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Functional Programing in Javascript

Xah Lee, 2009-01-28, 2010-10-30

This page shows you some functional programing examples in javascript. If you are not familiar with js, see: Javascript Basics.

Defining a Function

Here's how to define a function:

// defines a function
function f(n) {return n+1;};

Function without “return” returns “undefined”

If you want your function to return a value, you must use the “return” statement. A function without return value, when called, will return the builtin special value “undefined”. Example:

// defines a function
function f(n) {n;};

// call the function f
alert(f(3)); // result is “undefined”

Pure Function (aka Anonymous Function, “lambda”)

You can define a function without naming it. Example:

// defines a function without naming it
function (n) {return n+1;};

Function's Value is “function”

A function definition has a value. Its value is a special value of type “function”.

alert(
 typeof(
     function f() {return 1;}
 )
); // prints “function”

Assign a Function to Variable

You can assign a function to a variable.

// assign a function to a variable
var f = function (n) {return n+1;};
alert(f(2)); // prints 3

The above is effectively equivalent to this:

function f(n) {return n+1;};

Apply a Function to a Value

You can apply a function to value directly.

// apply a pure function to value directly
function (n) {return n+1;} (2);   // result value is 3

Function Returning a Function

You can have a function return another function.

// function returning a function
function f(n) {
    return function (x) {return (n.toString() + " and " + x.toString() ); };
}

alert (f(2) (7)); // prints “2 and 7”

So, for example, you can define a function f(n) that returns a function f(x) that computes nth power of x.

// function returning a function
function f(n) {
    return function (x) {return Math.pow(x,n); };
}

alert (f(2) (7)); // prints 49

In the above, we first call f(2), the result is a function that computes x^2. Then, we give this function a argument of 7, so the result is 49.

Recursion

Function can call itself. Here's a example of factorial.

function f(n) {
    if (n < 0)  { return -1; }
    if (n == 0) { return 1; } else return (n * f(n - 1));
}

alert(f(4)); // prints 24. (it's 4×3×2×1)

Function Composition

Because all the above features, javascript has some ability to do advanced functional programing. For example, we can define a function (and we call it simpleFunctionCompose), that takes 2 arguments, each is a function (call them f and g), and simpleFunctionCompose returns a new function whose behavior is equivalent to f(g(x)).

// function composition

// takes two single value functions f(x) and g(x) and returns a
// function that computes f(g(x))
function simpleFunctionCompose(f, g) { 
    return function (n) { return f(g(n)); };
}

// test
function h(n) { return n+1;}
function i(n) { return n*2;}

alert(simpleFunctionCompose(h,i)(3)); // prints 7