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Initial values-insertion draft
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@@ -10369,7 +10369,151 @@ <h3>Evaluation Semantics</h3>
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eval(D(G), Slice(L, start, length)) = Slice(eval(D(G), L), start, length)
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</pre>
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</div>
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<!-- ValuesInsertion -->
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<section>
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<h3>Value Insertion and `EXISTS`</h3>
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<p>The following sections contain draft of material for a revised
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"`exists`" operation.
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</p>
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<p>Background:</p>
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<ul>
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<li><a href="https://github.com/w3c/sparql-dev/blob/main/SEP/SEP-0007/sep-0007.md">SPARQL CG SEP-0007</a></li>
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</ul>
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<section>
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<h4>Syntax Restriction</h4>
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<p><i>Additional [[[#sparqlGrammar]]] note:</i></p>
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<blockquote>
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Any variable that is assigned to in the graph pattern of `EXISTS`/`NOT EXISTS` must not be in-scope.
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This applies to `BIND`, variables introduced by `AS` in a `SELECT` clause, variables in a `VALUES`
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clause, and variables intrucded by `AS` in `GROUP BY`.
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</blockquote>
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<p>Extend the "in-scope" rules to include the variables in-scope from the current row:</p>
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<table style="border-collapse: collapse; border-color: #000000; border-spacing:5px; border-width: 1px">
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<tbody>
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<tr>
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<th>Syntax Form</th>
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<th>In-scope variables</th>
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</tr>
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<tr>
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<td>`EXISTS` and `NOT EXISTS` filters </td>
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<td><code>v</code> is in-scope if it is in-scope for pattern to which the `FILTER` is applied.
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</td>
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</tr>
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</tbody>
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</table>
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<p class="note">
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This restriction means that <a href="#defn_valuesinsertion">values inserted</a>
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do not conflict with values assigned to varibales with the pattern.
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</p>
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</section>
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<section>
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<h4>Remapping</h4>
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<p>
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Remapping ensures that a variable name used inside a project expression,
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but which is not part of the results of the evaluation of the project expression,
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does not coincide with a variable mentioned anywhere else in the
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algebra expression of a query.
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</p>
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<p>
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Renaming these variables does not change the results of evalauting
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the project expresssion.
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</p>
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<div class="defn">
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<b>Definition: <span id="defn_projmap" name="defn_projmap">Projection Expression Variable Remapping</span></b>
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<p>
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For a projection algebra operation #sparqlProjection `Project(A, PV)` acting on algreg express `A` and with set of variables `PV`, define
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a partial mapping `F` from
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`<a href="#sparqlQueryVariables">V</a>`,
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the set of all variables, to `V` where:
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</p>
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<pre>F(v) = v1 if v is in PV, where v1 is a fresh variable
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F(v) = v if v is not in PV</pre>
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<p>
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Define the Projection Expression Variable Remapping `ProjectMap(P,PV)`
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</p>
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<pre>ProjectMap(Project(A, PV)) = Project(A1, PV)
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where A1 is the result of applying F
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to every variable mentioned in A.
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</pre>
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<p>
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The Projection Expression Variable Remapping yields an algrebra expression that
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evalautes to the same results as the Project argument. No variable of `ProjectMap(Project(A, PV))`
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that is not in `PV` is mentioned anywhere else in the algebra expression for the query.
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</p>
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</div>
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<p>This process is applied throughout the graph pattern of <code>EXISTS</code>:</p>
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<div class="defn">
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<b>Definition: <span id="defn_varrename" name="defn_varrename">Variable Remapping</span></b>
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<p>
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For any algebra expression `X`, define the Variable Remapping `PrjMap(X)`of algebra expression `X`:
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</p>
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<pre>PrjMap(X) = replace all project operations Project(P, PV)
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with ProjectMap(P,PV) for each projection in X.</pre>
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</div>
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<p>
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The outcome of `PrjMap` is independent of the order of replacement
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(e.g. bottom-up or top-down).
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Replacements may happen several times, depending on recusive order
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but each time a replacement is made, the variable not used anywhere else.
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</p>
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<p class="note">
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A variable inside a project expression that is not in the variables projected
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is not affected by value insertion because it is renamed apart.
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</p>
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</section>
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<section>
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<h4>Values Insertion</h4>
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<div class="defn">
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<div>
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<b>Definition: <span id="defn_valuesinsertion" name="defn_valuesinsertion">Values Insertion</span></b>
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<p>
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Define the Values Insertion function `ValuesInsert(X, μ)`
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</p>
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<pre>Let Table(μ) = { μ } and multiplicity( μ | Table(μ) = { μ } ) = 1
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Replace each occurence of `Y` in X where `Y` is one of
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<a href="#sparqlTranslateBasicGraphPatterns">Basic Graph Pattern</a>,
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<a href="#sparqlTranslatePathExpressions">Property Path Expression</a>,
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<a href="#sparqlTranslateGraphPatterns">`Graph(Var, pattern)`</a>
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with `join(Y, Table(μ))`.</pre>
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</div>
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<p>@@ rename as ???correllate</p>
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</div>
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<div class="example">
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<p>
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Examples
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</p>
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</div>
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</section>
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<section>
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<h4>Evaluation of EXISTS</h4>
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<div class="defn">
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<b>Definition: <span id="x-defn_evalExists" name="x-defn_evalExists">Evaluation of Exists</span></b>
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<p>
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Let `μ` be the current solution mapping for a filter, and `X` a graph pattern,
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define the Evaluation of Exists `exists(X)`
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</p>
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<pre>exists(X) = true
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if eval( D(G), ValuesInsert(PrjMap(X), μ) )
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is a non-empty solution sequence.
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exists(X) = false otherwise</pre>
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</div>
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</section>
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</section>
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<!-- ValuesInsertion -->
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</section>
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<section id="sparqlBGPExtend">
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<h3>Extending SPARQL Basic Graph Matching</h3>
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<p>The overall SPARQL design can be used for queries which assume a more elaborate form of

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