[om] A Proposal for extending OpenMath with structure sharing

[jhd at cs.bath.ac.uk]

On Wed, 3 Apr 2002, Michael Kohlhase wrote:
> I am still a bit confused by your example, mainly where the problem lies
> (in terms of the responsibility); I can see three possibilities:
> 
> 1) [Maple] did not get the implementation of subtraction of intervals or the
>    semantics of sharing right, i.e. it is a problem of equality like the
>    ones you presented in your CALCULEMUS paper.
Maple (almost explicitly) says that there are no semantics in sharing: if 
I write x:=interval(-1,1); y:=interval(-1,1); then, because of Maple's 
hashing, the two will share the same copy. So Maple cannot distinguish x-x 
from x-y, and is forced to say [-2,2]. Maple's view is that Sharing 
implies no semantics. See the recent quote from John Abbott on solving 
quartics.
> 2) [Interface] There is a problem in the interface of Maple to the outside
>    world.
Not necessarily, but it depends on the semantics of sharing.
> 3) There is some problem with the OpenMath semantics, that is only revealed
>    by the discussion of the sharing semantics. 
No - the point is that your proposal did not address the semantics. It is 
not clear whether OMR identifies syntactic sharing for compactness 
purposes (i.e. corresponds to Maple's sharing), or for genuine reasons of 
identity, as in John Abbott's example.
> From the discussion so far I have the feeling that it is 1; in this case it
> is not the problem of the OpenMath standard and we should not let the
> problem hinder us from proceeding. 
I would counter-propose two versions of OMR - one semantic and one 
syntactic, such that systems that do not understand semantic sharing can 
convert the second into the first, but can never export the second.
James
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