Playing about with arithmetic

Arithmetic.ts

type Count<A, S extends 0[] = []> = A extends S['length'] ? S : Count<A, [...S, 0]>
type Increment<A> = [...Count<A>, 0]['length']
type Decrement<A> = Count<A> extends [infer A, ...infer Rest] ? Rest['length'] : A
type Add<A, B> = [...Count<A>, ...Count<B>]['length']
type Multiply<A, B, S = 0> = B extends 0 ? S : Multiply<A, Decrement<B>, Add<S, A>>
type Power<A, B, S = A> = B extends 1 ? S : Power<A, Decrement<B>, Multiply<S, A>>
type Square<A> = Power<A, 2>
type Cube<A> = Power<A, 3>

type Incremented = Increment<10>
type Decremented = Decrement<5>
type Added = Add<10, 5>
type Multiplied = Multiply<10, 5>
type Squared = Square<2>
type Cubed = Cube<2>
type Power4 = Power<5, 4>