Anonymous function

In computer programming, an anonymous function (also function literal or lambda abstraction) is a function definition that is not bound to an identifier. Anonymous functions are often:[1]

  1. arguments being passed to higher-order functions, or
  2. used for constructing the result of a higher-order function that needs to return a function.

If the function is only used once, or a limited number of times, an anonymous function may be syntactically lighter than using a named function. Anonymous functions are ubiquitous in functional programming languages and other languages with first-class functions, where they fulfill the same role for the function type as literals do for other data types.

Anonymous functions originate in the work of Alonzo Church in his invention of the lambda calculus in 1936 (prior to electronic computers), in which all functions are anonymous.[2] In several programming languages, anonymous functions are introduced using the keyword lambda, and anonymous functions are often referred to as lambdas or lambda abstractions. Anonymous functions have been a feature of programming languages since Lisp in 1958 and an increasing number of modern programming languages support anonymous functions.

Anonymous functions are a form of nested function, in allowing access to variables in the scope of the containing function (non-local variables). This means anonymous functions need to be implemented using closures. Unlike named nested functions, they cannot be recursive without the assistance of a fixpoint operator (also known as an anonymous fixpoint or anonymous recursion) or binding them to a name.[3]

Uses

Anonymous functions can be used for containing functionality that need not be named and possibly for short-term use. Some notable examples include closures and currying.

Use of anonymous functions is a matter of style. Using them is never the only way to solve a problem; each anonymous function could instead be defined as a named function and called by name. Some programmers use anonymous functions to encapsulate specific, non-reusable code without littering the code with a lot of little one-line normal functions.

In some programming languages, anonymous functions are commonly implemented for very specific purposes such as binding events to callbacks, or instantiating the function for particular values, which may be more efficient, more readable, and less error-prone than a calling a more-generic named function.

All of the code in the following sections is written in Python 2.x (not 3.x).

Sorting

When attempting to sort in a non-standard way it may be easier to contain the comparison logic as an anonymous function instead of creating a named function. Most languages provide a generic sort function that implements a sort algorithm that will sort arbitrary objects. This function usually accepts an arbitrary comparison function that is supplied two items and the function indicates if they are equal or if one is "greater" or "less" than the other (typically indicated by returning a negative number, zero, or a positive number).

Consider sorting a list of strings by length of the string:

>>> a = ['house', 'car', 'bike']
>>> a.sort(lambda x,y: cmp(len(x), len(y)))
>>> print(a)
['car', 'bike', 'house']

The anonymous function in this example is the lambda expression:

lambda x,y: cmp(...)

The anonymous function accepts two arguments, x and y, and returns the comparison between them using the built-in function cmp(). Another example would be sorting items in a list by the name of their class (in Python, everything has a class):

>>> a = [10, 'number', 11.2]
>>> a.sort(lambda x,y: cmp(x.__class__.__name__, y.__class__.__name__))
>>> print(a)
[11.2, 10, 'number']

Note that 11.2 has class name "float", 10 has class name "int", and 'number' has class name "str". The sorted order is "float", "int", then "str".

Closures

Closures are functions evaluated in an environment containing bound variables. The following example binds the variable "threshold" in an anonymous function that compares the input to the threshold.

def comp(threshold):
    return lambda x: x < threshold

This can be used as a sort of generator of comparison functions:

>>> func_a = comp(10)
>>> func_b = comp(20)

>>> print func_a(5), func_a(8), func_a(13), func_a(21)
True True False False

>>> print func_b(5), func_b(8), func_b(13), func_b(21)
True True True False

It would be impractical to create a function for every possible comparison function and may be too inconvenient to keep the threshold around for further use. Regardless of the reason why a closure is used, the anonymous function is the entity that contains the functionality that does the comparing.

Currying

Main article: currying

Currying is the process of changing a function so that it takes fewer inputs (in this case, transforming a function that performs division by any integer into one that performs division by a set integer).

a
>>> def divide(x, y):
...     return x / y

>>> def divisor(d):
...     return lambda x: divide(x, d)

>>> half = divisor(2)
>>> third = divisor(3)

>>> print half(32), third(32)
16 10

>>> print half(40), third(40)
20 13

While the use of anonymous functions is perhaps not common with currying it still can be used. In the above example, the function divisor generates functions with a specified divisor. The functions half and third curry the divide function with a fixed divisor.

The divisor function also forms a closure by binding the "d" variable.

Higher-order functions

Python 2.x includes several functions that take anonymous functions as an argument. This section describes some of them.

Map

The map function performs a function call on each element of a list. The following example squares every element in an array with an anonymous function.

>>> a = [1, 2, 3, 4, 5, 6]
>>> print map(lambda x: x*x, a)
[1, 4, 9, 16, 25, 36]

The anonymous function accepts an argument and multiplies it by itself (squares it).

Filter

The filter function returns all elements from a list that evaluate True when passed to a certain function.

>>> a = [1, 2, 3, 4, 5, 6]
>>> print filter(lambda x: x % 2 == 0, a)
[2, 4, 6]

The anonymous function checks if the argument passed to it is even.

Fold

The fold/reduce function runs over all elements in a list (usually left-to-right), accumulating a value as it goes. A common usage of this is to combine all elements of a list into a single value, for example:

>>> a = [1, 2, 3, 4, 5]
>>> print reduce(lambda x,y: x*y, a)
120

This performs

\left( \left( \left( 1 \times 2 \right) \times 3 \right) \times 4 \right) \times 5 = 120.

The anonymous function here is the multiplication of the two arguments.

