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   Schemas, transformations and algebras

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One way of thinking about a schema (using "schema" in its generic sense 
rather than to refer to WXS, RNG, DTDs etc.) is as defining a possibly 
infinite set of document instances. And one way of thinking about a 
transformation (again, in its generic sense rather than to refer 
specifically to XSLT) is as defining a function from one set of 
documents/schema (the domain of the transformation) to another 
set/schema (the codomain). Thinking this way we can use functional 
notation for transforms, eg.,

  t: S1 -> S2

saying that transformation t takes members/instances of S1 onto 
members/instances of S2.

Now, suppose we want to compose two transforms,

  t1: S1 -> S2
  t2: S3 -> S4

to get,

  t3: S1 -> S4

In general we can only do this if S2 is a subset of S3. However, if the 
intersection of S2 and S3 is at least non-empty we can compose a 
restriction of t1 with t2, ie.,

  where S1' is a subset of S1
  and S2' is the image of S1' under t1
  and S2' is a subset of S3

we can compose,

  t1/S1': S1' -> S2'
  t2: S3 -> S4

to get,

  t3/S1': S1' -> S4

So far so good. But my question is, how, using the various XML schema 
languages, can I specify the restricted schema S1'? I'm fairly sure 
that this is straightforward to do in WXS using derivation by 
restriction. And I'm sure it can't be done with DTDs (you'd have to 
construct a completely new DTD to get the same effect). What I'm not 
sure about is whether or not there's any mechanism for this in RNG.

Is there? If not, should there be? Am I right wrt WXS?



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