MergeSort using TypeScript TypeSystem.

MergeSort.ts

type Compare<A extends number, B extends number, X extends any[]=[], Y extends any[]=[]> = X['length'] extends A
  ? Y['length'] extends B ? 0 : -1
  : Y['length'] extends B ? 1 : Compare<A, B, [any, ...X], [any, ...Y]>

type IsLower<A extends number, B extends number> = Compare<A, B> extends -1 ? true : false;
type IsHigher<A extends number, B extends number> = Compare<A, B> extends 1 ? true : false;

type Merge<A extends any[], B extends any[]> = A['length'] extends 0 ? B : (
  B['length'] extends 0 ? A : (
    IsLower<A[0], B[0]> extends true
    ? [A[0], ...Merge<TakeSince<A, 1>, B>]
    : [B[0], ...Merge<A, TakeSince<B, 1>>]
  )
)

type IntegerDivisionByTwo<N extends number, V extends any[] = [], P extends any[]=[]> = IsHigher<[...V, ...V]['length'], N> extends true
  ? P['length'] : IntegerDivisionByTwo<N, [any, ...V], V>;


type TakeUntil<L extends any[], N extends number, V extends any[]=[]> = V['length'] extends N ? V : (
  L extends [x: infer A, ...y: infer B] ? TakeUntil<B, N, [...V, A]> : []
);

type TakeSince<L extends any[], N extends number, V extends any[]=[]> = L extends [x: infer A, ...y: infer B] ? (
  V['length'] extends N ? [A, ...B] : TakeSince<B, N, [A, ...V]>
) : [];

type MergeSort<L extends any[]> = IsLower<L['length'], 2> extends true ? L : (
  IntegerDivisionByTwo<L['length']> extends infer N extends number ? (
    Merge<MergeSort<TakeUntil<L, N>>, MergeSort<TakeSince<L, N>>>
  ) : never
)

type Sort<L extends any[]> = MergeSort<L>;