The result of a fold need not be a single value—in fact, both map and filter can be created using fold. In map, the value that is accumulated is a new list, containing the results of applying a function to each element of the original list. In filter, the value that is accumulated is a new list containing only those elements that match the given condition.

List of languages

The following is a list of programming languages that fully support unnamed anonymous functions; support some variant of anonymous functions; and have no support for anonymous functions.

This table shows some general trends. First, the languages that do not support anonymous functions—C, Pascal, Object Pascal, Java—are all conventional statically typed languages. This does not, however, mean that statically typed languages are incapable of supporting anonymous functions. For example, the ML languages are statically typed and fundamentally include anonymous functions, and Delphi, a dialect of Object Pascal, has been extended to support anonymous functions. Second, the languages that treat functions as first-class functions—Dylan, JavaScript, Lisp, Scheme, ML, Haskell, Python, Ruby, Perl—generally have anonymous function support so that functions can be defined and passed around as easily as other data types. However, the new C++11 standard adds them to C++, even though this is a conventional, statically typed language.

This list is incomplete; you can help by expanding it.
Language Support Notes
ActionScript Green tickY
Ada Red XN Expression functions are a part of Ada2012
ALGOL 68 Green tickY
Brainfuck Red XN
Bash Green tickY A library has been made to support anonymous functions in Bash. [4]
C Red XN Support is provided in clang and along with the llvm compiler-rt lib. GCC support is given for a macro implementation which enables the possibility of usage. Details see below.
C# Green tickY
C++ Green tickY As of the C++11 standard
CFML Green tickY As of Railo 4[5] / ColdFusion 10[6]
Clojure Green tickY
COBOL Red XN Micro Focus's non-standard Managed COBOL dialect supports lambdas, which are called anonymous delegates/methods.[7]
Curl Green tickY
D Green tickY
Dart Green tickY
Delphi Green tickY
Dylan Green tickY
Eiffel Green tickY
Erlang Green tickY
F# Green tickY
Factor Green tickY "Quotations" support this[8]
Fortran Red XN
Frink Green tickY
Go Green tickY
Gosu Green tickY[9]
Groovy Green tickY[10]
Haskell Green tickY
Haxe Green tickY
Java Green tickY Supported in Java 8
JavaScript Green tickY
Julia Green tickY
Lisp Green tickY
Logtalk Green tickY
Lua Green tickY
MUMPS Red XN
Mathematica Green tickY
Maple Green tickY
Matlab Green tickY
Maxima Green tickY
OCaml Green tickY
Octave Green tickY
Object Pascal Green tickY Delphi, a dialect of Object Pascal, implements support for anonymous functions (formally, anonymous methods) natively since Delphi 2009. The Oxygene Object Pascal dialect also supports them.
Objective-C (Mac OS X 10.6+) Green tickY called blocks; in addition to Objective-C, blocks can also be used on C and C++ when programming on Apple's platform
Pascal Red XN
Perl Green tickY
PHP Green tickY As of PHP 5.3.0, true anonymous functions are supported; previously only partial anonymous functions were supported, which worked much like C#'s implementation.
PL/I Red XN
Python Green tickY Python supports anonymous functions through the lambda syntax, which supports only expressions (not statements).
R Green tickY
Racket Green tickY
Rexx Red XN
RPG Red XN
Ruby Green tickY Ruby's anonymous functions, inherited from Smalltalk, are called blocks.
Rust Green tickY
Scala Green tickY
Scheme Green tickY
Smalltalk Green tickY Smalltalk's anonymous functions are called blocks.
Standard ML Green tickY
Swift Green tickY Anonymous functions in Swift are called Closures.
TypeScript Green tickY
Tcl Green tickY
Vala Green tickY
Visual Basic .NET v9 Green tickY
Visual Prolog v 7.2 Green tickY
Wolfram Language Green tickY

Examples

Numerous languages support anonymous functions, or something similar.

C (non-standard extension)

The anonymous function is not supported by standard C programming language, but supported by some C dialects, such as gcc and clang.

GCC

GCC provides support for anonymous functions, mixed by nested functions and statement expressions. It has the form:

( { return_type anonymous_functions_name (parameters) { function_body } anonymous_functions_name; } )

The following example works only with GCC. Because of how macros are expanded, the l_body cannot contain any commas outside of parentheses; GCC treats the comma as a delimiter between macro arguments. The argument l_ret_type can be removed if __typeof__ is available; in the example below using __typeof__ on array would return testtype *, which can be dereferenced for the actual value if needed.

#include <stdio.h>

//* this is the definition of the anonymous function */
#define lambda(l_ret_type, l_arguments, l_body)         \
  ({                                                    \
   l_ret_type l_anonymous_functions_name l_arguments   \
   l_body                                            \
   &l_anonymous_functions_name;                        \
   })

#define forEachInArray(fe_arrType, fe_arr, fe_fn_body)                                            \
{                                                                                         \
  int i=0;                                                                                \
  for(;i<sizeof(fe_arr)/sizeof(fe_arrType);i++) {  fe_arr[i] = fe_fn_body(&fe_arr[i]); }  \
}

typedef struct __test
{
  int a;
  int b;
} testtype;

void printout(const testtype * array)
{
  int i;
  for ( i = 0; i < 3; ++ i )
    printf("%d %d\n", array[i].a, array[i].b);
  printf("\n");
}

int main(void)
{
  testtype array[] = { {0,1}, {2,3}, {4,5} };

  printout(array);
  /* the anonymous function is given as function for the foreach */
  forEachInArray(testtype, array,
    lambda (testtype, (void *item),
    {
      int temp = (*( testtype *) item).a;
      (*( testtype *) item).a = (*( testtype *) item).b;
      (*( testtype *) item).b = temp;
      return (*( testtype *) item);
    }));
  printout(array);
  return 0;
}

Clang (for C, C++, Objective-C, and Objective-C++)

Clang provides support for anonymous functions, called blocks. Blocks have the form:

^return_type ( parameters ) { function_body }

The type of the blocks above is return_type (^)(parameters).

