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Re: How to handle a where-list in MathML

From: Michael Kohlhase <m.kohlhase@jacobs-university.de>
Date: Thu, 07 Jun 2007 06:14:08 +0200
Message-ID: <46678610.7010501@jacobs-university.de>
To: David Carlisle <davidc@nag.co.uk>
Cc: r.muetzelfeldt@ed.ac.uk, www-math@w3.org

Dear all,

I really like David's representation it seems the cleanest so far, 
because it highlights the 'bound variables' character of a and b (for 
instance they can be renamed without changing the meaning of the 
expression).

To make things more explicit, it may be best to combine the two ideas 
and use a <csymbol > variant of lambda to make it clear that the 
beta-reduction David is talking about should maybe executed at different 
occasions than that for regular lambdas.

Michael

David Carlisle wrote:
> I agree with Robert that csymbol is probably better than ci but that
> otherwise that's a good encoding.
>
> An alternative viewpoint that I picked up in a previous life working in
> formal systems that essentially viewed everything as a lambda expression
> is that 
>    2*a+3*a^2+b+b^2 WHERE a=5+c*2, b=17-d
> is syntactic sugar for
>   (lamda a b. 2*a+3*a^2+b+b^2)(5+c*2, 17-d)
>
> that is first create the anonymous function of two variables
> representing the bound variables in your expression, then apply that
> function to the two  expressions which hold the definitions of the bound
> variables.
>
> This could be encoded directly in mathml as
>
> <apply>
> <lambda>
> <bvar><ci>a</ci></bvar>
> <bvar><ci>b</ci></bvar>
> <apply>
> <plus/>
> <!-- mathml for 2*a+3*a^2+b+b^2 -->
> </apply>
> </lambda>
> <apply>
> <plus/>
> <!-- mathml for 5+c*2-->
> </apply>
> <apply>
> <plus/>
> <!-- mathml for 17-d-->
> </apply>
> </apply>
>
>
> This has the advantage of being coded in core mathml without needing any
> csymbol defined operators, it has the possible disadvantages of being
> possibly harder to read by humans, and possibly more likely to be
> automatically "expanded out" by a system consuming the expression, just
> as
> <apply><plus/><mn>1</mn><mn>1</mn></apply>
> might not be the best encoding of the concept 1+1 if you want it to
> survive importing it into a CA system and not have it be seen as 2.
>
> David
>
>
>
>
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-- 
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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@jacobs-university.de http://kwarc.info/kohlhase 
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Received on Thursday, 7 June 2007 04:14:22 GMT

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