Re: DRAFT position paper
Nate Hayes wrote:
Arnold Neumaier wrote:
Nate Hayes wrote:
Arnold Neumaier wrote:
Nate Hayes wrote:
For those that may be interested, attached is the current draft of
the position paper John referred to.
Nate Hayes wrote:
> we propose an
> alternative, including by Proposition 1 (Motion 18) to make the
distinction
> between 1/0 and 1/Empty with decorations D_1 and D_0,
But your scheme fails to make a distinction between 1+1/0 and
1+1/Empty,
so your decorations for this distinction cannot be relied upon in a
longer calculation.
My scheme reports that both 1+1/0 and 1+1/Empty are ill-formed, as it
should be:
1/0 is undefined, and 1+undefined is ill-formed (as is 1/Empty).
Under these circumstances, what's the point of distinguishing between
undefined and ill-formed?
A user may want to trap the undefined operation in 1+1/0 to pinpoint the
location inside the lengthy computation where the evaluation ceased to
be real. Your scheme would not allow this.
How does your scheme allow this? There are no traps in the decoration
systems, only the final decoration. That this decoration is different
for f(0) and for g(0) is strange, and certainly doesn't help in
pinpointing the location of the 1/0 in the execution of either f or g.
The functions f(x):=1/x and g(x)=1+1/x are both defined everywhere
except at x=0, so f(0) and g(0) should both be undefined, or both
be ill-formed.
But it doesn't make sense to label f(0) undefined and g(0) ill-formed,
just because your scheme yields this artificial distinction.
Well, that is your opinion, and I don't accept it is a fact.
In my view, IEEE 1788 is a hardware-oriented computational standard
focusing on the individual arithmetic operations, and my scheme provides
information that is lost in your scheme.
useless, confusing information.
Users can safely ignore the
distinction if it is not useful to them, as demostrated in the example
of Section 5.3 of my paper. So it incurs no penalty to users that may
feel the way you do. However, if P1788 standardizes your scheme, users
will have no choice, since the relevant information will always be lost.
This information will be lost, but you haven't shown a reason why it
is relevant that the information is relevant. If it were relevant in
the evaluation of f(0) it surely is also relevant in the evaluation
of g(0), where your scheme lost it, too.