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improves definitions of all algebra operators that involve expressions #291

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improves definitions of all algebra operators that involve expressions
hartig Sep 25, 2025
0c316c4
better formatting of the conditions in the definition of Diff, as pro…
hartig Sep 27, 2025
a21e493
Update spec/index.html
hartig Sep 29, 2025
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Expand Up @@ -4694,6 +4694,15 @@ <h3>Operand Data Types</h3>
<section id="expression-evaluation">
<span id="evaluation"><!-- Legacy name --></span>
<h3>Expression Evaluation</h3>
<p>
A SPARQL expression is evaluated
with respect to a <a href="#defn_sparqlSolutionMapping">solution mapping</a>
and in the context of an <a href="#sparqlDataset">RDF dataset</a>
with an <a href="#defn_ActiveGraph">active graph</a>.
The result of such an evaluation is either
an <a data-cite="RDF12-CONCEPTS#dfn-rdf-term">RDF term</a> or
an [=error=].
</p>
<p>
SPARQL provides a subset of the functions and operators defined by
<a data-cite="XPATH-FUNCTIONS-31#">XPath and XQuery Functions and Operators</a>.
Expand Down Expand Up @@ -10048,16 +10057,18 @@ <h3>SPARQL Algebra</h3>
|D| be a <a href="#sparqlDataset">dataset</a>,
and |G| be the <a href="#defn_ActiveGraph">active graph</a>.
We define:</p>
<p><a href="#defn_algFilter" class="algFct">Filter</a>(<var>expr</var>, <var>Ω</var>, |D|, |G|) = { <var>μ</var> in <var>Ω</var> | <var>expr</var>(<var>μ</var>) is an expression that has an
[=effective boolean value=] of true }</p>
<div class="issue" data-number="254">
It is not clear what <var>expr</var>(<var>μ</var>) is, and it is not apparent in the formula that the expression |expr| is meant to be evaluated not only with respect to <var>μ</var> but also with respect to |D| with active graph |G|.</div>
<p><a href="#defn_algFilter" class="algFct">Filter</a>(<var>expr</var>, <var>Ω</var>, |D|, |G|) =
{ <var>μ</var> in <var>Ω</var> |
|expr|(<var>μ</var>, |D|, |G|) is an RDF term |t|
such that <a href="#func-ebv">EBV</a>(|t|) is `"true"^^xsd:boolean` }</p>
<p><a href="#defn_Multiplicity">multiplicity</a>( <var>μ</var> | <a href="#defn_algFilter" class="algFct">Filter</a>(<var>expr</var>, <var>Ω</var>, |D|, |G|) )
= <a href="#defn_Multiplicity">multiplicity</a>( <var>μ</var> | <var>Ω</var> )</p>
<blockquote>
Note that evaluating an <code>exists(pattern)</code> expression uses the dataset |D| and
active graph |G|. See the <a href="#defn_evalFilter">evaluation of filter</a>.
</blockquote>
<p>
where, for every solution mapping <var>μ</var>,
|expr|(<var>μ</var>, |D|, |G|) is the result of
<a href="#expression-evaluation">evaluating</a> expression |expr|
with respect to <var>μ</var>, in the context of dataset |D| with active graph |G|.
</p>
</div>
<div class="defn">
<p><b>Definition: <span id="defn_algJoin">Join</span></b></p>
Expand All @@ -10077,29 +10088,46 @@ <h3>SPARQL Algebra</h3>
of <var>μ</var> is the sum of the multiplicities from all possibilities.</p>
<div class="defn">
<p><b>Definition: <span id="defn_algDiff">Diff</span></b></p>
<p>Let <var>Ω<sub>1</sub></var> and <var>Ω<sub>2</sub></var> be multisets of solution mappings and <var>expr</var> be an
<a href="#expressions">expression</a>. We define:</p>
<p><a href="#defn_algDiff" class="algFct">Diff</a>(<var>Ω<sub>1</sub></var>, <var>Ω<sub>2</sub></var>, <var>expr</var>) = { <var>μ</var> | <var>μ</var> in <var>Ω<sub>1</sub></var> such that ∀ <var>μ'</var> in
<var>Ω<sub>2</sub></var>, either <var>μ</var> and <var>μ'</var> are not <a href="#defn_algCompatibleMapping">compatible</a> or <var>μ</var> and <var>μ'</var> are <a href="#defn_algCompatibleMapping">compatible</a> and
<var>expr</var>(merge(<var>μ</var>, <var>μ'</var>)) does not have an [=effective boolean value=] of true }</p>
<div class="issue" data-number="254">
It is not clear what <var>expr</var>(<var>μ</var>) is, and it is not apparent in the formula that the expression |expr| is meant to be evaluated not only with respect to <var>μ</var> but also with respect to |D| with active graph |G|.</div>
<p><a href="#defn_Multiplicity">multiplicity</a>( <var>μ</var> | <a href="#defn_algDiff" class="algFct">Diff</a>(<var>Ω<sub>1</sub></var>, <var>Ω<sub>2</sub></var>, <var>expr</var>) ) =
<p>Let <var>Ω<sub>1</sub></var> and <var>Ω<sub>2</sub></var> be multisets of solution mappings,
<var>expr</var> be an <a href="#expressions">expression</a>,
|D| be a <a href="#sparqlDataset">dataset</a>,
and |G| be the <a href="#defn_ActiveGraph">active graph</a>.
