[Tutor] Higher-Order Function Examples

[Steven D'Aprano]

Walter Prins wrote:
> 2011/2/14 Rafael Durán Castañeda <rafadurancastaneda at gmail.com>
> 
>> Could we consider sorted as an high order function?
>>
>> sorted_list = sorted(list_strings, key = str.lower)
>>
>>
> No because sorted() returns a list as a result.   A higher order function
> produces another function as a result, or takes one or more functions as a
> parameter.

By that definition, sorted *is* a higher-order function as it takes a 
key function as a parameter.

Typically, though, most people would consider that in order to count as 
a high order function, it must take another function as a main 
parameter, and not as an optional extra.

E.g. sorted doesn't make the cut, because you can call 
sorted(list_strings) without giving a key function. The key function is 
an optional extra that merely modifies the action of sorted, rather than 
an essential part of it.

On the other hand, once you really start to embrace the idea of 
functions-as-data, the distinction becomes less important. There are 
functions that take strings as arguments, and functions that take 
numbers as argument, and functions that take strings AND numbers as 
arguments... why should we single out functions that take functions as 
special? If functions are tools, then there's no fundamental difference 
between "ordinary tools" and "tools that make other tools". They're all 
just tools.

The difference between "ordinary functions" and "higher-order functions" 
is most important in languages that don't have higher-order functions.


-- 
Steven