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Definitions for Values Insertion #177

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Initial values-insertion draft
afs Jan 4, 2025
bc4c6a0
Add 'row in scope' approach
afs May 18, 2025
a1cec38
Updates from reviews
afs Aug 7, 2025
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Expand Up @@ -10640,7 +10640,211 @@ <h3>Evaluation Semantics</h3>
<a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), <a href="#defn_absSlice" class="absOp">Slice</a>(|L|, |start|, |length|) ) = <a href="#defn_algSlice" class="algFct">Slice</a>( <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), |L|), |start|, |length| )
</p>
</div>

<!-- ValuesInsertion -->
<section>
<h3>Values Insertion and `EXISTS`</h3>
<div class="ednote">
<p>The following subsections contain draft material for a revised
"`exists`" operation.
</p>
<p>
Background: <a href="https://github.com/w3c/sparql-dev/blob/main/SEP/SEP-0007/sep-0007.md">SPARQL CG SEP-0007</a>
</p>
</div>
<section>
<h4>Syntax Restriction</h4>
<p><i>Additional [[[#sparqlGrammar]]] note:</i></p>
<blockquote>
Any variable that is assigned to in the graph pattern of `EXISTS`/`NOT EXISTS` must not be in-scope.
This applies to `BIND`, variables introduced by `AS` in a `SELECT` clause, variables in a `VALUES`
clause, and variables introduced by `AS` in `GROUP BY`.
</blockquote>
<p>
Extend the "in-scope" rules to include the possible
variables that are in-scope for the current row:
</p>
<table style="border-collapse: collapse; border-color: #000000; border-spacing:5px; border-width: 1px">
<tbody>
<tr>
<th>Syntax Form</th>
<th>In-scope variables</th>
</tr>
<tr>
<td>`EXISTS` and `NOT EXISTS` filters </td>
<td><code>v</code> is in-scope if it is in-scope for the pattern to which the `FILTER` is applied.
</td>
</tr>
</tbody>
</table>
<div class="note">
<p>
This restriction means that inserted values
do not conflict with values assigned to variables within the pattern.
</p>
<p>
This operation is performed as part of query parsing.
</p>
</div>
</section>
<section>
<h4>Remapping</h4>
<p>
Remapping ensures that a variable name used inside a project expression,
but which is not part of the results of the evaluation of the project expression,
does not coincide with a variable mentioned anywhere else in the
algebra expression of a query.
</p>
<p>
Renaming these variables does not change the results of evaluating
the project expresssion.
</p>
<div class="defn">
<b>Definition: <span id="defn_projmap">Projection Expression Variable Remapping</span></b>
<p>
For a <a href="#sparqlProjection">projection algebra operation</a>
`Project(A, PV)` acting on algebra expression `A` and with set of variables `PV`,
define a mapping `F` from `V`,
<a href="#sparqlQueryVariables">the set of all variables</a>,
to `V` where:
</p>
<pre>F(v) = v1 if v is not in PV, where v1 is a fresh variable
F(v) = v if v is in PV</pre>
<p>
Define the Projection Expression Variable Remapping `ProjectMap(P, PV)`
</p>
<pre>ProjectMap(Project(A, PV)) = Project(A1, PV)
where A1 is the result of applying F
to every variable mentioned in A.
</pre>
<p>
The Projection Expression Variable Remapping yields an algrebra expression that
evaluates to the same results as the Project argument. No variable of `ProjectMap(Project(A, PV))`
that is not in `PV` is mentioned anywhere else in the algebra expression for the query.
</p>
</div>
<p>This process is applied throughout the graph pattern of <code>EXISTS</code>:</p>
<div class="defn">
<b>Definition: <span id="defn_varrename">Variable Remapping</span></b>
<p>
For any algebra expression `X`, define the Variable Remapping `PrjMap(X)`
of algebra expression `X`:
</p>
<pre>PrjMap(X) = replace all project operations Project(P, PV)
with ProjectMap(Project(A, PV), PV) for each projection in X.</pre>
</div>
<p>
The outcome of `PrjMap` is independent of the order of replacement
(whether "bottom-up" or "top-down") order.
Replacements may happen several times, depending on recursive order
but each time a replacement is made, the variable not used anywhere else.
</p>

