RE: I'm a bit lost Re: Meaning of decorations
Hi Baker,
The two main points I hope people will take time to consider before voting
on Motion 42:
-- P1788 should add EIN to the decoration system
-- While I believe Empty must remain a valid mathematical object of
the standard, define Empty to be not an element of overline-IR; so it would
no longer be necessary to distinguish NaI from Empty as two different
mathematical objects, ideas or concepts.
I am quite worried P1788 is becoming too unnecessarily complex (e.g., treat
constructors differently than out of domain evaluations, attempt to define
NaI and Empty as two separate mathematical objects with different
properties, etc.), while at the same time I see features and capabilities of
P1788 are vanishing (e.g., no decorated intersection or convex hull
operation, buggy compressed interval arithmetic, etc.).
In my view, all of these concerns and issues are fixed by adding the EIN
decoration and also by defining Empty not to be an element of overline-IR.
Nate
> -----Original Message-----
> From: stds-1788@xxxxxxxx [mailto:stds-1788@xxxxxxxx] On Behalf Of Ralph
Baker
> Kearfott
> Sent: Sunday, January 13, 2013 12:16 PM
> To: nh@xxxxxxxxxxxxxxxxx
> Cc: 'John Pryce'; 'Jürgen Wolff von Gudenberg'; 'Michel Hack'; 'stds-1788'
> Subject: I'm a bit lost Re: Meaning of decorations
>
> Nate, Jürgen, John, P-1788,
>
> I'm getting a bit lost by some of this, in the sense that
> I am missing the implications with regard to particular
> parts of the document we are collectively crafting.
> Furthermore, I am bothered by lack of a reference implementation
> (or, since we don't have a standard yet, a testbed implementation),
> or have I also missed this? My feeling is we need a bit
> more formality here to be able to progress. Hopefully, we
> can do so by moving actual text (rather than more position
> papers), due to our time constraints.
>
> Does someone wish to clarify or contribute?
>
> Baker
>
> On 01/12/2013 04:38 PM, Nathan T. Hayes wrote:
> > John Pryce wrote:
> >>>> I think "Hmm" on this one. What does "any defined and continuous
(dac)
> > interval
> >> range
> >>>> of floor([0,6])" mean? The only meaning I can see is "since floor()
> > isn't dac on the
> >>>> input [0,6], such a range doesn't exist; and if we insist on treating
> > this nonexistent
> >>>> thing as a set, it must be the empty set".
> >>> That is exactly my view... so why the "Hmmm"?
> >>
> >> Precisely because I think the argument I stated above, with which you
are
> > agreeing,
> >> makes no sense.
> >> Above, a certain kind of set does not exist: that is, the class of sets
> > having a certain
> >> property P is empty. You are arguing from that that you can take the
empty
> > set as
> >> being a set that has property P.
> >
> > No.
> >
> > Decorations describe a property that is true about the evaluation of a
> > function over an interval box.
> >
> > Two examples:
> >
> > sqrt(Empty) = Empty (1)
> > sqrt([-4,-1]) = Empty (2)
> >
> > Both (1) and (2) are Empty, but the Empty result is obtained for
different
> > reasons:
> >
> > -- in (1), the restriction of sqrt to Empty is defined and
> > continuous (DAC), but the result is Empty because the input was Empty;
and
> >
> > -- in (2), the restriction of sqrt to [-4,-1] is not defined (NDF)
> > so the result is Empty even though the input was nonempty.
> >
> > Decorations describe a property that is true about the evaluation of a
> > function over an interval box:
> >
> > -- (Empty,DAC) is a property that is true about evaluation of (1)
> >
> > -- (Empty,NDF) is a property that is true about evaluation of (2)
> >
> > Nate
> >
>
>
> --
>
> ---------------------------------------------------------------
> Ralph Baker Kearfott, rbk@xxxxxxxxxxxxx (337) 482-5346 (fax)
> (337) 482-5270 (work) (337) 993-1827 (home)
> URL: http://interval.louisiana.edu/kearfott.html
> Department of Mathematics, University of Louisiana at Lafayette
> (Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
> Box 4-1010, Lafayette, LA 70504-1010, USA
> ---------------------------------------------------------------