We define:</p>
<p><a href="#defn_algDiff" class="algFct">Diff</a>(<var>Ω<sub>1</sub></var>, <var>Ω<sub>2</sub></var>, <var>expr</var>, |D|, |G|)
= { <var>μ</var> in <var>Ω<sub>1</sub></var> | for every <var>μ'</var> in <var>Ω<sub>2</sub></var>,
any of the following conditions holds:</p>
<ul>
<li><var>μ</var> and <var>μ'</var> are not <a href="#defn_algCompatibleMapping">compatible</a>,</li>
<li><var>μ</var> and <var>μ'</var> are <a href="#defn_algCompatibleMapping">compatible</a>
and |expr|(merge(<var>μ</var>, <var>μ'</var>), |D|, |G|) is an [=error=], or</li>
<li><var>μ</var> and <var>μ'</var> are <a href="#defn_algCompatibleMapping">compatible</a>
and |expr|(merge(<var>μ</var>, <var>μ'</var>), |D|, |G|) is an RDF term |t|
for which <a href="#func-ebv">EBV</a>(|t|) is not `"true"^^xsd:boolean`.</li>
</ul>
<p>}</p>
<p><a href="#defn_Multiplicity">multiplicity</a>( <var>μ</var> | <a href="#defn_algDiff" class="algFct">Diff</a>(<var>Ω<sub>1</sub></var>, <var>Ω<sub>2</sub></var>, <var>expr</var>, |D|, |G|) ) =
<a href="#defn_Multiplicity">multiplicity</a>( <var>μ</var> | <var>Ω<sub>1</sub></var> )</p>
<p>
where, for every solution mapping <var>μ</var>,
|expr|(<var>μ</var>, |D|, |G|) is the result of
<a href="#expression-evaluation">evaluating</a> expression |expr|
with respect to <var>μ</var>, in the context of dataset |D| with active graph |G|.
</p>
</div>
<p>The evaluation of <var>expr</var>(merge(<var>μ</var>, <var>μ'</var>)) does not have an
[=effective boolean value=] of true if it evaluates to false or if it raises an error.</p>
<p><a href="#defn_algDiff" class="algFct">Diff</a> is used internally for the definition of <a href="#defn_algLeftJoin" class="algFct">LeftJoin</a>.</p>
<div class="defn">
<p><b>Definition: <span id="defn_algLeftJoin">LeftJoin</span></b></p>
<p>Let <var>Ω<sub>1</sub></var> and <var>Ω<sub>2</sub></var> be multisets of solution mappings and <var>expr</var> be an
<a href="#expressions">expression</a>. We define:</p>
<p><a href="#defn_algLeftJoin" class="algFct">LeftJoin</a>(<var>Ω<sub>1</sub></var>, <var>Ω<sub>2</sub></var>, <var>expr</var>) = <a href="#defn_algFilter" class="algFct">Filter</a>(<var>expr</var>, <a href="#defn_algJoin" class="algFct">Join</a>(<var>Ω<sub>1</sub></var>,
<var>Ω<sub>2</sub></var>)) ∪ <a href="#defn_algDiff" class="algFct">Diff</a>(<var>Ω<sub>1</sub></var>, <var>Ω<sub>2</sub></var>, <var>expr</var>)</p>
<p><a href="#defn_Multiplicity">multiplicity</a>( <var>μ</var> | <a href="#defn_algLeftJoin" class="algFct">LeftJoin</a>(<var>Ω<sub>1</sub></var>, <var>Ω<sub>2</sub></var>, <var>expr</var>) ) =
<a href="#defn_Multiplicity">multiplicity</a>( <var>μ</var> | <a href="#defn_algFilter" class="algFct">Filter</a>(<var>expr</var>, <a href="#defn_algJoin" class="algFct">Join</a>(<var>Ω<sub>1</sub></var>, <var>Ω<sub>2</sub></var>)) ) +
<p>Let <var>Ω<sub>1</sub></var> and <var>Ω<sub>2</sub></var> be multisets of solution mappings,
<var>expr</var> be an <a href="#expressions">expression</a>,
|D| be a <a href="#sparqlDataset">dataset</a>,
and |G| be the <a href="#defn_ActiveGraph">active graph</a>.
