Re: [xml-dev] Re: Schemas: Different Strokes From Different Folks

Hi,

To combine two schemas in Relax NG to form a union one will use a choice 
of two externalRef patterns, each pointing to a schema. The externalRef 
basically creates a new context and pattern Y from one schema is 
different from pattern Y from the other, thus the union in your example 
will generate only {a z, b}.

Best Regards,
George
--
George Cristian Bina
<oXygen/> XML Editor, Schema Editor and XSLT Editor/Debugger
http://www.oxygenxml.com

On 19/01/17 19:28, Henry S. Thompson wrote:
> John Cowan <> writes:
>
>> On Wed, Jan 18, 2017 at 4:17 PM, Henry S. Thompson <> wrote:
>>
>> I understood Murata to have proved for RELAX NG that given two XML
>>> languages, each (weakly) generated by a RELAX NG schema, the union _of
>>> the languages_ would be generated by the union of the schemata.
>>>
>>
>> Indeed, the proof is trivial.  Let a be the root pattern of schema A, and b
>> be the root pattern of schema B.  Then <choice><ref name="a"/><ref
>> name="b"/></choice> matches any document that matches either a or b or
>> both.  And since there are no constraints on the subpatterns of a choice
>> pattern other than those inherited from the context of the choice pattern
>> (which here is null), all such patterns are valid.
>
> <academicInterestOnly>
> Consider the following two CF-PSGs:
>
>  1) S -> X
>     X -> Y z
>     Y -> a
>
>  2) S -> Y
>     Y -> b
>
> (1) generates L1={a z}
> (2) generates L2=(b}
>
> (1) U (2) generates {a z, b, b z}, which is a proper superset of L1 U L2.
>
> It is straightforward to port this example to RELAX NG:
>
>   1) start = X
>      X = element x { Y , element z { empty } }
>      Y = element { element a { empty } }
>
>   2) start = Y
>      Y = element b { empty }
>
> with a parallel effect.
>
> So what you've offered above doesn't constitute the desired proof.
>
> The proof that context-free _languages_ are closed under union (see
> for example (first one Google offered me) [1]) involves a relabelling
> step for non-terminal symbols, precisely to avoid this 'capture'
> problem.  A similar step would obviously be possible for RELAX NG.
>
> So the class of RELAX NG _languages_ is closed under union, but it
> probably doesn't really make sense to say the _formalism_ is closed
> under union.
>
> </academicInterestOnly>
>
> ht
>