functional-programming Getting started with functional-programming Higher-order functions

Example

Higher-order functions take other functions as arguments and/or return them as results. They form the building blocks of functional programming. Most functional languages have some form of filter function, for example. This is a higher-order function, taking a list and a predicate (function that returns true or false) as arguments.

Functions that do neither of these are often referred to as first-order functions.

function validate(number,predicate) {
    if (predicate) {    // Is Predicate defined
        return predicate(number);
    }
    return false;
}

Here "predicate" is a function that will test for some condition involving its arguments and return true or false.

An example call for the above is:

validate(someNumber, function(arg) {
    return arg % 10 == 0;
    }
);

A common requirement is to add numbers within a range. By using higher-order functions we can extend this basic capability, applying a transformation function on each number before including it in the sum.

You want to add all integers within a given range (using Scala)

def sumOfInts(a: Int, b: Int): Int = {
  if(a > b) 0
  else a + sumOfInts(a+1, b)
}

You want to add squares of all integers within a given range

def square(a: Int): Int = a * a

def sumOfSquares(a: Int, b: Int): Int = {
  if(a > b) 0
  else square(a) + sumOfSquares(a + 1, b)
}

Notice these things have 1 thing in common, that you want to apply a function on each argument and then add them.

Lets create a higher-order function to do both:

def sumHOF(f: Int => Int, a: Int, b: Int): Int = {
  if(a > b) 0
  else f(a) + sumHOF(f, a + 1, b)
}

You can call it like this:

def identity(a: Int): Int = a

def square(a: Int): Int = a * a

Notice that sumOfInts and sumOfSquare can be defined as:

def sumOfInts(a: Int, b: Int): Int = sumHOF(identity, a, b)

def sumOfSquares(a: Int, b: Int): Int = sumHOF(square, a, b)

As you can see from this simple example, higher-order functions provide more generalized solutions and reducing code duplication.

I have used Scala By Example - by Martin Odersky as a reference.