type MongoFilter<T> = $and<T> | $or<T> | propertyRule<T>;

type logical<T> = $and<T> | $or<T>;

type $and<T> = { $and: Array<logical<T> | propertyRule<T>> }
type $or<T> = { $or: Array<logical<T> | propertyRule<T>> }

type propertyRule<T> = {
  [P in keyof T]?: T[P] | comparison<T[P]>
}

type comparison<V> = $eq<V> | $gt | $lt;

type $eq<V> = { $eq: V };
type $gt = { $gt: number };
type $lt = { $lt: number };

// See if MongoFilter works:
interface Person {
  id: number;
  name: string;
  age: number;
}

// should compile
let f1: MongoFilter<Person> = { $or: [{ id: 1 }, { name: 'dima' }] };
let f2: MongoFilter<Person> = { $and: [{ id: 1 }] };
let f3: MongoFilter<Person> = { id: 1 };

// should not compile
let w1: MongoFilter<Person> = { wrong: 1 }; // does not compile - good
let w2: MongoFilter<Person> = { $or: [{ wrong: 1 }] }; // compiles

let w1: MongoFilter<Person> = { $or: [{ wrong: 1 }] };