Anonymous subroutine

Anonymous function

In computing, an anonymous function (also function constant or function literal) is a function (or a subroutine) defined, and possibly called, without being bound to an identifier. Anonymous functions are convenient to pass as an argument to a higher-order function and are ubiquitous in languages with first-class functions.

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. The Y combinator can be utilised in these circumstances to provide anonymous recursion, which Church used to show that some mathematical questions are unsolvable by computation. (Note: this result was disputed at the time, and later Alan Turing - who became Church's student - provided a proof that was more generally accepted.)

Anonymous functions have been a feature of programming languages since Lisp in 1958. An increasing number of modern programming languages support anonymous functions, and some notable mainstream languages have recently added support for them, the most widespread being JavaScript also C# and PHP support anonymous functions. Anonymous functions were added to the C++ language as of C++0x

Some object-oriented programming languages have anonymous classes, which are a similar concept, but do not support anonymous functions. Java is such a language.

Uses

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

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 items in a list by the name of their class (in Python, everything has a class):

a = [10, '10', 10.0] a.sort(lambda x,y: cmp(x.__class__.__name__, y.__class__.__name__)) print a [10.0, 10, '10']

Note that 10.0 has class name " float ", 10 has class name " int ", and '10' has class name " str ". The sorted order is " float ", " int ", then " str ".

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 a list of strings by length of the string:

a = ['three', 'two', 'four'] a.sort(lambda x,y: cmp(len(x), len(y))) print a ['two', 'four', 'three']

which clearly has been sorted by length of the strings.

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:

a = comp(10) b = comp(20) print a(9), a(10), a(20), a(21) True False False False print b(9), b(10), b(20), b(21) True True False False

It would be very 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

Currying is transforming a function from multiple inputs to fewer inputs (in this case integer division).

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.

(It just so happens that the divisor function forms a closure as well as curries by binding the "d" variable.)

Higher-order functions

Map

The map function performs a function call on each element of an array. 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:

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

However, there is no reason why the result of a fold need 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 coming C++0x standard adds them to C++, even though this is conventional, statically typed language.

This list is incomplete; you can help by expanding it.

Examples

Numerous languages support anonymous functions, or something similar.

C# lambda expressions

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# 3.0 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 to denote 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.

D

 (x){return x*x;} 

Delphi (since v. 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.

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 

JavaScript

JavaScript supports anonymous functions.

alert((function(x){ return 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 can be used so that no value is returned:

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 equivalent to the following.

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

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 macro.

(lambda (arg) (* arg arg))

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 supports anonymous functions through the "fn" special form:

(fn [x] (+ x 3))

There is also a reader macro 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)))

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 

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.

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)

ML

The various dialects of ML support anonymous functions.

Objective Caml:

fun arg -> arg * arg

Standard ML:

 fn arg => arg * arg 

Octave

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 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.

{ say "I got called" }; # 1. fully anonymous, called as created my $squarer1 = -> $x { $x * $x }; # 2a. assigned to a variable, pointy block my $squarer2 = { $^x * $^x }; # 2b. assigned to a variable, twigil my $squarer3 = { my $x = shift @_; $x * $x }; # 2b. assigned to a variable, Perl 5 style # 3 curring sub add ($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.

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.

5.3

PHP 5.3 added a new class called Closure and magic method __invoke() that makes a class instance invocable. Lambda functions are a compiler "trick" that instantiates a new Closure instance that can be invoked as if the function were invokable.

$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 functions.

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.

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)

This example will print: 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) # Emits 100 cub = make_pow(3) print cub(10) # Emits 1000

R

Ruby

Ruby supports anonymous functions by using a syntactical structure called block. When passed to a method, a block is converted into an object of class Proc in some circumstances.

# Example 1: # Purely anonymous functions using blocks. ex = [16.2, 24.1, 48.3, 32.4, 8.5] 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] # Example 2: # First-class functions as an explicit object of Proc - ex = Proc.new { puts "Hello, world!" } ex.call # Hello, world!

Scala

In Scala, anonymous functions use the following syntax:

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

In certain contexts, such as when an anonymous function is passed as a parameter 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: 2 "returns 4"

Visual Basic

VB9, introduced in November 2007, supports anonymous functions through the lambda form. Combined with implicit typing, VB provides an economical syntax for anonymous functions. As with Python, in VB9, anonymous functions must be defined on a single line; they cannot be compound statements. Further, an anonymous function in VB must truly be a VB " Function " - it must return a value.

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

VB10, released April 12, 2010, adds 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()

Visual Prolog

Anonymous functions (in general anonymous predicates) were introduced in Visual Prolog in version 7.2. 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 }.

Mathematica

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

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

Additionally, Mathematica has an additional construct to for making recursive anonymous functions. The symbol '#0' refers to the entire function.

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

See also

References

External links

• Anonymous Methods - When Should They Be Used? (blog about anonymous function in Delphi)

Retrieved from : http://en.wikipedia.org/wiki/Anonymous_function