Compute all ordered combinations of a list of values at compile type in TypeScript

CombinationsOf.ts

type Tuple<X, Y> = [X, Y]
type Equal<X, Y> =
  (<T>() => T extends X ? 1 : 2) extends
  (<T>() => T extends Y ? 1 : 2) ? Tuple<true, Y> : Tuple<false, Y>
type Assert<T extends Tuple<true, any>> = T[1];

type AppendToAll<X, A extends Array<Array<any>>, R extends Array<any> = []> = 
  A extends []
  ? R
  : A extends [infer H extends Array<any>, ...infer T extends Array<Array<any>>]
    ? AppendToAll<X, T, [...R, [X, ...H]]>
    : never;

type CombinationsOf<A extends Array<any>> =
  A extends []
  ? [[]]
  : A extends [infer H, ...infer T]
    ? T extends []
      ? [...CombinationsOf<T>, [H]]
      : [...CombinationsOf<T>, ...AppendToAll<H, CombinationsOf<T>>]
    : never

type PermutationsOf<A extends Array<any>, L extends Array<any> = [], R extends Array<any> = []> = 
  A extends []
  ? R extends []
    ? [[]]
    : R
  : A extends [infer H, ...infer T]
    ? PermutationsOf<T, [H, ...L], [...R, ...AppendToAll<H, PermutationsOf<[...L, ...T]>>]>
    : never;

type ToUnionOfAll<A extends Array<any>, R extends any = never> = 
  A extends [] 
  ? R 
  : A extends [infer H, ...infer T] ? ToUnionOfAll<T, H | R> : never;

type PermutationsOfAll<A extends Array<any>, R extends Array<any> = []> =
  A extends []
  ? R
  : A extends [infer H extends Array<any>, ...infer T] 
    ? PermutationsOfAll<T, [...R, ...PermutationsOf<H>]>
    : never;

type CombinationsOfAsUnion<A extends Array<any>> = ToUnionOfAll<PermutationsOfAll<CombinationsOf<A>>>;

export type _ = [
  Assert<Equal<[], CombinationsOfAsUnion<[]>>>,
  Assert<Equal<[] | [1], CombinationsOfAsUnion<[1]>>>,
  Assert<Equal<[] | [1] | [2] | [1, 2] | [2, 1], CombinationsOfAsUnion<[1, 2]>>>,
  Assert<Equal<[] | [1] | [2] | [3] | [1, 2] | [2, 1] | [1, 3] | [2, 3] | [3, 1] | [3, 2] | [1, 2, 3] | [1, 3, 2] | [2, 1, 3] | [2, 3, 1] | [3, 2, 1] | [3, 1, 2], CombinationsOfAsUnion<[1, 2, 3]>>>,
]