A question on nomenclature

Reynolds, Gregg greynolds at datalogics.com
Wed Dec 8 16:32:04 GMT 1999

Sorry, just remembered the term

> I'd suggest good old ZF set terminolgy.  An expression that explicitly
> enumerates the members of a set is called an extension 
> expression, and an
> expression that logically describes the set is called a set 
> comprehension.
> So "{1, 2, 3}" is an extension expr., and "{ i : Z | 0 < i < }" is a
> comprehension expression denoting the same set.  (I believe 
> there are some
> other terms in use, such as intension, but these two terms 
> are common, and
> both are used in Z.)  

"Construction" is the other term I should have mentioned.

You might find Z's usage illuminating.  In Z, a schema is rigorously defined
as a named set of bindings, where a binding is function (set of ordered
pairs, not an algorithm) from names to values.  (They're also typed, so each
schema has a signature, defined as a function from names to types; the
values in the bindings must be of the appropriate type.)  There are several
ways to express a schema, but basically you can either write a construction
expression or an extension.  A schema construction expression looks
something like:

	+--[ FOO ]----
	|  i : Z
	|  0 < i < 4

meaning the name "FOO" is bound to the set of bindings of the name "i" to
integral (because of the type declaration using "Z") values satisfying the
predicate 0<i<4.

The same thing can be written using an extension expression, something like:

	FOO == { <| i == 1 |>, <| i == 2 |>, <| i == 4 |> }

"FOO" itself can be used as a type, as in the expression "f : FOO"; dot
notation is used to access the "components" of a schema:  "f.i".

What does this have to do with XML, you ask?  Well, nuttin' right now, but
it's possible to use Z's rigorous semantics to define other languages, e.g.
XML-langauges; some day in  the next millenium my pet project of expressing
a typed semantics for XML stuff using Z will bear fruit.  Maybe.

On the other hand, if "schema" is properly construed in terms of semantic
mappings, then Z provides a very handy, very carefully defined meta-language
for that right now.


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