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Re: Reasons (not) to vote Motion 27: NO

On 08/19/2011 12:17 AM, Vincent Lefevre wrote:

On 2011-08-18 17:30:21 +0200, Arnold Neumaier wrote:

One cannot give any useful guarantees for free expressions because
one cannot control the input decorations. They can carry decoration
information from ancient times that are completely irrelevant for the range
calculations.


On the contrary, AFAIK, this is the goal of decorations: to propagate
information from the input to the output.
If you apply the domain operator to the input (as a single vector), everything is alright. But if you have multiple inputs with unknown past, there is not ''the input''. 



Said that, I still don't think that 5.8.5 is correct. Consider:
   * xx and/or yy is Empty (so that the box (xx,yy) is empty).
   * f(x,y) = sqrt(x) + y
One gets:
   * After applying domain on the box (xx,yy), one gets (Empty,emp)
     for both components.


Oops, this is a typo in the text; according to the semantics in (Eval1),
upon which the proof of the FTDIA is based, domain should yield (Empty,ein).


Then this should be OK for bound expressions (but not for free
expressions).
If one deletes the decoration ein (which was not in the original set of decorations anyway, but was added because of prior demand), and uses emp instead, things also work alright for free expressions. 


> IMHO, the decoration system, defined by the specification of the
> individual operations, should be meaningful on free expressions.
> Motion 26 does probably too much by differentiating ein, emp and
> ill (is it really necessary to differentiate them?).
There is no harm in differentiating emp and ill, and it carries useful information.
I don't really care about ein; it was included only because the prior discussion had suggested it should be there. 


Arnold Neumaier