# Re: Suggested Corrections to 4.2.3.2 and 4.4.2.15

From: Stan Devitt <jsdevitt@stratumtek.com>
Date: Tue, 17 Jun 2003 17:20:54 -0400
Message-ID: <3EEF8636.3050004@stratumtek.com>


Andreas,

This again is in response to your messages from the last call review of
the working draft.

To assist us in preparing a Last Call report, we would appreciate it if
you could post a brief message acknowledging we have responded to the
points you've raised.

Stan Devitt
Math Working Group

>     * From: Andreas Strotmann
>     * Date: Apr 23 2003

> 4.2.3.2:

> I would like to suggest removing one line from the example quoted below
> from section 4.2.3.2, namely, the line containing the bvar qualifier:

> " It is also valid to use qualifier schema with a function not applied
> to an argument. For example, a function acting on integrable functions
> on the interval [0,1] might be denoted:
> <fn>
> <apply>
> <int/>
> <bvar><ci>x</ci></bvar>
> <lowlimit><cn>0</cn></lowlimit>
> <uplimit><cn>1</cn></uplimit>
> </apply>
> </fn>
> "

intended to be a curried expression, and not {\int_0^1 1 dx}

This has been clarified in the remarks by adding an example of how to
accomplish  the same thing without the deprecated fn by using a lambda
expression.

> I found that Maple quite reasonably interprets the apply element of the
> example as it stands now as $\int_0^1 dx$, which evaluates to 1.

> The problem is that the correct way to represent the concept of
> integrals over a particular interval is along the lines of the example
> in section 4.4.2.15 (Domain of Application):

> "The integral of a function f over an arbitrary domain C .
> <apply>
>   <int/>
>   <domainofapplication>
>     <ci> C </ci>
>   </domainofapplication>
>   <ci> f </ci>
> </apply>
> "

In several places throughout the text we have clarified that the most
general qualifier is the domainofapplication an that the others should
be thought of as abbreviations.  We have made this systematic throughout
the text across various examples that you refer to in your note that
were artificially restricte  to one or other of the shortened forms so
that qualifiers are now treated more uniformly.  Note that this does not
break any legacy data.

We did not deprecate the shorthand notations as they
serve two other important roles.

1.  New users looking for  a representation of \int_0^1 f(x) dx,
more quickly recognize the short form with uplimit and lowlimit
and may not be prepared to formalize this into a domain of application.
(It matches how they are used to writing their mathematics.)

2.  Each of the shortened forms maps naturally to a particular
presentation.  (e.g., upper and lower bounds with bound variables,
or intervals to {\int_0^1 f } or  bvar and condition of set
membership in C to {\int_{x\inC} f(x) dx }. )

> using a unary function as an argument to the integral operator.  The way
> the current example that I suggest fixed here stands, variables x in the
> argument to such a function would be crossing a variable binding barrier
> in a rather peculiar way that I don't think any semantics formalism
> could possibly allow in a systematic fashion.

Several examples discussing how domainofapplication and the
other representations of domain of integration are handled.

This representation corresponds roughly to the common usage
{\int_C f} and the notion of integrating a "function" over
a domain.

The underlying problem aluded to here is how to decide which
bound variable of the domain corresponds to which bound variable
of the integral and it surfaces in examples where the the
domainofapplication and the function are actually defined.

We have clarified this by using your suggestion of viewing the
domain as an "implicit" cartesian product in which the order
of the bound variables maps directly to the order of the
terms in the cartesian product.

> 4.4.2.15:

> I just realized that domainofapplication is not currently listed as a
> qualifier (as I had assumed) but as a regular element.  I don't think
> that that is a good idea -- it clearly has just as special a semantics
> as all the other qualifier elements, and should be a qualifier just like
> them.

In chapter 4, the only place where the qualifiers are listed as such
is in a table. (The same holds true for appendix C.)  This term
was missing from the qualifier rule in the validation grammar
(appendix B) and this has been fixed.

Text has also been added in several places to better clarify
the usage and interaction of the qualifiers and is discussed
in more detail in the detailed answers to one of your other
queries on this topic.

Received on Tuesday, 17 June 2003 17:18:41 GMT

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