Using the aforementioned blocks extension and libdispatch, the code could look simpler:

#include <stdio.h>
#include <dispatch/dispatch.h>

int main(void) {
  void (^count_loop)() = ^{
    for (int i = 0; i < 100; i++)
      printf("%d\n", i);
    printf("ah ah ah\n");
  };

/* Pass as a parameter to another function */
  dispatch_async(dispatch_get_global_queue(DISPATCH_QUEUE_PRIORITY_DEFAULT, 0), count_loop);

/* Invoke directly */
  count_loop();

  return 0;
}

The code with blocks should be compiled with -fBlocksRuntime and linked with -lBlocksRuntime

C++ (since C++11)

C++11 provides support for anonymous functions, called lambda expressions. A lambda expression has the form:

[capture](parameters) -> return_type { function_body }

An example lambda function is defined as follows:

[](int x, int y) -> int { return x + y; }

C++11 also supports closures. Closures are defined between square brackets [and ] in the declaration of lambda expression. The mechanism allows these variables to be captured by value or by reference. The following table demonstrates this:

[]        //no variables defined. Attempting to use any external variables in the lambda is an error.
[x, &y]   //x is captured by value, y is captured by reference
[&]       //any external variable is implicitly captured by reference if used
[=]       //any external variable is implicitly captured by value if used
[&, x]    //x is explicitly captured by value. Other variables will be captured by reference
[=, &z]   //z is explicitly captured by reference. Other variables will be captured by value

Variables captured by value are constant by default. Adding mutable after the parameter list makes them non-constant.

The following two examples demonstrate usage of a lambda expression:

std::vector<int> some_list{ 1, 2, 3, 4, 5 };
int total = 0;
std::for_each(begin(some_list), end(some_list), [&total](int x) {
	total += x;
});

This computes the total of all elements in the list. The variable total is stored as a part of the lambda function's closure. Since it is a reference to the stack variable total, it can change its value.

std::vector<int> some_list{ 1, 2, 3, 4, 5 };
int total = 0;
int value = 5;
std::for_each(begin(some_list), end(some_list), [&, value, this](int x) {
	total += x * value * this->some_func();
});

This will cause total to be stored as a reference, but value will be stored as a copy.

The capture of this is special. It can only be captured by value, not by reference. this can only be captured if the closest enclosing function is a non-static member function. The lambda will have the same access as the member that created it, in terms of protected/private members.

If this is captured, either explicitly or implicitly, then the scope of the enclosed class members is also tested. Accessing members of this does not require explicit use of this-> syntax.

The specific internal implementation can vary, but the expectation is that a lambda function that captures everything by reference will store the actual stack pointer of the function it is created in, rather than individual references to stack variables. However, because most lambda functions are small and local in scope, they are likely candidates for inlining, and thus will not need any additional storage for references.

If a closure object containing references to local variables is invoked after the innermost block scope of its creation, the behaviour is undefined.

Lambda functions are function objects of an implementation-dependent type; this type's name is only available to the compiler. If the user wishes to take a lambda function as a parameter, the type must be a template type, or they must create a std::function or a similar object to capture the lambda value. The use of the auto keyword can help store the lambda function,

auto my_lambda_func = [&](int x) { /*...*/ };
auto my_onheap_lambda_func = new auto([=](int x) { /*...*/ });

Here is an example of storing anonymous functions in variables, vectors, and arrays; and passing them as named parameters:

#include <functional>
#include <vector>
#include <iostream>

double eval(std::function <double(double)> f, double x = 2.0)
{
	return f(x);
}

int main()
{
	std::function<double(double)> f0    = [](double x){return 1;};
	auto                          f1    = [](double x){return x;};
	decltype(f0)                  fa[3] = {f0,f1,[](double x){return x*x;}};
	std::vector<decltype(f0)>     fv    = {f0,f1};
	fv.push_back                  ([](double x){return x*x;});
	for(int i=0;i<fv.size();i++)
		std::cout << fv[i](2.0) << std::endl;
	for(int i=0;i<3;i++)
		std::cout << fa[i](2.0) << std::endl;
	for(auto &f : fv)
		std::cout << f(2.0) << std::endl;
	for(auto &f : fa)
		std::cout << f(2.0) << std::endl;
	std::cout << eval(f0) << std::endl;
	std::cout << eval(f1) << std::endl;
	std::cout << eval([](double x){return x*x;}) << std::endl;
	return 0;
}

A lambda expression with an empty capture specification ([]) can be implicitly converted into a function pointer with the same type as the lambda was declared with. So this is legal:

auto a_lambda_func = [](int x) { /*...*/ };
void (* func_ptr)(int) = a_lambda_func;
func_ptr(4); //calls the lambda.

The Boost library provides its own syntax for lambda functions as well, using the following syntax:[11]

for_each(a.begin(), a.end(), std::cout << _1 << ' ');

C#

Support for anonymous functions in C# has deepened through the various versions of the language compiler. The C# language v3.0, released in November 2007 with the .NET Framework v3.5, has full support of anonymous functions. C# refers to them as "lambda expressions", following the original version of anonymous functions, the lambda calculus. See the C# 4.0 Language Specification, section 5.3.3.29, for more information.

