[om] A Proposal for extending OpenMath with structure sharing

[Andrew Solomon]

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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