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Re: PLease define 'collation'

From: Michael Brundage <xquery@comcast.net>
Date: Wed, 09 Jun 2004 23:14:12 -0700
To: Michael Kay <mhk@mhk.me.uk>, 'Igor Hersht' <igorh@ca.ibm.com>
Cc: XQuery Public Comments <public-qt-comments@w3.org>, <ashokmalhotra@alum.mit.edu>, <Stephen.Buxton@oracle.com>
Message-ID: <BCED4A44.2104%xquery@comcast.net>

> I was hoping that by saying it is a mapping to a sequence of
> integers then we can also imply some properties of functions like
> contains(), for example that contains(A,B) is true if A=B is true, and that
> startswith(A, B) implies A <= B.

The mathematician in me is required to reply with a proof that contains()
can never satisfy such a property.  The problem is that equality is
reflexive (symmetric), while string containment is not.

Assume contains(A, B) is true if and only if collation(A) = collation(B) is
true.  Then consider any two strings A and B such that contains(A, B) is
true but contains(B, A) is not (for example, "a" and "aa").  By the
hypothesis, contains(A, B) implies collation(A)=collation(B), but then by
the collation(B) = collation(A) so by hypothesis contains(B, A) is true, a
contradiction.

Therefore there cannot exist a collation for which contains(A, B) is true if
and only if collation(A) = collation(B).  [Note that this proof holds
regardless of what value space the collation maps into.]



Cheers,

Michael Brundage
xquery@comcast.net
Author, XQuery: The XML Query Language (Addison-Wesley, 2004)
Co-author, Professional XML Databases (Wrox Press, 2000)
Received on Thursday, 10 June 2004 02:14:52 UTC

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