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
--
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