What is the definition of a Higher-Order Function?

A higher-order function (HOF) is a function that meets at least one of the following criteria: it takes one or more functions as arguments, or it returns a function as its result. This concept is prevalent in both mathematics and computer science. In the realm of programming, higher-order functions allow functions to be used as arguments or returned as values, thereby treating functions as first-class citizens within the programming environment[2][3][6][7].

In practical terms, higher-order functions enable more abstract and potentially more concise code. They are fundamental in functional programming paradigms where operations like map, filter, and reduce are implemented as higher-order functions. These functions can manipulate other functions o...