Feat: infer parameter types for the implementation signature of an overloaded method

Suggestion

implicitly infer parameter types for the implementation signature of an overloaded method
This issue is a complement to #7763, #34319

🔍 Search Terms

TypeScript interface with multiple signatures;
infer params from different signatures;
implementation signature of an overloaded method;

✅ Viability Checklist

My suggestion meets these guidelines:

• This wouldn't be a breaking change in existing TypeScript/JavaScript code
• This wouldn't change the runtime behavior of existing JavaScript code
• This could be implemented without emitting different JS based on the types of the expressions
• This isn't a runtime feature (e.g. library functionality, non-ECMAScript syntax with JavaScript output, new syntax sugar for JS, etc.)
• This feature would agree with the rest of TypeScript's Design Goals.

⭐ Suggestion

Add an implicit inference to the params or restricted inference in some cases

📃 Motivating Example

Before, you can achieve simple

class Some {
  async request(action: 'auth', payload: AuthPayload): Promise<AuthResponse>
  async request(action: 'pub', payload: PubPayload): Promise<PubResponse>
  async request<S extends Values<SignalingRequests>>(
    ...params: Parameters<S>
  ): Promise<ReturnType<S>> {
    const [action, payload] = params
    switch (action) { /* ... */ }
  }
}
// redundant declarations
// declare Values<T> = T[keyof T]
declare type SignalingRequests = {
  auth: (action: 'auth', payload: AuthPayload) => AuthResponse
  pub: (action: 'pub', payload: PubPayload) => PubResponse
  // ...
}

Now you can use

class Some {
  async request(action: 'auth', payload: AuthPayload): Promise<AuthResponse>
  async request(action: 'pub', payload: PubPayload): Promise<PubResponse>
  async request(...params) {
    if (params[0] == 'auth') {
      const p: AuthPayload = params[1] // this works
    }
    // or you can write:
    const [action, payload] = params
    switch (action) {
      case 'auth':
        payload // AuthPayload
        break
      case 'pub':
        break
      default:
        // exhaustive check
        const nope: never = action
        throw 'nope'
    }
  }
}

💻 Use Cases

Prevent complex type annotation workarounds, simplify codes, make TypeScript sound again!

Best regards.

Beginne mit den motivierenden Beispielen für überladene Methoden in diesem Issue und lies dann die verwandten Issues #7763 und #34319. Bestimme die beabsichtigten Inferenzregeln für Implementierungsparameter und wie sich Narrowing über Overloads hinweg verhalten sollte; abgeschlossen ist die Aufgabe, wenn das Verhalten ausreichend genau spezifiziert ist, um die Implementierung und Tests anzuleiten.