Re: Motion 52: final "Expressions" text for vote

["G. William (Bill) Walster" <bill@xxxxxxxxxxx>]

Dan,

There have been lots of publications mainly regarding algorithms and 
implementation schemes.  However, as far as I am aware, there has not 
been a complete mathematical development of the foundations for 
computing with intervals that includes answers to questions like those I 
posted earlier.

Cheers,

Bill


On 11/23/13 10:24 AM, Dan Zuras Intervals wrote:
> > Date: Fri, 22 Nov 2013 11:15:00 -0800
> > From: "G. William (Bill) Walster" <bill@xxxxxxxxxxx>
> > To: "Kreinovich, Vladik" <vladik@xxxxxxxx>, Michel Hack <mhack@xxxxxxx>,
> >   stds-1788 <stds-1788@xxxxxxxxxxxxxxxxx>
> > Subject: Re: Motion 52: final "Expressions" text for vote
> >
> > 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.  . . .
> >
> > 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
> 	Bill,
>
> 	Have their not been publications over the years of various
> 	ways to implement intervals?  Can we not pick from one of them
> 	as a basis for our standard.  And I say 'basis' because there
> 	are clearly other things people would like in their standard.
>
> 	Yours,
>
> 				Dan Zuras