我想在Message和Response子类型之间创建一些抽象关系，这样我就可以有一个通用函数，它将Message作为参数，并返回Response。然而，每当函数被MessageTypeA类型调用时，我希望响应类型为ResponseTypeA，并希望TypeScript以某种方式确保这种关系。考虑以下TypeScript代码来说明问题：

type MessageTypeA = { a: string };
type MessageTypeB = { b: number };
type MessageTypeC = [number, number];

type Message = MessageTypeA | MessageTypeB | MessageTypeC;

type ResponseTypeA = { a: boolean; aa: number };
type ResponseTypeB = "hello" | "bye";
type ResponseTypeC = number;

type Reponse = ResponseTypeA | ResponseTypeB | ResponseTypeC;

type Pair<M extends Message, R extends Reponse> = {
  message: M;
  response: R;
};

// I know this should be some type of Map/Record instead
type ValidPairsMap =
  | Pair<MessageTypeA, ResponseTypeA>
  | Pair<MessageTypeB, ResponseTypeB>
  | Pair<MessageTypeC, ResponseTypeC>;

// Something like this, I know syntax is wrong here:
function sendMessageReturnResponse<T extends ValidPair>(
  message: typeof T.message
): typeof T.response {
  throw "idk how to do this";
}

function main() {
  let mesA: MessageTypeA = { a: "msg" };
  let resA: ResponseTypeA = sendMessageReturnResponse(mesA);
  // error: return value of sendMessageReturnResponse cannot be inferred to be ResponseTypeA
}

我可以做些什么来实现上述目标？