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

[c.a.rowley at open.ac.uk]

>>
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.
>>

That is not what sprang to my mind (although it might have been had I met C
before and knew that C was a set that had some vague connection with the
domain of f so that f might have some support in C.

The moral being that I find it very difficult to set up a specification for
P-->S that insists on:

  being anything beyond a trivial syntax for any P that a small group of us
  decide we do NOT understand;

  does profound and meaningful (but complex and both context and
  MML2-dependent) transformations to everything in the set {this usage was
  understood (in complete detail) by the wise seers of MML2} :-) ??

I agree that we have to provide some such transformation!  But the notion
of 'getting it right' becomes more elusive with every new example I see.

It is much too much like trying to 'align' natural language with a formal
grammar (actually, that is precisely what it is, if you push 'natural' only
a little).

chris






-----member-math-request at w3.org wrote: -----

To: jhd at cs.bath.ac.uk, member-math at w3.org, om3 at openmath.org
From: David Carlisle <davidc at nag.co.uk>
Sent by: member-math-request at w3.org
Date: 25/03/2009 12:19
Subject: Re: [Om3] Being pragmatic about the semantics of, eg,
variables and functions

>> <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

________________________________________________________________________
The Numerical Algorithms Group Ltd is a company registered in England
and Wales with company number 1249803. The registered office is:
Wilkinson House, Jordan Hill Road, Oxford OX2 8DR, United Kingdom.

This e-mail has been scanned for all viruses by Star. The service is
powered by MessageLabs.
________________________________________________________________________


---------------------------------------------------------------------------
The Open University is incorporated by Royal Charter (RC 000391), an exempt
charity in England & Wales and a charity registered in Scotland (SC 038302)