[Om3] trouble with container markup example

[Paul Libbrecht]

You are absolutely right Robert,

and I fear that both OpenMath and MathML content are having  
subset_suchthat (the set of things inside a reference set such that  
some condition holds) but miss

   set_of_expressions_such_that

To serve the purpose below ( {[0,x] | x in R} )
and many others where basically one constructs a set by applying  
functions to a few other sets. I think { [x,y] | x in R and y in R }  
is even more difficult.

Maybe James Davenport or Olga can help here.

paul

Le 11-févr.-09 à 22:59, Robert Miner a écrit :

>
> Thanks.  Yes, it was supposed to be a set of intervals.  In ASCII,  
> {[0,x] | x in R}
>
> But I don't think your formulation can be right either.  The  
> description of http://www.openmath.org/cd/set1.xhtml#suchthat says  
> the second argument is an expression returning a Boolean argument.   
> My reading was the suchthat is used to pick a subset out of another  
> set.  If we say W is the set of all intervals of the real line, then  
> I could do
>
> <apply>
>  suchthat
>  W
>  {expression that returns true for w in W if one of the endpoints is  
> 0}
> </apply>
>
> or something like that.  Basically, I guess I'm concluding this is  
> just a bad example because it is so hard to understand, and I'm  
> going to switch it to something easy.
>
> --Robert
>
>> -----Original Message-----
>> From: Paul Libbrecht [mailto:paul at activemath.org]
>> Sent: Wednesday, February 11, 2009 3:50 PM
>> To: Robert Miner
>> Cc: David Carlisle; m.kohlhase at jacobs-university.de; member-math at w3.org
>> Subject: Re: trouble with container markup example
>>
>> Robert,
>>
>> So we're talking about a set of intervals, right?
>> (at first I was reading this as yet another expression of an interval
>> itself!)
>>
>> I would agree that adding the domainofapplication element would be
>> cleaner but it does not sound strictly necessary.
>>
>> As for the strict variant, however, as per:
>>  http://www.openmath.org/cd/set1.xhtml#suchthat
>> the base set should be mentioned indeed
>>
>> so it should be
>>
>> <apply><csymbol cd="set1">suchthat</csymbol>
>>  <csymbol cd="setname1">R</csymbol>
>>  <bind><csymbol cd="fns1">lambda</csymbol>
>>    <bvar><ci>x</ci></bvar>
>>    <apply><csymbol cd="interval1">interval</csymbol>
>>      <cn>0</cn>
>>      <ci>x</ci>
>>    </apply>
>>  </bind>
>> </apply>
>>
>> hope it helps
>>
>> paul
>>
>> Le 11-févr.-09 à 18:55, Robert Miner a écrit :
>>> I've been pressing ahead with 4.3 and got up to the examples in  
>>> 4.3.1
>>> Container Markup for Constructor Symbols.
>>>
>>> One of them is the set of all intervals (0,x).  Both parts looked
>>> wrong
>>> to me.
>>>
>>> We had
>>>
>>> <set>
>>> <bvar><ci>x</ci></bvar>
>>> <interval><cn>0</cn><ci>x</ci></interval>
>>> </set>
>>>
>>> which doesn't define anything since the range of the bound variable
>>> isn't defined.  I think it should be
>>>
>>> <set>
>>> <bvar><ci>x</ci></bvar>
>>> <domainofapplication><reals/></domainofapplication>
>>> <interval><cn>0</cn><ci>x</ci></interval>
>>> </set>
>>>
>>> or
>>>
>>> <set>
>>> <bvar><ci>x</ci></bvar>
>>> <condition><apply><in/><ci>x</ci><reals/></apply></condition>
>>> <interval><cn>0</cn><ci>x</ci></interval>
>>> </set>
>>>
>>>
>>> However, the real trouble comes with the strict encoding.  It's
>>> currently
>>>
>>> <apply><csymbol cd="set1">suchthat</csymbol>
>>> <bind><csymbol cd="fns1">lambda</csymbol>
>>>   <bvar><ci>x</ci></bvar>
>>>   <apply><csymbol cd="interval1">interval</csymbol>
>>>     <cn>0</cn>
>>>     <ci>x</ci>
>>>   </apply>
>>> </bind>
>>> </apply>
>>>
>>> But this is clearly wrong, since "suchthat" is a function taking two
>>> arguments, a set and a Boolean valued expression on that set which
>>> determines a subset.  Was there some experimental MathML 3 version  
>>> of
>>> suchthat at some point?
>>>
>>> Anyway, I'm scarcely an expert, but I don't see how to do this
>> example
>>> without using something like big_union, and I don't want to get into
>>> that at this point.  Seems like a simpler example is in order.  I  
>>> can
>>> cook one up, but I wanted to be sure I was on solid ground first.
>>>
>>> --Robert
>>>
>>>
>>>
>
>

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