[Om3] Restarting the discussion!

[Michael Kohlhase]

Professor James Davenport wrote:
> [..]
>> MathML". The draft also defines the beginnings of a MathML CD format 
>> (compatible with OM, but extended wrt. the specific MathML needs), and 
>> most importantly, a notation definition format for MathML, based on the 
>> ideas that we discussed in Linz.
>>
>> The next large step for MathML3 will be to get the CDs in shape. The 
>> consensus is that the Math WG wants to achieve a joint CD document 
>> endorsed by the W3C and the OMSoc that presents the K-14 CDs (covering 
>> the current content MathML elements and the OpenMath "MathML CD group"). 
>>     
> So far, there is no concept of a 'CD document' as such, but if we have a 
> MathML3 CD group (as we probably should) his would cover it.
>   
The concept of a CD document is a little problematic for us (OM), since 
I do not really understand how normative (and immutable) such a document 
should be. So  we should really think about this one. But I am convinced 
that it would be good to have a joint document with W3C to document the 
synchronization effort.
>> I can see the following tasks that could more or less start immediately,
>>
>> 1. Identify the K-14 CDs among the OM CDs.
>>     
> This needs to be done, but it seems to me that the existing MathML CD 
> group is basically it.
>   
I agree with you there, but I would like to verify. Furthermore, I see a 
couple of inventory-taking tasks here:

   1. make an equivalence table of the symbols between OM2 and MathML2, 
   2. make a list of "homonymous" symbols, where the OM2 and MathML2
      names differ, but the concepts are equal
   3. make a list of "missing" symbols, where OM2 has something and
      MathML2 not, or vice versa
   4. make a list of "problem" symbols, where the mathematical concepts
      are dealt with differently.

An example of 4. are integrals, sums, .... which we have already 
discussed, but not have come to a real conclusion on.
I think that rereading the old OM/MathML compatibility report would go a 
long way. ARE THERE VOUNTEERS who would make these lists and report them 
to the list?

How to list members feel about using a wiki for this, (there is one in 
the trac system I could offer).
>> 2. think about a OM3 CD format, there were some wishes for addition
>>      a) notation definitions (see below).
>>      b) defMPs (see James' proposal from Linz)
>>      c) presentation MathML in CMPs
>>      d) more structure (e.g. the xhtml flow model) in CMPs
>>      e) ... please remind me...
>> 3) converge on the different intuitions in MathML and OM on e.g. 
>> integrals, sums, ...
>>     
> Right - I had some ideas on this over the summer.
>   

Great, let's hear them!
>> 4) extend the OM object model by conditions (needed for MathML)
>>     
> This one I don't understand.
>   
If you read the MathML3 draft (and of course MathML2 from which this 
comes, then you will see that a binding object in MathML has four 
children: a binding symbol (like OM), a set of bound variables (like 
OM), and a body (like OM), but between the bvars and the body, MathML 
also allows an optional <condition> element, that contains a restriction 
formula for the bound variables (unlike OM). An example is (please 
excuse me for using LaTeX)

\forall x,y: x>y p(x,y).
                  ___ --> condition

Since OM/MathML are totally open in what we allow for binding symbols, 
there is not a general way we can encode conditions. For the universal 
quantifier above, we can just say \forall x,y. x>y => p(x,y), but for 
\lambda x,y: x>y x^y, this is not possible; indeed we obtain a partial 
function.

So I think that we need to extend the notion of an OM binding object to 
accomodate for conditions in order to be compatible with MathML.

Michael
>> 5) ... please remind me
>>
>> And of course, we need volunteers, so please come forward.
>>
>> Another thing (task planning, etc.) I would like to use a bug tracker to 
>> support our project planning. I could supply a trac instance for that 
>> (and Paul always has a JIRA instance). Are there any preferences?
>>     
> I agree on the need, but have no strong preferences.
>   
>> Finally, the Math WG has weekly telephone conference, and that is quite 
>> effective. We could have them too, please tell me what you think,
>>     
> We could, and probably should nearer the time. I am about to get a new 
> desktop machine, which should have a sound card, so that I will be able to 
> Skype.
>
> James
>   

-- 
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 Prof. Dr. Michael Kohlhase,       Office: Research 1, Room 62 
 Professor of Computer Science     Campus Ring 12, 
 School of Engineering & Science   D-28759 Bremen, Germany
 Jacobs University Bremen*         tel/fax: +49 421 200-3140/-493140
 m.kohlhase at jacobs-university.de http://kwarc.info/kohlhase 
 skype: m.kohlhase   * International University Bremen until Feb. 2007
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