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In computer programming, an anonymous function (function literal, lambda abstraction, or lambda expression) is a function definition that is not bound to an identifier. Anonymous functions are often arguments being passed to higher-order functions, or 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 which all functions are anonymous, in 1936, before electronic computers. 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 a growing number of modern programming languages support anonymous functions.

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 calling a more-generic named function.

The following examples are written in Python 3.

Sorting
When attempting to sort in a non-standard way, it may be easier to contain the sorting 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 function that determines how to compare whether two elements equal or if one is greater or less than the other.

Consider this Python code sorting a list of strings by length of the string:

The anonymous function in this example is the lambda expression:

The anonymous function accepts one argument,, and returns the length of its argument, which is then used by the   method as the criteria for sorting. Another example would be sorting items in a list by the name of their class (in Python, everything has a class):

Note that  has class name " ",   has class name " ", and   has class name " ". The sorted order is " ", " ", then " ".

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.

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

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
Currying is the process of changing a function so that rather than taking multiple inputs, it takes a single input and returns a function which accepts the second input, and so forth. In this example, a function that performs division by any integer is transformed into one that performs division by a set integer.

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 variable.

Higher-order functions
A higher-order function is a function that takes a function as an argument. This is commonly used to customize the behavior of a generically defined function, often a looping construct or recursion scheme. Anonymous functions are a convenient way to specify such function arguments. The following examples are in Python 3.

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.

The anonymous function accepts an argument and multiplies it by itself (squares it). The above form is discouraged by the creators of the language, who maintain that the form presented below has the same meaning and is more aligned with the philosophy of the language:

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

The anonymous function checks if the argument passed to it is even. The same as with map form below is considered as more appropriate:

Fold
A fold function runs over all elements in a structure (for lists usually left-to-right, a "left fold", called  in Python), accumulating a value as it goes. A common use of this is to combine all elements of a structure into one value, for example:

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 one value. Instead, 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 support unnamed anonymous functions fully, or partly as some variant, or not at all.

This table shows some general trends. First, the languages that do not support anonymous functions (C, Pascal, Object Pascal) are all statically typed languages. However, statically typed languages can support 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, as has C++ (by the C++11 standard). Second, the languages that treat functions as first-class functions (Dylan, Haskell, JavaScript, Lisp, ML, Perl, Python, Ruby, Scheme) generally have anonymous function support so that functions can be defined and passed around as easily as other data types.

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
GNU Compiler Collection (GCC) supports anonymous functions, mixed by nested functions and statement expressions. It has the form:

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

Clang (C, C++, Objective-C, Objective-C++)
Clang supports anonymous functions, called blocks, which have the form:

The type of the blocks above is.

Using the aforementioned blocks extension and Grand Central Dispatch (libdispatch), the code could look simpler:

The code with blocks should be compiled with  and linked with

C++ (since C++11)
C++11 supports anonymous functions, called lambda expressions, which have the form:

An example lambda function is defined as follows:

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:

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

The following two examples demonstrate use of a lambda expression:

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

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

The capture of  is special. It can only be captured by value, not by reference. 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  is captured, either explicitly or implicitly, then the scope of the enclosed class members is also tested. Accessing members of  does not need explicit use of   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 need no added 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 parameter type must be a template type, or they must create a  or a similar object to capture the lambda value. The use of the  keyword can help store the lambda function,

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

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

C#
In C#, support for anonymous functions has deepened through the various versions of the language compiler. The language v3.0, released in November 2007 with .NET Framework v3.5, has full support of anonymous functions. C# names them lambda expressions, following the original version of anonymous functions, the lambda calculus.

// the first int is the x' type // the second int is the return type // 

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:

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  (in the   method):

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 unneeded 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:

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.

ColdFusion Markup Language (CFML)
CFML supports any statements within the function's definition, not simply expressions.

CFML supports recursive anonymous functions: CFML anonymous functions implement closure.

