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hartig merged 6 commits into from
Sep 22, 2025
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Adds links to algebraic syntax symbols within the Property Paths eval section #268

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74b1f52
snapshot of addressing #228 in Sec.18.5 'Property Path Patterns'
hartig Aug 20, 2025
cff3fb2
addresses #228 in Sec.18.5 'Property Path Patterns', and addresses #218
hartig Aug 21, 2025
8a36cfa
fixes HTML bug that made the Echidna run fail
hartig Aug 21, 2025
938aa01
Apply suggestions from code review (thanks @TallTed !!)
hartig Aug 22, 2025
0cf6b73
html readability fix
hartig Sep 16, 2025
ebf96de
Apply suggestions from code review
hartig Sep 21, 2025
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36 changes: 20 additions & 16 deletions spec/index.html
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Expand Up @@ -9713,22 +9713,25 @@ <h3>Property Path Patterns</h3>
<div id="pp-eval-notation">
<b>Notation</b>
</div>
<p>For every <a href="#defn_AlgebraicQueryExpression">algebraic query expression</a> of the form
<a href="#defn_absPath" class="absOp">Path</a>(|X|, |ppe|, |Y|) we write</p>
<p>To denote the evaluation of the property path pattern, for every <a href="#defn_AlgebraicQueryExpression">algebraic query expression</a> of the form
<a href="#defn_absPath" class="absOp">Path</a>(|X|, |ppe|, |Y|) </p>, we write the following:
<pre class="nohighlight">ppeval(<var>X</var>, <var>ppe</var>, <var>Y</var>)</pre>
<p>to denote the evaluation of the property path pattern. This produces a multiset of solution
<p>This produces a multiset of solution
mappings, each solution mapping having a binding for variables used (each of |X| and |Y| can
be a variable). Some operators only produce a set of solution mappings.</p>
<p>Write</p>
<table style="border-collapse: collapse; border-color: #000000; border-spacing: 10px ; border-width: 1px">
<tbody>
<tr>
<th>Write</th>
<th>When <code>|x|</code> is</th>
</tr>
<tr>
<td><code>|x|:term</code></td>
<td>when <code>|x|</code> is an RDF term</td>
<td>an RDF term</td>
</tr>
<tr>
<td><code>|x|:var</code></td>
<td>when <code>|x|</code> is a variable</td>
<td>a variable</td>
</tr>
</tbody>
</table>
Expand Down Expand Up @@ -9761,7 +9764,7 @@ <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>Informally, evaluating a Predicate Property Path is the same as executing a subquery
<code>SELECT * { |X| |iri| |Y|</i> }</code> at that point in the query evaluation.</p>
<code>SELECT&nbsp;*&nbsp;{&nbsp;|X|&nbsp;|iri|&nbsp;|Y|&nbsp;}</code> at that point in the query evaluation.</p>
<div class="defn">
<p><b>Definition: <span id="defn_evalPP_inverse">Evaluation of Inverse Property Path</span></b></p>
<p>Let |ppe| be an <a href="#defn_AlgebraicPropertyPathExpression">algebraic property path expression</a>, then:</p>
Expand All @@ -9771,7 +9774,7 @@ <h3>Property Path Patterns</h3>
<p><b>Definition: <span id="defn_evalPP_sequence">Evaluation of Sequence Property Path</span></b></p>
<p>Let <var>ppe<sub>1</sub></var> and <var>ppe<sub>2</sub></var> be <a href="#defn_AlgebraicPropertyPathExpression">algebraic property path expressions</a>. Let |V| be a fresh variable.</p>
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@afs afs Sep 21, 2025

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Minor: could we use the <var>V<var>:var notation here?

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@hartig hartig Sep 21, 2025

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Minor: could we use the <var>V<var>:var notation here?

I prefer the "Let V be a fresh variable" because that makes (at least a bit more) clear that it should be indeed a fresh variable, whereas <var>V<var>:var wouldn't say anything about V other than that it is a variable.

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@TallTed TallTed Sep 23, 2025

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I don't know that it matters, but I believe there's a missing / above, i.e., that <var>V<var>:var should be <var>V</var>:var.

