[Om3] STS, Arity, and RelaxNG Schema

[Michael Kohlhase]

Dear all,

triggered by James' remark that the Arity infringes on STS territory, I
have extended my RelaxNG generating code from MCD arities to full STS.
This is really quite fun (especially with nxml-mode in emacs), and works
well, see https://svn.openmath.org/OpenMath3/rnc for the current schema.

There are some things that came up.

   1. I copied the MathML--relevant STS files from OpenMath2 to
      OpenMath3 (without changing them) into cd/MathML directory for
      augmenting.
   2. I found some errors in the STS types (we might want to backport
      them to OM2). Has anybody ever implemented STS and used it for
      type-checking? Then these things should have popped up earlier....
         1. curl at veccalc1 had a wrong domain type
         2. factorof at integer1 had wrong function constructor
         3. moment at s_data1 seemed to be missing a range type
         4. mapsto at sts used the type AnyType at omtypes, which does not
            exist, I have changed it to Object at sts which does.
         5. in some places we use <OMV name="MatrixRow"/> and in others
            <OMS cd="omtypes" name="MatrixRow"/> I have eliminated the
            latter, since it does not exist in the CD.
   3. For this to work as an input help, we need multiple signature
      declarations per symbols, as we have them in MathML.
   4. We really need subtype  relations, they are easy to implement in
      schemas, but we do not have STS syntax for this. The subtype
      relations really carry a lot of the expressive power in STS.
   5. All of this tells me that we should really have all the types we
      use in the STS realized not as OMV but as OMS.

Well, this has turned out to be rather a lot of stuff, so I guess I will
give a talk about this in Barcelona.

Michael

-- 
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 Prof. Dr. Michael Kohlhase,       Office: Research 1, Room 62 
 Professor of Computer Science     Campus Ring 12, 
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 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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