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Re: Sequence type and other related questions

From: Paul Duffin <pduffin@volantis.com>
Date: Wed, 16 Jul 2003 17:49:08 +0100
Message-ID: <3F158204.60004@volantis.com>
To: Jerome Simeon <simeon@research.bell-labs.com>
CC: Torsten Grust <grust@inf.uni-konstanz.de>, www-ql@w3.org

Thanks ever so much. I had not come across a reference to it in the 
parts of the other XPath 2.0 and XQuery 1.0 documents I had read.

Jerome Simeon wrote:
> Paul,
> 
> The type system of XPath and XQuery is (based on) XML Schema. XML Schema
> provides types for sequences of items (or nodes). The connection between
> XML Schema and the XPath and XQuery type system is described in the
> XQuery 1.0 and XPath 2.0 Formal Semantics, which is what Torsten pointed
> you to.
> 
> For instance, the following XML Schema element declaration:
> 
> <xs:element name="a" type="T"/>
> <complexType name="T">
>   <xs:sequence>
>     <xs:element name="b" type="xs:string"/>
>     </xs:element name="c" type="xs:integer" maxOccurs="unbounded"/>
>   </xs:sequence>
> </complexType>
> 
> In the XQuery type system, this is written as:
> 
> define element a of type T
> define type T {
>   element b of type xs:string,
>   element c of type xs:integer+
> }
> 
> The key point here is that the content model of a complex type
> effectively acts as a 'type' for a sequence of items (nodes).
> 
> At the XQuery type system level, that means:
> 
>   element b of type xs:string, element c of type xs:integer+
> 
> is a type of a sequence of one element containing a string, followed by
> one or more elements c of type xs:integer.
> 
> Finally, there is a connection with 'SequenceTypes' in XQuery.
> SequenceTypes are used to refer to XML Schema types, but can also
> indicate a collection (using an occurrence indicator).
> 
> For instance:
> 
> The sequence type: element(a)+
> Corresponds to the type: element a+ in the XQuery type system.
> 
> However, sequence types cannot express all kinds of sequences from
> schema (they cannot express choice, all groups, or sequences of
> heterogeneous elements).
> 
> Hope this helps,
> - Jerome
> 
> On Tue, 2003-07-15 at 12:18, Paul Duffin wrote:
> 
>>Torsten,
>>     It does a little.
>>
>>I am more interested in the usage of this within XPath than in XQuery. I 
>>am not sure whether this mailing list is the right one to use it is just 
>>it is referred to from the same page that refers to the XPath/XQuery 
>>model and functions / operators.
>>
>>I cannot find anything within the XPath specifications that relate to 
>>this. The closest I found was the SequenceType but that does not appear 
>>to match what you describe below.
>>
>>Torsten Grust wrote:
>>
>>>Paul,
>>>
>>>  does the following help?
>>>
>>>On July 15 (11:03 +0100), Paul Duffin wrote with possible deletions:
>>>|
>>>| The section on sequences
>>>| (http://www.w3.org/TR/xpath-datamodel/#sequences) states that a sequence
>>>| that contains a single item is indistinguishable from the item itself.
>>>| Among other things this means that a sequence with one item in it has
>>>| the same type as that item. Therefore sequences must have types.
>>>|
>>>| This raises a couple of questions.
>>>|
>>>| What is the type of a sequence with two (or more) items in it which are
>>>| potentially different ?
>>>|
>>>| Is it just a generic sequence type, is it the type which is the closest
>>>| ancestor of all the item types, or something else ?
>>>
>>>For two items x and y of types s and t, respectively, the sequence
>>>value (x,y) has type s,t.  Note that (.,.) (the ``comma'') is used as
>>>a binary type constructor in forming the type s,t.
>>>
>>>As a derivation rule:
>>>
>>>                    E |- x:s   E |- y:t
>>>                   ---------------------
>>>                     E |- (x,y) : s,t
>>>
>>>
>>>What you refer to above (``closest ancestor'') might be related to
>>>approximations of such sequence types:
>>>
>>>The XQuery Formal Semantics sometimes compute (more or less rough)
>>>approximations of these types (e.g., during the typing of a for-bound
>>>variable).   An approximation of the type  s,t  is
>>>
>>>                              (s | t)+
>>>
>>>computed as
>>>
>>>                        prime (s,t) quantifier (s,t)
>>>                        \_________/ \______________/
>>>                          = s | t        = +
>>>
>>>Note that information about the order of s and t in the original type
>>>as well as information about the exact number of occurrences of s and
>>>t in the original type are lost.  We do however have
>>>
>>>                            s,t <: (s | t)+
>>>
>>>which ensures that typing the rest of program using the approximation
>>>is safe.
>>>
>>>| What is the type of an empty sequence ?
>>>
>>>The type of the empty sequence is the special type empty.
>>>
>>>
>>>Greetings,
>>>   --Torsten
>>>
>>>--
>>>  | Dr. Torsten Grust                          Torsten.Grust@uni-konstanz.de |
>>>  |                                   http://www.inf.uni-konstanz.de/~grust/ |
>>>  | Database Research Group, University of Konstanz (Lake Constance/Germany) |
>>>  |             (Please avoid sending me MS Word or PowerPoint attachments.) |
>>
Received on Wednesday, 16 July 2003 13:52:27 UTC

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