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hartig merged 2 commits into from
Jan 23, 2026
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Changes symbols L, P, P_1, and P_2 in 'Evaluation Semantics' section #347

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changes symbols L, P, P_1, and P_2 in 'Evaluation Semantics' section;…
hartig Jan 17, 2026
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A -> AQE and A' -> A
hartig Jan 23, 2026
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46 changes: 22 additions & 24 deletions spec/index.html
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Expand Up @@ -10714,12 +10714,10 @@ <h3>Evaluation Semantics</h3>
as defined in <a href="#func-filter-exists" class="sectionRef"></a>.</p>
<p>Further symbols used in the following definitions are:</p>
<ul>
<li>|P|, <var>P<sub>1</sub></var>, <var>P<sub>2</sub></var> : graph patterns</li>
<li>|L| : a solution sequence</li>
<li><var>A'</var>, <var>A<sub>1</sub></var>, <var>A<sub>2</sub></var> :
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@afs afs Jan 20, 2026

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Question: do we need A'?

It is only in three places - two in the first paragraph and in once in a note.

In, for example:

eval( D(G), Filter(F, A'), μctx ) = Filter( F, eval(D(G), A', μctx), D, G )

read fine to me as A (the LHS names a thing, and it appears in the RHS - its a scope)

If you want the distinction, use AQE at the top.

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@hartig hartig Jan 23, 2026

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I think the distinction is relevant and have applied your suggestion to use AQE at the top.

The distinction is relevant because the AQE at the top (previously A) denotes the algebraic query expression for which the different cases of the eval function are defined, whereas now A (previously A') is a sub-expression of AQE in some of these cases.

