Why does function overload fix type-narrowing issue?

Question

I have encountered an issue which basically involves narrowing the type returned from an object, accessed by its key. Let's say I have this an object whose values can be either number or string:

type Value = number | string;

enum DatumKey {
  numberDatum = 'numberDatum',
  stringDatum = 'stringDatum',
}

class DemoClass {
  private data = {
    [DatumKey.numberDatum]: 1337,
    [DatumKey.stringDatum]: 'foobar',
  }

  public getValue(key: DatumKey): Value {
    return this.data[key];
  }

  public doSomething(): void {
    const num: number = this.getValue(DatumKey.numberDatum); // TS expects `number | string`, I expect `number`
    const str: string = this.getValue(DatumKey.stringDatum); // TS expects `number | string`, I expect `string`

    console.log({ num, str });
  }
}

const dc = new DemoClass();
dc.doSomething();

See Typescript Playground example.

---

Failed approach

So, in order to narrow the type, I have attempted to use a generic type, and I can then tell getValue<...>() what kind of type am I expecting in return:

public getValue<T extends Value>(key: DatumKey): T {
  // Error here: Type 'Value' not assignable to type 'T'
  return this.data[key];
}

public doSomething(): void {
  const num: number = this.getValue<number>(DatumKey.numberDatum); // TS expects `number`, it's good!
  const str: string = this.getValue<string>(DatumKey.stringDatum); // TS expects `string`, it's good!
}

However, by doing so, I get an error from TypeScript:

Type 'Value' is not assignable to type 'T'.
  'Value' is assignable to the constraint of type 'T', but 'T' could be instantiated with a different subtype of constraint '{}'.
    Type 'string' is not assignable to type 'T'.
      'string' is assignable to the constraint of type 'T', but 'T' could be instantiated with a different subtype of constraint '{}'.

See Typescript Playground example.

---

Working approach

Then I came across a similar question here, which suggested that the use of function overloads to fix the issue. It does. However, I am not sure why does a function overload fix the issue:

public getValue<T extends Value>(key: DatumKey): T 
public getValue(key: DatumKey): Value {
  return this.data[key];
}

public doSomething(): void {
  const num = this.getValue<number>(DatumKey.numberDatum); // TS expects `number`, it's good!
  const str = this.getValue<string>(DatumKey.stringDatum); // TS expects `string`, it's good!
}

See Typescript Playground example.

Answer 1

Your working solution does not really works. Variables num and str are typed as Value not as respectively number and string.

A more robust solution:

enum DatumKey {
  numberDatum = 'numberDatum',
  stringDatum = 'stringDatum',
}

const data = {
  [DatumKey.numberDatum]: 1337,
  [DatumKey.stringDatum]: 'foobar',
};

function getValue<T extends keyof typeof data>(key: T): (typeof data)[T] {
  return data[key];
}

// You don't have to explicitly type num and str. They are automatically inferred 
const num = getValue(DatumKey.numberDatum);
const str = getValue(DatumKey.stringDatum);