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Adds definition of multiplicity for Extend operator #348

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38 changes: 24 additions & 14 deletions spec/index.html
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Original file line number Diff line number Diff line change
Expand Up @@ -10222,22 +10222,32 @@ <h3>SPARQL Algebra</h3>
|D| be a <a href="#sparqlDataset">dataset</a>,
and |G| be the <a href="#defn_ActiveGraph">active graph</a>.
We define:</p>
<p><a href="#defn_algExtend" class="algFct">Extend</a>(<var>Ω</var>, <var>var</var>, <var>expr</var>, |D|, |G|) = { |Extend|(<var>μ</var>, <var>var</var>, <var>expr</var>, |D|, |G|) | <var>μ</var> in <var>Ω</var> },</p>
<p>where, for every solution mapping <var>μ</var>,</p>
<p>|Extend|(<var>μ</var>, <var>var</var>, <var>expr</var>, |D|, |G|) = <var>μ</var> ∪ { (<var>var</var>, |expr|(<var>μ</var>, |D|, |G|)) }
if <var>var</var> not in dom(<var>μ</var>) and
|expr|(<var>μ</var>, |D|, |G|) is an RDF term,</p>
<p>|Extend|(<var>μ</var>, <var>var</var>, <var>expr</var>, |D|, |G|) = <var>μ</var>
if <var>var</var> not in dom(<var>μ</var>) and
|expr|(<var>μ</var>, |D|, |G|) is an [=error=],</p>
<p>|Extend|(<var>μ</var>, <var>var</var>, <var>expr</var>, |D|, |G|) is undefined
if <var>var</var> in dom(<var>μ</var>), and</p>
<p>|expr|(<var>μ</var>, |D|, |G|) is the result of
<p><a href="#defn_algExtend" class="algFct">Extend</a>(<var>Ω</var>, <var>var</var>, <var>expr</var>, |D|, |G|) = { |Extend|(<var>μ'</var>, <var>var</var>, <var>expr</var>, |D|, |G|) | <var>μ'</var> in <var>Ω</var> },</p>
<p>
<a href="#defn_Multiplicity">multiplicity</a>( <var>μ</var> |
<a href="#defn_algExtend" class="algFct">Extend</a>(<var>Ω</var>, |var|, |expr|, |D|, |G|) )
= <a href="#defn_Multiplicity">multiplicity</a>( <var>μ'</var> | <var>Ω</var> )
if there exists a solution mapping <var>μ'</var> in <var>Ω</var> such that
<var>μ</var> = |Extend|(<var>μ'</var>, <var>var</var>, <var>expr</var>, |D|, |G|),
</p>
<p>
<a href="#defn_Multiplicity">multiplicity</a>( <var>μ</var> |
<a href="#defn_algExtend" class="algFct">Extend</a>(<var>Ω</var>, |var|, |expr|, |D|, |G|) )
= 0 if no such solution mapping <var>μ'</var> exists in <var>Ω</var>,
</p>
<p>where, for every solution mapping <var>μ'</var>,</p>
<p>|Extend|(<var>μ'</var>, <var>var</var>, <var>expr</var>, |D|, |G|) = <var>μ'</var> ∪ { (<var>var</var>, |expr|(<var>μ'</var>, |D|, |G|)) }
if <var>var</var> not in dom(<var>μ'</var>) and
|expr|(<var>μ'</var>, |D|, |G|) is an RDF term,</p>
<p>|Extend|(<var>μ'</var>, <var>var</var>, <var>expr</var>, |D|, |G|) = <var>μ'</var>
if <var>var</var> not in dom(<var>μ'</var>) and
|expr|(<var>μ'</var>, |D|, |G|) is an [=error=],</p>
<p>|Extend|(<var>μ'</var>, <var>var</var>, <var>expr</var>, |D|, |G|) is undefined
if <var>var</var> in dom(<var>μ'</var>), and</p>
<p>|expr|(<var>μ'</var>, |D|, |G|) is the result of
<a href="#expression-evaluation">evaluating</a> expression |expr|
with respect to <var>μ</var>, in the context of dataset |D| with active graph |G|.
with respect to <var>μ'</var>, in the context of dataset |D| with active graph |G|.
</p>
<div class="issue" data-number="290">
We need to define <a href="#defn_Multiplicity">multiplicity</a>( <var>μ</var> | <a href="#defn_algExtend" class="algFct">Extend</a>(<var>Ω</var>, <var>var</var>, <var>expr</var>, |D|, |G|) )</div>
</div>
<p>Write [ <var>x</var> | <var>C</var> ] for a sequence of elements where <var>C</var> is a condition on <var>x</var>.</p>
<div class="defn">
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