Re: Comments on decoration ill, intersection and union

[Vincent Lefevre <vincent@xxxxxxxxxx>]

On 2012-12-14 20:34:25 -0600, Nathan T. Hayes wrote:
> Vincent Lefevre wrote:
> > On 2012-12-14 13:35:13 -0600, Nathan T. Hayes wrote:
> > > 	-- the input is nonempty, but the result is empty because of an
> > > intersection operation (as in the case of this particular example).
> > 
> > I have the impression that after an intersection one can obtain any
> > decoration just because of the intersection operation,
> 
> Can you explain this impression more specifically, perhaps with a concrete
> example? I don't understand what you mean.

Take your example (where you can replace DAC by another decoration).
We are in the case:

          -- the input is nonempty, but the result is empty because of an
  intersection operation (as in the case of this particular example).

What I don't like about giving decorations on the result of set
operations like intersection and union (hull) is that decorations make
sense only when there is a corresponding point function, but once you
have a set operation, you no longer have a point function, at least in
a canonical way.

Giving decorations in a particular case like intersection and union
might be interesting if existing practice shows that this is useful
and doesn't have significant drawbacks, but you only showed here is
that they are useful for some class of algorithms, about piecewise
functions. But what about all the other uses of intersection and
union? One doesn't know.

-- 
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)