Re: Motion 42: NO
Guillaume, P1788
On 6 Feb 2013, at 21:07, Guillaume Melquiond wrote:
> - I do not understand why intersectionDec and convexHullDec do not have
> symmetric behaviors with respect to propagating decorations...
I agree with the contradiction Nate has found in these in their present forms.
> - Sections 8.8.2 and 8.8.10 define decorations as both a property of the
> input intervals and the behavior of the function on these inputs. I am
> fine with decorations characterizing the behavior of the function, but
> not with taking inputs into account. More precisely, I feel that def,
> dac, and com, should not require the inputs to be nonempty, and com
> should not require the inputs to be bounded. They should only require
> that input intervals are part of the domain...
One reason for requiring nonempty was to make a tree in the containment
order, as I wrote to Nate:
Motion 42 Kaucher group
trv GAP
/ \ / \
emp def NDF DEF
/ \ | \
ill dac | DAC
\ \ /
com EIN
As I said, I think the tree model will prove easier for users to understand.
As for "com", classical intervals are nonempty & bounded, so those two
conditions are of the essence of recognising common evaluation. Please
explain what you propose as an alternative scheme.
> - I do not agree with com requiring the computed interval to be bounded
> at level 2. I feel that the boundedness should only be required at level
> 1. In particular, I do not see what is gained from stripping com in case
> of a harmless overflow.
This is indeed a serious question. Do we want to record (a) that an
evaluation actually *did* only use common intervals, or (b) that it
*would* have done so, if we had used infinite precision? I thought I
had a strong argument against the very attractive (b), but it
escapes me at present.
Arguments on either side please.
> What is the point of com if an unbounded
> interval from the point of view of the interval type is necessarily
> unbounded from the point of view of the decorations?...
It's a good point.
> - Finally, the emp decoration seems superfluous to me. There is no point
> in decorating a nonempty interval with an emp decoration (except maybe
> for wreaking havoc in an interval library), so the emp decoration could
> just as well be removed. An empty interval would then be decorated with
> trv when it does not designate a NaI.
Well, I'm all for simplification. The effect roughly is to remove any
reference to emp in the text, if possible, and where not possible, replace
by trv. Do we lose any knowledge thereby? You say not, because if evaluation
of an arithmetic expression f over box xx gives Empty, then (Dom(f)
intersect xx) must be empty, so we know "emp" is true and don't need
telling. Looks OK to me.
Anyone see a flaw in the proposal to abolish "emp"?
John