What does ^parents really tell you?

[Joseph Brenner]

If you look at the type diagram:

  https://docs.perl6.org/type/Str#___top

You can see that:
   Str is Cool is Any is Mu

But if you use the ^parents method on a string, you don't get
"Cool", instead you get "()":

   my $stringy = "abc";
   say $stringy.^name;      # Str
   say $stringy.^parents;   # ()

   say (Str).^parents;      # ()

So what exactly does ^parents tell you about?
Is there some other method you could use to trace the chain
of ancestors upwards?