Algebraic Data Types

Huh? What are they good for?

Posted by John Klingler on January 11, 2016

Algebraic data types, usually abbreviated ADTs, are a useful construct in programming to increase code clarity and reduce the likelihood of errors. Generally speaking, they’re somewhat similar to enums in Java, but Scala lends much more power to the construct. ADTs define a fixed set of all possible values of a given type. The classic example of an ADT in Scala is the Option type. An Option represents something that may or may not have a value. No value is None and some value is Some(). This is the functional version of returning an object or null from a method in Java, and is very useful for Java interoperability to eliminate NullPointerException’s.

To see how ADTs may be implemented in our code, we will begin with the example of the classic counting game FizzBuzz. The game begins with participants taking turns counting up from 1, but saying fizz instead of numbers which are multiples of 3, buzz instead of numbers which are multiples of 5, and fizzbuzz for numbers which are both. Now let’s look at how FizzBuzz could be written in Java:

public static void printIt(Integer i) {
  if (i % 3 == 0 && i % 5 == 0) {
  } else if (i % 3 == 0) {
  } else if (i % 5 == 0) {
  } else {

public static void main(String[] args) {
  for (int i = 1; i <= 100; i++) {

Nothing out of the ordinary here. If we just translated this into Scala, we’d have something similar to:

def printIt(i: Int): Unit =
  if (i % 3 == 0 && i % 5 == 0)
  else if (i % 3 == 0)
  else if (i % 5 == 0)

for (i <- 1 to 100) {

As experienced Scala developers, we would recognize there are more functional ways to accomplish this task. One way is:

val isMod: (Int, Int) => Boolean = (m, i) => i % m == 0
val mod3 = isMod(3, _)
val mod5 = isMod(5, _)

val fizzBuzzIt: Int => String = {
  case i if mod3(i) && mod5(i) => "FizzBuzz"
  case i if mod3(i)            => "Fizz"
  case i if mod5(i)            => "Buzz"
  case i                       => i.toString

Stream(1 to 100: _*).map(fizzBuzzIt).foreach(println)

So that works just fine and does exactly what we needed. But what if we want to share the FizzBuzzification functionality as a library? We could just publish our fizzBuzzIt function. However, if users wanted to do something different depending on whether it’s a Fizz or a Buzz, they’d have to resort to string matching which is brittle and definitely not type safe. One typo would result in incorrect behavior or, even worse, failures at runtime. While proper unit tests may catch these sorts of errors, it is just as likely they copied over the error or defined a constant with the typo. The tests would never catch it.

Here is where we can leverage ADTs to get the job done. First off, we need to define the type of our collection of values:

sealed abstract class FizzBuzzADT(i: Int) {
  override def toString: String = i.toString

There are two things to note here. First, we’ve defined a sealed class which tells the compiler that only classes within the same file are allowed to inherit from this class. This effectively prevents anyone from adding additional values to our type. This is important because adding more values somewhere might lead to unanticipated problems like a MatchError being thrown in a pattern match that doesn’t handle this new value. Secondly, we’ve declared shared functionality for all values with the toString method, standard OO stuff.

Now we need to define all of the possible values of our ADT. Remember, these all have to be in the same file as the trait:

case class Fizz(i: Int) extends FizzBuzzADT(i) {
  override val toString = "Fizz"

case class Buzz(i: Int) extends FizzBuzzADT(i) {
  override val toString = "Buzz"

case class FizzBuzz(i: Int) extends FizzBuzzADT(i) {
  override val toString = "FizzBuzz"

case class JustInt(i: Int) extends FizzBuzzADT(i)

We’ve defined Fizz, Buzz, FizzBuzz, and JustInt. It might not yet be clear why we’ve defined constructor arguments for Fizz, Buzz , and FizzBuzz, but it gives us some opportunities that we’ll discuss in a minute.

Now all we need is a way to create our values given any integer. The FizzBuzzADT companion object is the perfect place for this:

object FizzBuzzADT {
  def apply(i: Int): FizzBuzzADT = i match {
    case _ if i % 3 == 0 && i % 5 == 0 => FizzBuzz(i)
    case _ if i % 3 == 0               => Fizz(i)
    case _ if i % 5 == 0               => Buzz(i)
    case _                             => JustInt(i)

Here you see that the logic for determining whether the integer is a “Fizz”, “Buzz”, “FizzBuzz”, or just an integer hasn’t changed or gone away; instead of just printing the value, we’re mapping the integers to one of the values of our ADT. So to run our new FizzBuzz algorithm and print the values, we can use:

Stream(1 to 100: _*).map(FizzBuzzADT(_)).foreach(println)

So you’re probably thinking that this doesn’t look all that different from our “idiomatic Scala” implementation from above. Scala is supposed to be more concise. What did all that extra code buy us? Well, remember the constructor arguments to the case classes? Let’s say, for example, that we have a collection of FizzBuzzADT’s (but no access to the collection of integers from which it was created) and we only want to print something out if the original integer was even. We can do this using pattern matching:

val even: Int => Boolean = i => i % 2 == 0

// Pretend the Stream[Int] came from somewhere else
Stream(1 to 100: _*).map(FizzBuzzADT(_)).foreach {
  case a@Fizz(i) if even(i)     => println(a)
  case a@Buzz(i) if even(i)     => println(a)
  case a@FizzBuzz(i) if even(i) => println(a)
  case a@JustInt(i) if even(i)  => println(a)
  case _                        => // Be quiet

Certainly, we could have accomplished this example more effectively, by exposing the original integer as a value in the abstract class, but the purpose here was to demonstrate the power and flexibility of pattern matching with ADTs.

For another example, let’s suppose for a second that I don’t like Fizz. In fact, I hate it; I never want to see it. Let’s get rid of the Fizz:

Stream(1 to 100: _*).map(FizzBuzzADT(_)).foreach {
  case Fizz(_) => // Down with the bloody bad Fizz
  case x       => println(x)

In this case, we don’t really need pattern matching and we can accomplish the same thing more concisely:

Stream(1 to 100: _*).map(FizzBuzzADT(_)).filter(!_.isInstanceOf[Fizz]).foreach(println)

Sure, you could just as easily have ridded the world of Fizz with the implementation above:

Stream(1 to 100: _*).map(fizzBuzzIt).filter(_ != "Fizz").foreach(println)

But are you sure there’s not a typo? What if it’s decided that Fizz should be spelled Fisz? These all end up being runtime errors and who likes those? We have to write tests for these scenarios and even those tests are prone to the same problems. The ADT turns these runtime errors into compile time errors. Because we can’t even run tests if the code doesn’t compile, we’ve eliminated a whole class of tests. These tests weren’t truly valuable anyway as they validated library integration, not business functionality. So, in that sense, ADT’s also let us spend more brain cycles on business functionality.

Our simple FizzBuzz example demonstrates how ADTs can replace runtime with compile-time errors and transform a brittle algorithm to be type-safe. Hopefully I’ve demystified algebraic data types and shown how they’re valuable constructs you can employ in your code to build more robust applications.

All code shown can be found here or just git clone

posted on January 11, 2016 by
John Klingler