Algebraic Data Types & Typescript

Algebraic data types are a way of representing data by combining simple types using algebraic operations. There are two main kinds of algebraic types: product types and sum types. Discriminated unions are a specific implementation of sum types.

Product types (AND types)

Product types represent a combination of types.

type Shirt = {
    size: string
    sleeveLength: string
    shape: string
}

Sum types (OR types)

Sum types represent a choice between types.

type ShirtSize = "S" | "M" | "L" | "XL" | "XXL"
type SleeveLength = "Short" | "Long"

Compose

Compose small types from other small types.

type SleeveLength = "Short" | "Long"

type Shirt = {
    size: "S" | "M" | "L" | "XL" | "XXL"
    sleeveLength: SleeveLength
    shape: string
}

Pattern Matching

It's possible by adding a "kind" field to the product type.

type SleeveLength = "Short" | "Long"

type Shirt = {
    kind: "Shirt"
    size: "S" | "M" | "L" | "XL" | "XXL"
    sleeveLength: SleeveLength
    shape: string
}

type Jean = {
    kind: "Jean"
    hipSize: number
    legSize: number
    ...
}

type Clothing = Shirt | Jean

const clothing: Clothing = {
    kind: "Shirt",
    size: "L",
    sleeveLength: "Short",
    shape: "Straight",
}

const describeClothing = (clothing: Clothing) => {
    switch (clothing.kind) {
        case "Shirt": return "This is a shirt!"
        case "Jean": return "This is a jean!"
    }
}

You can go further by adding sections to kinds in order to combine Clothing and Shoes.

• kind: "Clothing/Shirt"
• kind: "Clothing/Jean"
• kind: "Shoes/Sneakers"
• kind: "Shoes/Boots"

type Product = {
    id: number
    price: Price
    item: Clothing | Shoes
}

OpenAPI

In OpenAPI specification, sum types are represented by oneOf.

Clothing:
  oneOf:
    - $ref: "#/components/schemas/Shirt"
    - $ref: "#/components/schemas/Jean"
  discriminator:
    propertyName: kind
    mapping:
      Shirt: "#/components/schemas/Shirt"
      Jean: "#/components/schemas/Jean"