RE: [boost] Re: set class

From: David Bergman (davidb_at_[hidden])
Date: 2002-08-30 14:13:20

Rich,

What I mean by the "without the algebraic semantics" is that your
"domains" should not be confused with the Algebraic Domains of the
computational side of Lattice Theory. Those "domains" are partially
ordered sets, where each element can be reached by taking all the
"approximations" beneath it and "combine them" (constructing a sup).

So, I was not suggesting getting rid of the conventional set operators,
which indeed can be regarded as algebraic if the algebra is the set
algebra with the the power set as its domain (oh, no, not another
occurrence of that word...) 

Yes, it might be a bit confusing with all the meanings of domain. I
summarize a few meanings:

1. (algebraic) domain - partially ordered sets with some computationally
sound qualities, such as being able to approximate each value as close
as needed in a finite number of steps
2. the domain of a function - the set from which a function takes its
elements, denoted "dom(f)"
3. (finite) domain in constraint programming - a finite set of
Goedel-codable elements (often integers) onto which one can stipulate
constraints, in the form of equalities, inequalities and compound
variants of those. These constraints can either act as guards in an
indeterministic computation rule, or can propagate through the system
actively as partial solutions
4. domain of an algebra - the unstructured underlying set onto algebraic
operations are applicable, one often uses a notation such as <S; '<',
'>'; '+', '*'; {0, 1}> 
5. domain as a pure set - "domain" is often used synonymously to "set"
6. (business) domain - a "softer" concept; a problem field, where our
solution is needed

When I talk about "domain" in the context of Spamjunk Set Library, I
mean (3) and even touch at (5).

If you want to learn more about any of these "domains", you can send me
an e-mail out-of Boost, since this mail is probably already straining
the "constraints" of this list...

/David

-----Original Message-----
From: boost-bounces_at_[hidden]
[mailto:boost-bounces_at_[hidden]] On Behalf Of spamjunk_at_[hidden]
Sent: Friday, August 30, 2002 2:45 PM
To: boost_at_[hidden]
Subject: RE: [boost] Re: set class

> Victor,
> 
> Not a bad suggestion at all. I think neither Prada or the few 
> Prologers out there (still using bags for holding solutions in 
> indeterministic
> problems) would reject the "bag" term completely.
> 
> What do you think of my old proposal: domain (without the algebraic 
> semantics...)?
> 
> /David
> 

I know Victor already addressed this somewhat, but won't client
programmers expect it to hold multiple elements of the same value?

Also:  when you say, "domain (without the algebraic semantics...)," you
aren't suggesting removing the mathematical operators from the class are
you?  Or are you refering to semantics specific to domains?  My
ignorance in certains fields of math again...

Rich

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