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Evaluation of property path patterns that contain triple patterns #396

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618c4c4
snapshot of extending the 'evaluation of PP patterns' to cover PP pat…
hartig Jun 23, 2026
cd14128
adds notes for issues #393, #394, and #395
hartig Jun 23, 2026
5f5d67d
snapshot of ZeroOrMorePath with triple patterns
hartig Jun 26, 2026
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88 changes: 85 additions & 3 deletions spec/index.html
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Expand Up @@ -8756,8 +8756,8 @@ <h3>Algebraic Syntax</h3>
<a href="#defn_absPath" class="absOp">Path</a>(|x|, |ppe|, |y|)
is an algebraic query expression if
|ppe| is an <a href="#defn_AlgebraicPropertyPathExpression">algebraic property path expression</a>,
|x| is an <a data-cite="RDF12-CONCEPTS#dfn-rdf-term">RDF term</a> or a <a href="#defn_QueryVariable">variable</a>, and
|y| is an <a data-cite="RDF12-CONCEPTS#dfn-rdf-term">RDF term</a> or a <a href="#defn_QueryVariable">variable</a>.</li>
|x| is an <a data-cite="RDF12-CONCEPTS#dfn-rdf-term">RDF term</a>, a <a href="#defn_QueryVariable">variable</a>, or a <a href="#defn_TriplePattern">triple pattern</a>, and
so is |y|.</li>
<li id="defn_absUnion">
<a href="#defn_absUnion" class="absOp">Union</a>(<var>A<sub>1</sub></var>, <var>A<sub>2</sub></var>)
is an algebraic query expression if
Expand Down Expand Up @@ -9247,7 +9247,8 @@ <h5>Translate Property Path Patterns</h5>
of the form <a href="#defn_absPath" class="absOp">Path</a>(...).</p>
<p>Notes:</p>
<ul>
<li>|x| and |y| are <a data-cite="RDF12-CONCEPTS#dfn-rdf-terms">RDF terms</a> or <a href="#defn_QueryVariable">variables</a>.</li>
<li>|x| is an <a data-cite="RDF12-CONCEPTS#dfn-rdf-terms">RDF term</a>, a <a href="#defn_QueryVariable">variable</a>, or a <a href="#defn_TriplePattern">triple pattern</a>.</li>
<li>|y| is an <a data-cite="RDF12-CONCEPTS#dfn-rdf-terms">RDF term</a>, a <a href="#defn_QueryVariable">variable</a>, or a <a href="#defn_TriplePattern">triple pattern</a>.</li>
<li>|var| is a fresh <a href="#defn_QueryVariable">variable</a>.</li>
<li>|ppe|, <var>ppe<sub>1</sub></var>, and <var>ppe<sub>2</sub></var> are <a href="#defn_AlgebraicPropertyPathExpression">algebraic property path expressions</a>.</li>
<li>These are only applied to property path patterns, not within property path
Expand Down Expand Up @@ -10008,6 +10009,10 @@ <h3>Property Path Patterns</h3>
<td><code>|x|:var</code></td>
<td>a variable</td>
</tr>
<tr>
<td><code>|x|:TP</code></td>
<td>a triple pattern</td>
</tr>
</tbody>
</table>
</div>
Expand Down Expand Up @@ -10047,6 +10052,34 @@ <h3>Property Path Patterns</h3>
ppeval(<var>X</var>:term, <a href="#defn_ppeLink" class="ppeOp">Link</a>(<var>iri</var>), <var>Y</var>:term) =
{ } if triple (<var>X</var>, <var>iri</var>, <var>Y</var>) is not in the active graph
</pre>
<p>If |X| is a triple pattern:</p>
<pre class="nohighlight">
ppeval(<var>X</var>:TP, <a href="#defn_ppeLink" class="ppeOp">Link</a>(<var>iri</var>), <var>Y</var>:term) = { }</pre>
<pre class="nohighlight">
ppeval(<var>X</var>:TP, <a href="#defn_ppeLink" class="ppeOp">Link</a>(<var>iri</var>), <var>Y</var>:var) = { }</pre>
<pre class="nohighlight">
ppeval(<var>X</var>:TP, <a href="#defn_ppeLink" class="ppeOp">Link</a>(<var>iri</var>), <var>Y</var>:TP) = { }</pre>
<p>If |X| is a variable and |Y| a triple pattern:</p>
<pre class="nohighlight">
ppeval(<var>X</var>:var, <a href="#defn_ppeLink" class="ppeOp">Link</a>(<var>iri</var>), <var>Y</var>:TP) =
{ (<var>X</var>, <var>xn</var>:term) &cup; <var>μ</var> | triple (<var>xn</var>, <var>iri</var>, <var>P</var>({<var>Y</var>}) ) is in the active graph,
where <var>P</var> = <var>μ</var>(<var>σ</var>) is a <a href="#defn_PatternInstanceMapping">pattern instance mapping</a>
with an <a data-cite="RDF12-SEMANTICS#dfn-instance">RDF instance mapping</a>&nbsp;<var>σ</var>
and a <a href="#defn_sparqlSolutionMapping">solution mapping</a>&nbsp;<var>μ</var>
such that dom(<var>μ</var>) is the set of all variables in <var>Y</var>
and {(<var>X</var>, <var>xn</var>:term)} and <var>μ</var> are <a href="#defn_algCompatibleMapping">compatible</a> }</pre>
<p>If |X| is an RDF term and |Y| a triple pattern:</p>
<pre class="nohighlight">
ppeval(<var>X</var>:term, <a href="#defn_ppeLink" class="ppeOp">Link</a>(<var>iri</var>), <var>Y</var>:TP) =
{ <var>μ</var> | triple (<var>X</var>, <var>iri</var>, <var>P</var>({<var>Y</var>}) ) is in the active graph,
where <var>P</var> = <var>μ</var>(<var>σ</var>) is a <a href="#defn_PatternInstanceMapping">pattern instance mapping</a>
with an <a data-cite="RDF12-SEMANTICS#dfn-instance">RDF instance mapping</a>&nbsp;<var>σ</var>
and a <a href="#defn_sparqlSolutionMapping">solution mapping</a>&nbsp;<var>μ</var>
such that dom(<var>μ</var>) is the set of all variables in <var>Y</var> }</pre>
<div class="issue" data-number="393">
All of these cases above are incomplete in the sense that they do not mention the multiplicities of the solution mappings.
Moreover, for cases in which |X| or |Y| is a blank node, the formulas are even wrong.
</div>
<p>Informally, evaluating a Predicate Property Path is the same as executing a subquery
<code>SELECT&nbsp;*&nbsp;{&nbsp;|X|&nbsp;|iri|&nbsp;|Y|&nbsp;}</code> at that point in the query evaluation.</p>
<div class="defn">
Expand Down Expand Up @@ -10114,6 +10147,13 @@ <h3>Property Path Patterns</h3>
either (<var>yn</var> in <a href="#defn_nodeSet">nodes</a>(<var>G</var>) and <var>xn</var> = <var>yn</var>)
or {(<var>X</var>, <var>xn</var>), (<var>Y</var>, <var>yn</var>)} in ppeval(<var>X</var>, <var>ppe</var>, <var>Y</var>) }</pre>
</div>
<div class="issue" data-number="394">
<p>The previous definition does not correctly cover cases in which |X| or |Y| are a blank node.</p>
<p>Moreover, the definition needs to be explicit about the multiplicity of the resulting solution mappings.
Is the result of `ppeval`(<var>X</var>, <a href="#defn_ppeZeroOrOnePath" class="ppeOp">ZeroOrOnePath</a>(<var>ppe</var>), <var>Y</var>)
just a set of solution mappings?
The question is relevant because `ppeval`(<var>X</var>, <var>ppe</var>, <var>Y</var>) may produce a multiset of solution mappings.</p>
</div>
<p>We define an auxiliary function, <a href="#defn_evalALP">ALP</a>, used in the definitions of <a href="#defn_evalZeroOrMorePath">ZeroOrMorePath</a> and
<a href="#defn_evalOneOrMorePath">OneOrMorePath</a>. Note that the algorithm given here serves to specify the feature. An
implementor is free to implement evaluation by any method that produces the same results
Expand Down Expand Up @@ -10165,8 +10205,34 @@ <h3>Property Path Patterns</h3>
ppeval(<var>x</var>:term, <a href="#defn_ppeZeroOrMorePath" class="ppeOp">ZeroOrMorePath</a>(<var>ppe</var>), <var>y</var>:term) =
{ { } } if { (<var>vy</var>:var,<var>y</var>) } in ppeval(<var>x</var>, <a href="#defn_ppeZeroOrMorePath" class="ppeOp">ZeroOrMorePath</a>(<var>ppe</var>), <var>vy</var>)
{ } otherwise