// the first int is the x' type
// the second int is the return type
// <see href="http://msdn.microsoft.com/en-us/library/bb549151.aspx" />
Func<int,int> foo = x => x*x;
Console.WriteLine(foo(7));

While the function is anonymous, it cannot be assigned to an implicitly typed variable, because the lambda syntax may be used for denoting an anonymous function or an expression tree, and the choice cannot automatically be decided by the compiler. E.g., this does not work:

// will NOT compile!
var foo = (int x) => x*x;

However, a lambda expression can take part in type inference and can be used as a method argument, e.g. to use anonymous functions with the Map capability available with System.Collections.Generic.List (in the ConvertAll() method):

// Initialize the list:
var values = new List<int>() { 7, 13, 4, 9, 3 };
// Map the anonymous function over all elements in the list, return the new list
var foo = values.ConvertAll(d => d*d) ; 
// the result of the foo variable is of type System.Collections.Generic.List<Int32>

Prior versions of C# had more limited support for anonymous functions. C# v1.0, introduced in February 2002 with the .NET Framework v1.0, provided partial anonymous function support through the use of delegates. This construct is somewhat similar to PHP delegates. In C# 1.0, Delegates are like function pointers that refer to an explicitly named method within a class. (But unlike PHP the name is not required at the time the delegate is used.) C# v2.0, released in November 2005 with the .NET Framework v2.0, introduced the concept of anonymous methods as a way to write unnamed inline statement blocks that can be executed in a delegate invocation. C# 3.0 continues to support these constructs, but also supports the lambda expression construct.

This example will compile in C# 3.0, and exhibits the three forms:

    public class TestDriver
    {
        delegate int SquareDelegate(int d);
        static int Square(int d)
        {
            return d*d;
        }
 
        static void Main(string[] args)
        {
            // C# 1.0: Original delegate syntax required 
            // initialization with a named method.
            SquareDelegate A = new SquareDelegate(Square);
            System.Console.WriteLine(A(3));
 
            // C# 2.0: A delegate can be initialized with
            // inline code, called an "anonymous method." This
            // method takes an int as an input parameter.
            SquareDelegate B = delegate(int d) { return d*d; };
            System.Console.WriteLine(B(5));
 
            // C# 3.0. A delegate can be initialized with
            // a lambda expression. The lambda takes an int, and returns an int. 
            // The type of x is inferred by the compiler.
            SquareDelegate C = x => x*x;
            System.Console.WriteLine(C(7));
 
            // C# 3.0. A delegate that accepts a single input and
            // returns a single output can also be implicitly declared with the Func<> type.
            System.Func<int,int> D = x => x*x;
            System.Console.WriteLine(D(9));
        } 
    }

In the case of the C# 2.0 version, the C# compiler takes the code block of the anonymous function and creates a static private function. Internally, the function gets a generated name, of course; this generated name is based on the name of the method in which the Delegate is declared. But the name is not exposed to application code except by using reflection.

In the case of the C# 3.0 version, the same mechanism applies.

CFML 

fn = function(){
  // statements
};

CFML supports any statements within the function's definition, not simply expressions.

CFML supports recursive anonymous functions:

factorial = function(n){
    return n > 1 ? n * factorial(n-1) : 1;
};

CFML anonymous functions implement closure.

D

D uses inline delegates to implement anonymous functions. The full syntax for an inline delegate is

return_type delegate(arguments){/*body*/}

If unambiguous, the return type and the keyword delegate can be omitted.

(x){return x*x;}
delegate (x){return x*x;} // if more verbosity is needed
(int x){return x*x;} // if parameter type cannot be inferred
delegate (int x){return x*x;} // ditto
delegate double(int x){return x*x;} // if return type must be forced manually

Since version 2.0, D allocates closures on the heap unless the compiler can prove it is unnecessary; the scope keyword can be used for forcing stack allocation. Since version 2.058, it is possible to use shorthand notation:

x => x*x;
(int x) => x*x;
(x,y) => x*y;
(int x, int y) => x*y;

An anonymous function can be assigned to a variable and used like this:

auto sqr = (double x){return x*x;};
double y = sqr(4);

Dart

Dart supports anonymous functions.

var sqr = (x) => x * x;
print(sqr(5));

or

print(((x) => x * x)(5));

Delphi

Delphi introduced anonymous functions since version 2009.

program demo;

type
  TSimpleProcedure = reference to procedure;
  TSimpleFunction = reference to function(x: string): Integer;

var
  x1: TSimpleProcedure;
  y1: TSimpleFunction;

begin
  x1 := procedure
    begin
      Writeln('Hello World');
    end;
  x1;   //invoke anonymous method just defined

  y1 := function(x: string): Integer
    begin
      Result := Length(x);
    end;
  Writeln(y1('bar')); 
end.

Erlang

Erlang uses a syntax for anonymous functions similar to that of named functions.

% Anonymous function bound to the Square variable
Square = fun(X) -> X * X end.

% Named function with the same functionality
square(X) -> X * X.

Go

Go supports anonymous functions.

foo := func(x int) int {
	return x * x
}
fmt.Println(foo(10))

Haskell

Haskell uses a concise syntax for anonymous functions (lambda expressions).

