Re: Bare decorations (was ...level 2 datums)
Nate
On 25 Oct 2010, at 06:09, Nate Hayes wrote:
>> It is possible to discuss Level 2 in the abstract, but there is NO way to
>> define a specific Level 2 floating-point or interval datatype without
>> describing it by some sort of formula, which usually amounts to a
>> representation.
>
> I'm sorry, John, but this is not true.
>
> It is done all the time. A good reference is Bertrand Meyer's book on
> object-oriented design where he describes an abstract datatype (ADT) purely
> in mathematical terms by:
>
> -- its types (i.e., its mathematical sets)
> -- its functions
> -- its axioms
> -- its preconditions (if any)
I have read books on OO design; indeed I consulted one of Grady Booch's while composing that last email. Maybe what's at issue is what my words "amounts to a representation" mean. So I ask you
How can one specify the set F of level 2 datums of IEEE 754's
"binary32" datatype in a representation-free way?
The specification must enable one to answer the question "how many such datums are there?", i.e. to find the cardinality of F explicitly -- a boring but valid level 2 question.
John