The What? and Why? of functional programming

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When I talk to fellow programmers about functional programming it’s often about something specific, but occasionally that person will suddenly turn the conversation around and ask “So what actually is functional programming, anyway?”. I will talk about some specific features of FP but I will also cover something more general, a tagline or soundbite with which I could give people an instant sense of the philosophy behind functional programming and how it differs from object-oriented programming. As we will see, however, you can get a lot of the benefits of functional programming even if you don’t program in a function language.

Literally speaking, functional programming means that the basic units of your application (i.e. the bits that you compose together to make a complete program) are functions (as opposed to Object-Oriented Programming when they are classes). However, when it comes to the philosophies of the two, I think we can be a bit broader than that to contrast the two:

The main goal of a code unit in object-oriented / imperative programming is to perform actions

The main goal of a code unit in functional programming is to compute results

Why is this distinction important? It’s why functional programming values concepts such as immutability and purity (which have a whole host of benefits).

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Property-based testing

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Unit testing. We all do it. Some of us even practice TDD (although I wish I had a penny for each time I see a company claiming that they practice TDD when what they actually mean is “We write unit tests.”).

Test Driven Design means that your development is actually driven by your tests. It doesn’t mean that you write unit tests (although that is required), it doesn’t mean that you write your tests first (although that is also required), but it means that the desired behaviour is implemented incrementally, one test at a time. This normally means that, for each cycle of this method, a single test is written and then the simplest possible implementation is written that will make that test pass. After each test is added and passes (along with the rest of the test suite covering that particular piece of functionality) the developer is free to refactor the code–after all, up until this point the code has grown quite organically and is likely of poor quality. This repeated process is often referred to as Red-Green-Refactor: first the test is added and fails (the test is “red”), then the implementation is augmented until the test passes (the test “goes green”) and then the dev can refactor to improve code quality.

There are many, many different aspects to writing tests, each of which has a hand in how readable, maintainable, comprehensive, useful and correct your test suite is. These include (but are far from limited to): black-box / gray-box / white-box philosophy, mocking strategies, outside-in or inside-out…

But one aspect I don’t hear many people talking about (outside of the functional programming community at least) is how you pick your test cases. It might not seem that important–just throw some example data at the test and assert that for each of those inputs the expected output is produced. Simple, right?

A ha, dear reader. Allow me to throw a spanner in the works.

This doesn’t always work (at least, not well). Let’s go for the most basic of examples:

How would you unit test the + operator?

Examples? 1 + 0? 2 + 2? 423798 + 278? Where do you stop? How would a developer, following TDD by the book, incrementally implement that function?

When designing tests it’s often helpful to pretend that the person writing the tests and the person completing the implementation of the function are different people. Let us play the part of the coder who has been tasked with implementing the “add” function as above. The signature of the function is agreed and the tester throws their first test case at us: 0 + 0. So, we dutifully write the most simple case that will solve that:

let add x y = 0

The test passes. Yay! Now, here comes the second test case: 1, 0 which should equal 1. So:

let add x y =
    if x = 1 then 1 else 0

Okay, that’s fine. It’s early days yet! So. 2, 2 = 4?

let add x y = 
    if x = 1 then 1
    elif x = 2 then 4
    else 0

Hmmm, it doesn’t look like we’re being driven towards a real implementation here. Maybe let’s try one more test case?

let add x y = 
    if x = 1 then 1
    elif x = 2 then 4
    elif x = 423798 && y = 278 then 424076
    else 0

No, this isn’t working. We’re solving each case as they come in, but we’re not getting anywhere: the if/else statement is just going to grow and grow and grow. We’re stuck in a loop of: tester adds an example, implementation solves that one particular example.

So, how do you choose your test examples? Wouldn’t it be better if you could randomly generate inputs to your test? It would certainly stop the implementation from devolving into a series of hard-coded values, but then what would you assert? This is something that has fascinated me for a while now.

Allow me to introduce Property-Based Testing.

In this context the word property is used in the mathematical way; a property means some quality, attribute, feature or characteristic that a function, or its input and output, has. In short, property-based testing doesn’t assert what the output is, it instead asserts the the output has some property / characteristic. Sometimes the property you are checking is dependent on the input having some property as well (this may or may not be the same property as you expect to see in the output). An example of this might be:

For any two positive numbers x and y, x + y must be positive

You can see here that we are now able to write an assertion that is true for all inputs to the program. For this particular property–that the output of the function is positive–we have placed a constraint on the input (x and y must be positive). We are now able to automatically generate the input data for our tests because we don’t need to know what the data is in advance.