We define:</p>
<p><a href="#defn_algLeftJoin" class="algFct">LeftJoin</a>(<var>Ω<sub>1</sub></var>, <var>Ω<sub>2</sub></var>, <var>expr</var>, |D|, |G|) = <a href="#defn_algFilter" class="algFct">Filter</a>(<var>expr</var>, <a href="#defn_algJoin" class="algFct">Join</a>(<var>Ω<sub>1</sub></var>,
<var>Ω<sub>2</sub></var>), |D|, |G|) ∪ <a href="#defn_algDiff" class="algFct">Diff</a>(<var>Ω<sub>1</sub></var>, <var>Ω<sub>2</sub></var>, <var>expr</var>, |D|, |G|)</p>
<p><a href="#defn_Multiplicity">multiplicity</a>( <var>μ</var> | <a href="#defn_algLeftJoin" class="algFct">LeftJoin</a>(<var>Ω<sub>1</sub></var>, <var>Ω<sub>2</sub></var>, <var>expr</var>, |D|, |G|) ) =
<a href="#defn_Multiplicity">multiplicity</a>( <var>μ</var> | <a href="#defn_algFilter" class="algFct">Filter</a>(<var>expr</var>, <a href="#defn_algJoin" class="algFct">Join</a>(<var>Ω<sub>1</sub></var>, <var>Ω<sub>2</sub></var>), |D|, |G|) ) +
<a href="#defn_Multiplicity">multiplicity</a>( <var>μ</var> | <a href="#defn_algDiff" class="algFct">Diff</a>(<var>Ω<sub>1</sub></var>, <var>Ω<sub>2</sub></var>,
<var>expr</var>) )</p>
<var>expr</var>, |D|, |G|) )</p>
</div>

<div class="defn">
Expand Down Expand Up @@ -10128,14 +10156,28 @@ <h3>SPARQL Algebra</h3>
pattern <code>P</code>.</p>
<div class="defn">
<p><b>Definition: <span id="defn_algExtend">Extend</span><span id="defn_extend"><!-- obsolete id --></span></b></p>
<p>Let <var>μ</var> be a solution mapping, <var>Ω</var> a multiset of solution mappings, <var>var</var> a variable
and <var>expr</var> be an <a href="#expressions">expression</a>, then we define:</p>
<p><a href="#defn_algExtend" class="algFct">Extend</a>(<var>μ</var>, <var>var</var>, <var>expr</var>) = <var>μ</var> ∪ { (<var>var</var>, <var>value</var>) | <var>var</var> not in dom(<var>μ</var>) and <var>value</var> = <var>expr</var>(<var>μ</var>) }</p>
<div class="issue" data-number="254">
It is not clear what <var>expr</var>(<var>μ</var>) is, and it is not apparent in the formula that the expression |expr| is meant to be evaluated not only with respect to <var>μ</var> but also with respect to |D| with active graph |G|.</div>
<p><a href="#defn_algExtend" class="algFct">Extend</a>(<var>μ</var>, <var>var</var>, <var>expr</var>) = <var>μ</var> if <var>var</var> not in dom(<var>μ</var>) and expr(<var>μ</var>) is an error</p>
<p><a href="#defn_algExtend" class="algFct">Extend</a> is undefined if <var>var</var> in dom(<var>μ</var>).</p>
<p><a href="#defn_algExtend" class="algFct">Extend</a>(<var>Ω</var>, <var>var</var>, <var>expr</var>) = { <a href="#defn_algExtend" class="algFct">Extend</a>(<var>μ</var>, <var>var</var>, <var>expr</var>) | <var>μ</var> in <var>Ω</var> }</p>
<p>Let <var>μ</var> be a solution mapping, <var>Ω</var> a multiset of solution mappings,
<var>var</var> be a variable,
<var>expr</var> be an <a href="#expressions">expression</a>,
|D| be a <a href="#sparqlDataset">dataset</a>,
and |G| be the <a href="#defn_ActiveGraph">active graph</a>.
