Re: [Om3] trouble with container markup example

[Paul Libbrecht]

You are absolutely right Robert,




  set_of_expressions_such_that

To serve the purpose below ( {[0,x] | x in R} )


Maybe James Davenport or Olga can help here.

paul

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

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 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.

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

</apply>



--Robert

{expression that returns true for w in W if one of the endpoints is 0} 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.

-----Original Message-----
From: Paul Libbrecht [mailto:p...@activemath.org]
Sent: Wednesday, February 11, 2009 3:50 PM
To: Robert Miner
Cc: David Carlisle; m.kohlh...@jacobs-university.de; member-m...@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

suchthat at some point?

Anyway, I'm scarcely an expert, but I don't see how to do this

determines a subset. Was there some experimental MathML 3 version of

example

without using something like big_union, and I don't want to get into

cook one up, but I wanted to be sure I was on solid ground first.

--Robert

that at this point. Seems like a simpler example is in order. I can

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