ppeval(<var>X</var>:TP, <a href="#defn_ppeZeroOrMorePath" class="ppeOp">ZeroOrMorePath</a>(<var>ppe</var>), <var>vy</var>:var) =
{ <var>μ</var> &cup; {(<var>vy</var>, <var>n</var>)} |
<var>μ</var> is a <a href="#defn_sparqlSolutionMapping">solution mapping</a> with dom(<var>μ</var>) = vars(<var>X</var>) and
(<var>vy</var>, <var>n</var>) in ppeval(<var>P</var>(<var>X</var>), <a href="#defn_ppeZeroOrMorePath" class="ppeOp">ZeroOrMorePath</a>(<var>ppe</var>), <var>vy</var>),
where vars(<var>X</var>) is the set of all variables in <var>X</var> and
<var>P</var> = <var>μ</var>(<var>σ</var>) is a <a href="#defn_PatternInstanceMapping">pattern instance mapping</a>
with an arbitrary <a data-cite="RDF12-SEMANTICS#dfn-instance">RDF instance mapping</a>&nbsp;<var>σ</var>
such that <var>P</var>(<var>X</var>) is a <a data-cite="RDF12-CONCEPTS#dfn-triple-term">triple term</a> in <a href="#defn_nodeSet">nodes</a>(<var>G</var>)
and {(<var>vy</var>, <var>n</var>)} and <var>μ</var> are <a href="#defn_algCompatibleMapping">compatible</a> }

