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Merge pull request #124 from w3c/AlternativeToPR122
Improves the section about the Sum set function
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‎spec/index.html

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@@ -9703,16 +9703,25 @@ <h5>Sum</h5>
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be 6.0 (float).</p>
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<div class="defn">
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<p><b>Definition: <span id="defn_aggSum">Sum</span></b></p>
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<pre class="code nohighlight">numeric Sum(sequence S)</pre>
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<p>L = Flatten(S)</p>
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<p>Sum(S) = Sum(L)</p>
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<p>Sum(L) = op:numeric-add(L<sub>1</sub>, Sum(L<sub>2..n</sub>)) if <a href="#defn_Card">Card</a>(L) &gt;
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1<br>
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Sum(L) = op:numeric-add(L<sub>1</sub>, 0) if <a href="#defn_Card">Card</a>(L) = 1<br>
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Sum(L) = "0"^^xsd:integer if <a href="#defn_Card">Card</a>(L) = 0</p>
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<p>In this way, Sum( (1, 2, 3) ) = op:numeric-add(1, op:numeric-add(2,
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op:numeric-add(3, 0))).</p>
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<pre class="code nohighlight">numeric <var>Sum</var>(sequence <var>S</var>)</pre>
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<p><var>Sum</var>(<var>S</var>) = <var>SumList</var>(<var>L</var>),</p>
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<p>where <var>L</var> = Flatten(<var>S</var>) and
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<var>SumList</var>(<var>L</var>) is defined recursively as follows.</p>
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<ul>
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<li>If <a href="#defn_Card">Card</a>(<var>L</var>) = 0, then
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<var>SumList</var>(<var>L</var>) = "0"^^<code>xsd:integer</code>.</li>
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<li>If <a href="#defn_Card">Card</a>(<var>L</var>) = 1, then
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<var>SumList</var>(<var>L</var>) = <a data-cite="XPATH-FUNCTIONS-31#func-numeric-add">op:numeric-add</a>(<var>L</var><sub>1</sub>, 0).</li>
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<li>If <a href="#defn_Card">Card</a>(<var>L</var>) > 1, then
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<var>SumList</var>(<var>L</var>) = <a data-cite="XPATH-FUNCTIONS-31#func-numeric-add">op:numeric-add</a>(<var>L</var><sub>1</sub>,
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<var>SumList</var>(<var>L</var><sub>2..n</sub>)).</li>
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</ul>
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<p>Note that <var>L</var><sub>1</sub> is the first element in
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<var>L</var>, and <var>L</var><sub>2..n</sub> is <var>L</var>
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without its first element.</p>
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</div>
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<p>In this way, <var>Sum</var>( [(1), (2), (3)] ) = <var>SumList</var>( (1, 2, 3) ) =
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op:numeric-add(1, op:numeric-add(2, op:numeric-add(3, 0))).</p>
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</section>
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<section id="aggAvg">
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<h5>Avg</h5>
@@ -9734,12 +9743,19 @@ <h5>Min</h5>
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arbitrarily typed expressions.</p>
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<div class="defn">
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<p><b>Definition: <span id="defn_aggMin">Min</span></b></p>
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<pre class="code nohighlight">term Min(sequence S)</pre>
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<p>L = Flatten(S)</p>
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<p>Min(S) = Min(L)</p>
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<p>The flattened list L of values is ordered as per the <code>ORDER BY ASC</code> clause.</p>
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<p>Min(L) = L<sub>1</sub> if <a href="#defn_Card">Card</a>(L) > 0<br>
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Min(L) = error if <a href="#defn_Card">Card</a>(L) = 0</p>
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<pre class="code nohighlight">term <var>Min</var>(sequence <var>S</var>)</pre>
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<p><var>Min</var>(<var>S</var>) = <var>MinList</var>(<var>L</var>),</p>
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<p>where <var>L</var> is the list of values obtained by Flatten(<var>S</var>)
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and then ordered as per the <code>ORDER BY ASC</code> clause,
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and <var>MinList</var>(<var>L</var>) is defined as follows.</p>
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<ul>
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<li>If <a href="#defn_Card">Card</a>(<var>L</var>) = 0, then
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<var>MinList</var>(<var>L</var>) = error.</li>
