From: Michael Kay <mhk@mhk.me.uk>

Date: Thu, 10 Jun 2004 09:18:31 +0100

To: "'Michael Brundage'" <xquery@comcast.net>, "'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: <20040610081908.32886A175F@frink.w3.org>

Date: Thu, 10 Jun 2004 09:18:31 +0100

To: "'Michael Brundage'" <xquery@comcast.net>, "'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: <20040610081908.32886A175F@frink.w3.org>

> > > 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. I should have been more formal. By "if" I didn't mean "if and only if". The property I was after was compare(A, B, C) = 0 implies contains(A, B, C) It does seem to me that a collation without this property is likely to be problematic. Michael Kay > > 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 04:19:08 UTC

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