Typescript Union Permutation, count of keys in an object, count of cases in an Union

Permutation.d.ts

/**
 * @example
 * type P = Permutation<1 | 2 | 3>
 * // [1, 2, 3] | [1, 3, 2] | [2, 1, 3] | [2, 3, 1] | [3, 1, 2] | [3, 2, 1]
 */
export type Permutation<U, T = U> = [U] extends [never]
  ? []
  : T extends unknown
  ? [T, ...Permutation<Exclude<U, T>>]
  : never

/**
 * @example
 * type C = UnionCount<'a' | 'b' | 'c'>
 * // 3
 */
export type UnionCount<U> = Permutation<U>['length']

/**
 * @example
 * type C = KeyCount<{ x: 1, y: 2 }>
 * // 2
 */
export type KeyCount<T> = UnionCount<keyof T>