ppeval(<var>X</var>:TP, <a href="#defn_ppeZeroOrMorePath" class="ppeOp">ZeroOrMorePath</a>(<var>ppe</var>), <var>Y</var>:term) = ? <em>(TODO)</em>

ppeval(<var>vx</var>:var, <a href="#defn_ppeZeroOrMorePath" class="ppeOp">ZeroOrMorePath</a>(<var>ppe</var>), <var>Y</var>:TP) = ? <em>(TODO)</em>

ppeval(<var>X</var>:term, <a href="#defn_ppeZeroOrMorePath" class="ppeOp">ZeroOrMorePath</a>(<var>ppe</var>), <var>Y</var>:TP) =
{ <var>μ</var> | <var>μ</var> is a <a href="#defn_sparqlSolutionMapping">solution mapping</a> with dom(<var>μ</var>) = vars(<var>Y</var>)
such that <var>μ</var>(<var>σ</var>(<var>Y</var>)) in <a href="#defn_evalALP">ALP</a>(<var>X</var>, <var>ppe</var>)
where <var>σ</var> is an arbitrary <a data-cite="RDF12-SEMANTICS#dfn-instance">RDF instance mapping</a>
and vars(<var>Y</var>) is the set of all variables in <var>Y</var> }

ppeval(<var>X</var>:TP, <a href="#defn_ppeZeroOrMorePath" class="ppeOp">ZeroOrMorePath</a>(<var>ppe</var>), <var>Y</var>:TP) = ? <em>(TODO)</em>
</pre>
</div>
<div class="issue">
The previous definition needs to be extended to cover cases in which |X| or |Y| is a triple pattern.
Notice that this will add five more cases to the definition!
</div>
<div class="defn">
<p><b>Definition: <span id="defn_evalOneOrMorePath">Evaluation of OneOrMorePath</span></b></p>
<p>Let <var>ppe</var> be an <a href="#defn_AlgebraicPropertyPathExpression">algebraic property path expression</a>.
Expand Down Expand Up @@ -10198,6 +10264,10 @@ <h3>Property Path Patterns</h3>
{ } otherwise
</pre>
</div>
<div class="issue">
The previous definition needs to be extended to cover cases in which |x| or |y| is a triple pattern.
Notice that this will add five more cases to the definition!
</div>
<div class="defn">
<p><b>Definition: <span id="eval_negatedPropertySet">Evaluation of NegatedPropertySet</span></b></p>
<pre class="nohighlight">
Expand All @@ -10213,6 +10283,16 @@ <h3>Property Path Patterns</h3>
{ <var>μ</var> | ∃ triple(<var>μ'</var>(<var>μ</var>, <var>x</var>), <var>p</var>, <var>μ'</var>(<var>μ</var>, <var>y</var>)) in <var>G</var>, such that the IRI of <var>p</var> ∉ <var>S</var> }
</pre>
</div>
<div class="issue">
The previous definition needs to be extended to cover cases in which |x| or |y| is a triple pattern.
</div>
<div class="issue" data-number="395">
<p>The previous definition does not correctly cover cases in which |x| or |y| are a blank node.</p>
<p>Moreover, the definition needs to be explicit about the multiplicity of the resulting solution mappings.
Is the result of `ppeval`(<var>x</var>, <a href="#defn_ppeNPS" class="ppeOp">NPS</a>(<var>S</var>), <var>y</var>)
just a set of solution mappings?
The question is relevant because there may be multiple such <var>p</var> ∉ <var>S</var> (and, also, |x| or |y| may be a blank node).</p>
</div>
</section>
<section id="sparqlAlgebra">
<h3>SPARQL Algebra</h3>
Expand Down Expand Up @@ -13035,6 +13115,8 @@ <h2>Changes between SPARQL 1.1 Query Language and SPARQL 1.2 Query Language</h2>
<ul>
<li>Update grammar for triple terms, reifiers, reified triples, annotation syntax, and triple term functions
in <a href="#sparqlGrammar" class="sectionRef"></a></li>
<li>Extend the <a href="#PropertyPathPatterns">evaluation of property path patterns</a>
to cover <a href="#defn_PropertyPathPattern">property path patterns</a> that contain triple patterns.</li>
<li>Add functions related to <a data-cite="RDF12-CONCEPTS#dfn-triple-term">triple terms</a> to
<a href="#func-triple-terms" class="sectionRef"></a>:
`TRIPLE`, `isTRIPLE`, `SUBJECT`, `PREDICATE`, `OBJECT`</li>
Expand Down
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