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| {{merge from|Procedural parameter|date=May 2012}}
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| {{inline citations|date=September 2013}}
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| In [[mathematics]] and [[computer science]], a '''higher-order function''' (also '''functional form''', '''functional''' or '''functor''') is a [[function (mathematics)|function]] that does at least one of the following:
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| *takes one or more functions as an input
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| *outputs a function
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| All other functions are ''first-order functions''. In mathematics higher-order functions are also known as ''[[operator (mathematics)|operators]]'' or ''[[functional (mathematics)|functionals]]''. The [[derivative]] in [[calculus]] is a common example, since it maps a function to another function.
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| In the [[lambda calculus|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 values with types of the form <math>(\tau_1\to\tau_2)\to\tau_3</math>.
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| The <code>[[map (higher-order function)|map]]</code> 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 the 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 (programming language)|C]] standard [[function (computer science)|function]] <code>qsort</code> is an example of this.
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| Other examples of higher-order functions include [[fold (higher-order function)|fold]], [[function composition (computer science)|function composition]], [[integral|integration]], and the constant-function function λ''x''.λ''y''.''x''.
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| ==Example== | |
| ''The following examples are not intended to compare and contrast programming languages, since each program performs a different task.''
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| This [[Python (programming language)|Python]] program defines the higher-order function <code>twice</code> which takes a function and an arbitrary object (here a number), and applies the function to the object twice. This example prints 13: twice(f, 7) = f(f(7)) = (7 + 3) + 3.
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| <source lang="python">
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| def f(x):
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| return x + 3
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| def twice(function, x):
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| return function(function(x))
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| print(twice(f, 7))
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| </source>
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| This [[Haskell (programming language)|Haskell]] code is the equivalent of the Python program above.
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| <source lang="haskell"> | |
| f = (+3)
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| twice function = function . function
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| main = print (twice f 7)
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| </source> | |
| In this [[Scheme (programming language)|Scheme]] example the higher-order function <code>g()</code> takes a number and returns a function. The function <code>a()</code> takes a number and returns that number plus 7 (e.g. ''a''(3)=10).
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| <source lang="scheme">
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| (define (g x)
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| (lambda (y) (+ x y)))
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| (define a (g 7))
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| (display (a 3))
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| </source>
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| In this [[Erlang (programming language)|Erlang]] example the higher-order function <code>or_else</code>/2 takes a list of functions (<code>Fs</code>) and argument (<code>X</code>). It evaluates the function <code>F</code> with the argument <code>X</code> as argument. If the function <code>F</code> returns false then the next function in <code>Fs</code> will be evaluated. If the function <code>F</code> returns <code>{false,Y}</code> then the next function in <code>Fs</code> with argument <code>Y</code> will be evaluated. If the function <code>F</code> returns <code>R</code> the higher-order function <code>or_else</code>/2 will return <code>R</code>. Note that <code>X</code>, <code>Y</code>, and <code>R</code> can be functions. The example returns <code>false</code>.
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| <source lang="erlang">
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| or_else([], _) -> false;
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| or_else([F | Fs], X) -> or_else(Fs, X, F(X)).
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| or_else(Fs, X, false) -> or_else(Fs, X);
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| or_else(Fs, _, {false, Y}) -> or_else(Fs, Y);
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| or_else(_, _, R) -> R.
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| or_else([fun erlang:is_integer/1, fun erlang:is_atom/1, fun erlang:is_list/1],3.23).
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| </source>
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| In this [[JavaScript]] example the higher-order function <code>ArrayForEach</code> takes an array and a method in as arguments and calls the method on every element in the array. That is, it [[Map (higher-order function)|Map]]s the function over the array elements.
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| <source lang="javascript"> | |
| function ArrayForEach(array, func) {
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| for (var i = 0; i < array.length; i++) {
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| if (i in array) {
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| func(array[i]);
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| }
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| }
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| }
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| function log(msg) {
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| console.log(msg);
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| }
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| ArrayForEach([1,2,3,4,5], log);
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| </source>
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| This [[Ruby (programming language)|Ruby ]] code is the equivalent of the Python program above.