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@hartig hartig Sep 23, 2025

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@TallTed

I don't know that it matters, but I believe there's a missing / above, i.e., that <var>V<var>:var should be <var>V</var>:var.

Yes, that would have mattered. However, in the end I decided not to implement this proposed change anyway, as also indicate in my previous reply here.

<pre class="nohighlight"><var>A</var> = <a href="#defn_algJoin" class="algFct">Join</a>( ppeval(<var>X</var>, <var>ppe<sub>1</sub></var>, <var>V</var>), ppeval(<var>V</var>, <var>ppe<sub>2</sub></var>, <var>Y</var>) )</pre>
<pre class="nohighlight">ppeval(<var>X</var>, <a href="#defn_ppeSeq" class="ppeOp">seq</a>(<var>ppe<sub>1</sub></var>,<var>ppe<sub>2</sub></var>), <var>Y</var>) = <a href="#defn_algProject" class="algFct">Project</a>(<var>A</var>, <var>PV</var>)</pre>
<pre class="nohighlight">ppeval(<var>X</var>, <a href="#defn_ppeSeq" class="ppeOp">seq</a>(<var>ppe<sub>1</sub></var>, <var>ppe<sub>2</sub></var>), <var>Y</var>) = <a href="#defn_algProject" class="algFct">Project</a>(<var>A</var>, <var>PV</var>)</pre>
<p>where |PV| = { |v| ∈ {|X|,|Y|} | |v| is a variable}.</p>
<div class="issue" data-number="266"><a href="#defn_algJoin" class="algFct">Join</a> produces a multiset of solution mappings but <a href="#defn_algProject" class="algFct">Project</a> expects a sequence as its first argument. Moreover, <a href="#defn_algProject" class="algFct">Project</a> produces a sequence but ppeval(..) should be a multiset.</div>
</div>
Expand All @@ -9788,7 +9791,7 @@ <h3>Property Path Patterns</h3>
<p><b>Definition: <span id="defn_evalPP_alternative">Evaluation of Alternative Property Path</span></b></p>
<p>Let <var>ppe<sub>1</sub></var> and <var>ppe<sub>2</sub></var> be <a href="#defn_AlgebraicPropertyPathExpression">algebraic property path expressions</a>.
<pre class="nohighlight">
ppeval(<var>X</var>, <a href="#defn_ppeAlt" class="ppeOp">alt</a>(<var>ppe<sub>1</sub></var>,<var>ppe<sub>2</sub></var>), <var>Y</var>) =
ppeval(<var>X</var>, <a href="#defn_ppeAlt" class="ppeOp">alt</a>(<var>ppe<sub>1</sub></var>, <var>ppe<sub>2</sub></var>), <var>Y</var>) =
<a href="#defn_algUnion" class="algFct">Union</a>( ppeval(<var>X</var>, <var>ppe<sub>1</sub></var>, <var>Y</var>), ppeval(<var>X</var>, <var>ppe<sub>2</sub></var>, <var>Y</var>) )
</pre>
</div>
Expand All @@ -9811,23 +9814,23 @@ <h3>Property Path Patterns</h3>
Let <var>G</var> be the <a href="#defn_ActiveGraph">active graph</a>.</p>
<pre class="nohighlight">
ppeval(<var>X</var>:term, <a href="#defn_ppeZeroOrOnePath" class="ppeOp">ZeroOrOnePath</a>(<var>ppe</var>), <var>Y</var>:var) =
{ (<var>Y</var>, <var>yn</var>) | <var>yn</var> = <var>X</var> or {(<var>Y</var>, <var>yn</var>)} in ppeval(<var>X</var>,<var>ppe</var>,<var>Y</var>) }
{ (<var>Y</var>, <var>yn</var>) | <var>yn</var> = <var>X</var> or {(<var>Y</var>, <var>yn</var>)} in ppeval(<var>X</var>, <var>ppe</var>, <var>Y</var>) }
</pre>
<pre class="nohighlight">
ppeval(<var>X</var>:var, <a href="#defn_ppeZeroOrOnePath" class="ppeOp">ZeroOrOnePath</a>(<var>ppe</var>), <var>Y</var>:term) =