<a href="#defn_AlgebraicQueryExpression">algebraic query expressions</a></li>
<li>|F| : an <a href="#expressions">expression</a></li>
</ul>
<div class="issue" data-number="308">
|L| should not be a solution sequence but an <a href="#defn_AlgebraicQueryExpression">algebraic query expression</a>.</div>
<div class="issue" data-number="225">
The definitions in this section do not cover the cases in which
|A| is a sequence or a multiset of solution mappings.</div>
Expand All @@ -10739,49 +10737,49 @@ <h3>Evaluation Semantics</h3>
</div>
<div class="defn">
<p><b>Definition: <span id="defn_evalFilter">Evaluation of Filter</span></b></p>
<p><a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absFilter" class="absOp">Filter</a>(|F|, |P|), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algFilter" class="algFct">Filter</a>( |F|, <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), |P|, <var>μ<sub>ctx</sub></var>), |D|, |G| )</p>
<p><a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absFilter" class="absOp">Filter</a>(|F|, <var>A'</var>), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algFilter" class="algFct">Filter</a>( |F|, <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>A'</var>, <var>μ<sub>ctx</sub></var>), |D|, |G| )</p>
</div>
<div class="defn">
<p><b>Definition: <span id="defn_evalJoin">Evaluation of Join</span></b></p>
<p><a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absJoin" class="absOp">Join</a>(<var>P<sub>1</sub></var>, <var>P<sub>2</sub></var>), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algJoin" class="algFct">Join</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>P<sub>1</sub></var>, <var>μ<sub>ctx</sub></var>), <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>P<sub>2</sub></var>, <var>μ<sub>ctx</sub></var>) )</p>
<p><a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absJoin" class="absOp">Join</a>(<var>A<sub>1</sub></var>, <var>A<sub>2</sub></var>), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algJoin" class="algFct">Join</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>A<sub>1</sub></var>, <var>μ<sub>ctx</sub></var>), <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>A<sub>2</sub></var>, <var>μ<sub>ctx</sub></var>) )</p>
</div>
<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|), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algLeftJoin" class="algFct">LeftJoin</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>P<sub>1</sub></var>, <var>μ<sub>ctx</sub></var>), <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>P<sub>2</sub></var>, <var>μ<sub>ctx</sub></var>), |F|, |D|, |G| )
<a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absLeftJoin" class="absOp">LeftJoin</a>(<var>A<sub>1</sub></var>, <var>A<sub>2</sub></var>, |F|), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algLeftJoin" class="algFct">LeftJoin</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>A<sub>1</sub></var>, <var>μ<sub>ctx</sub></var>), <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>A<sub>2</sub></var>, <var>μ<sub>ctx</sub></var>), |F|, |D|, |G| )
</p>
</div>
<div class="defn">
<p><b>Definition: <span id="defn_evalUnion">Evaluation of Union</span></b></p>
<p><a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absUnion" class="absOp">Union</a>(<var>P<sub>1</sub></var>, <var>P<sub>2</sub></var>), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algUnion" class="algFct">Union</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>P<sub>1</sub></var>, <var>μ<sub>ctx</sub></var>), <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>P<sub>2</sub></var>, <var>μ<sub>ctx</sub></var>) )</p>
<p><a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absUnion" class="absOp">Union</a>(<var>A<sub>1</sub></var>, <var>A<sub>2</sub></var>), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algUnion" class="algFct">Union</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>A<sub>1</sub></var>, <var>μ<sub>ctx</sub></var>), <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>A<sub>2</sub></var>, <var>μ<sub>ctx</sub></var>) )</p>
</div>
<div class="defn">
<p><b>Definition: <span id="defn_evalGraph">Evaluation of Graph</span></b></p>
<p>For every |x| that is
an <a data-cite="RDF12-CONCEPTS#dfn-iri">IRI</a> or
a <a href="#defn_QueryVariable">variable</a>,
<a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absGraph" class="absOp">Graph</a>(|x|, |P|), <var>μ<sub>ctx</sub></var> )
<a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absGraph" class="absOp">Graph</a>(|x|, <var>A'</var>), <var>μ<sub>ctx</sub></var> )
is defined as follows:</p>
<ul>
<li>If |x| is an IRI
that is a <a data-cite="RDF12-CONCEPTS#dfn-graph-name">graph name</a> in |D|,
<div class="indentedFormula">
<a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absGraph" class="absOp">Graph</a>(|x|, |P|), <var>μ<sub>ctx</sub></var> )
<a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absGraph" class="absOp">Graph</a>(|x|, <var>A'</var>), <var>μ<sub>ctx</sub></var> )
=
<a href="#defn_eval" class="evalFct">eval</a>( |D|(<var>G<sub>|x|</sub></var>), |P|, <var>μ<sub>ctx</sub></var> ),
<a href="#defn_eval" class="evalFct">eval</a>( |D|(<var>G<sub>|x|</sub></var>), <var>A'</var>, <var>μ<sub>ctx</sub></var> ),
</div>
where <var>G<sub>|x|</sub></var> is the RDF graph of the named graph with name |x| in |D|.
</li>
<li>If |x| is an IRI
that is not a <a data-cite="RDF12-CONCEPTS#dfn-graph-name">graph name</a> in |D|,
<div class="indentedFormula">
<a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absGraph" class="absOp">Graph</a>(|x|, |P|), <var>μ<sub>ctx</sub></var> )
<a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absGraph" class="absOp">Graph</a>(|x|, <var>A'</var>), <var>μ<sub>ctx</sub></var> )
is the empty multiset.
</div>
</li>
<li>If |x| is a variable,
<div class="indentedFormula">
<a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absGraph" class="absOp">Graph</a>(|x|, |P|), <var>μ<sub>ctx</sub></var> )
<a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absGraph" class="absOp">Graph</a>(|x|, <var>A'</var>), <var>μ<sub>ctx</sub></var> )
=
<var>Ω</var>,
</div>
Expand All @@ -10790,7 +10788,7 @@ <h3>Evaluation Semantics</h3>
<var>Ω</var> := the empty multiset
for each <a data-cite="RDF12-CONCEPTS#dfn-graph-name">graph name</a> <var>gn</var> in <var>D</var> (recall that a graph name may be an IRI or a blank node)
<var>G'</var> := the RDF graph of the named graph with name <var>gn</var> in <var>D</var>
<var>Ω'</var> := <a href="#defn_eval" class="evalFct">eval</a>( <var>D</var>(<var>G'</var>), <var>P</var>, <var>μ<sub>ctx</sub></var> )
<var>Ω'</var> := <a href="#defn_eval" class="evalFct">eval</a>( <var>D</var>(<var>G'</var>), <var>A'</var>, <var>μ<sub>ctx</sub></var> )
<var>Ω</var> := <a href="#defn_algUnion" class="algFct">Union</a>( <var>Ω</var>, <a href="#defn_algJoin" class="algFct">Join</a>(<var>Ω'</var>, <var>μ</var>) ), where <var>μ</var> = {<var>x</var> → <var>gn</var>}
the result is <var>Ω</var>
</pre>
Expand All @@ -10801,7 +10799,7 @@ <h3>Evaluation Semantics</h3>
<div id="defn_evalGroup">