<div class="note">
<p>
A variable inside a project expression that is not in the variables projected
is not affected by the values insertion operation because it is renamed apart.
</p>
<p>
This operation is as part of the <a href="#sparqlQuery">translation to the SPARQL
algebra</a>.
</p>
</div>
</section>
<section>
<h4>Values Insertion</h4>
<p>
Alternative 1: rewrite the algebra during
<a href="#sparqlQuery">translation to the SPARQL algebra</a>
to include a function that evaluates to the current row.
</p>

<div class="defn">
<div>
<b>Definition: <span id="defn_correlate">Values In Scope</span></b>
<p>
Define the function `BindingInScope()`.
Evaluation of `BindingInScope()` results in a table of one row,
being the current binding of the enclosing filter.
</p>
</div>
<p class="ednote">Need to define `BindingInScope`</p>
</div>

<div class="defn">
<div>
<b>Definition: Access to the current binding</b>
<p>
During <a href="#sparqlQuery">translation to the SPARQL algebra</a>
</p>
<p class="ednote">Define putting in the `BindingInScope` operator</p>
<pre>
Replace each occurence of Y where Y is one of
<a href="#sparqlTranslateBasicGraphPatterns">Basic Graph Pattern</a>,
<a href="#sparqlTranslatePathPatterns">Property Path Patterns</a>,
<a href="#sparqlTranslateGraphPatterns">Graph(Var, pattern)</a>,
<a href="#https://www.w3.org/TR/sparql12-query/#sparqlTranslateGraphPatterns">Inline Data</a>
with join(Y, BindingInScope()).</pre>
</div>
<div class="note">
c.f. section <a href="#sparqlTranslateGraphPatterns">Translate Graph Patterns</a>
where an empty basic graph pattern start any
<a href="#rGroupGraphPattern">GroupGraphPattern</a>.
It happens before the <a href="#sparqlSimplification">simplification step</a>.
</div>
</div>

<div class="example">
<p>
Examples
</p>
</div>

<p>
Alternative 2: rewrite the algebra during execution. This corresponds to the
<a href="https://github.com/w3c/sparql-dev/blob/main/SEP/SEP-0007/sep-0007.md">original SEP-0007 proposal</a>.
</p>
<div class="defn">
<div>
<b>Definition: <span id="defn_insertvalues">Insert Values</span></b>
<p>
Define the function `InsertValues(X, μ)`
</p>
<pre>Let Table(μ) = { μ } and multiplicity( μ | Table(μ) = { μ } ) = 1

Replace each occurence of Y in X where Y is one of
<a href="#sparqlTranslateBasicGraphPatterns">Basic Graph Pattern</a>,
<a href="#sparqlTranslatePathPatterns">Property Path Patterns</a>,
<a href="#sparqlTranslateGraphPatterns">Graph(Var, pattern)</a>,
<a href="#https://www.w3.org/TR/sparql12-query/#sparqlTranslateGraphPatterns">Inline Data</a>
with join(Y, Table(μ)).</pre>

</div>
</div>
</section>

<section>
<h4>Evaluation of EXISTS</h4>
<div class="defn">
<b>Definition: <span id="x-defn_evalExists">Evaluation of Exists</span></b>
<p>
Let `μ` be the current solution mapping for a filter, and `X` a graph pattern,
define the Evaluation of Exists `exists(X)`
</p>
<p class="ednote">
@@ Set up the current row for `BindingdInScope`.
</p>
<pre>exists(X) = true
if eval( D(G), μ)
is a non-empty solution sequence.
exists(X) = false otherwise</pre>
</div>
</section>
</section>
<!-- ValuesInsertion -->

</section>

<section id="sparqlBGPExtend">
<h3>Extending SPARQL Basic Graph Matching</h3>
<p>The overall SPARQL design can be used for queries which assume a more elaborate form of
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