polymorphic lens in TypeScript 2.8

polylens.ts

/**
 * Gives you an object type compatible with given key type TKey.
 *
 * For example,
 *
 *   type Example = ObjFor<'a'>
 *
 * is expanded to
 *
 *   type Example = {
 *     a: any;
 *   }
 */
type ObjFor<K, T = any> = {
  [P in keyof (K extends keyof infer O ? O : never)]: T
}

type Len<T> = T extends any[] ? T['length'] : never

/**
 * Returns an object type compatible with a given nested key sequence KS.
 *
 * For example,
 *
 *   type ExampleSeq = ObjForSeq<['a', 'b', 'c']>
 *
 * is expanded to
 *
 *   type ExmapleSeq = {
 *     a: {
 *       b: {
 *          c: any;
 *       };
 *     };
 *   }
 */
// @TODO is there a way to do a cons on an array at the type level?
type ObjForSeq<KS extends string[]> = Len<KS> extends 4
  ? ObjFor<KS[0], ObjFor<KS[1], ObjFor<KS[2], ObjFor<KS[3]>>>>
  : Len<KS> extends 3
    ? ObjFor<KS[0], ObjFor<KS[1], ObjFor<KS[2]>>>
    : Len<KS> extends 2
      ? ObjFor<KS[0], ObjFor<KS[1]>>
      : Len<KS> extends 1
        ? ObjFor<KS[0]>
        : never

type PropType<O, K extends keyof O> = O[K]

/**
 * Creates a polymorphic lens that looks at property k of an object.
 *
 * The type of object and the type of property is determined at use site.
 * If the object doesn't have a property K, the lens is incompatible and
 * the usage will not compile.
 */
function key<K extends string>(k: K) {
  return {
    get: <O extends ObjFor<K, PropType<O, K>>>(o: O): PropType<O, K> =>
      o[k],

    set: <O extends ObjFor<K, PropType<O, K>>>(o: O, v: PropType<O, K>): O =>
      Object.assign({}, o, { [k]: v })
  }
}

const example = {
  a: 5,
  b: '6',
  c: { d: false }
}

const a_ = key('a')

const _1: number = a_.get(example)

// Argument of type '{ hello: number; }' is not assignable to parameter of type '{ a: any; }'.
//   Object literal may only specify known properties, and 'hello' does not exist in type '{ a: any; }'.
const _2 = a_.get({ hello: 5 })

const _3: string = a_.get({ a: 'a string' })

const _4: { a: string } = a_.set({ a: 'hello' }, 'hallo')

// Argument of type '"hello"' is not assignable to parameter of type 'number'.
const _5 = a_.set(example, 'hello')

const _6: typeof example = a_.set(example, 6)

const _7: boolean = key('d').get(key('c').get(example))