Re: Friendly amendment to Motion 25
> From: "Nate Hayes" <nh@xxxxxxxxxxxxxxxxx>
> To: "Dan Zuras Intervals" <intervals08@xxxxxxxxxxxxxx>
> Subject: Re: Friendly amendment to Motion 25
> Date: Sat, 28 May 2011 18:25:23 -0500
>
> Dan Zuras wrote:
> > In section 2.4 you state that the domain for min & max shall
> > be the same as for add. Indeed, I am fairly sure that the
> > domain for min & max must be strictly LARGER than that for
> > add. Min & max must be defined for empty operands & non-
> > empty results whereas add is not. That is, min & max of a
> > non-empty operand together with an empty operand must be the
> > non-empty operand. So min & max return results in a domain
> > where add would return empty. Min & max of both empty
> > operands is empty just as it is in add. I'll leave it to
> > your sense of parsimony of definition to decide whether that
> > case is outside the domain of min & max or inside it &
> > defined to be empty.
>
> Hi Dan,
>
> I understand what you are speaking about.
>
> >From discussions I've witnessed between you and Nick, I gather that in IEEE
> 754 the correctness of such a result is topic of a longstanding debate. I'm
> not taking sides as it pertains to IEEE 754. In regards to IEEE 1788,
> though, this would certainly lead to failure of certain important interval
> algorithms. So just to be clear: the description given in Motion 25 is
> really designed to ensure the result of interval min and max is empty if at
> least one operand is empty, just as it is for addition.
I understand but disagree.
Still, that might not be a problem. Given that it has
no relation to the rest of your motion, may I suggest you
remove references to min & max so that we may have this
discussion at some later date & avoid needless conflict
with the rest of your motion.
>
>
> >
> > You make no mention of it but it must be true that union &
> > intersection also differ from add in their domains of
> > validity.
>
> Yes. The motion text specifically does not mention intersection and union,
> though. I thought this should probably be in a future motion.
Agreed. So should it be with min & max.
>
>
> > And we still have no decoration for 'ill'.
>
> Yes. The motion is a Level 1 document. Given the Level 1 model P1788 is
> currently embracing, there is no operation or result that can be ill-formed
> (that I'm aware of). This observation actually comes from Dominique. Clearly
> when we get to Level 3 and Level 4 we will need to re-introduce ill-formed
> somehow. However, I think its wise to finish the Level 1 model before
> attempting to do this (let us walk before we run).
This is a reasonable approach which I accept.
>
> I suppose some of these answers may or may not be to your liking, but I hope
> at least I've provided some clarity.
>
> Sincerely,
>
> Nate
You have now & I accept your approach so far as it goes.
I would still like to see the table in section 3 filled
out with examples. As it is, there is much that is
non-obvious if not incorrect.
I'm am still troubled by the lack of the subset property
& its obvious effect on our proof of the FTDIA. So far
as I know this property is necessary for FTDIA to be true
much less provable.
You mention some approach in section 3.3 that suggests
the subset property might NOT be necessary in that you
know of some other property that suffices.
Since I cannot scrutinise what I cannot see, can you
at least outline this new result for us?
Pulling out max & min & outlining how the FTDIA proof
might go without the subset property being true might
go a long way to eliminating the controversy of this
motion & getting it passed.
IMHO, of course.
Dan
P.S. - BTW, & this is just a nit, I would rename the
decoration numbers D4,...,D0 to D0,...,D4. That way
the subset property would be in the 'same direction'
conceptually as the decoration property. I find it
is difficult to reverse the sense of the relation in
my head. But it is just a pedagogical point & may
have no meaning at all if you find you can eliminate
the need for property ordering to prove the FTDIA.