Algebraic data types

Algebraic data types are types created from the combination of other types. They are common in statically types functional programming languages such as Haskell and OCaml. Rust also has algebraic data types in the form of enums and structs.

The main classes of algebraic data types are product types (tuples, records etc) and sum types (enums, tagged unions, disjoint unions etc). Usually, languages with algebraic data types also provide Pattern matching mechanisms to operate on them.

I really like to have algebraic data types. It makes the type system rich enough to encode complex domain knowledge, making it easy to verify program behavior at compile time.

This Rust example shows how to use enums with pattern matching to achieve a polymorphic behavior when calculating the area of a geometric shape.

use std::f32::consts::PI;
 
enum Shape {
    Rectangle { width: u32, height: u32 },
    Circle { radius: u32 },
}
 
impl Shape {
    fn area(&self) -> f32 {
        match self {
            Shape::Circle { radius } => PI * (radius.pow(2) as f32),
            Shape::Rectangle { width, height } => (width * height) as f32,
        }
    }
}