{ (<var>X</var>, <var>xn</var>) | <var>xn</var> = <var>Y</var> or {(<var>X</var>, <var>xn</var>)} in ppeval(<var>X</var>,<var>ppe</var>,<var>Y</var>) }
{ (<var>X</var>, <var>xn</var>) | <var>xn</var> = <var>Y</var> or {(<var>X</var>, <var>xn</var>)} in ppeval(<var>X</var>, <var>ppe</var>, <var>Y</var>) }
</pre>
<pre class="nohighlight">
ppeval(<var>X</var>:term, <a href="#defn_ppeZeroOrOnePath" class="ppeOp">ZeroOrOnePath</a>(<var>ppe</var>), <var>Y</var>:term) =
{ {} } if <var>X</var> = <var>Y</var> or ppeval(<var>X</var>,<var>ppe</var>,<var>X</var>) is not empty
{ } otherwise</pre>
<pre class="nohighlight">
ppeval(<var>X</var>:var, <a href="#defn_ppeZeroOrOnePath" class="ppeOp">ZeroOrOnePath</a>(<var>ppe</var>), <var>Y</var>:var) =
{ (<var>X</var>, <var>xn</var>) (<var>Y</var>, <var>yn</var>) | 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>
{ (<var>X</var>, <var>xn</var>) (<var>Y</var>, <var>yn</var>) | 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>
<p>We define an auxiliary function, <a href="#defn_evalALP_1">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
implementation is free to implement evaluation by any method that produces the same results
implementor is free to implement evaluation by any method that produces the same results
for the query overall. The <a href="#defn_ppeZeroOrMorePath" class="ppeOp">ZeroOrMorePath</a> and <a href="#defn_ppeOneOrMorePath" class="ppeOp">OneOrMorePath</a> forms return matches based on
distinct nodes connected by the path.</p>
<p>The matching algorithm is based on following all paths, and detecting when a graph node
Expand All @@ -9840,7 +9843,8 @@ <h3>Property Path Patterns</h3>
<p><b>Definition: <span id="defn_evalALP_1">Function ALP</span></b></p>
<pre class="nohighlight">
Let <var>ppe</var> be an <a href="#defn_AlgebraicPropertyPathExpression">algebraic property path expression</a>.
Let <var>eval</var>(<var>x</var>:term, <var>ppe</var>) be the evaluation of <var>ppe</var>, starting at RDF term <var>x</var>,
Let <var>eval</var>(<var>x</var>:term, <var>ppe</var>) be the evaluation of <var>ppe</var>,
starting at RDF term <var>x</var>,
and returning a multiset of RDF terms reached
by repeated matches of <var>ppe</var>.

Expand Down Expand Up @@ -9912,13 +9916,13 @@ <h3>Property Path Patterns</h3>
<pre class="nohighlight">
Write <var>μ'</var> as the extension of a solution mapping:
<var>μ'</var>(<var>μ</var>, <var>x</var>) = <var>μ</var>(<var>x</var>) if <var>x</var> is a variable
<var>μ'</var>(<var>μ</var>, <var>t</var>) = <var>t</var> if <var>t</var> is a RDF term
<var>μ'</var>(<var>μ</var>, <var>t</var>) = <var>t</var> if <var>t</var> is an RDF term
</pre>
<pre class="nohighlight">
Let <var>x</var> and <var>y</var> be variables or RDF terms, <var>S</var> a set of IRIs,
and <var>G</var> the <a href="#defn_ActiveGraph">active graph</a>.

ppeval(<var>x</var>, <a href="#defn_ppeNPS" class="ppeOp">NPS</a>(<var>S</var>), <var>y</var>) = { <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> }
ppeval(<var>x</var>, <a href="#defn_ppeNPS" class="ppeOp">NPS</a>(<var>S</var>), <var>y</var>) = { <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>
</section>
Expand Down
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