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| <source lang="ruby">
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| f1 = ->(x){ x + 3 }
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| def twice(f, x); f.call(f.call(x)) end
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| print twice(f1, 7)
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| </source>
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| ==Alternatives==
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| In programming languages that support [[function pointer]]s, one can emulate higher-order functions to some extent. Such languages include the [[C (programming language)|C]] and [[C++]] family. An example is the following C code which computes an approximation of the integral of an arbitrary function:
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| <source lang=c>
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| // Compute the integral of f() within the interval [a,b]
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| double integral(double (*f)(double x), double a, double b)
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| {
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| double sum, dt;
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| int i;
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| // Numerical integration: 0th order approximation
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| sum = 0.0;
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| dt = (b - a) / 100.0;
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| for (i = 0; i < 100; i++)
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| sum += (*f)(i * dt + a) * dt;
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| return sum;
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| }
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| </source> | |
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| Another example is the function [[qsort]] from C standard library.
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| In other [[imperative programming]] languages it is possible to achieve some of the same algorithmic results as are obtained through use of 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:
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| *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.
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| *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.
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| [[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.
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| 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 [[structs]] can provide more flexibility with this method.
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| An example of using a simple stack based record in [[Free Pascal]] with a function that returns a function:
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| <source lang=pascal>
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| program example;
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| type
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| int = integer;
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| Txy = record x, y: int; end;
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| Tf = function (xy: Txy): int;
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|
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| function f(xy: Txy): int;
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| begin
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| Result := xy.y + xy.x;
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| end;
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| function g(func: Tf): Tf;
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| begin
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| result := func;
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| end;
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| var
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| a: Tf;
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| xy: Txy = (x: 3; y: 7);
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| begin
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| a := g(@f); // return a function to "a"
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| writeln(a(xy)); // prints 10
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| end.
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| </source> | |
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| 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).
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| ==See also==
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| *[[First-class function]]
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| *[[Combinatory logic]]
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| *[[Function-level programming]]
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| *[[Functional programming]]
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| *[[Kappa calculus]] - a formalism for functions which ''excludes'' higher-order functions
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| *[[Strategy pattern]]
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| *[[Higher order message]]s
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| ==External links==
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| *[http://ergodicity.iamganesh.com/2006/08/07/higher-order-functions/ Higher-order functions and variational calculus]
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| *[http://boost.org/doc/html/lambda.html Boost Lambda Library for C++]
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| *[http://hop.perl.plover.com/book/ Higher Order Perl]
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| [[Category:Functional programming]]
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| [[Category:Lambda calculus]]
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| [[Category:Higher-order functions| ]]
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| [[Category:Subroutines]]
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| [[Category:Articles with example Python code]]
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| [[Category:Articles with example Haskell code]]
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| [[Category:Articles with example Scheme code]]
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| [[Category:Articles with example Erlang code]]
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| [[Category:Articles with example JavaScript code]]
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| [[Category:Articles with example C code]]
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| [[Category:Articles with example Pascal code]]
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If you"re making an project, then you are going to need at least one voice actor, and you will have to find out what to question them about their skill sets. Which means you need to shop for your voice actoror stars in the plural, because the case may possibly be-armed with a character number complete with a brief, one-sentence description of every character"s voice requirements. Don"t just hire a voice actor and desire you"ll discover she may do things you need. Be taught further about Search Engines Optimisation For Companies - Khabawiki by navigating to our witty encyclopedia. As each screen actor is different from his peers, each speech actor can be as different from every other. All things considered, if the business had forged Jack Nicholson as Vito Corleone, The Godfather could have been a different movie, even if Nicholson were Italian.
Whether you are casting a genuine character, a complicated character with apparent contradictions in his naturethe rogue with a gentle, gooey center, for instanceor an like Gandalf of the Ring Trilogy and Dumbledore of the Harry Potter series, you need to understand what a actor needs to have the ability to do in order to deliver that character to life. Screenwriters is a striking resource for more concerning when to flirt with it. You need to understand what areas of the voice are negotiable and which aren"t.
A character"s age or feature, for example, are usually not negotiable unless you are ready to change the very heart of one"s creation. If you require a accent, but find a actor who does British accents, but who is a master at pulling off other difficult features of the character, it is perfectly okay to change the character to match the actorif you"ve found a treasure of an actor. You have to make the call in the end, but you have to at the very least know what you need initially, even when you find you"re unable to get it. Clicking online video production seemingly provides cautions you should tell your pastor.
You could even need special skills from the voice actor, like having the ability to perform a child"s voice. Chances are, you are maybe not likely to have the ability to locate a daughter or son who is a voice actor, all things considered. But there are things you can do to generate the impression. Bart Simpson, as an example, is voiced by Nancy Cartwright.
All you could really need when casting can be a fundamental concept of the character"s voice: gender, age, accent or absence thereof, and things such as clean, tough, low, large, squeaky, sultry--that sort of thing. And you have to know very well what type of person he"s, whether he is confident, sly, whatever. Then go shopping and see what happens..
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