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Merge pull request #221 from w3c/Issue217
Consider bnode graph names in evaluation of Graph
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‎spec/index.html

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@@ -107,6 +107,7 @@
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div.defn p { margin-top: 1ex ; margin-bottom: 1.5ex ;}
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div.defn ul { margin-top: 1ex ; margin-bottom: 1.5ex ; }
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span.definedTerm {font-weight: bold;}
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div.indentedFormula { margin-left: 5ex ; margin-top: 2mm ; margin-bottom: 2mm ; }
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div.grammarExtract
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{ border: thin solid #888888;
@@ -9472,8 +9473,6 @@ <h3>Basic Graph Patterns</h3>
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<p>Write <var>Ω<sub>0</sub></var> for the multiset consisting of exactly the empty mapping
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<var>μ<sub>0</sub></var>, with multiplicity 1. This is the join identity.</p>
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<p>Write <var>μ</var>(<var>x</var>) for the solution mapping variable <var>x</var> to RDF term <var>t</var> : { (<var>x</var>, <var>t</var>) }.</p>
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<p>Write <var>Ω</var>(<var>x</var>) for the multiset consisting of exactly <var>μ</var>(<var>?x</var>-&gt;<var>t</var>), that is, <code>{ { (x, t) } }</code>
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with multiplicity 1.</p>
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<div class="defn">
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<p><b>Definition: <span id="defn_algCompatibleMapping">Compatible Mappings</span></b></p>
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<p>Two solution mappings μ<sub>1</sub> and μ<sub>2</sub> are compatible if, for every
@@ -10312,9 +10311,8 @@ <h5>Sample</h5>
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<h3>Evaluation Semantics</h3>
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<p id="defn_eval">We define <a href="#defn_eval" class="evalFct">eval</a>(|D|(|G|), |A|) as the evaluation of an algebra expression |A| with
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respect to a <a href="#sparqlDataset">dataset</a> |D| having <a href="#defn_ActiveGraph">active graph</a> |G|. The active graph is initially the default
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graph of |D|. Further symbols and notation used in the following definitions are:</p>
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graph of |D|. Further symbols used in the following definitions are:</p>
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<ul>
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<li>|D|[|i|] : Denotes the graph with IRI |i| in dataset |D|</li>
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<li>|P|, <var>P<sub>1</sub></var>, <var>P<sub>2</sub></var> : graph patterns</li>
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<li>|L| : a solution sequence</li>
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<li>|F| : an expression</li>
@@ -10368,25 +10366,46 @@ <h3>Evaluation Semantics</h3>
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</div>
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<div class="defn">
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<p><b>Definition: <span id="defn_evalGraph">Evaluation of Graph</span></b></p>
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<pre class="code nohighlight">
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if <var>IRI</var> is a graph name in <var>D</var>
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<a href="#defn_eval" class="evalFct">eval</a>( <var>D</var>(<var>G</var>), Graph(<var>IRI</var>,<var>P</var>) ) = <a href="#defn_eval" class="evalFct">eval</a>( <var>D</var>(<var>D</var>[<var>IRI</var>]), <var>P</var> )
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</pre>
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<pre class="code nohighlight">
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if <var>IRI</var> is not a graph name in <var>D</var>
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<a href="#defn_eval" class="evalFct">eval</a>( <var>D</var>(<var>G</var>), Graph(<var>IRI</var>,<var>P</var>) ) = the empty multiset
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</pre>
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<pre class="code nohighlight">
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<a href="#defn_eval" class="evalFct">eval</a>( <var>D</var>(<var>G</var>), Graph(<var>var</var>,<var>P</var>) ) =
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Let <var>R</var> be the empty multiset
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foreach IRI <var>i</var> in <var>D</var>
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<var>R</var> := <a href="#defn_algUnion" class="algFct">Union</a>(<var>R</var>, <a href="#defn_algJoin" class="algFct">Join</a>( <a href="#defn_eval" class="evalFct">eval</a>(<var>D</var>(<var>D</var>[<var>i</var>]), <var>P</var>) , Ω(<var>var</var>-&gt;<var>i</var>) ) )
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the result is <var>R</var>
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</pre>
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<p>For every |x| that is
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an <a data-cite="RDF12-CONCEPTS#dfn-IRI">IRI</a> or
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a <a href="#defn_QueryVariable">variable</a>,
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<a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), Graph(|x|, |P|) )
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is defined as follows:</p>
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<ul>
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<li>If |x| is an IRI
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that is a <a data-cite="RDF12-CONCEPTS#dfn-graph-name">graph name</a> in |D|,
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<div class="indentedFormula">
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<a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), Graph(|x|, |P|) )
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=
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<a href="#defn_eval" class="evalFct">eval</a>( |D|(<var>G<sub>|x|</sub></var>), |P| ),
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</div>
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where <var>G<sub>|x|</sub></var> is the RDF graph of the named graph with name |x| in |D|.
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</li>
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<li>If |x| is an IRI
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that is not a <a data-cite="RDF12-CONCEPTS#dfn-graph-name">graph name</a> in |D|,
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<div class="indentedFormula">
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<a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), Graph(|x|, |P|) )
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is the empty multiset.
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</div>
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</li>
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<li>If |x| is a variable,
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<div class="indentedFormula">
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<a href="#defn_eval" class="evalFct">eval</a>( |D|(|G|), Graph(|x|, |P|) )
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=
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<var>Ω</var>,
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</div>
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where <var>Ω</var> is the multiset of solution mappings produced by the following algorithm:
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<pre class="code nohighlight" style="font-family: sans-serif;">
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<var>Ω</var> := the empty multiset
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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)
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<var>G'</var> := the RDF graph of the named graph with name <var>gn</var> in <var>D</var>
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<var>Ω'</var> := <a href="#defn_eval" class="evalFct">eval</a>( <var>D</var>(<var>G'</var>), <var>P</var> )
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<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>}
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the result is <var>Ω</var>
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</pre>
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</li>
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</ul>
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</div>
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<p>The evaluation of graph uses the <a href="#defn_algUnion" class="algFct">Union</a> operator. The multiplicity of a
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solution mapping is the sum of the multiplicities of that solution mapping in each <a href="#defn_algJoin" class="algFct">Join</a>
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operation.</p>
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<div class="defn">
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<div id="defn_evalGroup">
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<b>Definition: Evaluation of Group</b>

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