Make all fields in an interface readonly in a nested way

I know that, we can use Readonly< T> to redeclare all fields of T as readonly, as in: [Typescript: extending an interface and redeclaring the existing fields as readonly

What about nested fields? For example:

interface School {
  teachers: Array<Teacher>;
  students: Array<Student>;
}

interface Teacher {
  teacherId: number;
  personInfo: PersonInfo;
}

interface Student {
  studentId: number;
  personInfo: PersonInfo;
}

interface PersonInfo {
  name: string;
  age: number
}

How to create a SchoolReadonly type, in which all nested fields are readonly.

A simple test case:

var s: SchoolReadonly = {
  teachers: [{teacherId: 1, personInfo: {name: "John", age: 40}}],
  students: [{studentId: 1, personInfo: {name: "Dan", age: 20}}]
}

s.teachers[0].personInfo.name = "John2"; //should produce readonly error
s.students[0].personInfo.age = 22; //should produce readonly error

As a constraint, I do not want to add Readonly directly to the School, Teacher, Student and PersonInfo interfaces.

You can use generics and type aliases, it's a lot of code, but it will do the trick:

interface School<T extends Teacher<PersonInfo>, S extends Student<PersonInfo>> {
    teachers: Array<T>;
    students: Array<S>;
}

type EditableSchool = School<EditableTeacher, EditableStudent>;
type ReadonlySchool = Readonly<School<ReadonlyTeacher, ReadonlyStudent>>;

interface Teacher<P extends PersonInfo> {
    teacherId: number;
    personInfo: P;
}

type EditableTeacher = Teacher<PersonInfo>;
type ReadonlyTeacher = Readonly<Teacher<Readonly<PersonInfo>>>;

interface Student<P extends PersonInfo> {
    studentId: number;
    personInfo: P;
}

type EditableStudent = Student<PersonInfo>;
type ReadonlyStudent = Readonly<Student<Readonly<PersonInfo>>>;

interface PersonInfo {
    name: string;
    age: number
}

var s: ReadonlySchool = {
  teachers: [{teacherId: 1, personInfo: {name: "John", age: 40}}],
  students: [{studentId: 1, personInfo: {name: "Dan", age: 20}}]
}

s.teachers = null;
s.teachers[0].personInfo.name = "John2"; // Cannot assign to 'name' because it is a constant or a read-only property
s.students[0].personInfo.age = 22; // Cannot assign to 'age' because it is a constant or a read-only property

(code in playground)

---

Edit

If you want s.teachers[0] = nul to fail then you need to also change the Array to ReadonlyArray, so:

interface School<T extends Teacher<PersonInfo>, Ta extends ArrayLike<T>, S extends Student<PersonInfo>, Ts extends ArrayLike<S>> {
    teachers: Ta;
    students: Ts;
}

type EditableSchool = School<EditableTeacher, Array<EditableTeacher>, EditableStudent, Array<EditableStudent>>;
type ReadonlySchool = Readonly<School<ReadonlyTeacher, ReadonlyArray<ReadonlyTeacher>, ReadonlyStudent, ReadonlyArray<ReadonlyStudent>>>;

The rest is the same, but then:

s.teachers = null; // Cannot assign to 'teachers' because it is a constant or a read-only property
s.teachers[0] = null; // Index signature in type 'ReadonlyArray<Readonly<Teacher<Readonly<PersonInfo>>>>' only permits reading

True, it's not a simple solution and is very verbose, but I don't think that a simple generic solution exists, at least for now, for the problem.
Consider:

type ReadyonlyDeep<T> = {
    readonly [P in keyof T]: ReadyonlyDeep<T[P]>;
}

This works great as long as the object has only other simple objects:

interface A {
    b: B
}

interface B {
    str: string;
}

let a: ReadyonlyDeep<A>;
a.b.str = "fe"; // Cannot assign to 'str' because it is a constant or a read-only property

But if you introduce an array:

interface B {
    str: string;
    moreB: B[];
}

Then:

a.b.moreB = []; // Cannot assign to 'moreB' because it is a constant or a read-only property
a.b.moreB[0].str = "hey"; // this is fine though

It probably isn't an easy problem to solve.