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Merge pull request #132 from w3c/Issue131
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More accurate definition of the Group operator
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@hartig
hartig authored Dec 8, 2023
2 parents 580f1f7 + dcfccc7 commit 826c5d9
Showing 1 changed file with 30 additions and 23 deletions.
53 changes: 30 additions & 23 deletions spec/index.html
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Expand Up @@ -9533,8 +9533,6 @@ <h3>SPARQL Algebra</h3>
<p><a href="#defn_Multiplicity">multiplicity</a>( μ | ToMultiSet(Ψ) ) =
<a href="#defn_Multiplicity">multiplicity</a>( μ | Ψ )</p>
</div>
<p>ListEval is a function which is used to evaluate a list of expressions against a
solution and return a list of the resulting values.</p>
<div class="defn">
<div id="defn_algToMultiset">
<b>Definition: ToMultiset</b>
Expand All @@ -9558,21 +9556,41 @@ <h4>Aggregate Algebra</h4>
<div id="defn_algGroup">
<b>Definition: Group</b>
</div>
<p>Group evaluates a list of expressions against a solution sequence Ψ, producing a
<p>Group evaluates a list of expressions against a solution sequence <var>Ψ</var>, producing a
partial function from keys to solution sequences.</p>
<p>Group(exprlist, Ψ) = { ListEval(exprlist, μ) → [ μ' | μ' in Ψ, ListEval(exprlist, μ)
= ListEval(exprlist, μ') ] | μ in Ψ }</p>
<p>Group(<var>exprlist</var>, <var>Ψ</var>) = {
<a href="#defn_ListEval">ListEval</a>(<var>exprlist</var>, <var>μ</var>)
→ [ <var>μ'</var> | <var>μ'</var> in <var>Ψ</var> such that
<a href="#defn_ListEval">ListEval</a>(<var>exprlist</var>, <var>μ'</var>) and
<a href="#defn_ListEval">ListEval</a>(<var>exprlist</var>, <var>μ</var>)
are the same ] | <var>μ</var> in <var>Ψ</var> },</p>
<p>where two lists <var>L</var> and <var>L'</var> (as produced by
the <a href="#defn_ListEval">ListEval</a> function) are considered
the same iff they have the same number of elements and, for every
position&nbsp;<var>k</var> within the two lists, either of the
following two conditions is true:</p>
<ul>
<li>the element at the <var>k</var>-th position of
<var>L</var> is an RDF term; the element at the <var>k</var>-th
position of <var>L'</var> is also an RDF term; and these two
RDF terms are the <a href="#func-sameTerm">same term</a></li>
<li>the element at the <var>k</var>-th position of <var>L</var>
is an error, and the element at the <var>k</var>-th position of
<var>L'</var> is also an error</li>
</ul>
</div>
<div class="defn">
<p><b>Definition: ListEval</b></p>
<p><b>Definition: <span id="defn_ListEval">ListEval</span></b></p>
<p>ListEval((expr<sub>1</sub>, ..., expr<sub>n</sub>), μ) returns a list
(e<sub>1</sub>, ..., e<sub>n</sub>), where e<sub>i</sub> = expr<sub>i</sub>(μ) or
error.</p>
<p>ListEval retains errors resulting from the evaluation of the list elements.</p>
</div>
<p>Note that, although the result of a ListEval can be an error, and errors may be used
<p>Note that, although the result of <a href="#defn_ListEval">ListEval</a>
may contain errors, and errors may be used
to group, solutions containing error values are removed at projection time.</p>
<p>ListEval((unbound), μ) = (error), as the evaluation of an unbound expression is an
<p>Note also that the result of <a href="#defn_ListEval">ListEval</a>((unbound), <var>μ</var>)
is the list (error), as the evaluation of an unbound expression is an
error.</p>
<p>Aggregation, a function which calculates a scalar value as an output of the aggregate
expression. It is used in the SELECT clause, the HAVING evaluation process, and in ORDER
Expand All @@ -9594,30 +9612,19 @@ <h4>Aggregate Algebra</h4>
&nbsp;&nbsp;&nbsp;= { (key, F(Ψ)) | key → Ψ in { key<sub>1</sub>→Ψ<sub>1</sub>, ...,
key<sub>m</sub>→Ψ<sub>m</sub> } }</p>
<p>where<br>
&nbsp;&nbsp;M(Ψ) = [ ListEval(exprlist, μ) | μ in Ψ ]<br>
&nbsp;&nbsp;M(<var>Ψ</var>) = [ <a href="#defn_ListEval">ListEval</a>(exprlist, <var>μ</var>) | <var>μ</var> in <var>Ψ</var> ]<br>
&nbsp;&nbsp;F(Ψ) = func(M(Ψ), scalarvals), for non-<code>DISTINCT</code><br>
&nbsp;&nbsp;F(Ψ) = func(Dedup(M(Ψ)), scalarvals), for <code>DISTINCT</code></p>
<p>with Dedup(M(Ψ)) being an order-preserving, duplicate-free version of the sequence M(Ψ); that is, Dedup(M(Ψ)) is a sequence of lists that has the following four properties
(where each such list in this sequence may contain RDF terms and
errors, as it is produced by the ListEval function).</p>
errors, as it is produced by the <a href="#defn_ListEval">ListEval</a> function).</p>
<ol>
<li>For every list&nbsp;<var>L</var> in M(Ψ) there exists a
list&nbsp;<var>L'</var> in Dedup(M(Ψ)) such that <var>L</var>
and <var>L'</var> are the same,
where two lists <var>L</var> and <var>L'</var> from M(Ψ) are
considered the same iff they have the same number of elements
and, for every position&nbsp;<var>k</var> within the two lists,
any of the following two conditions is true:
<ul>
<li>either the element at the <var>k</var>-th position of
<var>L</var> is an RDF term, the element at the <var>k</var>-th
position of <var>L'</var> is also an RDF term, and these two
RDF terms are the <a href="#func-sameTerm">same term</a>;</li>
<li>or the element at the <var>k</var>-th position of <var>L</var>
is an error and the element at the <var>k</var>-th position of
<var>L'</var> is also an error.</li>
</ul>
</li>
considered the same as specified in the definition of the
<a href="#defn_algGroup">Group operator</a>.</li>
<li>For every list&nbsp;<var>L</var> in Dedup(M(Ψ)) there exists
a list&nbsp;<var>L'</var> in M(Ψ) such that <var>L</var> and
<var>L'</var> are the same.</li>
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