After a long time learning and working with object-oriented programming, I took a step back to think about system complexity.

`“Complexity is anything that makes software hard to understand or to modify.`

“?—?John Outerhout

Doing some research, I found functional programming concepts like immutability and pure function. Those concepts are big advantages to build side-effect-free functions, so it is easier to maintain systems?—?with some other benefits.

In this post, I will tell you more about functional programming, and some important concepts, with a lot of code examples. In Javascript!

### What is functional programming?

Functional programming is a programming paradigm?—?a style of building the structure and elements of computer programs?—?that treats computation as the evaluation of mathematical functions and avoids changing-state and mutable data?—?

### Pure functions

The first fundamental concept we learn when we want to understand functional programming is **pure functions**. But what does that really mean? What makes a function pure?

So how do we know if a function is `pure`

or not? Here is a very strict definition of purity:

- It returns the same result if given the same arguments (it is also referred as
`deterministic`

) - It does not cause any observable side effects

#### It returns the same result if given the same arguments

Imagine we want to implement a function that calculates the area of a circle. An impure function would receive `radius`

as the parameter, and then calculate `radius * radius * PI`

:

Why is this an impure function? Simply because it uses a global object that was not passed as a parameter to the function.

Now imagine some mathematicians argue that the `PI`

value is actually `42`

and change the value of the global object.

Our impure function will now result in `10 * 10 * 42`

= `4200`

. For the same parameter (`radius = 10`

), we have a different result. Let’s fix it!

TA-DA ?! Now we’ll always pass the`PI`

value as a parameter to the function. So now we are just accessing parameters passed to the function. No `external object`

.

- For the parameters
`radius = 10`

&`PI = 3.14`

, we will always have the same the result:`314.0`

- For the parameters
`radius = 10`

&`PI = 42`

, we will always have the same the result:`4200`

#### Reading Files

If our function reads external files, it’s not a pure function?—?the file’s contents can change.

#### Random number generation

Any function that relies on a random number generator cannot be pure.

#### It does not cause any observable side effects

Examples of observable side effects include modifying a global object or a parameter passed by reference.

Now we want to implement a function to receive an integer value and return the value increased by 1.

We have the `counter`

value. Our impure function receives that value and re-assigns the counter with the value increased by 1.

**Observation**: mutability is discouraged in functional programming.

We are modifying the global object. But how would we make it `pure`

? Just return the value increased by 1. Simple as that.

See that our pure function `increaseCounter`

returns 2, but the `counter`

value is still the same. The function returns the incremented value without altering the value of the variable.

If we follow these two simple rules, it gets easier to understand our programs. Now every function is isolated and unable to impact other parts of our system.

Pure functions are stable, consistent, and predictable. Given the same parameters, pure functions will always return the same result. We don’t need to think of situations when the same parameter has different results?—?because it will never happen.

#### Pure functions benefits

The code’s definitely easier to test. We don’t need to mock anything. So we can unit test pure functions with different contexts:

- Given a parameter
`A`

? expect the function to return value`B`

- Given a parameter
`C`

? expect the function to return value`D`

A simple example would be a function to receive a collection of numbers and expect it to increment each element of this collection.

We receive the `numbers`

array, use `map`

incrementing each number, and return a new list of incremented numbers.

For the `input`

`[1, 2, 3, 4, 5]`

, the expected `output`

would be `[2, 3, 4, 5, 6]`

.

### Immutability

Unchanging over time or unable to be changed.

When data is immutable, its **state cannot change** **after it’s created.** If you want to change an immutable object, you can’t. Instead, **you create a new object with the new value.**

In Javascript we commonly use the `for`

loop. This next `for`

statement has some mutable variables.

For each iteration, we are changing the `i`

and the `sumOfValue`

**state**. But how do we handle mutability in iteration? Recursion!

So here we have the `sum`

function that receives a vector of numerical values. The function calls itself until we get the list empty (our recursion `base case`

). For each “iteration” we will add the value to the `total`

accumulator.

With recursion, we keep our **variables** immutable. The `list`

and the `accumulator`

variables are not changed. It keeps the same value.

