P1788 members
In the next day or two I expect to circulate to you, after the Officers have had a chance to comment, a draft of most of the description of Level 1 (omitting the decorations material and some lesser items), asking you to vote for its acceptance as standard text.
It also contains a revised clause 4 "Structure of the standard in levels", to help refresh our memory of what the levels mean.
Included in the Level 1 text but excluded from the vote, and called "provisional", 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.