高阶函数的"阶(order)"到底是什么意思? 递归函数有"阶"吗?

cdsfiui

是不是说f.g.h这样的调用嵌套就是三阶函数?
这个阶(order)到底是一个静态的定义，还是一个动态的衡量?

递归函数在执行的时候，反复调用自己，就像是f.f.f.f.f.f，那它岂不是"无穷阶"?

love_wisdom

复合函数是高阶函数，但是高阶函数不一定是复合函数。

love_wisdom

比如说微分运算可以建一个函数变换成另外一个函数，这就是典型的高阶函数。

MMMIX

回复 1# cdsfiui


    https://en.wikipedia.org/wiki/Higher-order_function

另外，和 higher-order 对应的是 first-order：https://en.wikipedia.org/wiki/First-order

In mathematics and other formal sciences, first-order or first order most often means either:
* "linear" (a polynomial of degree at most one), as in first-order approximation and other calculus uses, where it is contrasted with "polynomials of higher degree", or
* "without self-reference", as in first-order logic and other logic uses, where it is contrasted with "allowing some self-reference" (higher-order logic)

其中的 order 在这里并不是个单独的概念。