curry.ts

function add2(a: number, b: number) {
  return a + b;
}

function add4(a: number, b: number, c: number, d: number) {
    return a + b + c + d;
}

function concat(a: string, b: string) {
  return (a + b).length;
}

function slice<T>(arr: T[], from: number) {
  return arr.slice(from);
}

type AddOne<T extends number> = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13][T];
type Arity<F extends (...args: any) => any> = Parameters<F> extends {
  length: infer R;
}
  ? R
  : never;

type CurriedFunction<
  F extends (...args: any) => any,
  From extends number = 0
> = Parameters<F>[From] extends undefined
  ? ReturnType<F>
  : (x: Parameters<F>[From]) => CurriedFunction<F, AddOne<From>>;

type CurriedAdd2 = CurriedFunction<typeof add2>;
type CurriedAdd4 = CurriedFunction<typeof add4>;
type CurriedConcat = CurriedFunction<typeof concat>;
type CurriedSlice = CurriedFunction<typeof slice>; // unknown[] :((((((