Re: Is T an ancestor of T?

[Georg Bauhaus <sb463ba@l1-hrz.uni-duisburg.de>]

Bj�rn Persson <spam-away@nowhere.nil> wrote:
: Georg Bauhaus wrote:

: 
: Then I'd say "ancestor" is also clearly defined: "If a type T2 is a 
: descendant of a type T1, then T1 is called an ancestor of T2." So if T 
: is a descendant of T, then T is an ancestor of T.
: 

So far so good. As a tree has a root at one and and 
trees at the other ends (so there is no end)
the definition cannot be mirrored so to speak.

:> However,
:> "The ultimate ancestor of a type is the
:>  ancestor of the type that is not a descendant of any other type."
: 
: The one ancestor that isn't a descendant of any type other than itself, 
: that is, the one that isn't derived, is the ultimate ancestor. At least 
: that's how I read that.

Yes, I think that too, but I don't see it in either in the RM nor in the
AARM sentences you quoted. (Which of course means I must be missing
something.)

: 10.b
: A specific type is an ancestor of itself.

o.K.

: 10.c
: Discussion: The terms root, parent, ancestor, and ultimate ancestor are 
: all related. For example:
: 
: 10.d
:     * Each type has at most one parent, and one or more ancestor types; 
: each type has exactly one ultimate ancestor.

So we know there is exactly one ultimate ancestor for each type T.
If T is at the root of a derivation hierarchy of height 0,
is there a named type that is the ultimate ancestor of T?
Is it T? By 10.d I would say yes. By the last sentence of (10),
the ultimate ancestor (T) "is not a descendant of any other type".
So if T is the ultimate ancestor, it is not a descendant of T.
Which it is by the first sentence of (10).
I must be missing something. Specific types?

Then if D is new T with ..., is T the ultimate ancestor of D?
(Again I would agree that it is.)

If T is the ultimate ancestor of T (and T is the ultimate
ancestor of D if D had been defined), can GNAT be right when
(T with n => 0) is accepted as an extension aggregate of specific
type T? I still don't think so.

 (type T is tagged record
     n: Natural;
  end record;)