为什么要更高层次的程序？ [英] Why higher order procedures?

问题描述

所以如果一种语言提供了更高阶的过程，那么我可以有返回过程的过程。例如：

So if a language provides higher order procedure then I can have procedure that returns procedure. Something like:

(define (Proc a b c)
  (lambda (x) ( #| method body here in terms of a b c and x |# )))

要创建新的过程，

(define ProcA (Proc a1 b1 c1)) ; Would create ProcA that has 1 argument

类似的任务可以在不支持高阶通过定义 Proc ，它需要4个而不是3个参数，并调用此过程来定义 ProcA ，如：

Similar task could be done in a language which does not support higher order procedure by defining Proc that takes 4 instead of 3 arguments and calling this procedure to define ProcA, like:

(define (Proc a b c x) ( #| method body -- does not return any procedure |# )
(define (ProcA x) (Proc a1 b1 c1 x))

那么为什么有更多的fuzz

So why is there so much fuzz about higher order procedure? Am I missing something?

推荐答案

这是一个很好的观察，一个函数返回另一个函数是相同的函数，换句话说，从A到B的函数是逻辑意义的证明，A意味着B，或者：

It's a good observation that a function that returns another function is the same as a function that takes two arguments. This is called "Currying". Put another way, a function from A to B is proof of a logical implication, that A implies B, or:

A => B.

B表示C，则A和B表示C，或者：

As you note, if A implies that B implies C, then A and B implies C, or:

(A => (B => C)) <==> ((A, B) => C)

但是高阶函数不一定是函数返回另一个函数。 高阶函数是以另一个函数作为其参数的函数。这是一个重要的区别，HOFs是非常强大的编程工具。

But a higher order function is not necessarily a function that returns another function. A higher-order function is a function that takes another function as its argument. This is an important difference, and HOFs are immensely powerful programming tools.

例如，考虑这个Haskell函数：

For example, consider this Haskell function:

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

这个高阶函数使用一个函数 f 并将其应用于列表中的每个元素。在没有HOF的语言中，你可以用循环或类似的东西做这个函数，但是在有HOF的语言中，你可以为列表中的每个元素调用 f 用这样的简单调用：

This higher-order function takes a function f and applies it to every element in a list. In languages without HOFs, you would do what this function does with a loop or something similar, but in a language that has HOFs, you can call f for every element in the list with a simple call like this:

map f myList

当然，语言中的控制结构可以逼近高阶函数，但具有高阶函数的语言可让您发明自己的控制结构 。计划肯定有资格。

Sure, control constructs in languages let you approximate higher-order functions, but a language that has higher-order functions lets you invent your own control constructs. Scheme certainly qualifies.

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