**Observation**: Yes! We can use `reduce`

to implement this function. We will cover this in the `Higher Order Functions`

topic.

It is also very common to build up the final **state** of an object. Imagine we have a string, and we want to transform this string into a `url slug`

.

In OOP in Ruby, we would create a class, let’s say, `UrlSlugify`

. And this class will have a `slugify!`

method to transform the string input into a `url slug`

.

Beautiful! It’s implemented! Here we have imperative programming saying exactly what we want to do in each `slugify`

process?—?first lower case, then remove useless white spaces and, finally, replace remaining white spaces with hyphens.

But we are mutating the input state in this process.

We can handle this mutation by doing function composition, or function chaining. In other words, the result of a function will be used as an input for the next function, without modifying the original input string.

Here we have:

`toLowerCase`

: converts the string to all lower case`trim`

: removes whitespace from both ends of a string`split`

and`join`

: replaces all instances of match with replacement in a given string

We combine all these 4 functions and we can `"slugify"`

our string.

### Referential transparency

Let’s implement a `square function`

:

This pure function will always have the same output, given the same input.

Passing `2`

as a parameter of the `square function`

will always returns 4. So now we can replace the `square(2)`

with 4. That’s it! Our function is `referentially transparent`

.

Basically, if a function consistently yields the same result for the same input, it is referentially transparent.

**pure functions + immutable data = referential transparency**

With this concept, a cool thing we can do is to memoize the function. Imagine we have this function:

And we call it with these parameters:

The `sum(5, 8)`

equals `13`

. This function will always result in `13`

. So we can do this:

And this expression will always result in `16`

. We can replace the entire expression with a numerical constant and memoize it.

### Functions as first-class entities

The idea of functions as first-class entities is that functions are **also** treated as values **and** used as data.

Functions as first-class entities can:

- refer to it from constants and variables
- pass it as a parameter to other functions
- return it as result from other functions

The idea is to treat functions as values and pass functions like data. This way we can combine different functions to create new functions with new behavior.

Imagine we have a function that sums two values and then doubles the value. Something like this:

Now a function that subtracts values and the returns the double:

These functions have similar logic, but the difference is the operators functions. If we can treat functions as values and pass these as arguments, we can build a function that receives the operator function and use it inside our function. Let’s build it!

Done! Now we have an `f`

argument, and use it to process `a`

and `b`

. We passed the `sum`

and `subtraction`

functions to compose with the `doubleOperator`

function and create a new behavior.

### Higher-order functions

When we talk about higher-order functions, we mean a function that either:

- takes one or more functions as arguments, or
- returns a function as its result

The `doubleOperator`

function we implemented above is a higher-order function because it takes an operator function as an argument and uses it.

You’ve probably already heard about `filter`

, `map`

, and `reduce`

. Let’s take a look at these.

### Filter

Given a collection, we want to filter by an attribute. The filter function expects a `true`

or `false`

value to determine if the element **should or should not** be included in the result collection. Basically, if the callback expression is `true`

, the filter function will include the element in the result collection. Otherwise, it will not.

A simple example is when we have a collection of integers and we want only the even numbers.

**Imperative approach**

An imperative way to do it with Javascript is to:

- create an empty array
`evenNumbers`

- iterate over the
`numbers`

array - push the even numbers to the
`evenNumbers`

array

We can also use the `filter`

higher order function to receive the `even`

function, and return a list of even numbers:

One interesting problem I solved on Hacker Rank FP Path was the **Filter Array problem**. The problem idea is to filter a given array of integers and output only those values that are less than a specified value `X`

.

An imperative Javascript solution to this problem is something like:

We say exactly what our function needs to do?—?iterate over the collection, compare the collection current item with `x`

, and push this element to the `resultArray`

if it pass the condition.

**Declarative approach**

But we want a more declarative way to solve this problem, and using the `filter`

higher order function as well.

A declarative Javascript solution would be something like this:

Using `this`

in the `smaller`

function seems a bit strange in the first place, but is easy to understand.

`this`

will be the second parameter in the `filter`

function. In this case, `3`

(the `x`

) is represented by `this`

. That’s it.