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Definitions for Values Insertion #177

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145 changes: 145 additions & 0 deletions spec/index.html
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Original file line number Diff line number Diff line change
Expand Up @@ -10425,7 +10425,152 @@ <h3>Evaluation Semantics</h3>
eval(D(G), Slice(L, start, length)) = Slice(eval(D(G), L), start, length)
</pre>
</div>

<!-- ValuesInsertion -->
<section>
<h3>Values Insertion and `EXISTS`</h3>
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Values Insertion reads very oddly to me. Can this be changed (throughout) to Value Insertion?

Suggested change
<!-- ValuesInsertion -->
<section>
<h3>Values Insertion and `EXISTS`</h3>
<!-- ValueInsertion -->
<section>
<h3>Value Insertion and `EXISTS`</h3>

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It is inserting multiple values.

<p>The following sections contain draft of material for a revised
"`exists`" operation.
</p>
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<p>The following sections contain draft of material for a revised
"`exists`" operation.
</p>
<p>This section contains draft material for a revised
"`exists`" operation.
</p>

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This is a DRAFT pull request.

These are process notes. They will be removed.

<p>
Background: <a href="https://github.com/w3c/sparql-dev/blob/main/SEP/SEP-0007/sep-0007.md">SPARQL CG SEP-0007</a>
</p>

<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 variables in-scope from the current row:</p>
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<p>Extend the "in-scope" rules to include the variables in-scope from the current row:</p>
<p>Extend the "in-scope" rules to include the 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>
<p class="note">
This restriction means that <a href="#defn_valuesinsertion">values inserted</a>
do not conflict with values assigned to variables with the pattern.
</p>
</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" name="defn_projmap">Projection Expression Variable Remapping</span></b>
<p>
For a projection algebra operation #sparqlProjection `Project(A, PV)` acting on algreg express `A` and with set of variables `PV`, define
a partial mapping `F` from
`<a href="#sparqlQueryVariables">V</a>`,
the set of all variables, to `V` where:
</p>
<pre>F(v) = v1 if v is in PV, where v1 is a fresh variable
F(v) = v if v is not in PV</pre>
<p>
Define the Projection Expression Variable Remapping `ProjectMap(P,PV)`
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Define the Projection Expression Variable Remapping `ProjectMap(P,PV)`
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" name="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(P, PV) for each projection in X.</pre>
</div>
<p>
The outcome of `PrjMap` is independent of the order of replacement
(e.g. bottom-up or top-down).
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(e.g. bottom-up or top-down).
(e.g., bottom-up or top-down).

Replacements may happen several times, depending on recursive order
but each time a replacement is made, the variable not used anywhere else.
</p>

<p class="note">
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.
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Suggested change
is not affected by the values insertion operation because it is renamed apart.
is not affected by the value insertion operation because it is renamed apart.

</p>
</section>

<section>
<h4>Values Insertion</h4>
<div class="defn">
<div>
<b>Definition: <span id="defn_valuesinsertion" name="defn_valuesinsertion">Values Insertion</span></b>
<p>
Define the Values Insertion function `ValuesInsert(X, μ)`
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If, as I suggested above, Values Insertion is being changed to Value Insertion, then ValuesInsert should likewise be changed to ValueInsert

Suggested change
Define the Values Insertion function `ValuesInsert(X, μ)`
Define the Value Insertion function `ValueInsert(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="#sparqlTranslatePathExpressions">Property Path Expression</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>
<p>@@ rename as ???correllate</p>
</div>

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

<section>
<h4>Evaluation of EXISTS</h4>
<div class="defn">
<b>Definition: <span id="x-defn_evalExists" name="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>
<pre>exists(X) = true
if eval( D(G), ValuesInsert(PrjMap(X), μ) )
is a non-empty solution sequence.
exists(X) = false otherwise</pre>
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exists(X) = false otherwise</pre>
Otherwise, exists(X) = false.</pre>

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The style here is that for function definition, with each case being aligned. It is not running text.

</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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