[om] A Proposal for extending OpenMath with structure sharing

[Andreas Strotmann]

Michael,

I think the problem is specific to the question of sharing.  The question
is: What is the semantic interpretation of a syntactic sharing, is it
something like

A)  interpret(ref(label)) = deref'(label) where deref' is dereferencing
         on the semantic layer
    (syntactic sharing => semantic sharing)

or is it

B)  interpret(ref(label)) = interpret(deref(label))
    (syntactic sharing does not imply semantic sharing necessarily)

My interpretation is therefore most closely related to your version [2]
below.

My point is that OpenMath needs to explicitly state which one of these two
possible interpretations of syntactic sharing it wants.  If it wants to be
Maple-friendly, interpretation B is the one that would be advisable, but
the other one would be a possible choice, too.

Note that B) is also the only choice that I can see is compatible with
avoiding changing the OpenMath Standard itself, since right now the
standard does not say anything at all about the semantics of common
sub-trees in an OM Object (the way I understand that document).

 -- Andreas
>
> > > 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?
> > Worse, since Maple always shares (syntactically), should it export shared,
> > even if it attaches no semantics ot the sharing, since the reader may
> > attach semantics to the sharing.
>
> 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.
>
> 2) [Interface] There is a problem in the interface of Maple to the outside
>    world.
>
> 3) There is some problem with the OpenMath semantics, that is only revealed
>    by the discussion of the sharing semantics.
>
> >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.
>
>      Michael
>
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