D
D uses inline delegates to implement anonymous functions. The full syntax for an inline delegate is If unambiguous, the return type and the keyword delegate can be omitted. Since version 2.0, D allocates closures on the heap unless the compiler can prove it is unnecessary; the  keyword can be used for forcing stack allocation. Since version 2.058, it is possible to use shorthand notation: An anonymous function can be assigned to a variable and used like this:

Dart
Dart supports anonymous functions. or

Delphi
Delphi introduced anonymous functions in version 2009.

PascalABC.NET
PascalABC.NET supports anonymous functions using lambda syntax

Elixir
Elixir uses the closure  for anonymous functions.

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

Go
Go supports anonymous functions.

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

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).

The following are all equivalent:

Haxe
In Haxe, anonymous functions are called lambda, and use the syntax.

Java
Java supports anonymous functions, named Lambda Expressions, starting with JDK 8.

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 one statement or a statement block.

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), as in the following example:

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

Java 8 introduced another mechanism named method reference (the :: operator) to create a lambda on an existing method. A method reference doesn't indicate the number or types of arguments because those are extracted from the abstract method of the functional interface. In the example above, the functional interface  declares an abstract method , so the compiler looks for a method   in the class.

Java Limitations
Java 8 lambdas have the following limitations:


 * Lambdas can throw checked exceptions, but such lambdas will not work with the interfaces used by the Collection API.
 * Variables that are in-scope where the lambda is declared may only be accessed inside the lambda if they are effectively final, i.e. if the variable is not mutated inside or outside of the lambda scope.

JavaScript
JavaScript/ECMAScript supports anonymous functions.

ES6 supports "arrow function" syntax, where a => symbol separates the anonymous function's parameter list from the body:

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. 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:

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  unlike an anonymous function.

Use void to avoid new pages for arbitrary anonymous functions: or just:

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: and Representing " " by, the form of the constructs are a parenthetical within a parenthetical  and a parenthetical applied to a parenthetical.

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  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  ). In a very broad non-rigorous sense (especially since global bindings are compromised), an arbitrary sequence of braced JavaScript statements,, can be considered to be a fixed point of More correctly but with caveats,

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


 * without surrounding 's is generally not legal
 * does not "forget"  globally unlike


 * 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 anonymous functions are defined using the syntax ,

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.

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" can be abbreviated as #'. Also, macro lambda exists, which expands into a function form:

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

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

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

Scheme
Scheme's named functions is simply syntactic sugar for anonymous functions bound to names: expands (and is equivalent) to

Clojure
Clojure supports anonymous functions through the "fn" special form: There is also a reader syntax to define a lambda:

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

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 is just syntactical sugar for

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

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

So, for instance:

Also, Mathematica has an added construct to make recursive anonymous functions. The symbol '#0' refers to the entire function. The following function calculates the factorial of its input: For example, 6 factorial would be:

MATLAB, Octave
Anonymous functions in MATLAB or Octave are defined using the syntax. Any variables that are not found in the argument list are inherited from the enclosing scope.

Maxima
In Maxima anonymous functions are defined using the syntax ,

ML
The various dialects of ML support anonymous functions.

OCaml
OCaml functions do not have to have names; they may be anonymous. For example, here is an anonymous function that increments its input: fun x -> x+1. Here, fun is a keyword indicating an anonymous function, x is the argument, and -> separates the argument from the body.

We now have two ways we could write an increment function:

They are syntactically different but semantically equivalent. That is, even though they involve different keywords and put some identifiers in different places, they mean the same thing.

Anonymous functions are also called lambda expressions, a term that comes out of the lambda calculus, which is a mathematical model of computation in the same sense that Turing machines are a model of computation. In the lambda calculus, fun x -> e would be written λx.e. The λ  denotes an anonymous function.

It might seem a little mysterious right now why we would want functions that have no names. Don't worry; we'll see good uses for them later in the course. In particular, we will often create anonymous functions and pass them as input to other functions.

Syntax.

Static semantics.

If by assuming that x1:t1 and x2:t2 and ... and xn:tn, we can conclude that e:u, then fun x1 ... xn -> e : t1 -> t2 -> ... -> tn -> u. Dynamic semantics.

An anonymous function is already a value. There is no computation to be performed.

