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Sure, Vladik.Any standard for how to implement computing with mathematically defined objects will be ambiguous unless the definition of the objects and the results of operations on, and functions of them are unambiguously defined. It has been clear, at least to me, from the outset that the current P1788 effort was doomed because such a mathematical foundation has yet to be developed. Such a foundation must be completely independent of any implementation considerations.
Instead of concentrating on the mathematical foundation, what has been attempted is to define the mathematics and its implementation simultaneously. This is extremely difficult because existing hardware and languages impose constraints on any implementation that then become imposed on the mathematics. This causes confusion, misunderstandings, and results in an extremely unclear, ambiguous, and baroque draft standard, which in my opinion is what exists.
As evidenced by many discussions including the recent ones on Motion 52, I believe without a clear mathematically sound foundation on which to base any interval implementation, we will only hurt our credibility in the larger mathematical and scientific communities by continuing on the current P1788 path.
A way to put computing with intervals on a solid mathematical foundation is to wait to consider implementation details, including language syntax and semantics, until the mathematical foundation for its implementation is published in "Mathematics of Computation."
<http://www.ams.org/publications/journals/journalsframework/mcom> This is my motion and the reason for it. Cheers, Bill On 11/22/13 10:43 AM, Kreinovich, Vladik wrote:
Can you please explain what you mean? ________________________________________ From: stds-1788@xxxxxxxx [stds-1788@xxxxxxxx] on behalf of G. William (Bill) Walster [bill@xxxxxxxxxxx] Sent: Friday, November 22, 2013 10:24 AM To: Michel Hack; stds-1788 Subject: Re: Motion 52: final "Expressions" text for vote How can a standard for computing with intervals be constructed if the result of evaluating any given numerical expression that contains intervals is ambiguous? I do not believe it can, and therefore, I believe such a construction is premature. As evidence of this fact, I the recent discussion concerning the content of Motion 52 is more than sufficient proof. Therefore, I move that all work on a standard for computing with intervals be suspended until such an unambiguous interval mathematical foundation is developed and published in "The Mathematics of Computation."