algebraic data types

A common language feature in functional programming languages that allows easily declaring types that are a sum of products.

Examples in various languages:

data Stuff = Foo {_a :: Int, _b :: Bool} | Bar (Maybe Foo)

(* no guarantee this works; I barely remembered OCaml when I wrote this *)
type stuff = foo of (int, bool) | bar of (foo option)

enum Stuff {
  case foo(a: Int, b: Bool)
  case bar(Foo?)
}

```rust
// same as the OCaml, still good enough to demonstrate basic syntax
enum stuff {
  Foo(i32, bool),
  Bar(Box<stuff>)
}

Algebraic data types tend to make it easy to describe data that might come in several different shapes, and also are very good at representing tree like structures.

Essentially they’re a single feature bundling together:

• structs/record types
• coproducts / variants / enums
• recursive (µ) types
• nominative (ν) types

Common object oriented programming languages use a lot of boilerplate when representing ADTs because they represent these as class hierarchies.