 \x -> x * x

Lambda expressions are fully integrated with the type inference engine, and support all the syntax and features of "ordinary" functions (except for the use of multiple definitions for pattern-matching, since the argument list is only specified once).

 map (\x -> x * x) [1..5] -- returns [1, 4, 9, 16, 25]

The following are all equivalent:

 f x y = x + y
 f x = \y -> x + y
 f = \x y -> x + y

Haxe

In Haxe the anonymous functions are called lambda they are using the syntax function(argument-list) expression; .

var f = function(x) return x*x;
f(8); // 64

(function(x,y) return x+y)(5,6); // 11

Java

Java supports anonymous functions beginning with JDK 8.[12] In Java, anonymous functions are known as Lambda Expressions.

A lambda expression consists of a comma separated list of the formal parameters enclosed in parentheses, an arrow token (->), and a body. Data types of the parameters can always be omitted, as can the parentheses if there is only one parameter. The body can consist of a single statement or a statement block.[13]

// with no parameter
() -> System.out.println("Hello, world.")

// with a single parameter (This example is an identity function).
a -> a

// with a single expression
(a, b) -> a + b

// with explicit type information
(long id, String name) -> "id: " + id + ", name:" + name

// with a code block
(a, b) -> { return a + b; }

// with multiple statements in the lambda body. It requires a code block.
// This example also includes two nested lambda expressions (the first one is also a closure).
(id, defaultPrice) -> {
  Optional<Product> product = productList.stream().filter(p -> p.getId() == id).findFirst();
  return product.map(p -> p.getPrice()).orElse(defaultPrice);
}

Lambda expressions are converted to "functional interfaces" (defined as interfaces that contain only one abstract method in addition to one or more default or static methods[13]), as in the following example:

public class Calculator {
    interface IntegerMath {
        int operation(int a, int b);

        default IntegerMath swap() {
          return (a, b) -> operation(b, a);
        }
    }

    private static int apply(int a, int b, IntegerMath op) {
        return op.operation(a, b);
    }

    public static void main(String... args) {
        IntegerMath addition = (a, b) -> a + b;
        IntegerMath subtraction = (a, b) -> a - b;
        System.out.println("40 + 2 = " + apply(40, 2, addition));
        System.out.println("20 - 10 = " + apply(20, 10, subtraction));
        System.out.println("10 - 20 = " + apply(20, 10, subtraction.swap()));    
    }
}

In this example, a functional interface called IntegerMath is declared. Lambda expressions that implement IntegerMath are passed to the apply() method to be executed. Default methods like swap define methods on functions.

JavaScript

JavaScript/ECMAScript supports anonymous functions.

alert((function(x){
	return x*x;
})(10));

In ES6:

alert((x => x*x)(10));

This construct is often used in Bookmarklets. For example, to change the title of the current document (visible in its window's title bar) to its URL, the following bookmarklet may seem to work.

javascript:document.title=location.href;

However, as the assignment statement returns a value (the URL itself), many browsers actually create a new page to display this value.

Instead, an anonymous function, that does not return a value, can be used:

javascript:(function(){document.title=location.href;})();

The function statement in the first (outer) pair of parentheses declares an anonymous function, which is then executed when used with the last pair of parentheses. This is almost equivalent to the following, which populates the environment with f unlike an anonymous function.

javascript:var f = function(){document.title=location.href;}; f();

Use void() to avoid new pages for arbitrary anonymous functions:

javascript:void(function(){return document.title=location.href;}());

or just:

javascript:void(document.title=location.href);

JavaScript has syntactic subtleties for the semantics of defining, invoking and evaluating anonymous functions. These subliminal nuances are a direct consequence of the evaluation of parenthetical expressions. The following constructs which are called immediately-invoked function expression illustrate this:

(function(){ ... }())

and 

(function(){ ... })()

Representing "function(){ ... }" by f, the form of the constructs are a parenthetical within a parenthetical (f()) and a parenthetical applied to a parenthetical (f)().

Note the general syntactic ambiguity of a parenthetical expression, parenthesized arguments to a function and the parentheses around the formal parameters in a function definition. In particular, JavaScript defines a , (comma) operator in the context of a parenthetical expression. It is no mere coincidence that the syntactic forms coincide for an expression and a function's arguments (ignoring the function formal parameter syntax)! If f is not identified in the constructs above, they become (()) and ()(). The first provides no syntactic hint of any resident function but the second MUST evaluate the first parenthetical as a function to be legal JavaScript. (Aside: for instance, the ()'s could be ([],{},42,"abc",function(){}) as long as the expression evaluates to a function.)

Also, a function is an Object instance (likewise objects are Function instances) and the object literal notation brackets, {} for braced code, are used when defining a function this way (as opposed to using new Function(...)). In a very broad non-rigorous sense (especially since global bindings are compromised), an arbitrary sequence of braced JavaScript statements, {stuff}, can be considered to be a fixed point of

(function(){( function(){( ... {( function(){stuff}() )} ... )}() )}() )

More correctly but with caveats, 

( function(){stuff}() ) ~=
   A_Fixed_Point_of(
      function(){ return function(){ return ... { return function(){stuff}() } ... }() }()
   )

Note the implications of the anonymous function in the JavaScript fragments that follow:

Performance metrics to analyze the space and time complexities of function calls, call stack, etc. in a JavaScript interpreter engine implement easily with these last anonymous function constructs. From the implications of the results, it is possible to deduce some of an engine's recursive versus iterative implementation details, especially tail-recursion.

Julia

In Julia programming language anonymous functions are defined using the syntax (arguments)->(expression),

julia> f = x -> x*x; f(8)
64
julia> ((x,y)->x+y)(5,6)
11

Lisp

Lisp and Scheme support anonymous functions using the "lambda" construct, which is a reference to lambda calculus. Clojure supports anonymous functions with the "fn" special form and #() reader syntax.

