Re: Level 2 query, number 2
Michel, Baker, George etc.
On 4 Sep 2011, at 23:37, Michel Hack wrote:
>> 1. Every (bare) interval type T must have a loss-free way to write
>> any datum (i.e. interval) in T as text, and to read that text
>> back to recover the original datum exactly.
>
> Assuming we're going back to the same representation (e.g. on the same
> platform). Even then it needs the concept of recovery conversion
With respect, I think Michel's reply, and subsequent ones from Baker & George, are transverse to the main question I asked. For one thing they relate mainly to my "solution 5b"; not 5a or 5c. In fact isn't 5b a sort of encryption of the binary data? It's only because of our decimal heritage that we don't consider it weird.
We have chosen to lumber ourselves with... delete that, I know it is for a good reason -- chosen to support ... interval types beyond basic IEEE754 inf-sup. My basic point is philosophical with legal overtones:
Is the (documented) text representation of some exotic interval
type a sufficient basis for a "contract" between the supplier and
the user of that type?
(Maybe a figurative contract, but possibly a real one: I buy your
special interval hardware and you warrant it does X, Y, Z.)
Enabling data interchange between machines is useful but secondary. If what I ask for is done -- i.e. if there is an algorithm to convert text string to mathematical interval and back -- it is NECESSARILY possible, even from my laptop to a base 7 machine implemented by little green men on Mars scribbling on slates.
Inward versus outward rounding seems, to me, a complete red herring. Suppose I'm talking about FP datums whose internal format is 3-bit binary and I map the numbers 0, 0.125, 0.25, 0.375, ..., 0.875, 1, by round-to-nearest, to 1-digit decimal strings "0", ".1", ".3", ".4", ..., ".9", "1". Then I think converting back to 3-bit binary using round-to-nearest recovers the original numbers in each case.
Using the same method for intervals in the obvious way, xx = [0.25,0.625] converts to "[.3, .6]" converts back to xx. The fact that the interval [.3, .6] doesn't enclose xx is irrelevant. This particular text representation wasn't intended to be interpreted that way.
My question is about a "contract". Maybe not well expressed, and I hope someone can say it better.
John