mgeier / arts

Arithmetic in Rust's Type System

Arithmetic in Rust's Type System

Based on some basic ideas from math, we use deeply nested genenics to represent numbers and then apply traits like functions to do arithmetic! Here's how we'd multiply two numbers:

trait Mul {
    type Product;
}

impl<T> Mul for (T, Zero) {
    type Product = Zero;
}

impl<T> Mul for (Zero, Succ<T>) {
    type Product = Zero;
}

impl<T, U> Mul for (Succ<T>, Succ<U>)
where
    (T, Succ<U>): Mul,
    (Succ<U>, <(T, Succ<U>) as Mul>::Product): Add,
{
    // x * y = x + (x - 1) * y
    type Product = <(Succ<U>, <(T, Succ<U>) as Mul>::Product) as Add>::Sum;
}

Then doing <(encode!(***), encode!(****)) as Mul>::Product::VALUE would give the actual integer 12, even though everything in the previous expression is a type!

Here's a blog post that explains it in much more detail: Doing First Grade Math in Rust's Type System

License

This project (more like formula sheet) is licensed under the GNU General Public License v3.0, because math is for everyone.