A brief look at programming paradigms

Overview

If you've spent any significant amount of time programming, then you've probably heard discussions about imperative, functional, and declarative programming. These discussions are often mired in technical knowledge and require a fair amount of intuition when trying to grasp the differences between the examples placed in front of us. These different programming styles, usually called programming "paradigms", are discussed as if they exist within a vacuum with complete and total isolation from one another. This only furthers the confusion and frustration among newer programmers especially, which runs counter to the goal of instructing them.

In this post I'll be taking a look at the oft-neglected intersections where these paradigms meet with the hope that the differences between them will be better understood by reframing our existing knowledge of programming basics.

Note: I'll be using PHP for my code examples and will try to provide comments when necessary to point out language quirks.

Understanding Fundamentals is Imperative

Let's start by first reviewing the most basic, fundamental programming paradigm: imperative programming. The term is a bit strange, but the important thing to understand about it is that imperative programming refers to writing software as a series of instructions where you tell the computer how to solve a specific task. For example, if we need to add together a bunch of numbers inside of an array, we might write code that looks like this:

$numbers = [ 8, 31, 5, 4, 20, 78, 52, 18, 96, 27 ];
$sum = 0;
foreach($numbers as $number) {
    $sum += $number;
}

This is a pretty typical example that you've probably encountered in some form or another at some point in your programming studies or career--iterate over an array one element at a time from the first element to the last and add the current element to some accumulating variable that starts at 0. The kind of loop you use may differ, but the general format of the solution looks the same. This is very similar to the way the computer itself performs the task, so the code here is just a relatively human-friendly version of the actual steps the computer performs. This is the essence of imperative programming, the basic building blocks of everything you learn early on.

Abstract Concepts

As the software we write gets larger and more complex, we then tend to rely on "abstractions" to simplify our code and make it easier to understand, reuse, and maintain. For example, if we've written a program that adds arrays of numbers together, then we probably aren't doing that in only one place. Maybe we've written a tool that generates reports on large data sets, such as calculating the total number of sales for a particular quarter, gross profit, net profit, remaining inventory, and any number of other important business-related metrics. Summing numbers could be so common that you use it in 30 different places, so to avoid having to maintain 30 separate instances of our number adding code from above, we define a function:

function sum($numbers) {
    $sum = 0;
    foreach($numbers as $number) {
        $sum += $number;
    }

    return $sum;
}

We do this so frequently in our code that it becomes second nature. We attach so many names and terms to it, too: DRY, abstraction layers, code reuse, separation of concerns, etc. But one thing experienced programmers learn is to write their functions and object and interface methods in such a way that anyone who uses them doesn't need to care about the underlying implementation details, and instead only need to worry about the method name, expected arguments (if any), expected return type (if any), and expected behavior. In other words, they don't need to understand how the function or method completes the intended action, they only need to declare what action they want performed.

A Declaration of Understanding

Anyone who has looked into the concept of the declarative programming paradigm should find those last words familiar: "they don't need to understand how the function or method completes the intended action, they only need to declare what action they want performed". This is the oft-touted explanation of what declarative programming is, the difference between detailing "how" and declaring "what", and I believe that it's this great similarity that causes imperative and declarative programming to become heavily entwined in a programmer's mind and makes it difficult to understand. Take this common example that authors tend to use to try to detail the difference between declarative and imperative programming:

// imperative
function sum($numbers) {
    $sum = 0;
    foreach($numbers as $number) {
        $sum += 0;
    }

    return $sum;
}

// declarative
function sum($numbers) {
    return array_reduce($numbers, fn($x, $y) => $x + $y, 0);
}

The authors will go on to state that in the imperative example, you tell the computer how to sum the numbers, whereas in the declarative example you don't tell the computer how to do it since you don't know anything about the reduce implementation, but intuitively it still feels as if you're telling the computer how to perform its task--you're still defining a function and deciding what its underlying implementation details are, i.e. the steps it needs to take to perform the task, even if its details are abstracted away behind function or method calls that could have varying implementation details of their own. So how the hell is this any different from defining functions like we do in imperative programming?

The answer is simple: it isn't. We've used so many names and terms to describe functions and methods in our ordinary imperative programming, but the truth is that a well-defined function or method serves as a declarative interface to an imperative implementation. Put differently, declarative programming is defining and utilizing simple interfaces that describe what you want accomplished while the underlying implementation details are inevitably written using imperative code.

Functional Differences

Now we can finally tackle one of the biggest trends in programming right now: the functional programming paradigm. But to understand this paradigm, it's important to understand what a "function" is... from a mathematical perspective.

Yes, I know, math tends to be a enthusiasm sink for many, but don't worry, we're not actually going to be doing math. We only need to understand how math treats functions. Specifically, math functions usually look something like f(x) = {insert expression here}, which is loosely equivalent to the following code:

function f($x) {
    return {insert expression here};
}

The important thing to note about functions in math is that you can run them a theoretically infinite number of times on the same input x and still get the same return result. Unlike in a lot of the programs we can write, math functions don't produce side effects. Files aren't written to or destroyed, database entries aren't deleted, some global counter somewhere isn't incremented, and your x doesn't suddenly change. The idea behind functional programming is to embody some of that nature of mathematical functions because they're predictable and always reproducible, and therefore simple to test as well. For example, take the following:

// not functional
function increment(&$x) { // pass by reference--$x will be modified outside of this function!
    $x++;
}

$x = 1;
increment($x);
increment($x);
increment($x);

// functional
function increment($x) { // pass by value--$x will NOT be modified outside of this function!
    return $x + 1;
}

$x = 1;
$y = increment($x);
$y = increment($x);
$y = increment($x);

Note that the first example will change the value of $x on each call, meaning each subsequent call of increment($x) produces a different result. Meanwhile the second example doesn't change $x and so the return value of increment($x) is always the same. This may seem like a silly example, but in larger, more complex software this can be significant. So now that we have an understanding of functions from a mathematical perspective, we have everything we need to actually understand what functional programming is.

