[Om3] Definite Integrals (was Re: [Fwd: MathML CDs])

[Michael Kohlhase]

Professor James Davenport wrote:
> On Thu, 5 Jul 2007, Michael Kohlhase wrote:
>   
>> I have seen that James introduced symbols for the MathML qualifiers upperbound
>> and lowerbound. I do not think that this is a good way of doing things. I
>>     
> I resent that (only joking, Michael). They ARE in MathML.
>   
Dear James, a piece of background for our discussions here. In content 
MathML3 (I mean the published draft at 
http://www.w3.org/TR/2007/WD-MathML3-20070427/) we have distinguished 
"canonical MathML" and "legacy MathML" (names to be reconsidered), the 
former is CD-based in syntax, and is the basis for OpenMath alignment. 
The latter is a convenience extension to keep backwards compatibility 
and write down things in a easy-to-understand way. It's meaning is given 
in form of canonical MathML. <upperbound> and <lowerbound> are part of 
the latter, and we do not have to align them with MathML.

Introducing constructor symbols for these seems like a bad idea, since 
they only have a meaning inside integral, sum, and product... They are 
purely representational, and I dislike that.
> Oh - I see, this is a portmanteau of defint and interval, and I am not 
> sure i like that.
>   
yes it is, and I agree that the only redeeming feature with an 
applicative integral operator is that it allows us to get rid of 
interval. I am not really fighting for this, but in the presentation 
process (the ntn files), we do not really have a way of distinguishing 
$\int_{[0,1]}\sin(x)dx$ and $\int_0^1\sin(x)dx$. If you say that we 
should not cater to presentation in cMathML/OM, then I would have to 
agree. Distinguishing defint and defintbounds is not one of my top 
priorities.

I do want to stress that we need binding forms of the integral, and that 
the set (and possibly bounds) arguments should be part of a complex 
binding operator.

Michael
>> <OMA>
>> <OMS name="defintbounds" cd="newint"/>
>> <OMI>0</OMI>
>> <OMI>1</OMI>
>> <OMBIND>
>> <OMS cd="fn1" name="lambda"/>
>> <OMBVAR><OMV name="x"/></OMBVAR>
>> <OMA><OMS cd="specfun1" name="sin"/><OMV name="x"/></OMA>
>> </OMBIND>
>> </OMA>
>>
>> for $\int_0^1\sin(x) dx$ in traditional OM representation
>>     
> James
>   

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 Prof. Dr. Michael Kohlhase,       Office: Research 1, Room 62 
 Professor of Computer Science     Campus Ring 12, 
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 m.kohlhase at jacobs-university.de http://kwarc.info/kohlhase 
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