Sum numbers, but in the type system!

sum.ts

type SameLenTuple<N extends number, T extends any[] = []> = number extends N
  ? never
  : T["length"] extends N
  ? T
  : SameLenTuple<N, [0, ...T]>;

type ConcatTuples<T1 extends any[], T2 extends any[]> = [...T1, ...T2];

type TupleToLen<T extends any[]> = T["length"];

type Sum<N extends number, M extends number> = [number] extends [N | M]
  ? number
  : TupleToLen<ConcatTuples<SameLenTuple<N>, SameLenTuple<M>>> & number;

type three = Sum<0, 3>; // 3
type five = Sum<2, three>; // 2

type num = Sum<number, 2>; // number