Introduction to Algebraic Data Types

July 14, 2020 ยท 4 minute read

The demo code:

One of the concepts in functional programming that trips up beginners is Algebraic Data Types (ADT). I am going to go through some examples and relate it to some concepts that would be familiar to Object Oriented Programming (OOP).

For this introduction I will be using TypeScript for the OOP examples and Elm for the functional examples.

Let's start with an example.

type Animal = Cat | Dog

An Animal can be either a Cat or a Dog, but you can't just be an animal. You need to be a type of an animal, the classic "is a" relationship. This is a bit similar to abstract classes in OOP languages.

abstract class Animal {
	abstract speak(): string;

class Cat extends Animal {
	speak(): string {
		return "meow";

class Dog extends Animal {
	speak(): string {
		return "bark";

// can't make an abstract Animal
// const myAnimal = new Animal();
const myCat = new Cat();


Now you could make a function that generically takes any type of Animal as an argument.

function feedAnimal(animal: Animal): string {
	return "thanks for the food! " + animal.speak(); 


Similarly, let's translate this to Elm.

animalSpeak : Animal -> string
animalSpeak animal =
    case animal of
        Cat ->

        Dog ->
feedAnimal : Animal -> string
feedAnimal animal =
    "thanks for the food! " ++ animalSpeak(animal)

Why are they useful?

When working on a new feature or a refactor with a strongly typed language I will often start by changing the data structures and then let the compiler tell me where my code fails to compile. When my code compiles again my job is mostly done.

You can do this by leveraging classes and using them as types but it is a lot easier and compact to have a robust type system built into the language. There is usually a lot of boiler code needed to get some better type safety in languages like Java or TypeScript. See this stackoverflow question.

Animal Names

Since there are no classes or member variables in a language like Elm we use records instead.

type alias AnimalRecord =
    { type_ : Animal
    , name : String

felix = AnimalRecord Cat "Felix"

When I write TypeScript I actually prefer using interfaces instead of defining classes. The reason for this preference is that I like to separate the structure of the data from the operations on that data.

I will, in fact, claim that the difference between a bad programmer and a good one is whether he considers his code or his data structures more important. Bad programmers worry about the code. Good programmers worry about data structures and their relationships.

So it would look like this:

interface AnimalRecord {
    type_ : Animal;
    name : string;

const felix : AnimalRecord = {
    type_: new Cat(),
    name : "Felix",


One core idea of functional programming is immutability. You can get more immutability in TypeScript by declaring class members or interfaces as immutable.

An example with error handling

I wrote about this in another post Exceptions considered harmful.

Let's use the Either type from purify-ts to deal with errors in our code. The TypeScript compiler can help us if we give it the right information.

Below is the type signature for Either (almost). See Neverthrow's Result type signature is a bit easier to read but has less functionality.

type Either<E, T> = Left<E, T> | Right<T, E>

An Either can be one of Left which holds the error or it can be Right which holds the successful return value.

// might be one of an Error or a result string
function getUsernameFromDB(id : number) : Either<Error, string> {
    const username : string;
    const error : Error;
    try {
        username = DB.getUserById(id);
    } catch(e) {
        error = e;

    if (error) {
        return Left(error); // error values are always Left
    } else {
        return Right(username); // Right is "right" or the correct value
    // could use Either.encase instead
    // see
    // return Either.encase(() => DB.getUserByID(id));

const result = getUsernameFromDB(1);
// now the compiler forces you to deal with the error
    Left: error => error.toString(),
    Right: value => value,

Here are the docs of caseOf statements for

When I first encountered ADT in Elm it looked so foreign. Once I got used to them I wished that every language I used had them. The compiler now becomes your best friend.

You can get fancier with TypeScript that I did in this post to get something closer to Elms ADTs using union types. See TypeScript also has type guards that aid in handling these types.