To see how this might work, let’s write the above property in a more formal language:

For all x, y
where x > 0
and y > 0
it follows that: x + y > 0

It almost looks as if we are now following a Gherkin-style BDD syntax for our tests! Okay, so now we understand what a property is we need to come up with a way of discovering more properties.

Continuing with the mathematical example of addition, your function might have the concept of *identity*. From https://en.wikipedia.org/wiki/Function_(mathematics)#Identity_function, “The unique function over a set X that maps each element to itself is called the identity function for X”, meaning “a function who’s output is always equal to its input”. For addition this is simply “+ 0”, and is a property that we can check.

For all x
it follows that x + 0 = x

There are more mathematical properties that would be useful to check, such as commutativity:

For all x, y:
it follows that x + y = y + x

Associativity:

For all x, y, z
it follows that (x + y) + z = x + (y + z)

Given these properties, it’s now much harder to write an implementation of (+) that is incorrect yet passes all our tests.

This is all very good in theory, but how does this actually work? How do we actually implement this? In part 2 of this series we’ll go through a worked example with something a bit harder than addition: the Diamond Kata.

Code comments

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I read a blog post by Jeff Atwood some time ago (warning: this is an old post: https://blog.codinghorror.com/coding-without-comments/) that got me thinking about code comments again. I forget how I came across the blog post but it made me realise that I never, ever comment.

I used to think that comments were an essential part of software development because that’s what I was taught at university and, if I’m honest, they’re still a good idea for junior developers. I have found, though, that in most codebases comments are merely an excuse for poorly-written code. In fact, I would almost go so far as to say that the definition of well-written code is code that needs no comments.

I’d like to clear one thing up before we really begin: I’m talking about comments, not documentation. XML or JavaDoc comments for intellisense are fantastic–if done correctly–for documenting the public surface of your API. From now on when I use the word ‘comment’ I’m talking about double-slashed comments (// such as this) in the middle of a piece of code.

When do we see comments?

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Does null equal null?

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There are few subjects in programming that are contentious enough to cause heated discussions whenever they come up in conversations, blog posts or Stack Overflow answers. The canonical example of one of these subjects is ‘tabs vs spaces’, but I’ve found another one. It’s something that you may not have thought about before (except occasionally when crafting a SQL query), so let me introduce today’s topic: Does null equal null?

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Why records must be sealed

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When most people (and I include myself in this) start to learn a functional programming language like F#, they are immediately surprised by the lack of inheritance. It’s such a mainstay of our daily programming that we’re initially nonplussed when it’s taken away… In this post I want to talk about the problems introduced by mixing inheritance with the notion of structural equality, and thus why any language which implements the concept of a record type must also prohibit inheritance of such a type.

For the record (ahem), a record is a type where one simply declares the shape of the class (i.e. the names and types of the public members), and then the constructor, equality and hashcode methods are generated for you by the compiler. An example in F# might be this:

type PersonName = { firstName : string; surname : string }

which is roughly equivalent to the following C#:

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Roslyn analyzers

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I’ve finally decided to get in on that sweet, sweet Roslyn action and write myself an analyzer (please forgive the American spelling–since I’m programming against a series of types defined in American I’ve decided to use their spelling).

You’ll probably know I’m a big fan of functional programming and I’m trying to write my C# in a more functional style; I’ve found that you can get many of the benefits of functional programming even though you’re not writing in a functional language.
As it turns out, sometimes removing certain features from your programming language (or, at least, disallowing certain actions) can actually improve your code. An easy example of this is the goto statement; despite the fact that the C# language supports goto nobody uses it because it’s widely regarded as a harmful thing to do.

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Some functional types in C#

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Update: I now have a project on GitHub containing this code at https://github.com/Richiban/Richiban.Func Check this repository for up to date code.

Continuing with my long-running train of thought in bringing some functional programming concepts to my C# projects, I have implemented a type called Optional, roughly equivalent to `Option` from F# or `Maybe a` from Haskell. If you’re not familiar with these concepts, then imagine Nullable from .NET, but applicable to all types (not just value types). The whole idea is that, rather than using a null reference of T to represent a missing value you use a new type–Optional–that can exist in one of two states: it either contains a value of T or does not.

This is a very important difference that I will explain over the course of this post. First, let’s look at the type definition itself. It’s quite long, so feel free to skim-read it at this point and refer back to it at later points in the post.

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