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Add 'row in scope' approach
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‎spec/index.html

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@@ -10645,7 +10645,7 @@ <h3>Evaluation Semantics</h3>
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<section>
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<h3>Values Insertion and `EXISTS`</h3>
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<div class="ednote">
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<p>The following subsections contain draft of material for a revised
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<p>The following subsections contain draft material for a revised
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"`exists`" operation.
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</p>
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<p>
@@ -10660,7 +10660,10 @@ <h4>Syntax Restriction</h4>
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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 introduced 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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<p>
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Extend the "in-scope" rules to include the possible
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variables that are in-scope for the current row:
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</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>
@@ -10674,10 +10677,15 @@ <h4>Syntax Restriction</h4>
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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 variables within the pattern.
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</p>
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<div class="note">
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<p>
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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 variables within the pattern.
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</p>
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<p>
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This operation is performed as part of query parsing.
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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>Remapping</h4>
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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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<b>Definition: <span id="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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<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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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
@@ -10716,7 +10724,7 @@ <h4>Remapping</h4>
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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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<b>Definition: <span id="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)`
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of algebra expression `X`:
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Replacements may happen several times, depending on recursive 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 the values insertion operation because it is renamed apart.
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</p>
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<div class="note">
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<p>
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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 the values insertion operation because it is renamed apart.
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</p>
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<p>
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This operation is as part of the <a href="#sparqlQuery">translation to the SPARQL
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algebra</a>.
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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>Values Insertion</h4>
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<p>
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Alternative 1: rewrite the algebra during
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<a href="#sparqlQuery">translation to the SPARQL algebra</a>
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to include a function that evaluates to the current row.
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</p>
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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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<b>Definition: <span id="defn_correlate">Values In Scope</span></b>
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<p>
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Define the Values Insertion function `ValuesInsert(X, μ)`
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Define the function `BindingInScope()`.
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Evaluation of `BindingInScope()` results in a table of one row,
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being the current binding of the enclosing filter.
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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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</div>
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</div>
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<div class="defn">
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<div>
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<b>Definition: Access to the current binding</b>
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<p>
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During <a href="#sparqlQuery">translation to the SPARQL algebra</a>
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</p>
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<pre>
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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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<a href="#https://www.w3.org/TR/sparql12-query/#sparqlTranslateGraphPatterns">Inline Data</a>
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with `join(Y, Table(μ))`.</pre>
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with `join(Y, BindingInScope())`.</pre>
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</div>
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<div class="note">
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c.f. section <a href="#sparqlTranslateGraphPatterns">Translate Graph Patterns</a>
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where an empty basic graph pattern start any
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<a href="#rGroupGraphPattern">GroupGraphPattern</a>.
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It happens before the <a href="#sparqlSimplification">simplification step</a>.
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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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<p>
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Alternative 2: rewrite the algebra during execution. This corresponds to the
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<a href="https://github.com/w3c/sparql-dev/blob/main/SEP/SEP-0007/sep-0007.md">original SEP-0007 proposal</a>.
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</p>
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<div class="defn">
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<div>
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<b>Definition: <span id="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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<a href="#https://www.w3.org/TR/sparql12-query/#sparqlTranslateGraphPatterns">Inline Data</a>
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with `join(Y, Table(μ))`.</pre>
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</div>
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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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<b>Definition: <span id="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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if eval( D(G), ValuesInScope(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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