Daniel Duan

Swift Algebraic Data Types

The Basics

Algebraic Data Type is a fancy name for “a type creaded by combining other types” in programming languages. One aspect of the “algebraic-ness” is how many potential new values there are for the new type, given a set of type as its building block.

To better illustrate this, consider the following example in Swift.

enum StarkChild { case Rickon, Bran, Arya, Sansa, Robb, Jon }

enum Direwolf { case Shaggydog, Summer, Nymeria, Lady, Greywind, Ghost }

enum Actor {
    case Wolf(Direwolf)
    case Person(StarkChild)

struct Parters {
    var wolf: Direwolf
    var person: StarkChild

StarkChild and Direwolf each has 6 potential values. Combining them, we get two new types.

Question: how many potentiol values are there for Actor? How many for Parters?

An Actor can be either a StarkChild or a DireWolf, therefore it has `6

A Partners requires us to select one value from Child and one from DireWolf, resulting in 6 * 6 = 36 potential values – the product of Child’s and DireWolf’s values.

Actor, an enum, is a sum type. Parters, a struct, is a product type. Here, Parters could easily be defined as a class or a tuple and remain a product type. Because we can create product or sum types in these direct ways, we can say Swift has first class support for Algebraic Data Types.

The Crossovers

However, the story doesn’t stop here. In Swift, an enum’s option can have multiple values. If it happens to be the only option, then this enumeffectively becomes a product type:

// there are 6 * 6 = 36 potential values for Parters
enum Parters {
    case Value(wolf: DireWolf, person: StarkChild)

Incidentally, this makes enum similar to data in Haskell, where product and sum types can be created with a unified construct – data.

In C and C++, unions are the closest thing to sum types. However, union is hardly used to combine arbitrary types due to its lack of associated values. What do people do in need of sum types? They make do with product types. Here’s one way to achive that in Swift:

// Actor.value can have only 6 + 6 = 12 potential values thanks to
// manual enforcement
class Actor {
    var child: StarkChild?
    var wolf: Direwolf?

    var value: Any {
        get {
            return child == nil ? wolf! : child!
        set(newValue) {
            if newValue is StarkChild {
                child = (newValue as! StarkChild)
                wolf = nil
            if newValue is Direwolf {
                wolf = (newValue as! Direwolf)
                child = nil

    init(wolf: Direwolf) {
        self.wolf = wolf
    init(child: StarkChild) {
        self.child = child
    init() {
        fatalError("must initialize with a child or a wolf")

It’s… ugly.

Recursion Types

Besides sum and product, another common class of algebraic type is recursion types. The interesting bit here is that Swift struggles to support it. In WWDC 2015, it was announced that enums can be defined recursively in Swift 2:

enum Tree {
    case Empty
    indirect case Node(Tree, Tree)

As of this writing, Xcode 7 beta 3 has not delivered this feature yet. Also, it’s a good bet that indirect is not going to be available in tuple aliases, such as:

typealias Node = (indirect Node, indirect Node)

I hope this is on the Swift team’s (understandably) gigantic todo list 😉.