In the untyped lambda calculus, all functions are higher-order; in a typed lambda calculus, from which most functional programming languages are derived, higher-order functions are generally those with types containing more than one arrow. In functional programming, higher-order functions that return other functions are said to be curried.
map function found in many functional programming languages is one example of a higher-order function. It takes as arguments a function f and a list of elements, and as result, returns a new list with f applied to each element from the list. Another very common kind of higher-order function in those languages which support them are sorting functions which take a comparison function as a parameter, allowing the programmer to separate the sorting algorithm from the comparisons of the items being sorted. The C standard function,
qsort, is an example of this.
Similar code in D (programming language) 2.0: Function g returns delegate to anonymous function which in this case becomes closure. Returned delegate is of type int returning int, but in can be simply converted into a template.
In another example, this Pascal program takes a function as its first argument also, and prints 100 :
Macros can also be used to achieve some of the effects of higher order functions. However, macros cannot easily avoid the problem of variable capture; they may also result in large amounts of duplicated code, which can be more difficult for a compiler to optimize. Macros are generally not strongly typed, although they may produce strongly typed code.
Objects in the object-oriented programming paradigm can be used as higher order functions – a method of an object acts in many ways like a function, and a method may take objects (containing methods) as arguments or return objects with methods. Objects often carry additional run-time overhead compared to pure functions, however. Language syntax can introduce additional difficulties; an object must be created to hold any parameters that are functions, and any resulting function must also have an associated object. However, languages that offer stack objects or structs (as opposed to just heap based) can make it easier to utilize an object as if it were a function too.
An example of using a simple stack based record in Freepascal with a function that returns a function:
The function a() takes a Txy record as input and returns the integer value of the sum of the record's x and y fields (3 + 7).
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