<b>Definition: Evaluation of Group</b>
</div>
<p><a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absGroup" class="absOp">Group</a>(|exprlist|, |P|), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algGroup" class="algFct">Group</a>( |exprlist|, <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), |P|, <var>μ<sub>ctx</sub></var>) )</p>
<p><a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absGroup" class="absOp">Group</a>(|exprlist|, <var>A'</var>), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algGroup" class="algFct">Group</a>( |exprlist|, <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>A'</var>, <var>μ<sub>ctx</sub></var>) )</p>
</div>
<div class="defn">
<div id="defn_evalAggregation">
Expand All @@ -10821,43 +10819,43 @@ <h3>Evaluation Semantics</h3>
<div class="defn">
<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|), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algExtend" class="algFct">Extend</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), |P|, <var>μ<sub>ctx</sub></var>), |var|, |expr|, |D|, |G| )
<a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absExtend" class="absOp">Extend</a>(<var>A'</var>, |var|, |expr|), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algExtend" class="algFct">Extend</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>A'</var>, <var>μ<sub>ctx</sub></var>), |var|, |expr|, |D|, |G| )
</p>
</div>
<div class="defn">
<p><b>Definition: <span id="defn_evalList">Evaluation of ToList</span></b></p>
<p><a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absToList" class="absOp">ToList</a>(|P|), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algToList" class="algFct">ToList</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), |P|, <var>μ<sub>ctx</sub></var>) )</p>
<p><a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absToList" class="absOp">ToList</a>(<var>A'</var>), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algToList" class="algFct">ToList</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>A'</var>, <var>μ<sub>ctx</sub></var>) )</p>
</div>
<div class="defn">
<p><b>Definition: <span id="defn_evalDistinct">Evaluation of Distinct</span></b></p>
<p><a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absDistinct" class="absOp">Distinct</a>(|L|), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algDistinct" class="algFct">Distinct</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), |L|, <var>μ<sub>ctx</sub></var>) )
<p><a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absDistinct" class="absOp">Distinct</a>(<var>A'</var>), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algDistinct" class="algFct">Distinct</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>A'</var>, <var>μ<sub>ctx</sub></var>) )
</p>
</div>
<div class="defn">
<p><b>Definition: <span id="defn_evalReduced">Evaluation of Reduced</span></b></p>
<p><a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absReduced" class="absOp">Reduced</a>(|L|), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algReduced" class="algFct">Reduced</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), |L|, <var>μ<sub>ctx</sub></var>) )
<p><a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absReduced" class="absOp">Reduced</a>(<var>A'</var>), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algReduced" class="algFct">Reduced</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>A'</var>, <var>μ<sub>ctx</sub></var>) )
</p>
</div>
<div class="defn">
<p><b>Definition: <span id="defn_evalProject">Evaluation of Project</span></b></p>
<p><a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absProject" class="absOp">Project</a>(|L|, |vars|), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algProject" class="algFct">Project</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), |L|, <var>μ<sub>ctx</sub></var>), |vars| )
<p><a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absProject" class="absOp">Project</a>(<var>A'</var>, |vars|), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algProject" class="algFct">Project</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>A'</var>, <var>μ<sub>ctx</sub></var>), |vars| )
</p>
</div>
<div class="defn">
<p><b>Definition: <span id="defn_evalOrderBy">Evaluation of OrderBy</span></b></p>
<p><a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absOrderBy" class="absOp">OrderBy</a>(|L|, |condition|), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algOrderBy" class="algFct">OrderBy</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), |L|, <var>μ<sub>ctx</sub></var>), |condition| )
<p><a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absOrderBy" class="absOp">OrderBy</a>(<var>A'</var>, |condition|), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algOrderBy" class="algFct">OrderBy</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>A'</var>, <var>μ<sub>ctx</sub></var>), |condition| )
</p>
</div>
<div class="defn">
<p><b>Definition: <span id="defn_evalToMultiSet">Evaluation of ToMultiSet</span></b></p>
<p><a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absToMultiset" class="absOp">ToMultiset</a>(|L|), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algToMultiSet" class="algFct">ToMultiSet</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), |L|, <var>μ<sub>ctx</sub></var>) )</p>
<p><a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absToMultiset" class="absOp">ToMultiset</a>(<var>A'</var>), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algToMultiSet" class="algFct">ToMultiSet</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>A'</var>, <var>μ<sub>ctx</sub></var>) )</p>
</div>
<div class="defn">
<p><b>Definition: <span id="defn_evalSlice">Evaluation of Slice</span></b></p>
<p><a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absSlice" class="absOp">Slice</a>(|L|, |offset|), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algSlice" class="algFct">Slice</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), |L|, <var>μ<sub>ctx</sub></var>), |offset| )
<p><a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absSlice" class="absOp">Slice</a>(<var>A'</var>, |offset|), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algSlice" class="algFct">Slice</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>A'</var>, <var>μ<sub>ctx</sub></var>), |offset| )
</p>
<p>
<a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absSlice" class="absOp">Slice</a>(|L|, |offset|, |limit|), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algSlice" class="algFct">Slice</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), |L|, <var>μ<sub>ctx</sub></var>), |offset|, |limit| )
<a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absSlice" class="absOp">Slice</a>(<var>A'</var>, |offset|, |limit|), <var>μ<sub>ctx</sub></var> ) = <a href="#defn_algSlice" class="algFct">Slice</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), <var>A'</var>, <var>μ<sub>ctx</sub></var>), |offset|, |limit| )
</p>
</div>
</section>
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