Definite or indefinite article for non-singletons?

[Peter Otten]

Chris Angelico wrote:

> When talking about indistinguishable objects, is it correct to talk
> about "the <x>" or "an <x>"?
> 
> Example:
> 
> def f(s):
>     """Frob a thing.
> 
>     If s is an empty string, frobs all the things.
>     OR
>     If s is the empty string, frobs all the things.
>     """

Slightly OT: 

While I would write "an empty string" but happily accept "the empty string" 
I stumbled upon "all *the* things". Shouldn't it be "all things"?

Real question as I'm not a native speaker.