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Re: Proposed definition of ExprMultiSet

From: Andy Seaborne <andy.seaborne@talis.com>
Date: Mon, 29 Mar 2010 22:57:28 +0100
Message-ID: <4BB12248.20805@talis.com>
To: Axel Polleres <axel.polleres@deri.org>
CC: SPARQL Working Group <public-rdf-dawg@w3.org>


On 26/03/2010 9:57 AM, Axel Polleres wrote:
> short clarification request:
>
>> { eval(expr,μ) | μ in Ω such that eval(μ(expr)) is defined }
>
> by "is defined" you mean "is unequal to 'error'", yes?

Does not generate an error.  As eval is RDF term-valued, if it generates 
an error, it is not defined on the input.

	Andy

>
> What I mean to ask here... when I read the current section on Filter evaluation
> http://www.w3.org/2009/sparql/docs/query-1.1/rq25.xml#evaluation
> to me it seems that eval is always "defined", but it could be an error for reasons of mistyping or
> values being unbound.
>
> Thanks for clarification on whether/what I might have overlooked here!
>
> Axel
>
> On 7 Mar 2010, at 17:42, Andy Seaborne wrote:
>
>> ISSUE-53
>>
>> I propose the following to define ExprMultiSet:
>>
>> -------
>>
>> Let Ω be a partition.
>>
>> ExprMultiSet(Ω) =
>>     { eval(expr,μ) | μ in Ω such that eval(μ(expr)) is defined }
>>     UNION
>>     { e | μ in Ω such that  eval(μ(expr)) is undefined }
>>
>> where "e" is some symbol that is distinct from all RDF terms.
>>
>> card[x]:
>>     if DISTINCT:
>>        card[x] = 1 if there exists μ in Ω such that x =  eval(μ(expr))
>>        card[x] = 0 otherwise
>>     else
>>        card[x] = count of μ in Ω such that x =  eval(μ(expr))
>>
>> --------
>>
>> "e" just records error evaluations.
>>
>> This is the most flexible definition. An alternative is
>>
>> ExprMultiset(Ω) =
>>     { eval(expr,μ) | μ in Ω such that eval(expr,μ) is defined }
>>
>> which is hard-coding dropping errors and unbounds during evaluation. But
>> the aggregate can't know there were some errors.
>>
>> Another possibility is that a yes/no flag indicating a error was seen.
>> But this might as well be the count of errors, which is equivalent to
>> the flexible definition given.
>>
>> By the way, this is in no way a recipe for implementation.  Aggregation
>> can be done over all groups in parallel during query execution.
>>
>>
>>
>> For the last publication, it was noted
>>
>> http://lists.w3.org/Archives/Public/public-rdf-dawg/2009OctDec/0646.html
>>
>> Unbound and error are the same. The current design so far has it that
>> any error means that the multiset is invalid and that group is not
>> considered.
>>
>> We didn't have time to propose a solid design to address ISSUE-53 - the
>> potential design at the time of publication was that any error when
>> calculating the ExprMultiset from a partition meant that
>>
>> SUM of {1, 2, unbound} is an error.
>> COUNT of {1, 2, unbound} is an error.
>>
>> I don't think that is a useful form for COUNT(?x).  It does seem to mean
>> that COUNT(?x) is either COUNT(*) or error; it can't be anything else.
>>
>> COUNT(?x) can not be zero because zero arises when there are no ?x but
>> there are solutions in the partition.  If there are no solutions in the
>> partition then there is no group key and no grouping happens.
>>
>> For each aggregate we can decide what happens about unbounds and errors.
>>
>> I would like to see:
>>
>> COUNT(*) = size of multiset.
>> COUNT(DISTINCT *) = size of set after removing any e (i.e. skip undefs).
>>
>> COUNT(?x) = number of times ?x is defined in each group
>>       0<= COUNT(?x)<= COUNT(*)
>>
>> COUNT(DISTINCT ?x) = number of times ?x is uniquely defined in each group
>>
>> I'm less worried about SUM(?x) but I'd prefer that
>>
>>     SUM(?x) = op:numeric-add of defined values of ?x, skips unbounds
>>
>> rather that the rigid form we currently have.
>>
>> Previously, one of the difficulties raised for this design was that the
>> operation to add two numbers wasn't op:numeric-add because that could
>> not cope the errors (there were related datatyping issues as well).
>>
>> With the definition of ExprMultiSet above, op:numeric-add can be used to
>> define SUM.  There is step between getting the ExprMultiSet and the
>> calculation of aggregation.  This step, for SUM (and COUNT(?x)), removes
>> any errors.
>>
>> GROUP_CONCAT(?x) = concatenation
>> and now GROUP_CONCAT of an empty set can be defined as "".
>>
>> -------------
>> Some examples:
>>
>> Does anyone want to suggest we design to get different results in any of
>> these cases?
>>
>>
>> --Data:
>>
>> @prefix :<http://example/>  .
>>
>> :x1 a :T .
>> :x1 :p 1 .
>> :x1 :p 2 .
>>
>> :x2 a :T .
>> :x2 :p 9 .
>>
>> :x3 a :T .
>> :x3 :p 5 .
>> :x3 :q "x" .
>>
>> :x4 a :T .
>> :x4 :q "z".
>>
>>
>> --
>>
>>
>> -- Query 1:
>>     1 PREFIX  :<http://example/>
>>     2
>>     3 SELECT  ?x (count(*) AS ?C)
>>     4 WHERE
>>     5   { ?x<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>  :T
>>     6     OPTIONAL
>>     7       { ?x :p ?v}
>>     8   }
>>     9 GROUP BY ?x
>>    10 ORDER BY str(?x)
>>
>> -----------
>> | x   | C |
>> ===========
>> | :x1 | 2 |
>> | :x2 | 1 |
>> | :x3 | 1 |
>> | :x4 | 1 |
>> -----------
>>
>> -- Query 2:
>>
>> Change line 3 to:
>>       SELECT  ?x (count(?v) AS ?C)
>>
>> -----------
>> | x   | C |
>> ===========
>> | :x1 | 2 |
>> | :x2 | 1 |
>> | :x3 | 1 |
>> | :x4 | 0 |
>> -----------
>>
>> -- Query 3:
>>
>> Change line 3 to:
>>       SELECT  ?x (sum(?v) AS ?C)
>>
>> -----------
>> | x   | C |
>> ===========
>> | :x1 | 3 |
>> | :x2 | 9 |
>> | :x3 | 5 |
>> | :x4 | 0 |
>> -----------
>>
>> The :x4 row is zero because there were no valid numbers to add together.
>>
>> -- Different query OPTIONAL part - now has ?p
>>
>>     1 PREFIX  :<http://example/>
>>     2
>>     3 SELECT  ?x (sum(?v) AS ?C)
>>     4 WHERE
>>     5   { ?x<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>  :T
>>     6     OPTIONAL
>>     7       { ?x ?any ?v}
>>     8   }
>>     9 GROUP BY ?x
>>    10 ORDER BY str(?x)
>>
>> -----------
>> | x   | C |
>> ===========
>> | :x1 | 3 |
>> | :x2 | 9 |
>> | :x3 | 5 |
>> | :x4 | 0 |
>> -----------
>>
>> The case  where ?v is "Z2 and "x" have been skipped.
>>
>>          Andy
>>
>>
>>
>>
>>
>>
>
Received on Monday, 29 March 2010 21:58:03 GMT

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