[om] A Proposal for extending OpenMath with structure sharing

[Michael Kohlhase]

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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