First-class function

In computer science, a programming language is said to support first-class functions (or function literal) if it treats functions as first-class objects. Specifically, this means that the language supports constructing new functions during the execution of a program, storing them in data structures, passing them as arguments to other functions, and returning them as the values of other functions. This concept doesn't cover any means external to the language and program (metaprogramming), such as invoking a compiler or an eval function to create a new function.

These features are a necessity for the functional programming style, in which (for instance) the use of higher-order functions is a standard practice. A simple example of a higher-ordered function is the map or mapcar function, which takes as its arguments a function and a list, and returns the list formed by applying the function to each member of the list. For a language to support map, it must support passing a function as an argument.

There are certain implementation difficulties in passing functions as arguments and returning them as results. Historically, these were termed the funarg problems, the name coming from "function argument".

1 Availability
2 Examples
3 See also

Availability

Languages which are strongly associated with functional programming, such as Lisp, Scheme, ML, and Haskell, all support first-class functions. Other languages which also support them include Perl, Python, PHP, Lua, Tcl/Tk, ECMAScript (JavaScript, ActionScript), Ruby, Io, Scala, and Nemerle.

Most modern, natively compiled programming languages (e.g. C, C++, C#, and Pascal) support function pointers, which can be stored in data structures and passed as arguments to other functions. Nevertheless, they are not considered to support first-class functions since, in general, functions cannot be created dynamically during the execution of a program without using reflection, which has an enormous performance impact. This could be mitigated by caching in some cases. The closest analog would be a dynamically compiled function created by a just-in-time compiler, which is compiled as an array of machine language instructions in memory and then cast to a function pointer, such as in C#. However, this technique is specific to the underlying managed framework architecture and is therefore not portable. But if using windows, C# has a delegate type which is a type safe function pointer. The C++ programming language supports user-defined operators, including the '()' operator, which allows first-class objects to be treated as functions. Those objects can be manipulated just like any other first-class object in C++, but such manipulations do not include changing the function itself at runtime. Additionally, real Lambdas (see Lambda Calculus) have no language support in the last C++ standard (although there may be in C++0x). C# supports lambdas in many uses, including anonymous methods. C# Version 3 adds a lamdba expression lexer and parser which run at compile-time and then a lambda code-generation portion of the compiler which executes at run-time.[1]

Examples

Lisp

(lambda (a b) (* a b)) ; function literal
((lambda (a b) (* a b)) 4 5) ; function is passed 4 and 5

ALGOL 68

PROC newton = (REAL x, error, PROC (REAL) REAL f, f prime) REAL:
# Newton's method #
  IF f(x) <= error
  THEN x
  ELSE newton (x - f(x) / f prime (x), error, f, f prime)
  FI;

print((
  newton(0.5, 0.001, (REAL x) REAL: x**3 - 2*x**2 + 6, (REAL x) REAL: 3*x**2 - 4**x),
  newline
));

ECMAScript

function(message) { print(message); } // function literal
SomeObject.SomeCallBack=function(message) { print(message); } // function literal assigned to callback

Note that the callee keyword in ECMAScript makes it possible to write recursive functions without naming them.

Python

Python does not have a (full) function literal, because the lambda keyword can only be followed by an expression and not statements.

lambda x:x*x # function literal 
map(lambda x:x*x,range(1,11)) # array of first ten square numbers;
                              # same as [x*x for x in range(1,11)]

However, functions can be created dynamically; they live in the same namespace as ordinary variables, and thus it is possible to assign a function to a variable:

>>> code="""def f(a):
...  if isinstance(a, int):
...   print a**2
...  else:
...   print a, 'is not an integer number'
... """
>>> exec(code)
>>> f(3)
9
>>> g=f
>>> g(3)
9
>>> g(3.0)
3.0 is not an integer number
>>>

It is also possible to create a simple function which returns any function.

There is also the possibility to make code with same functionality as there is in the Javascript section below:

import math
 
def make_derivative(f, deltaX):
    assert deltaX != 0.0, 'deltaX could not be zero'
    return lambda x: (f(x+deltaX) - f(x)) / deltaX
 
cos=make_derivative(math.sin, 0.0000000001)
 
# cos(0)     ~> 1.0
# cos(math.pi/2)  ~> 0.0

Javascript

Javascript supports both first class functions and lexical scope.

// f: function that takes a number and returns a number
// deltaX: small positive number
// returns a function that is an approximate derivative of f
function makeDerivative( f, deltaX )
{
    var deriv = function(x)
    { 
       return ( f(x + deltaX) - f(x) )/ deltaX;
    }
    return deriv;
}
var cos = makeDerivative( Math.sin, 0.000001);
// cos(0)     ~> 1
// cos(pi/2)  ~> 0

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