Simple calculator made in ts

calculator.ts

type Reverse<A> =
  `${A}` extends `${infer AH}${infer AT}`
    ? `${Reverse<AT>}${AH}` : A

type Digs = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
type DigsNext<I = Digs, R = {}> =
  I extends [infer Head, infer Next, ...infer Tail]
    ? DigsNext<[Next, ...Tail], R & Record<Head, Next>>
    : { [K in keyof R]: R[K] }
type DigsPrev = { [K in keyof DigsNext as DigsNext[K]]: K }
type ToNumber<
  S extends string,
  L extends number[] = []>
  = `${L['length']}` extends S
  ? L['length']
  : ToNumber<S, [...L, 0]>

type GreaterThan<
  T extends number,
  U extends number,
  C extends unknown[] = []
  > =
  T extends U
    ? false
    : C['length'] extends T
      ? false
      : C['length'] extends U
        ? true
        : GreaterThan<T, U, [...C, 1]>;
type AddOne<A> =
  A extends `${infer AH}${infer AT}`
    ? AH extends '9' ? `0${AddOne<AT>}` : `${DigsNext[AH]}${AT}`
    : `1`
type SubOne<A> =
  A extends `${infer AH}${infer AT}`
    ? AH extends '0' ? `9${SubOne<AT>}` : `${DigsPrev[AH]}${AT}`
    : never
type Sub<
  A extends string,
  B extends string,
  R extends string = "0"
  > =
  B extends R
    ? A
    : Sub<SubOne<A>, B, AddOne<R>>;

type Add<A, B> =
  A extends `${infer AH}${infer AT}` ?
    B extends `${infer BH}${infer BT}`
      ? BH extends '0' ? `${AH}${Add<AT, BT>}` : Add<AddOne<A>, SubOne<B>>
      : A : B
type Mul<A, B, R = '0'> =
  A extends '0' ? R :
    B extends '0' ? R :
      A extends `${infer AH}${infer AT}`
        ? AH extends '0' ? Mul<AT, `0${B}`, R> : Mul<SubOne<A>, B, Add<R, B>>
        : R

type Multiply<A extends string | number | bigint, B extends string | number | bigint> =
  Reverse<Mul<Reverse<A>, Reverse<B>>>

type Division<
  W extends string,
  D extends string,
  Q extends string = '0'
  > =
  W extends '0'
    ? Q
    : Division<Sub<W, D>, D, AddOne<Q>>

type Power<
  V extends string,
  P extends string,
  A extends string = V> =
  P extends '1'
    ? A
    : P extends '0'
      ? '1'
      : Power<V, SubOne<P>, Multiply<V, A>>




// Log<10, 100> = 2
type Log<
  B extends string,
  L extends string,
  I extends string = "0",
  PA extends string = "0"> =
  L extends "1"
    ? "0"
    : L extends PA
      ? I
      : GreaterThan<ToNumber<PA>,ToNumber<L>> extends true
        ? never
        : Log<B, L, AddOne<I>, Power<B, AddOne<I>>>;

const $: Power<'2', '4'> = "16";
const _: Power<'2', '3'> = "8";

type OpDict<A extends string, B extends string>  = {
  'Div': Division<A, B>,
  'Mul': Multiply<A, B>,
  'Sum': Add<A, B>,
  'Sub': Sub<A, B>,
  'Log': Log<A, B>,
  'Pow': Power<A, B>
};

type Calculator
  <Operation extends keyof OpDict<string, string>,
    A extends string = '0',
    B extends string = '0'
    > = OpDict<A, B>[Operation];

const teste: Calculator<'Mul', '2', '2'> // 4
const teste: Calculator<'Mul', '2', '8'> // 16
const teste: Calculator<'Sum', '2', '4'> // 6
const teste: Calculator<'Sub', '9', '4'> // 5