[Om3] Being pragmatic about the semantics of, eg, variables and functions

[David Carlisle]

>> <apply><cn>1</cn><condition><pi/></condition><cn>2</cn></apply>
>>
>> is valid mathml which perhaps means the function 1 applied to 2,
>But as I understand it, the P->S would fail to convert this. Am I wrong
>here? This is a key illustration.

Why should it fail? (what would failure mean?)

The implemented conversion via xslt may fail but it has bugs, which I'm
slowly trying to iron out. When it does "fail" it doesn't report any
error it just silently loses subterms (because it  fails to have
sufficiently general xpaths to look up all the combinations).
Whatever we think the rewrite to strict mathml should be I think that
just silently discarding "unexpected" constructs is not a good thing,
so if that happens it's a bug...



Structurally the above is the same as the example in the current
editor's draft

http://www.w3.org/Math/Group/draft-spec/chapter4.html#contm.domainofapplication.qualifier

<apply><csymbol>f</csymbol>
  <domainofapplication>
    <csymbol>C</csymbol>
  </domainofapplication>
  <ci>x</ci>
</apply>


(or at least it would be once you treat the condition as specifying a
domainofapplication.) the suggested mapping of an f (with no bound
variable) to a domain is something that you might write as

f|_C (x)

That is, (f restricted to C) applied to x.

Currently it suggests using fns3:domainofapplication as the symbol to
denote restriction (this symbol not defined yet) there is an ednote
about that which says:

    Editorial note  	 

    David, actually there's a domainofapplication in fns1 intended for
    mathml compat, or so I wrote in 1999... domainofapplication however
    it has a different signature, returning the domain rather than
    restricting a function to a given domain. perhaps this symbol should
    be called fns1#restriction rather than fns?#domainofapplication ?



But in any case the transformation isn't affected by the fact that
<cn>1</cn> is a pretty strange function.

This is no different from the fact that the simple case without
condition


<apply><cn>1</cn><cn>2</cn></apply>

is already Strict Content MathML, just as

<OMA>
 <OMI>1</OMI>
 OMI>2</OMI>
</OMA>

is valid (if meaningless) OpenMath.



David

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