TS Type-level Fizzbuzz

typelevel-fizzbuzz.ts

type Count<A, S extends 0[] = []> = A extends S["length"]
  ? S
  : Count<A, [...S, 0]>;

type IncC<A> = [...Count<A>, 0];
type DecC<A> = Count<A> extends [infer _H, ...(infer R)] ? R : [];

// Basic Arithmetic
type Inc<A> = IncC<A>["length"]; 
type Dec<A> = DecC<A>["length"];

type Add<A, B> = B extends 0 ? A : Add<Inc<A>, Dec<B>>;
type Sub<A, B> = B extends 0 ? A : Sub<Dec<A>, Dec<B>>;
type Mul<A, B, R = 0> = B extends 0 ? R : Mul<A, Dec<B>, Add<R, A>>;
type Div_<A, B, R = 0> = A extends 0 ? R : Div_<Sub<A, B>, B, Inc<R>>;
type Div<A, B> = Mul<B, Div_<A, B>> extends A
  ? Div_<A, B> 
  : Dec<Div_<A, B>>; 
type Mod<A, B> = Sub<A, Mul<B, Div<A, B>>>;

// Logical operators
type Equal<A, B> = A extends B ? B extends A ? true : false : false;
type And<A, B> = A extends true ? B extends true ? true : false : false;
type Or<A, B> = A extends true 
  ? true 
  : (B extends true ? true : false);

// Fizzbuzzin'
type Mod5<A> = Equal<0, Mod<A, 5>> extends true ? true : false;
type Mod3<A> = Equal<0, Mod<A, 3>> extends true ? true : false;
type Mod15<A> = And<Mod5<A>, Mod3<A>> extends true ? true : false;

type NumberToFizzBuzz<N> = Mod15<N> extends true 
  ? "fizzbuzz" 
  : (Mod5<N> extends true 
      ? "buzz" 
      : (Mod3<N> extends true 
          ? "fizz" 
          : N));

type FizzBuzzTo<N, R extends any[] = []> = N extends 0 
  ? R 
  : FizzBuzzTo<Dec<N>, [NumberToFizzBuzz<N>, ...R]>

type FizzBuzz = FizzBuzzTo<29>; // breaks after 29, foiled by the type instantiation limit