Motion P1788/M0030.01:Level_1_constructors -- discussion period begins
P-1788:
Since Motion 30 has been made by John Pryce and
seconded by Dan Zuras, the discussion period now
begins, and will end after Saturday, December 24, 2011.
I append the motion, along with a comment from John.
Discussion on this motion will proceed according to the rules for
position papers.
Juergen: Please place the motion and associated information
in the appropriate place on the web page, as
you have aptly done in the past.
Acting secretary: Please record the transaction in the minutes.
As usual, please contact me if you need the password to the private
area of the P-1788 web site.
Best regards,
Baker (acting as chair, P-1788)
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[Here is] the following specification of *constructors*. It is
very close to what the Vienna proposal has (except Vienna
doesn't distinguish Level 1 from Level 2). Separately from the
"acceptance as standard text" motion, I hereby submit an
(ordinary) motion as below.
I have a query however. When a constructor call "fails", should
the call
(a) return Empty, as currently written;
(b) return a "Not an Interval" value, which must then exist at
Level 1; or
(c) not return any value, i.e. the function is simply undefined
at this input argument?
E.g. text2interval("rubbish").
John Pryce
Motion
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The standard shall specify constructors at Level 1 as described below.
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Proposed Level 1 text on Constructors
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The following operations shall be provided, that create an
interval from non-interval data.
The operation nums2interval(l,u), where l and u are
extended-real values, returns the set {x in R | l <= x <= u}. If
(see subclause 5.2) the conditions l <= u , l < +oo and u -oo
hold, this set is the nonempty interval [l,u] and the operation
is said to succeed. Otherwise the operation is said to fail, and
returns Empty.
Success and failure are used in specifying how decorations are
set by the corresponding finite-precision operations on
decorated intervals.
The operation num2interval(x) is equivalent to nums2interval(x,
x). It fails if and only if x is infinite.
The operation text2interval(t) succeeds and returns the interval
denoted by the text string t, if t denotes an interval.
Otherwise, it fails and returns Empty.
[Note. Since Level 1 is mainly for human-human communication,
any understandable t is acceptable, e.g. "[3.1,4.2]" or
"[2\pi,\infty]”. Rules for the strings t accepted at an
implementation level are given in the Level 2 Subclause 6.11 on
I/O and may optionally be followed.]
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I won't give a Rationale, because the above seems
self-explanatory, but it may help to say that in the Level 2
text I aim to circulate shortly, the finite-precision
constructors are specified roughly thus:
A. There shall be a version of each Level 1 constructor for each
supported or available interval type T, explicit or implicit,
and it shall return the T-interval hull of what the Level 1
constructor returns.
B. Until we have sorted out decorations I can't say whether
finite-precision constructors shall return a bare or a
decorated interval, or whether both kinds exist. I have
sympathy with Dan Zuras' view that only decorated interval
constructors should exist.
C. The Level 2 Subclause 6.11 referred to above describes "the
strings t accepted" thus:
- Vienna section 6.2 square brackets form, like "[3.4e1,
5.6e1]", is required (to be accepted).
- The strings "Empty" and "Entire" are required, also "empty"
etc.
- Vienna 6.3 "Centered intervals", like "<2.3+-0.005", are
recommended.
- Vienna 6.4 "Uncertain numbers", like "1.23_" and "1.2?e3",
are recommended.
- Vienna 6.5 "Exact numbers", like "-5/7" and "0.71428" and
"Pi", are required.
- Vienna 6.6 and 6.7 look excellent but I haven't a view on
them yet.
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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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