fizzbuzz in typescripts type system

type-golf.ts

// typescript v4.1.3

type _0 = 0;
type Increment<N> = [N, 1];
type Eq<A, B extends A> = true;

type _1 = Increment<_0>;
type _2 = Increment<_1>;
type _3 = Increment<_2>;
type _4 = Increment<_3>;
type _5 = Increment<_4>;
type _6 = Increment<_5>;
type _7 = Increment<_6>;
type _8 = Increment<_7>;
type _9 = Increment<_8>;
type _10 = Increment<_9>;
type _11 = Increment<_10>;
type _12 = Increment<_11>;
type _13 = Increment<_12>;
type _14 = Increment<_13>;
type _15 = Increment<_14>;

type Negative = -1

type Decrement<N>
  = N extends Increment<infer M> ? M
  : Negative;

type Subtract<N, S>
  = S extends _0 ? N
  : Subtract<Decrement<N>, Decrement<S>>;

type IsDivisibleBy<N, D>
  = N extends Negative ? false
  : N extends _0 ? true
  : IsDivisibleBy<Subtract<N, D>, D>;

type And<A, B>
  = A extends false ? false
  : B extends false ? false
  : true;

type IsDivisibleBy3<N> = IsDivisibleBy<N, _3>;
type IsDivisibleBy5<N> = IsDivisibleBy<N, _5>;
type IsDivisibleBy15<N> = And<IsDivisibleBy3<N>, IsDivisibleBy5<N>>;

type FizzBuzzNth<N>
    = IsDivisibleBy15<N> extends true
    ? "FizzBuzz"
    : IsDivisibleBy3<N> extends true
    ? "Fizz"
    : IsDivisibleBy5<N> extends true
    ? "Buzz"
    : N;

type Unshift<A, B extends any[]> = [A, ...B];

type FizzBuzzUpTo<N, O extends any[] = []>
    = N extends _0
    ? O
    : FizzBuzzUpTo<Decrement<N>, Unshift<FizzBuzzNth<N>, O>>;

type test = [
  Eq<
    FizzBuzzUpTo<_15>,
    [
      _1, _2, "Fizz", _4, "Buzz", "Fizz", _7, _8, "Fizz", "Buzz", _11, "Fizz", _13, _14, "FizzBuzz"
    ]
  >
];