"closure" WAS RE: [xtm-wg] Reification of topic map constructs

[Sam Hunting <sam_hunting@yahoo.com>]

[sam]
> > I understand that a topic map engine does not operate directly on
> > the topic map markup, but only on a graph that contains properties
> > (some emergent) that derive from the markup. (This is why the graph

> > is not isomorphic to the topic map document, which is counter-
> > intuitive to someone brought up on the DOM, for example.)
> > So far, so good -- but what is "closure" (on a postcard, please)
> > and what is the test to pass that tells me that I have achieved it?

[daniel]
> CLOSURE ON A POSTCARD:
> 
> A set is said to be closed under a family of operations if performing
> those operations on members of the set always yields results that are
> members of the set.
> 

OK. This is simple enough for me to understand (which really means that
I am no longer userful as a guinea pig or proxy for the Desperate Topic
Map hacker, I fear. We need new blood!)

[daniel]
> EXAMPLE 5: The set of topic maps will be closed under the operations
> of merging and querying. (i.e. merging and querying topic maps will
> always yield topic maps.)

I would amend the above to read "topic map graph" (using "graph" as a
placeholder for the idea of the results of a process appplied to a
topic map document). In Dallas, the use of similar words for components
of topic map documents, and the results of processing topic maps
documents was a constant, subtle, yet extremely painful source of
confusion. 

> EXAMPLE 6: The set of XTM documents will be closed under the
> operations of parsing, then merging and querying, then serializing.
> (i.e.  parsing, then merging and querying, then serializing XTM
> documents will always yield XTM documents)

An XTM document is not by definition serialized?

> "will exist in memory" should perhaps read "is available for further
> processing and may optionally be serialized as an XTM document."

Good. Thank you.

[sam]
> >I'm not sure how to test this.<snip>
> >So how do I know that the forms are exactly the same?

[daniel] 
> I didn't mean they're identical in structure; just that they're of
> the same *nature* (closure again!)

That's what I mean to say, although I see this is not at all evident
from my words. For an XTM document, it is easy to see how closure is
tested -- that's what validation is for. But how do I test a "graph"?
It isn't sufficient to test the (an?) XTM document derived from the
graph, because the topic map document and the topic map graph are not
necessarily isomorphic.

S.



=====
<?-- "To imagine a language is to imagine a form of life."
     - Ludwig Wittgenstein, Philosophical Investigations -->

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