Editing Higher-order function (section)

=== Alternatives ===
====Function pointers====
[[Function pointer]]s in languages such as [[C (programming language)|C]], [[C++]], [[Fortran]], and [[Pascal (programming language)|Pascal]] allow programmers to pass around references to functions. The following C code computes an approximation of the integral of an arbitrary function:

<syntaxhighlight lang="c">
#include <stdio.h>

double square(double x)
{
    return x * x;
}

double cube(double x)
{
    return x * x * x;
}

/* Compute the integral of f() within the interval [a,b] */
double integral(double f(double x), double a, double b, int n)
{
    int i;
    double sum = 0;
    double dt = (b - a) / n;
    for (i = 0;  i < n;  ++i) {
        sum += f(a + (i + 0.5) * dt);
    }
    return sum * dt;
}

int main()
{
    printf("%g\n", integral(square, 0, 1, 100));
    printf("%g\n", integral(cube, 0, 1, 100));
    return 0;
}
</syntaxhighlight>

The [[qsort]] function from the C standard library uses a function pointer to emulate the behavior of a higher-order function.

====Macros====
[[Macro (computer science)|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.

====Dynamic code evaluation====
In other [[imperative programming]] languages, it is possible to achieve some of the same algorithmic results as are obtained via higher-order functions by dynamically executing code (sometimes called ''Eval'' or ''Execute'' operations) in the scope of evaluation. There can be significant drawbacks to this approach:
*The argument code to be executed is usually not [[type system#Static typing|statically typed]]; these languages generally rely on [[type system#Dynamic typing|dynamic typing]] to determine the well-formedness and safety of the code to be executed.
*The argument is usually provided as a string, the value of which may not be known until run-time. This string must either be compiled during program execution (using [[just-in-time compilation]]) or evaluated by [[interpreter (computing)|interpretation]], causing some added overhead at run-time, and usually generating less efficient code.

====Objects====
In [[object-oriented programming]] languages that do not support higher-order functions, [[object (computer science)|objects]] can be an effective substitute. An object's [[method (computer science)|methods]] act in essence like functions, and a method may accept objects as parameters and produce objects as return values. Objects often carry added run-time overhead compared to pure functions, however, and added [[boilerplate code]] for defining and instantiating an object and its method(s). Languages that permit [[stack-based memory allocation|stack]]-based (versus [[dynamic memory allocation|heap]]-based) objects or [[Record (computer science)|structs]] can provide more flexibility with this method.

An example of using a simple stack based record in [[Free Pascal]] with a function that returns a function:

<syntaxhighlight lang="pascal">
program example;

type 
  int = integer;
  Txy = record x, y: int; end;
  Tf = function (xy: Txy): int;
     
function f(xy: Txy): int; 
begin 
  Result := xy.y + xy.x; 
end;

function g(func: Tf): Tf; 
begin 
  result := func; 
end;

var 
  a: Tf;
  xy: Txy = (x: 3; y: 7);

begin  
  a := g(@f);     // return a function to "a"
  writeln(a(xy)); // prints 10
end.
</syntaxhighlight>

The function <code>a()</code> takes a <code>Txy</code> record as input and returns the integer value of the sum of the record's <code>x</code> and <code>y</code> fields (3 + 7).

====Defunctionalization====
[[Defunctionalization]] can be used to implement higher-order functions in languages that lack  [[first class function|first-class functions]]:

<syntaxhighlight lang="cpp">
// Defunctionalized function data structures
template<typename T> struct Add { T value; };
template<typename T> struct DivBy { T value; };
template<typename F, typename G> struct Composition { F f; G g; };

// Defunctionalized function application implementations
template<typename F, typename G, typename X>
auto apply(Composition<F, G> f, X arg) {
    return apply(f.f, apply(f.g, arg));
}

template<typename T, typename X>
auto apply(Add<T> f, X arg) {
    return arg  + f.value;
}

template<typename T, typename X>
auto apply(DivBy<T> f, X arg) {
    return arg / f.value;
}

// Higher-order compose function
template<typename F, typename G>
Composition<F, G> compose(F f, G g) {
    return Composition<F, G> {f, g};
}

int main(int argc, const char* argv[]) {
    auto f = compose(DivBy<float>{ 2.0f }, Add<int>{ 5 });
    apply(f, 3); // 4.0f
    apply(f, 9); // 7.0f
    return 0;
}
</syntaxhighlight>

In this case, different types are used to trigger different functions via [[function overloading]]. The overloaded function in this example has the signature <code>auto apply</code>.