(lambda (arg) (* arg arg))

Common Lisp

Common Lisp has the concept of lambda expressions. A lambda expression is written as a list with the symbol "lambda" as its first element. The list then contains the argument list, documentation or declarations and a function body. Lambda expressions can be used inside lambda forms and with the special operator "function".

(function (lambda (arg) (do-something arg)))

"function" can be abbreviated as #'. Additionally there is a macro "lambda", which expands into a function form:

; using sharp quote
#'(lambda (arg) (do-something arg))
; using the lambda macro:
(lambda (arg) (do-something arg))

One typical use of anonymous functions in Common Lisp is to pass them to higher-order functions like "mapcar". "mapcar" applies a function to each element of a list and returns a list of the results.

(mapcar #'(lambda (x) (* x x))
        '(1 2 3 4))
; -> (1 4 9 16)

The "lambda form" in Common Lisp allows a "lambda expression" to be written in a function call:

((lambda (x y)
   (+ (sqrt x) (sqrt y)))
 10.0
 12.0)

Anonymous functions in Common Lisp can also later be given global names:

(setf (symbol-function 'sqr)
      (lambda (x) (* x x)))
; which allows us to call it using the name SQR:
(sqr 10.0)

Scheme

Interestingly, Scheme's "named functions" is simply syntactic sugar for anonymous functions bound to names:

(define (somename arg)
  (do-something arg))

expands (and is equivalent) to

(define somename
  (lambda (arg)
    (do-something arg)))

Clojure

Clojure supports anonymous functions through the "fn" special form:

(fn [x] (+ x 3))

There is also a reader syntax to define a lambda:

# (+ % %2 %3) ; Defines an anonymous function that takes three arguments and sums them.

Like Scheme, Clojure's "named functions" are simply syntactic sugar for lambdas bound to names:

(defn func [arg] (+ 3 arg))

expands to:

(def func (fn [arg] (+ 3 arg)))

Lua

In Lua (much as in Scheme) all functions are anonymous. A "named function" in Lua is simply a variable holding a reference to a function object.[14]

Thus, in Lua

function foo(x) return 2*x end

is just syntactical sugar for

foo = function(x) return 2*x end

An example of using anonymous functions for reverse-order sorting:

table.sort(network, function(a,b)
  return a.name > b.name
end)

Wolfram Language/Mathematica

The Wolfram Language is the programming language of Mathematica. Anonymous Functions are important in programming Mathematica. There are several ways to create them. Below are a few anonymous functions that increment a number. The first is the most common. '#1' refers to the first argument and '&' marks the end of the anonymous function.

     #1+1&
     Function[x,x+1]
     x \[Function] x+1

So, for instance:

    f:= #1^2&;f[8]
     64
    #1+#2&[5,6]
     11

Additionally, Mathematica has an additional construct to for making recursive anonymous functions. The symbol '#0' refers to the entire function. The following function calculates the factorial of its input:

     If[#1 == 1, 1, #1 * #0[#1-1]]&

MATLAB/Octave

Anonymous functions in GNU Octave or MATLAB are defined using the syntax @(argument-list)expression. Any variables that are not found in the argument list are inherited from the enclosing scope.

 > f = @(x)x*x; f(8)
 ans =  64
 > (@(x,y)x+y)(5,6) % Only works in Octave
 ans =  11

Maxima

In Maxima anonymous functions are defined using the syntax lambda(argument-list,expression),

 f: lambda([x],x*x); f(8);
 64

 lambda([x,y],x+y)(5,6);
 11

ML

The various dialects of ML support anonymous functions.

OCaml

fun arg -> arg * arg

F#

(fun x -> x * x) 20 // 400

Standard ML

fn arg => arg * arg

Perl

Perl 5

Perl 5 supports anonymous functions, as follows:

(sub { print "I got called\n" })->();         # 1. fully anonymous, called as created

my $squarer = sub { my $x = shift; $x * $x }; # 2. assigned to a variable

sub curry {
    my ($sub, @args) = @_;
    return sub { $sub->(@args, @_) };         # 3. as a return value of another function
}

# example of currying in Perl programming
sub sum { my $tot = 0; $tot += $_ for @_; $tot } # returns the sum of its arguments
my $curried = curry \&sum, 5, 7, 9;
print $curried->(1,2,3), "\n";    # prints 27 ( = 5 + 7 + 9 + 1 + 2 + 3 )

Other constructs take "bare blocks" as arguments, which serve a function similar to lambda functions of a single parameter, but don't have the same parameter-passing convention as functions -- @_ is not set.

my @squares = map { $_ * $_ } 1..10;   # map and grep don't use the 'sub' keyword
my @square2 = map $_ * $_, 1..10;      # parentheses not required for a single expression

my @bad_example = map { print for @_ } 1..10; # values not passed like normal Perl function

Perl 6

In Perl 6, all blocks (even the ones associated with if, while, etc.) are anonymous functions. A block that is not used as an rvalue is executed immediately.

