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Motion P1788/M0052:Clause6Text (expressions) -- discussion period begins



P-1788:

Since Motion 52 has been made by John Pryce and seconded
by Vincent Lefevre, the discussion period now begins.
The discussion period will continue until after October 25.

This motion is processed as a standard text motion.  That is,
we will be voting on the actual wording, and a 2/3 majority is
required for passage.  The motion may be changed during the
discussion period, but not during voting.  I have appended
John's most recent rationale, and I have attached a copy
of the current draft, which includes clause 6.

Juergen: Please record the status of this motion on the
          web page containing your list of motions and links
          to the actual motions.

Sincerely,

Ralph Baker Kearfott (acting chair)
===============================================================
===============================================================
Motion
==============================================
Clause 6 "Expressions and the functions they define"
be accepted as standard text.
====================================================

Rationale.

This clause is central, since it aims to explain why and how
interval arithmetic is actually useful for getting enclosures. It
is in Chapter 1 because if one sticks to common intervals the
conclusions apply to all flavors. (Nate Hayes' recent document
shows how much more complicated and subtle the FTIA becomes, in
the Kaucher flavor.)
3We used to have a formal definition of "expression", offered by
Arnold Neumaier. It was essentially the "algebraic expression"
in the current §6.

Then, as part of migrating this material to Chapter 1, I had
(re)written this with an informal definition of what an
expression is, on the grounds that a formal definition would
constrain a language, which is not 1788's job.

Prof Wolfram Kahl (Ned's colleague at McMaster U. and a
languages expert) pointed out that this fear is misguided. The
concept "expression" as used in the FTIA is nothing to do with a
language - one could apply the FTIA to results of an interval
program written in machine code, say.

"Expression" in a language typically is a special case of
"expression" as used by the FTIA, under some restrictions. But a
serious FTIA application will have expressions made up of a
number of lines of code, each containing an expression in the
language-sense. And the expression to which the FTIA is applied
is the one created by a particular run of the code. The
computational graph - or the code list, which is essentially a
linearly ordered CG - is the most insightful way to represent
this.

So I rewrote it again, with more precise definitions than in the
previous version.

===============================================================
===============================================================

--

---------------------------------------------------------------
R. Baker Kearfott,    rbk@xxxxxxxxxxxxx   (337) 482-5346 (fax)
(337) 482-5270 (work)                     (337) 993-1827 (home)
URL: http://interval.louisiana.edu/kearfott.html
Department of Mathematics, University of Louisiana at Lafayette
(Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
Box 4-1010, Lafayette, LA 70504-1010, USA
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