function object (functor) (2) : first-class funtion

http://en.wikipedia.org/wiki/First-class_function

 

In computer science, a programming language is said to support first-class functions^[1] (also called function literals, function types) 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.

Python

Python creates functions by the def statement or the lambda expression. Although lambda expressions cannot create functions that use statements in their definition as they are confined to be just expressions, they are flexible enough to show that they create first class functions as well as if the more powerful def statement were used

>>> #some built in functions and their inverses >>> from math import sin, cos, acos, asin >>> # Add a user defined function and its inverse >>> cube = lambda x: x * x * x >>> croot = lambda x: x ** (1/3.0) >>> # First class functions allow run-time creation of functions from functions >>> # return function compose(f,g)(x) == f(g(x)) >>> compose = lambda f1, f2: ( lambda x: f1(f2(x)) ) >>> # first class functions should be able to be members of collection types >>> funclist = [sin, cos, cube] >>> funclisti = [asin, acos, croot] >>> # Apply functions from lists as easily as integers >>> [compose(inversef, f)(.5) for f, inversef in zip(funclist, funclisti)] [0.5, 0.49999999999999989, 0.5] >>> 

 

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 ) { return function (x) { return ( f(x + deltaX) - f(x) )/ deltaX; }; } var cos = makeDerivative( Math.sin, 0.000001); // cos(0) ~> 1 // cos(pi/2) ~> 0 

 

 

http://en.wikipedia.org/wiki/First-class_object

An object is first-class when it^{[citation needed]}:

• can be stored in variables and data structures
• can be passed as a parameter to a subroutine
• can be returned as the result of a subroutine
• can be constructed at runtime
• has intrinsic identity (independent of any given name)