[om] A Proposal for extending OpenMath with structure sharing

Andrew Solomon andrews at it.uts.edu.au
Wed Apr 3 13:25:50 CEST 2002

```Now that everyone else has understood this, can someone explain it to me?:)

I have no idea what subtraction of intervals is (probably a
deficiency in my real analysis education).

So, if someone would be so kind, I would like to have:
an example of syntactic sharing, an example of semantic sharing, and
an explanation of where they differ.

Sorry to be slow,

Andrew

On Tue, Apr 02, 2002 at 10:40:24AM -0500, Michael Kohlhase wrote:
>
> I think that Steve's Response to James objection makes the issue very
> clear. The term "syntactic sharing" coincides with my view on sharing, and
> I really think it is unproblematic, as it is only a matter of the XML
> encoding. If this change were adopted, we should maybe add James' example
> as an explanatory note.
>
> However, this does raise the question of what a phrasebook (e.g. for maple)
> should do upon receiving a syntactically shared OM object. Should it
> explode the object, just to be sure to adhere to the semantics?
>
>      Michael
>
>
>
> > Delivered-To: kohlhase+ at cs.cmu.edu
> > Sender:  owner-om at openmath.org
> > Precedence: bulk
> >
> > > I assume that JHD mean the interval from -1 to 1  by [-1,1].
> > > Then JHD asserts that if x= [-1,1],  then  x-x is zero, while
> > > [-1,1]- [-1,1]  is [-2,2].
> > > I think that x-x pretty much has to be [-2,2],  which of course includes
> > > one
> > > value of  0.
> > > Consider the extension of JHD's rule yielding 0:  p(x) where p is a
> > > program
> > > would not be the result of evaluating each operation as an interval
> > > operation,
> > > but the value [a,b] where a= min(p(x),x in [-1,1]), b = max ....
> > > Now this would be very neat, but might not be computable.
> > >
> >
> > I think this tells us that there are two notions of interval needed here. One
> > trully represents the whole set, and the x= [-1,1], x-x  should be [-2,2]. The
> > other represents an unknown value in the set, and then x = [-1,1], x-x should
> > be 0.
> >
> > Regarding sharing, I can see no possible problem with a  "syntactic" sharing,
> > wherte the OM tree is the unshared one, but repeated, syntactically identical
> > subtrees are merged for economy of space or bandwidth.  On the other hand,
> > gzip will more-or-less do this for you anyway.
> >
> > A "sematic" sharing, creating an OM DAG is a little bit tricky, because
> > existing CDs have not been written with it in mind, so, for instance, we are
> > not clear which kind of intervals we have. Since we don't have a notion of
> > evaluation at OM level at all, the problem passes down to individual symbols,
> > and we would have to go through our whole collection of such checking for any
> > issues. That would not be a huge job. but it would be a job.
> >
> > 	Steve
> >
> >
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