[Om] Specification of functions, preserving function signatures

[W Naylor]

I've just discovered a bug on the OpenMath site (this is the mirror at 
http://openmath.activemath.org/ as the official one seems to be down 
today!) There are currently two versions of fn3, the one at:

http://openmath.activemath.org/cd/fns3.xhtml

which I am refering to, this seems to have come out of a paper due to 
Arjeh Cohen, "CD experiences" May 9th 2003, and one from Mike Dewar on the 
contributed site:

http://openmath.activemath.org/cd/contrib/cd/fns3.xhtml

this is about properties of functions,

cheers,

Bill

On Thu, 8 Dec 2005, W Naylor wrote:

> 
> Hi all,
> 
> as part of my project, I am implementing an OpenMath phrasebook for aldor 
> (http://www.aldor.org/). I am looking at mappings for function objects, 
> these can be specified using:
> 
> <OMBIND>
>   <OMS cd="fns1" name="lambda"/>
> ...
> 
> however this holds no typing information. One possible solution is to use 
> attribution where the attribute is 
> <OMS cd="ecc" name="type"/>
> this has role 'semantic-attribution' so preserves semantic information, an 
> example would be f:Z->N x +-> x^2 as
> <OMATR>
>   <OMATP>
>     <OMS cd="ecc" name="type"/>
>     <OMS cd="setname1" name="N"/>
>   </OMATP>
>   <OMBIND>
>     <OMS cd="fns1" name="lambda"/>
>     <OMBVAR>
>       <OMATR>
>         <OMATP>
>           <OMS cd="ecc" name="type"/>
>           <OMS cd="setname1" name="Z"/>
>         </OMATP>
>         <OMV name="x"/>
>       </OMATR>
>     </OMBVAR>
>     <OMA>
>       <OMS cd="arith1" name="power"/>
>       <OMV name="x"/>
>       <OMI>2</OMI>
>     </OMA>
>   </OMBIND>
> </OMATR>
> 
> (I personally find this a bit ugly)
> 
> Another possibility is to use the function symbol from fns3
> 
> <OMA>
>   <OMS cd="fns3" name="function"/>
>   <OMS cd="setname1" name="Z"/>
>   <OMS cd="setname1" name="N"/>
>   <OMBIND>
>     <OMS cd="fns1" name="lambda"/>
>     <OMBVAR>
>       <OMV name="x"/>
>     </OMBVAR>
>     <OMA>
>       <OMS cd="arith1" name="power"/>
>       <OMV name="x"/>
>       <OMI>2</OMI>
>     </OMA>
>   </OMBIND>
> </OMA>
> 
> I find the second solution nicer (the type information is kept together, 
> though multiple arguments will involve cross products ... not so nice on 
> the aldor side :-| ), however fns3 is an experimental CD, whereas 
> semantic-attribution is in the OM2 specification.
> 
> I would appreciate other peoples opinion/experience on this matter
> 
> cheers,
> 
> Bill
>  
> 
> -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
> -
> -                  Dr. W.A. Naylor
> -
> -                  http://www.cs.bath.ac.uk/~wn
> -                  http://orcca.on.ca/~bill
> -
> -                  work tel: +44 1225 386183
> -
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> 
> 

-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
-
-                  Dr. W.A. Naylor
-
-                  http://www.cs.bath.ac.uk/~wn
-                  http://orcca.on.ca/~bill
-
-                  work tel: +44 1225 386183
-
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*