Re: Equivalent keys/elements in Ada.Containers Maps and Sets

["Adam Beneschan" <adam@irvine.com>]

On Jan 23, 4:43 pm, "Randy Brukardt" <r...@rrsoftware.com> wrote:

> > This function "<" is a strict ordering relation for T, as required for
> > Ada.Containers.Ordered_Maps/Sets. But the "equivalence" relation induced
> > by this "<" is not transitive: X and Y are "equivalent" (both X < Y and
> > Y < X are False) and Y and Z are "equivalent" (both Y < Z and Z < Y are
> > False) but X and Z are not "equivalent" (because X < Z is True).

> I don't believe this function meets the requirements. It has to be the case
> that the function is reversible (we can't know the order of the operands)
> and it can't be the case that
>    neither (X < Z) nor (Z < X) nor (X = Z) (where "=" means equivalent).
>
> One of these three things has to hold, or the function is not acceptable.

This doesn't make sense to me.  "Equivalent" is defined in terms of "<"
(A.18.9(78/2)), and it's defined in such a way that

   neither (X < Z) nor (Z < X) nor (X === Z)

[using === for "equivalent"] will tautologically be true.  Thus, it's
logically impossible to come up with a function "<" that is
"unacceptable" according to the last criterion you state.

As far as I can tell from the wording of the RM (A.18.9(79/2)), the
function "<" that Niklas wrote does indeed meet the requirements: it's
irreflexive (A < A is false for all A), asymmetric (A < B and B < A are
not both true, for all A and B), and transitive (A < B and B < C
implies A < C, for all A, B, and C---because, in this case, there are
no such A, B, and C for which the first two relations hold).  If there
is some other requirement that "<" should meet but doesn't, then that
requirement is missing from the RM.

                          -- Adam