binary tree in typescript type system

binary-tree-type.ts

type Equal<L, R> = L extends R ? true : false;
type GreaterThan<L, R, C extends number[] = []> = L extends R
  ? false
  : C["length"] extends L
  ? false
  : C["length"] extends R
  ? true
  : GreaterThan<L, R, [...C, 1]>;

interface INode<V extends number | null, L, R> {
  left: L;
  right: R;
  value: V;
}

type EmptyNode = INode<null, null, null>;

type N<V extends number, Node = EmptyNode> = Node extends EmptyNode | null
  ? INode<V, null, null>
  : Node extends INode<infer NextV, infer L, infer R>
  ? Equal<V, NextV> extends true
    ? Node
    : GreaterThan<V, NextV> extends true
    ? INode<NextV, N<V, L>, R>
    : INode<NextV, L, N<V, R>>
  : never;

type BinaryTree<T extends number[]> = 
  T extends [infer C, ...(infer R)]
  ? C extends number
    ? R extends []
      ? N<C>
      : R extends number[]
        ? N<C, BinaryTree<R>>
        :never
    : never
  : never

type B = BinaryTree<[10, 4, 3, 5, 4]> // INode<4, INode<5, INode<10, null, null>, null>, INode<3, null, null>>
type A = N<10, N<4, N<3, N<5, N<4>>>>>; // INode<4, INode<5, INode<10, null, null>, null>, INode<3, null, null>>