We define:</p>
<p><a href="#defn_algExtend" class="algFct">Extend</a>(<var>Ω</var>, <var>var</var>, <var>expr</var>, |D|, |G|) = { |Extend|(<var>μ</var>, <var>var</var>, <var>expr</var>, |D|, |G|) | <var>μ</var> in <var>Ω</var> },</p>
<p>where, for every solution mapping <var>μ</var>,</p>
<p>|Extend|(<var>μ</var>, <var>var</var>, <var>expr</var>, |D|, |G|) = <var>μ</var> ∪ { (<var>var</var>, |expr|(<var>μ</var>, |D|, |G|)) }
if <var>var</var> not in dom(<var>μ</var>) and
|expr|(<var>μ</var>, |D|, |G|) is an RDF term,</p>
<p>|Extend|(<var>μ</var>, <var>var</var>, <var>expr</var>, |D|, |G|) = <var>μ</var>
if <var>var</var> not in dom(<var>μ</var>) and
|expr|(<var>μ</var>, |D|, |G|) is an [=error=],</p>
<p>|Extend|(<var>μ</var>, <var>var</var>, <var>expr</var>, |D|, |G|) is undefined
if <var>var</var> in dom(<var>μ</var>), and</p>
<p>|expr|(<var>μ</var>, |D|, |G|) is the result of
<a href="#expression-evaluation">evaluating</a> expression |expr|
with respect to <var>μ</var>, in the context of dataset |D| with active graph |G|.
</p>
<div class="issue" data-number="290">
We need to define <a href="#defn_Multiplicity">multiplicity</a>( <var>μ</var> | <a href="#defn_algExtend" class="algFct">Extend</a>(<var>Ω</var>, <var>var</var>, <var>expr</var>, |D|, |G|) )</div>
</div>
<p>Write [ <var>x</var> | <var>C</var> ] for a sequence of elements where <var>C</var> is a condition on <var>x</var>.</p>
<div class="defn">
Expand Down Expand Up @@ -10631,7 +10673,7 @@ <h3>Evaluation Semantics</h3>
<div class="defn">
<p><b>Definition: <span id="defn_evalLeftJoin">Evaluation of LeftJoin</span></b></p>
<p>
<a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absLeftJoin" class="absOp">LeftJoin</a>(<var>P<sub>1</sub></var>, <var>P<sub>2</sub></var>, |F|) ) = <a href="#defn_algLeftJoin" class="algFct">LeftJoin</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>P<sub>1</sub></var>), <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>P<sub>2</sub></var>), |F| )
<a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absLeftJoin" class="absOp">LeftJoin</a>(<var>P<sub>1</sub></var>, <var>P<sub>2</sub></var>, |F|) ) = <a href="#defn_algLeftJoin" class="algFct">LeftJoin</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>P<sub>1</sub></var>), <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>P<sub>2</sub></var>), |F|, |D|, |G| )
</p>
</div>
<div class="defn">
Expand Down Expand Up @@ -10702,9 +10744,9 @@ <h3>Evaluation Semantics</h3>
</div>
<p>Note that if <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>A<sub>i</sub></var>) is an error, it is ignored.</p>
<div class="defn">
<p><b>Definition: <span id="defn_evalExtend">Evaluation of <a href="#defn_absExtend" class="absOp">Extend</a></span></b></p>
<p><b>Definition: <span id="defn_evalExtend">Evaluation of Extend</span></b></p>
<p>
<a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absExtend" class="absOp">Extend</a>(|P|, |var|, |expr|) ) = <a href="#defn_algExtend" class="algFct">Extend</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), |P|), |var|, |expr| )
<a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absExtend" class="absOp">Extend</a>(|P|, |var|, |expr|) ) = <a href="#defn_algExtend" class="algFct">Extend</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), |P|), |var|, |expr|, |D|, |G| )
</p>
</div>
<div class="defn">
Expand Down Expand Up @@ -12652,6 +12694,9 @@ <h2>Changes between SPARQL 1.1 Query Language and SPARQL 1.2 Query Language</h2>
from <i>eval</i> to <i>reachableTerms</i>.</li>
<li>Add section <a href="#sparql-error" class="sectionRef"></a> about SPARQL expression evaluation errors</a>.</li>
<li>Rename section "Filter evaluation" as <a href="#expression-evaluation" class="sectionRef"></a>.</li>
<li>Improve definitions of all algebra operators that involve expressions
(<a href="#defn_algFilter" class="algFct">Filter</a>, <a href="#defn_algDiff" class="algFct">Diff</a>,
<a href="#defn_algLeftJoin" class="algFct">LeftJoin</a>, and <a href="#defn_algExtend" class="algFct">Extend</a>).</li>
</ul>
</li>
<li>
Expand Down
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