[om] A Proposal for extending OpenMath with structure sharing

[Andrew Solomon]

Thanks to Steve and James - everything is now clear (assuming James meant X-Y = [-2,2]).

I also agree that syntactic sharing is probably a triviality and maybe it doesn't need to be
considered in the OM standard at all, but only at the encoding layer?  It would surely be no problem
to do it automatically e.g with gzip as Steve said.

Now to my next stage of catching up.  On the subject of semantic sharing, Steve wrote:
> 
> Note that Random might also be specified otherwise. Since we don't have a 
> notion of evaluation at OpenMath level, each Symbol, for which it is relevant 
> would need to define how shared instances  behaved in various contexts. 

The idea of semantic sharing seems no longer to have anything to do with
DAGs instead of trees (which is a data compression issue) but more to do with
identity in terms of bound variables.

Back to Steve's example, to do semantic sharing, wouldn't you just want
to define something like a binding symbol "assign"? (Not sure if OM
can accommodate this yet, but...)

Assign[x, Random(Integer)].(x - x)

Is there so much latitude in how identity is defined in various places that this could be 
ambiguous? Why would this need to be defined in each situation?

Andrew




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