# Algebraic Data Types — Functional Programming Concepts

Source: https://www.geekswithgeeks.com/en/functional-programming/ty-adt

> Sum and product types, discriminated unions in TypeScript.

## AND types and OR types

A **product type** combines several values at once: a record or tuple such as `{ x: number; y: number }` holds an x **and** a y. A **sum type** is exactly one of several alternatives: a shape is a circle **or** a rectangle. Together they are **algebraic data types** (ADTs). Haskell, Rust, OCaml and Kotlin (sealed classes) have them built in. TypeScript models sum types as **discriminated unions**: each variant has a literal tag field such as `kind`, and the compiler narrows the type when you check it. ADTs let you make illegal states unrepresentable, for example a request that cannot be both loading and failed.

## Making illegal states unrepresentable

Algebraic data types, pattern matching and Option/Result types model data precisely and force every case to be handled.

![Three ideas: sum and product types, exhaustive matching, Option and Result.](assets/figures/functional-programming/section-6-map.svg) — Figure 6.1 — Types, matching and explicit absence or failure.

## Replacing flags with a union

Booleans allow impossible combinations; a union does not.

```typescript
// Before: 2 x 2 x optional fields allows nonsense states
type RequestStateLoose = {
  loading: boolean;
  error?: string;
  data?: string[];
};

// After: a sum type of product types
type RequestState =
  | { kind: 'idle' }
  | { kind: 'loading' }
  | { kind: 'failed'; error: string }
  | { kind: 'loaded'; data: string[] };

type Shape =
  | { kind: 'circle'; radius: number }
  | { kind: 'rect'; width: number; height: number };
```

## The same type in Haskell

`data Shape = Circle Double | Rect Double Double` declares a sum type with two constructors; each constructor holds a product of fields.

**Quiz:** What is a sum type?

- [ ] A number type used for addition
- [ ] A record that holds several fields at once
- [x] A value that is exactly one of several tagged alternatives
- [ ] A list of all possible values

*Answer:* A value that is exactly one of several tagged alternatives. Sum = OR, product = AND.