# 1. fully anonymous, called as created
{ say "I got called" };

# 2. assigned to a variable
my $squarer1 = -> $x { $x * $x };             # 2a. pointy block
my $squarer2 = { $^x * $^x };                 # 2b. twigil
my $squarer3 = { my $x = shift @_; $x * $x }; # 2b. Perl 5 style

# 3. currying
sub add ($m, $n) { $m + $n }
my $seven   = add(3, 4);
my $add_one = &add.assuming(m => 1);
my $eight   = $add_one($seven);

PHP

Prior to 4.0.1, PHP had no anonymous function support.[15]

PHP 4.0.1 to 5.3

PHP 4.0.1 introduced the create_function which was the initial anonymous function support. This function call creates a new randomly named function and returns its name (as a string)

$foo = create_function('$x', 'return $x*$x;');
$bar = create_function("\$x", "return \$x*\$x;");
echo $foo(10);

It is important to note that the argument list and function body must be in single quotes or the dollar signs must be escaped. Otherwise PHP will assume "$x" means the variable $x and will substitute it into the string (despite possibly not existing) instead of leaving "$x" in the string. For functions with quotes or functions with lots of variables, it can get quite tedious to ensure the intended function body is what PHP interprets.

It must also be noted that each invocation of create_function will create a new function which exists for the rest of the program, and cannot be "garbage collected". If one uses this to create anonymous functions many times, e.g. in a loop, it will irreversibly use up memory in the program.

PHP 5.3

PHP 5.3 added a new class called Closure and magic method __invoke() that makes a class instance invocable.[16]

$x = 3;
$func = function($z) { return $z *= 2; };
echo $func($x); // prints 6

In this example, $func is an instance of Closure and echo $func() is equivalent to $func->__invoke($z). PHP 5.3 mimics anonymous functions but it does not support true anonymous functions because PHP functions are still not first-class objects.

PHP 5.3 does support closures but the variables must be explicitly indicated as such:

$x = 3;
$func = function() use(&$x) { $x *= 2; };
$func();
echo $x; // prints 6

The variable $x is bound by reference so the invocation of $func modifies it and the changes are visible outside of the function.

Prolog's dialects

Logtalk

Logtalk uses the following syntax for anonymous predicates (lambda expressions):

{FreeVar1, FreeVar2, ...}/[LambdaParameter1, LambdaParameter2, ...]>>Goal

A simple example with no free variables and using a list mapping predicate is:

| ?- meta::map([X,Y]>>(Y is 2*X), [1,2,3], Ys).
Ys = [2,4,6]
yes

Currying is also supported. The above example can be written as:

| ?- meta::map([X]>>([Y]>>(Y is 2*X)), [1,2,3], Ys).
Ys = [2,4,6]
yes

Visual Prolog

Anonymous functions (in general anonymous predicates) were introduced in Visual Prolog in version 7.2.[17] Anonymous predicates can capture values from the context. If created in an object member it can also access the object state (by capturing This).

mkAdder returns an anonymous function, which has captured the argument X in the closure. The returned function is a function that adds X to its argument:

clauses
    mkAdder(X) = { (Y) = X+Y }.

Python

Python supports simple anonymous functions through the lambda form. The executable body of the lambda must be an expression and can't be a statement, which is a restriction that limits its utility. The value returned by the lambda is the value of the contained expression. Lambda forms can be used anywhere ordinary functions can, however these restrictions make it a very limited version of a normal function. Here is an example:

>>> foo = lambda x: x*x
>>> print(foo(10))
100

In general, Python convention encourages the use of named functions defined in the same scope as one might typically use an anonymous functions in other languages. This is acceptable as locally defined functions implement the full power of closures and are almost as efficient as the use of a lambda in Python. In this example, the built-in power function can be said to have been curried:

>>> def make_pow(n):
...     def fixed_exponent_pow(x):
...         return pow(x, n)
...     return fixed_exponent_pow
...
>>> sqr = make_pow(2)
>>> print (sqr(10))
100
>>> cub = make_pow(3)
>>> print (cub(10))
1000

R

For more details on this topic, see R (programming language).

In GNU R the anonymous functions are defined using the syntax function(argument-list)expression .

> f <- function(x)x*x; f(8)
[1] 64
> (function(x,y)x+y)(5,6)
[1] 11

Ruby

For more details on this topic, see Ruby (programming language) § Blocks and iterators.

Ruby supports anonymous functions by using a syntactical structure called block. There are two data types for blocks in Ruby. Procs behave similarly to closures, whereas lambdas behave more analogous to an anonymous function.[18] When passed to a method, a block is converted into a Proc in some circumstances.

irb(main):001:0> # Example 1:
irb(main):002:0* # Purely anonymous functions using blocks.
irb(main):003:0* ex = [16.2, 24.1, 48.3, 32.4, 8.5]
=> [16.2, 24.1, 48.3, 32.4, 8.5]
irb(main):004:0> ex.sort_by { |x| x - x.to_i } # Sort by fractional part, ignoring integer part.
=> [24.1, 16.2, 48.3, 32.4, 8.5]
irb(main):005:0> # Example 2:
irb(main):006:0* # First-class functions as an explicit object of Proc -
irb(main):007:0* ex = Proc.new { puts "Hello, world!" }
=> #<Proc:0x007ff4598705a0@(irb):7>
irb(main):008:0> ex.call
Hello, world!
=> nil
irb(main):009:0> # Example 3:
irb(main):010:0* # Function that returns lambda function object with parameters
irb(main):011:0* def is_multiple_of(n)
irb(main):012:1>   lambda{|x| x % n == 0}
irb(main):013:1> end
=> nil
irb(main):014:0> multiple_four = is_multiple_of(4)
=> #<Proc:0x007ff458b45f88@(irb):12 (lambda)>
irb(main):015:0> multiple_four.call(16)
=> true
irb(main):016:0> multiple_four[15]
=> false

Scala

In Scala, anonymous functions use the following syntax:[19]

 (x: Int, y: Int) => x + y

In certain contexts, like when an anonymous function is a parameter being passed to another function, the compiler can infer the types of the parameters of the anonymous function and they can be omitted in the syntax. In such contexts, it is also possible to use a shorthand for anonymous functions using the underscore character to introduce unnamed parameters.

 val list = List(1, 2, 3, 4)
 list.reduceLeft( (x, y) => x + y ) 
// Here, the compiler can infer that the types of x and y are both Int. 
// Therefore, it does not require type annotations on the parameters of the anonymous function.

 list.reduceLeft( _ + _ )   
// Each underscore stands for a new unnamed parameter in the anonymous function. 
// This results in an even shorter equivalent to the anonymous function above.

