Getting started with functional-programming

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Remarks

Functional programming is a programming paradigm which models computations (and thus programs) as the evaluation of mathematical functions. It has its roots in lambda calculus, which was developed by Alonzo Church in his research on computability.

Functional programming has some interesting concepts:

  • Higher Order functions
  • Purity
  • Recursion
  • Laziness
  • Referential Transparency
  • Currying
  • Functors
  • Monads
  • Memoization & Tail-call Optimization
  • Functional Unit Testing

Some examples of functional programming languages are Lisp, Haskell, Scala and Clojure, but also other languages, like Python, R and Javascript allow to write (parts of) your programs in a functional style. Even in Java, functional programming has found its place with Lambda Expressions and the Stream API which were introduced in Java 8.

Currying

Currying is the process of transforming a function that takes multiple arguments into a sequence of functions that each has only a single parameter. Currying is related to, but not the same as, partial application.

Let's consider the following function in JavaScript:

var add = (x, y) => x + y
 

We can use the definition of currying to rewrite the add function:

var add = x => y => x + y
 

This new version takes a single parameter, x , and returns a function that takes a single parameter, y , which will ultimately return the result of adding x and y .

var add5 = add(5)
var fifteen = add5(10) // fifteen = 15
 

Another example is when we have the following functions that put brackets around strings:

var generalBracket = (prefix, str, suffix) => prefix + str + suffix
 

Now, every time we use generalBracket we have to pass in the brackets:

var bracketedJim = generalBracket("{", "Jim", "}") // "{Jim}"
var doubleBracketedJim = generalBracket("{{", "Jim", "}}") // "{{Jim}}"
 

Besides, if we pass in the strings that are not brackets, our function still return a wrong result. Let's fix that:

var generalBracket = (prefix, suffix) => str => prefix + str + suffix
var bracket = generalBracket("{", "}")
var doubleBracket = generalBracket("{{", "}}")
 

Notice that both bracket and doubleBracket are now functions waiting for their final parameter:

var bracketedJim = bracket("Jim") // "{Jim}"
var doubleBracketedJim = doubleBracket("Jim") // "{{Jim}}"
 

Higher-order functions

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.

Immutability

In traditional object-oriented languages, x = x + 1 is a simple and legal expression. But in Functional Programming, it's illegal.

Variables don't exist in Functional Programming. Stored values are still called variables only because of history. In fact, they are constants. Once x takes a value, it's that value for life.

So, if a variable is a constant, then how can we change its value?

Functional Programming deals with changes to values in a record by making a copy of the record with the values changed.

For example, instead of doing:

var numbers = [1, 2, 3];
numbers[0] += 1; // numbers = [2, 2, 3];
 

You do:

var numbers = [1, 2, 3];
var newNumbers = numbers.map(function(number) {
    if (numbers.indexOf(number) == 0)
        return number + 1
    return number
});
console.log(newNumbers) // prints [2, 2, 3]
 

And there are no loops in Functional Programming. We use recursion or higher-order functions like map , filter and reduce to avoid looping.

Let's create a simple loop in JavaScript:

var acc = 0;
for (var i = 1; i <= 10; ++i)
    acc += i;
console.log(acc); // prints 55
 

We can still do better by changing acc 's lifetime from global to local:

function sumRange(start, end, acc) {
    if (start > end)
        return acc;
    return sumRange(start + 1, end, acc + start)
}
console.log(sumRange(1, 10, 0)); // 55
 

No variables or loops mean simpler, safer and more readable code (especially when debugging or testing - you don't need to worry about the value of x after a number of statements, it will never change).

Pure functions

Pure functions are self-contained, and have no side effects. Given the same set of inputs, a pure function will always return the same output value.

The following function is pure:

function pure(data) {
    return data.total + 3;
}
 

However, this function is not pure as it modifies an external variable:

function impure(data) {
    data.total += 3;
    return data.total;
}
 

Example:

data = {
    total: 6
};

pure(data);   // outputs: 9
impure(data); // outputs: 9 (but now data.total has changed)
impure(data); // outputs: 12
 

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Friday, May 5, 2017
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