[Om3] binary vs n-ary relations

[Professor James Davenport]

On Thu, September 25, 2008 10:26 am, David Carlisle wrote:
>>   <apply>
>>    <csymbol cd="logic1">and</csymbol>
>>    <apply><csymbol cd="relation1">eq</csmbol>a
>> b(xml:id="foo")</csmbol></apply>
>>    <apply><csymbol cd="relation1">eq</csmbol><share href="foo"/>
>> c</csmbol></apply>
>>   </apply>
>>
>> I must say that I like this a lot.
>
> Normally Michael liking something is reason enough to object, but he may
> have a point here.
>
> The default presentation (at least the presentation currently used in the
> CDs) goes via cmml -> OM -> pmml and currently if
>
> <apply><eq/> a b c </apply>
>
> maps to a thing with binary and and = then it will have a default
> presentation of
>
> (a = b) and (b = c)
>
> which isn't really what you want.
>
> I could make the OM->pmml stylesheet try to spot that adjacent terms are
> identical and if so use the compressed layout
> a = b = c
> but that would mean in general comparing arbitrary XMl fragments for
> equality which is a bit painful, and sometimes you may _want_ the
> expanded layout.
Exactly on both counts.
> On the other hand spotting that OMR usage is easy/quick and so it would
> be easy to generate that from <apply><eq/> a b c </apply> and conversely
> easy to give it a default presentation mathml layout of
> a = b = c
>
Furthermore, it's a GOOD use of OMR, sinc ethe point of the a=b=c notation
is precisely to say that it's the SAME b that is equal to both a and ac,
which is what OMR provides.


James Davenport
Hebron & Medlock Professor of Information Technology
Formerly RAE Coordinator and Undergraduate Director of Studies, CS Dept
Lecturer on CM30070, 30078, 50209, 50123, 50199
Chairman, Powerful Computing WP, University of Bath
OpenMath Content Dictionary Editor
IMU Committee on Electronic Information and Communication