How to get literal paths of an object TypeScript

1_all-vertexes-of-tree.ts

// Vertexes = "user" | "user.address" | "user.address.state" | "user.address.city" | "user.phone"
type Vertexes = VertexesOfTree<{
  user: {
    address: {
      state: string,
      city: string
    },
    phone: number
   } }>

export type VertexesOfTree<T extends {}, P extends string = ``> = T extends {
  [K in infer A]: any
}
  ? A extends string
    ? T[A] extends object
      ? `${P}${A}` | VertexesOfTree<T[A], `${P}${A}.`>
      : `${P}${A}`
    : never
  : never;

2_all-vertexes-of-tree-with-support-arrays.ts

/* Vertexes =
  `users` |
  `users[${number}].address` |
  `users[${number}].address.state` |
  `users[${number}].address.city` |
  `users[${number}].address.postcode` |
  `users[${number}].address.postcode.zip` |
  `users[${number}].phone` |
  `users[${number}].friends` |
  `users[${number}].friends[${number}].name`*/
type Vertexes = VertexesOfTree<{
  users: {
    address: {
      state: string;
      city: string;
      postcode: {
        zip: number
      }
    };
    phone: number;
    friends: {
      name: string
    }[]
  }[];
}>;

export type VertexesOfTree<T, P extends string = ``> = T extends any[]
  ? VertexesOfTree<T[number], `${P}[${number}].`>
  : T extends object
  ? T extends { [K in infer A]: any }
    ? A extends string
      ? T[A] extends object
        ? `${P}${A}` | VertexesOfTree<T[A], T[A] extends any[] ? `${P}${A}` : `${P}${A}.`>
        : `${P}${A}`
      : never
    : never
  : never;

3_terminal-vertexes-of-tree.ts

// TerminalVertexes = "user.address.state" | "user.address.city" | "user.phone"
type TerminalVertexes = TerminalVertexesOfTree<{
  user: {
    address: {
      state: string,
      city: string
    },
    phone: number
   } }>

export type TerminalVertexesOfTree<T extends {}, P extends string = ``> = T extends {
  [K in infer A]: any
}
  ? A extends string
    ? T[A] extends object
      ? TerminalVertexesOfTree<T[A], `${P}${A}.`>
      : `${P}${A}`
    : never
  : never;

4_termina-vertexes-of-tree-with-support-arrays.ts

/* TerminalVertexes =
  `users[${number}].address.state` |
  `users[${number}].address.city` |
  `users[${number}].address.postcode.zip` |
  `users[${number}].phone` |
  `users[${number}].friends[${number}].name`*/
type TerminalVertexes = TerminalVertexesOfTree<{
  users: {
    address: {
      state: string;
      city: string;
      postcode: {
        zip: number
      }
    };
    phone: number;
    friends: {
      name: string
    }[]
  }[];

export type TerminalVertexesOfTree<T, P extends string = ``> = T extends any[]
  ? TerminalVertexesOfTree<T[number], `${P}[${number}].`>
  : T extends object
  ? T extends { [K in infer A]: any }
    ? A extends string
      ? T[A] extends object
        ? TerminalVertexesOfTree<T[A], T[A] extends any[] ? `${P}${A}` : `${P}${A}.`>
        : `${P}${A}`
      : never
    : never
  : never;

You can learn more about template literal here: https://www.typescriptlang.org/docs/handbook/2/template-literal-types.html