📈 Higher Order Functions (Functional Programming)

What is Higher Order Function ?

Higher Order function is a function which meets atleast one of the following criteria.

1. Takes function as a argument

function x() {
    console.log("x function");
}

function y(x) {   // y is the higher order function
    x();
}

2. Return function as a argument

function x() {
    return function() {
     console.log("function returns from another function");   
    }
}

const z = x();
z();

Higher-order functions are a fundamental concept in functional programming, and they provide a way to write more modular and reusable code. They enable you to pass behavior (functions) around, making your code more flexible and expressive.

Consider this example

1. function to calculate area of a circle

const radius = [1,2,3,4];

const calculateArea = function(radius) {
    const output = [];
    for(let i=0;i<radius.length;i++) {
        output.push(Math.PI * radius[i] * radius[i]);
    }
    return output;
}

console.log(calculateArea(radius));

2. function to calculate circumference of a cirlce

const radius = [1,2,3,4];

const calculateArea = function(radius) {
    const output = [];
    for(let i=0;i<radius.length;i++) {
        output.push(Math.PI * radius[i] * radius[i]);
    }
    return output;
}

const calculateCircumference = function(radius) {
    const output = [];
    for(let i=0;i<radius.length;i++) {
        output.push(2 * Math.PI * radius[i]);
    }
    return output;
}

console.log(calculateCircumference(radius));

3. Also includes diameter

const radius = [1,2,3,4];

const calculateArea = function(radius) {
    const output = [];
    for(let i=0;i<radius.length;i++) {
        output.push(Math.PI * radius[i] * radius[i]);
    }
    return output;
}

const calculateCircumference = function(radius) {
    const output = [];
    for(let i=0;i<radius.length;i++) {
        output.push(2 * Math.PI * radius[i]);
    }
    return output;
}

const calculateRadius = function(radius) {
    const output = [];
    for(let i=0;i<radius.length;i++) {
        output.push(radius[i] * radius[i]);
    }
    return output;
}

console.log(calculateRadius(radius));

This is a valid program, but we need to write in more functional way.

Problems in this code

Repeating: all 3 functions have same functionality, but only thing changes is logic.

Optimized Code

To make a code more optimized and more functional, we need to abstract function in which it is reusable not repeatable.

The function which is abstract is area.
We need generic function to maintain all execution, calculate.

const radius = [1,2,3,4];

const area = function(radius) {
    return Math.PI * radius * radius;
}

const circumference = function(radius) {
    return 2 * Math.PI * radius;
}

const diameter = function(radius) {
    return radius * radius;
}

const caculate = function(radius, callback) {
    let output = [];
    for(let i=0;i<radius.length;i++) {
        output.push(callback(radius[i]));
    }
    return output;
}

console.log(calculate(radius, area));
console.log(calculate(radius, circumference));
console.log(calculate(radius, diameter));

In this above code calculate is higher order function.

Why we need Higher Order Function

Abstraction
Code Reusability
Flexibility
Functional Composition.
Callback Function
map, filter, reduce.
closure and state
currying

Implementation of `map` behind

const radius = [1,2,3,4];

const area = function(radius) {
    return Math.PI * radius * radius;
}

const circumference = function(radius) {
    return 2 * Math.PI * radius;
}

const diameter = function(radius) {
    return radius * radius;
}

Array.prototype.calculate = function(callback) {
    let output = [];
    for(let i=0;i<radius.length;i++) {
        output.push(callback(radius[i]));
    }
    return output;
}

console.log(radius.calculate(area));

Extending Array Prototype:

The calculate method is added to the prototype of the Array object. This method takes a callback function (callback) as an argument and applies it to each element of the array (radius). The results are stored in an output array, which is then returned.