noImplicitReturnType [Suggestion]

We have noImplicitReturns which is great and helps tick up silly mistakes but it woud great to have noImplicitReturnType as well.

So what would noImplicitReturnType do?
Currently we can write a function like so:

function life () {
    return 42;
}
let x = life(); // Number

So all is great, TypeScript works out the return type nicely for us.

function life (x: boolean) {
    if (x) {
        return 'hi';
    } else {
        return 42;
    }
}
let y = life(true); // Number / String

This is where things start to go a little crazy. TypeScript records y as of type number | string which is of course acurate. But what if i wanted this function to only return strings?

We already have support for that with limited modifications

function life (x: boolean): string {
    if (x) {
        return 'hi';
    } else {
        return 42; // Type '42' is not assignable to type 'string'.
    }
}
let y = life(true);

And as a result TypeScript nicly throws an error.

So my suggestion is that in much the same way as with noImplicitAny and let enforcing strict typeing an argument is added in the form of noImplicitReturnType which for my first example (only a single return) wouldn't have any effect but for the second would throw an error instead of typing the function as number | string

Start by comparing the existing noImplicitReturns and noImplicitAny options with the proposed noImplicitReturnType behavior described in the examples. Determine the intended diagnostics for functions whose inferred return type is a union, and define what would count as complete for the new compiler option; the issue names no files or tests.