Snippet from CS3110, Cornell, taught by Michael R. Clarkson, Robert L. Constable, Nate Foster, Michael D. George, Dan Grossman, Daniel P. Huttenlocher, Dexter Kozen, Greg Morrisett, Andrew C. Myers, Radu Rugina, and Ramin Zabih.

F#
F# supports anonymous functions, as follows:

Standard ML
Standard ML supports anonymous functions, as follows: fn arg => arg * arg

Next Generation Shell
Next Generation Shell has several syntaxes for anonymous functions due to their prevalence in the language and different use cases.

Syntaxes: Anonymous functions usage examples:

Perl 5
Perl 5 supports anonymous functions, as follows:

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

PHP
Before 4.0.1, PHP had no anonymous function support.

PHP 4.0.1 to 5.3
PHP 4.0.1 introduced the  which was the initial anonymous function support. This function call makes a new randomly named function and returns its name (as a string)

The argument list and function body must be in single quotes, or the dollar signs must be escaped. Otherwise, PHP assumes " " means the variable  and will substitute it into the string (despite possibly not existing) instead of leaving " " 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.

Each invocation of  makes a new function, which exists for the rest of the program, and cannot be garbage collected, using memory in the program irreversibly. If this is used to create anonymous functions many times, e.g., in a loop, it can cause problems such as memory bloat.

PHP 5.3
PHP 5.3 added a new class called  and magic method   that makes a class instance invocable.

In this example,  is an instance of   and   is equivalent to. 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:

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

Logtalk
Logtalk uses the following syntax for anonymous predicates (lambda expressions): A simple example with no free variables and using a list mapping predicate is: Currying is also supported. The above example can be written as:

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 ).

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

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:

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:

R
In R the anonymous functions are defined using the syntax.

Raku
In Raku, all blocks (even those 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
 * 2) assigned to a variable
 * 3) currying
 * 4) WhateverCode object
 * 1) currying
 * 2) WhateverCode object
 * 1) WhateverCode object

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

Rust
In Rust, anonymous functions are called closures. They are defined using the following syntax:

For example:

With type inference, however, the compiler is able to infer the type of each parameter and the return type, so the above form can be written as:

With closures with a single expression (i.e. a body with one line), the curly braces may be omitted:

Closures with no input parameter are written like so:

Closures may be passed as input parameters of functions that expect a function pointer:

However, one may need complex rules to describe how values in the body of the closure are captured. They are implemented using the,  , and   traits:


 * : the closure captures by reference . They are used for functions that can still be called if they only have reference access (with ) to their environment.
 * : the closure captures by mutable reference . They are used for functions that can be called if they have mutable reference access (with ) to their environment.
 * : the closure captures by value . They are used for functions that are only called once.

With these traits, the compiler will capture variables in the least restrictive manner possible. They help govern how values are moved around between scopes, which is largely important since Rust follows a lifetime construct to ensure values are "borrowed" and moved in a predictable and explicit manner.

The following demonstrates how one may pass a closure as an input parameter using the  trait:

Scala
In Scala, anonymous functions use the following syntax:

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.

Smalltalk
In Smalltalk anonymous functions are called blocks and they are invoked (called) by sending them a "value" message. If arguments are to be passed, a "value:...value:" message with a corresponding number of value arguments must be used. Smalltalk blocks are technically closures, allowing them to outlive their defining scope and still refer to the variables declared therein.

Swift
In Swift, anonymous functions are called closures. The syntax has following form: For example:

For sake of brevity and expressiveness, the parameter types and return type can be omitted if these can be inferred: Similarly, Swift also supports implicit return statements for one-statement closures: 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.):

Tcl
In Tcl, applying the anonymous squaring function to 2 looks as follows: 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 where  is the expansion prefix (new in Tcl 8.5). The command prefix in the above example is apply  Command names can be bound to command prefixes by means of the   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  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  command. Lambdas do not support currying, unless paired with an  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 one line; they cannot be compound statements. Further, an anonymous function in VB.NET must truly be a VB.NET  - it must return a value. 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.

Z Shell
The Z Shell has two variants of anonymous function definitions, built after the Bourne and Korn shell variants of regular function definitions: