[Om3] trouble with container markup example

[Robert Miner]

Thanks. 

--Robert

> -----Original Message-----
> From: Paul Libbrecht [mailto:paul at activemath.org]
> Sent: Wednesday, February 11, 2009 4:08 PM
> To: Robert Miner
> Cc: OM3 Mailing list; member-math at w3.org Group WG
> Subject: Re: trouble with container markup example
> 
> 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
> >>>
> >>>
> >>>
> >
> >