Functional programming is a subset of declarative programming. Just like in declarative programming, you use simple interfaces to tell the program what you want to do rather than how to do it. But unlike declarative programming as a whole, functional programming imposes some additional restrictions on what you should and shouldn't do:

• You should encapsulate behavior in pure functions, which always give a consistent output for a given input and don't have side effects.

• You should write functions in such a way that you can compose them together, allowing you to combine and chain behavior to produce new functions or use the output of one as the input for another.

• You should avoid side effects as much as possible.

• You should avoid mutable state (e.g. changing the values in a variable).

• You should avoid sharing state between components.

These restrictions would require an entirely separate post on their own to properly cover and have been covered so many times in so many ways by others elsewhere that it would be superfluous for me to try to add anything more. It's important to note, however, that these restrictions are imposed because they provide some key benefits. By avoiding side effects and by avoiding mutable and shared states, the code you write becomes more predictable and tracing the behavior of an algorithm becomes far simpler. By writing pure, composable functions, you create reusable building blocks that can be strung together in virtually any configuration with predictable results. This makes writing, reading, maintaining, and debugging code easier and less error-prone.

That said, I feel that it's important to note that in the real world when writing practical software that users can interact with, it's simply not possible to completely avoid side effects or mutable state. The very act of creating and updating database entries is itself an act of mutating state, which runs contrary to functional programming principles and is essential for many important software projects. But even if you can't adhere strictly to functional programming principles, it's possible to benefit significantly from being aware of them and integrating them into your own software development strategies.

Let's consider a more practical example to illustrate this. Imagine that you've built a social media website and you're trying to test a push notification system that will be triggered when your user receives a new message. Now imagine your code and unit tests look something like this:

function sendNotification(&$message) { // pass by reference--$message will be modified outside of this function!
    $notification_system = new NotificationSystem();
    if(!$message['sent_push_notification']) {
        $notification_system->sendPushNotification($message);
        $message['sent_push_notification'] = true;
    }
}

function testSendNotification() {
    $message = [
        'user_id'=>'{some_id}',
        'contents'=>'Hi!',
        'sent_push_notification'=>false
    ];

    sendNotification($message);
    sendNotification($message);
}

At a quick glance you probably wouldn't be aware of why the second message didn't send, but the fact that our sendNotification() function mutates the state of the data provided to it is the culprit. This is code that doesn't adhere to functional programming principles since the data provided to it is mutated. As a result, running the function multiple times on the same variable doesn't result in the same behavior as the first call. If we wanted to work around this without adhering to functional programming principles then we would need to manually set $message['sent_push_notification'] = false; between function calls, which makes our unit tests potentially more error-prone. Alternatively we can make a simple change to adhere better to those functional principles:

function sendNotification($message) { // pass by value--$message will NOT be modified outside of this function!
    $notification_system = new NotificationSystem();
    if(!$message['sent_push_notification']) {
        $notification_system->sendPushNotification($message);
        $message['sent_push_notification'] = true;
    }

    return $message;
}

function testSendNotification() {
    $message = [
        'user_id'=>'{some_id}',
        'contents'=>'Hi!',
        'sent_push_notification'=>false
    ];

    sendNotification($message);
    sendNotification($message);
}

Now both notifications will be sent out, which is what we would intuitively expect. You should also notice that the above is also a blend of imperative, declarative, and functional programming. Our function definitions have imperative code, our sendNotification() function adheres to the functional programming principle of avoiding mutable state (well, mostly), and our NotificationSystem object provides a declarative interface for sending a push notification for a message.

Final Thoughts

By viewing these three paradigms not as completely separate concepts but as layers on top of one another, where functional programming is a type of declarative programming which is implemented using imperative programming, we can stop being confused by their similarities and instead find clarification in them. By understanding that imperative programming is the backbone of everything, that declarative programming is just simplifying that backbone with simple interfaces, and that functional programming is simply adding some additional guidelines and restrictions to the way you write code to make it more consistent, reusable, and predictable, we can start to see that we're not choosing one programming paradigm over another, but instead choosing how much consideration we place on the design of the programs we write. Except in purely functional languages, functional programming isn't some alien concept distinct from imperative or declarative programming, but is instead a natural evolution of the two.

There are a lot of details I've glossed over here. Each of these programming paradigms is far too detailed to include a proper analysis in an already lengthy post that tries to separate them from each other and clarify their differences. Blog articles exist in a thousand different places that can do each one far more justice than I can, and programming languages exist that completely cut imperative programming out of the picture. But for your average programmer slinging JavaScript, C, Rust, PHP, or what have you, I hope that this serves as a crucial starting pointing to understanding just what in the hell these functional programming enthusiasts are on about.