Smalltalk

In Smalltalk anonymous functions are called blocks

[ :x | x*x ] value: 4
"returns 16"

Swift

In Swift, anonymous functions are called closures.[20] The syntax has following form:

{ (parameters) -> returnType in
  statement
}

For example:

{ (s1: String, s2: String) -> Bool in
  return s1 > s2
}

For sake of brevity and expressiveness, the parameter types and return type can be omitted if these can be inferred:

{ s1, s2 in return s1 > s2 }

Similarly, Swift also supports implicit return statements for single-statement closures:

{ s1, s2 in s1 > s2 }

Finally, the parameter names can be omitted as well; when omitted, the parameters are referenced using shorthand argument names, consisting of the $ symbol followed by their position (e.g. $0, $1, $2, etc.):

{ $0 > $1 }

Tcl

In Tcl, applying the anonymous squaring function to 2 looks as follows:[21]

apply {x {expr {$x*$x}}} 2
# returns 4

It should be observed that this example involves two candidates for what it means to be a "function" in Tcl. The most generic is usually called a command prefix, and if the variable f holds such a function, then the way to perform the function application f(x) would be

{*}$f $x

where {*} is the expansion prefix (new in Tcl 8.5). The command prefix in the above example is apply {x {expr {$x*$x}}} Command names can be bound to command prefixes by means of the interp alias command. Command prefixes support currying. Command prefixes are very common in Tcl APIs.

The other candidate for "function" in Tcl is usually called a lambda, and appears as the {x {expr {$x*$x}}} part of the above example. This is the part which caches the compiled form of the anonymous function, but it can only be invoked by being passed to the apply command. Lambdas do not support currying, unless paired with an apply to form a command prefix. Lambdas are rare in Tcl APIs.

Visual Basic .NET

Visual Basic.NET 2008 introduced anonymous functions through the lambda form. Combined with implicit typing, VB provides an economical syntax for anonymous functions. As with Python, in VB.NET, anonymous functions must be defined on a single line; they cannot be compound statements. Further, an anonymous function in VB.NET must truly be a VB.NET "Function" - it must return a value. 

Dim foo = Function(x) x * x
Console.WriteLine(foo(10))

Visual Basic.NET 2010 added support for multiline lambda expressions and anonymous functions without a return value. For example, a function for use in a Thread.

Dim t As New System.Threading.Thread(Sub()
    For n as Integer = 0 to 10   'Count to 10
        Console.WriteLine(n)     'Print each number
    Next
    End Sub)
t.Start()

See also

References

  1. ↑ "Higher order functions". learnyouahaskell.com. Retrieved 3 December 2014.
  2. ↑ Fernandez, Maribel (2009), Models of Computation: An Introduction to Computability Theory, Undergraduate Topics in Computer Science, Springer Science & Business Media, p. 33, ISBN 9781848824348, The Lambda calculus ... was introduced by Alonzo Church in the 1930s as a precise notation for a theory of anonymous functions
  3. ↑ "Lecture 29: Fixpoints and Recursion". CS3110 Spring 2012 :: Data Structures and Functional Programming. Cornell University - Computer Science. Retrieved 3 December 2014.
  4. ↑ "Bash lambda".
  5. ↑ "Closure support".
  6. ↑ "Whats new in ColdFusion 10".
  7. ↑ "Managed COBOL Reference". Micro Focus Documentation. Micro Focus. Retrieved 25 February 2014.
  8. ↑ "Quotations - Factor Documentation". Retrieved 26 December 2015. A quotation is an anonymous function (a value denoting a snippet of code) which can be used as a value and called using the Fundamental combinators.
  9. ↑ "Gosu Documentation" (PDF). Retrieved 4 March 2013.
  10. ↑ "Groovy Documentation". Retrieved 29 May 2012.
  11. ↑ Järvi, Jaakko; Powell, Gary (n.d.). "Chapter 16. Boost.Lambda". Boost Documentation. Boost. Retrieved December 22, 2014.
  12. ↑ http://www.oracle.com/technetwork/java/javase/8-whats-new-2157071.html
  13. 1 2 The Java Tutorials: Lambda Expressions, docs.oracle.com
  14. ↑ "Programming in Lua - More about Functions". Archived from the original on 14 May 2008. Retrieved 2008-04-25.
  15. ↑ http://php.net/create_function the top of the page indicates this with "(PHP 4 >= 4.0.1, PHP 5)"
  16. ↑ http://wiki.php.net/rfc/closures
  17. ↑ "Anonymous Predicates". in Visual Prolog Language Reference
  18. ↑ Sosinski, Robert (2008-12-21). "Understanding Ruby Blocks, Procs and Lambdas". Reactive.IO. Retrieved 2014-05-30.
  19. ↑ http://www.scala-lang.org/node/133
  20. ↑ https://developer.apple.com/library/prerelease/ios/documentation/swift/conceptual/swift_programming_language/Closures.html
  21. ↑ apply manual page, retrieved 2012-09-06.

External links

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