换为相应的lambda表达式:

So we can now replace the (.)s with corresponding lambda expressions:

(\f g x -> f (g x)) (.) (.)

所以现在我们可以执行一些替换:

So now we can perform some replacements:

   (\f g x -> f (g x)) (.) (.)
-> (\x -> (.) ((.) x))
-> (\x -> (\q r y -> q (r y)) ((.) x))
-> (\x -> (\r y -> ((.) x) (r y)))
-> (\x r y -> ((.) x) (r y))
-> (\x r y -> ((\s t u -> s (t u)) x) (r y))
-> (\x r y -> (\t u -> x (t u)) (r y))
-> (\x r y -> (\u -> x ((r y) u)))
-> \x r y u -> x ((r y) u))
-> \x r y u -> x (r y u)

所以从根本上讲，这意味着我们惊讶的猫头鹰算子等于:

So basically it means that our surprised owl operator, is equal to:

surprised_owl :: (y -> z) -> (a -> b -> y) -> a -> b -> z
surprised_owl f g x y = f (g x y)  -- renamed variables

如果现在我们通过提供的功能(两次(+))对它进行专门化处理，我们将得到:

And if we now specialize this with the fuctions provided (two times (+)), we get:

f = surprised_owl (+) (+)

如此:

f x y = (+) ((+) x y)

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