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

[Michael Kohlhase]

James Davenport wrote:
> On Fri, 6 Jul 2007, Michael Kohlhase wrote:
>   
>> Professor James Davenport wrote:
>>     
>>> On Thu, 5 Jul 2007, Michael Kohlhase wrote:
>>>       
>> 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. Its 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.
>>     
> [ I assume you meant OpenMath, not MathML, at the end.
>   
yes, I should have been more explicit.
> OK. So legacy-C to canonical-C is nothing to do with OM, and W need only
> worry about canonical-C to OM. That makes life a lot easier (and calcmml1
> redundant). I'll have another stab, concentrating on the defint-binder.
>
>   
good.
>> 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.
>>     
> Agreed - I only added them because I thought we had to. Happily junked.
>   
good.
>>> 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.
>>     
> Right. On the lines of my MKM paper, I would argue that this is purely a
> presentational issue, and is some-one wants to invent a
> presentation-oriened decoration for it, that's fine by me.
> I'll ignore defintbounds until further notice.
>
>   
Hmmm, but not having defintbounds puts me into a spot with presentation 
in another place. I would like to argue that the presentation of a 
complex term only depends on the top-level symbol. Defint in our case. 
In the bounds case, we have to look deep into the interval to find the 
bounds for presentation (and thus go two levels deep). This wreaks my 
hypothesis, and it is the only case (except $\sin^2(x)$), where I can 
see this happening.  And in  the sin case, I am not sure whether  it is 
not the pointwise power function  at work here so  what we are really 
seeing  is  $ppower(sin,2)(x)$ which is  equivalent to $power(sin(x),2$. 
What do you think?

Michael
>> 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.
>>     
> Not sure what you mean by 'set', unless you mean writing [0,1] as a set.
> But I agree with your general point.
>
> I'll go re-read MathML-C3.0 again with this enlightemnment.
>   
Please do not look at the cds there too closely, up till now, they are 
just a place for putting the junk we extracted from all over the spec.

Michael
> James
>
>   

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 Prof. Dr. Michael Kohlhase,       Office: Research 1, Room 62 
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