Discriminating union with generic type

Question

I'm having issues working with discriminated union and generic types.

I have a discriminated union type as follows:

interface A {
  type: 'A',
  payload: string,
}

interface B {
  type: 'B',
  payload: number,
}

type ALL = A | B;

I'd like to write a function that has a return type of the given payload. The problem is that this function doesn't infer the type of payload:

function doStuff <T extends ALL>(input: T): T['payload'] {
  switch (input.type) {
    case 'A':
      // TS2345: Argument of type 'string | number' is not assignable to parameter of type 'number'. Type 'string' is not assignable to type 'number'.
      return processStringPayload(input.payload);
    case 'B':
      // TS2345: Argument of type 'string | number' is not assignable to parameter of type 'number'. Type 'string' is not assignable to type 'number'.
      return processNumberPayload(input.payload);
  }
}

function processStringPayload(payload: string): string {
  return payload;
}

function processNumberPayload(payload: number): number {
  return payload;
}

Additionally, the return type is not respected:

function doStuff <T extends ALL>(input: T): T['payload'] {
  switch (input.type) {
    case 'A':
      // 'A' should only support returning string
      return 123;
    case 'B':
      // 'B' should only support returning number
      return 'some string'
  }
}

Edit: I am having this problem using TS 4.0. As mentioned in the comments, TS 4.3+ has improvements to discriminated unions.