[Om3] paper sources

[jhd at cs.bath.ac.uk]

> You pointed me at the MathML 3.0 spec. and I've looked at it in a bit
> more detail.
> It seems that MathML3 has merged the MathML and OpenMath ideas.  The
> semantics of an expression would be expressed using content
> dictionaries, similar to the OpenMath spec.
Essentially, yes.
>
> Do you know of any examples that are axiom-related?
No - the OM and MathML communities AS SUCH try not to produce
system-related examples.
> The key problem, which I'm sure you're aware, is that types are not
> apparent in the syntax. Thus 2 mod 5, exports at '2'.  Is it possible
> to encode the type towers so that they get recreated? Axiom does not
> have "expression trees" (section C.2.2).
I would rather say that 'types are not NECESSARILY apparent in the syntax'.
Types as such can be encoded, e.g.
<OMA>
  <OMS Name="Zm" cd="setname2"/>
  <OMI> 5 </OMI>
</OMA>
Then the question is how to handle them. This, as far as I recall, has not
been explicitly addressed in the OM world, hence I am copying various
OM-ers.
(1) Export this as a set membership:
    <OMA>
      <OMS name="in" cd="set1"/>
      <OMI> 2 </OMI>
      as above
    </OMA>
    I am not happy with this, since I can see a system (not Axiom)
    interpreting this as 'true' (or indeed as 'false').
(2) <OMATTR>
      <OMATP>
         <OMS name="type" cd="axiom"/>
         as above
      </OMATP>
      <OMI> 2 </OMI>
    </OMATTR>
(3) As (2), but make the 'type' symbol not be axiom-specific, since the
    concept is common to Magma, GAP etc.
(4) <OMA>
      <OMS name="typedobject" cd="axiom"/>
      <OMI> 2 </OMI>
      as above
    </OMA>
(5) As (4), but make the 'typed' symbol not be axiom-specific, since the
    concept is common to Magma, GAP etc.

Of these, I suspect my preference is for 5, followed by 3,2,4.
Thoughts?
James