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<li>If <a href="#defn_Card">Card</a>(<var>L</var>) > 0, then
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<var>MinList</var>(<var>L</var>) = <var>L</var><sub>1</sub>,
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where <var>L</var><sub>1</sub> is the first element in
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<var>L</var>.</li>
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</ul>
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</div>
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</section>
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<section id="aggMax">
@@ -9750,12 +9766,19 @@ <h5>Max</h5>
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arbitrarily typed expressions.</p>
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<div class="defn">
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<p><b>Definition: <span id="defn_aggMax">Max</span></b></p>
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<pre class="code nohighlight">term Max(sequence S)</pre>
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<p>L = Flatten(S)</p>
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<p>Max(S) = Max(L)</p>
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<p>The flattened list L of values is ordered as per the <code>ORDER BY DESC</code> clause.</p>
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<p>Max(L) = L<sub>1</sub> if <a href="#defn_Card">Card</a>(L) > 0<br>
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Max(L) = error if <a href="#defn_Card">Card</a>(L) = 0</p>
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<pre class="code nohighlight">term <var>Max</var>(sequence <var>S</var>)</pre>
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<p><var>Max</var>(<var>S</var>) = <var>MaxList</var>(<var>L</var>),</p>
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<p>where <var>L</var> is the list of values obtained by Flatten(<var>S</var>)
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and then ordered as per the <code>ORDER BY DESC</code> clause,
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and <var>MaxList</var>(<var>L</var>) is defined as follows.</p>
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<ul>
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<li>If <a href="#defn_Card">Card</a>(<var>L</var>) = 0, then
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<var>MaxList</var>(<var>L</var>) = error.</li>
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<li>If <a href="#defn_Card">Card</a>(<var>L</var>) > 0, then
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<var>MaxList</var>(<var>L</var>) = <var>L</var><sub>1</sub>,
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where <var>L</var><sub>1</sub> is the first element in
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<var>L</var>.</li>
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</ul>
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</div>
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</section>
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<section id="aggGroupConcat">
@@ -9766,20 +9789,38 @@ <h5>GroupConcat</h5>
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SEPARATOR.</p>
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<div class="defn">
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<p><b>Definition: <span id="defn_aggGroupConcat">GroupConcat</span></b></p>
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<pre class="code nohighlight">literal GroupConcat(sequence S, function scalarvals)</pre>
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<p>If the scalarvals argument is absent from GROUP_CONCAT, then scalarvals is taken to
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be the empty function.</p>
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<p>|separator| = scalarvals("separator") if scalarvals is defined for the argument "separator"</p>
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<p>|separator| = the "space" character, unicode codepoint U+0020, if scalarvals is undefined for the argument "separator"</p>
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<p>L = Flatten(S)</p>
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<p>GroupConcat(S, scalarvals) = GroupConcat(L, |separator|)</p>
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<p>GroupConcat(L, sep) = "" if <a href="#defn_Card">Card</a>(L) = 0</p>
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<p>GroupConcat(L, sep) = CONCAT("", L<sub>1</sub>) if
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<a href="#defn_Card">Card</a>(L) = 1</p>
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<p>GroupConcat(L, sep) = CONCAT(L<sub>1</sub>, sep, GroupConcat(L<sub>2..n</sub>,
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sep)) if <a href="#defn_Card">Card</a>(L) &gt; 1</p>
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</div>
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<p>For example, GroupConcat([("a"), ("b"), ("c")], {"separator" → "."}) = "a.b.c".</p>
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<pre class="code nohighlight">literal <var>GroupConcat</var>(sequence <var>S</var>, function <var>scalarvals</var>)</pre>
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<p>If the <var>scalarvals</var> argument is absent from <code>GROUP_CONCAT</code>,
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then <var>scalarvals</var> is taken to be the empty function.</p>
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<p>Let <var>sep</var> be a string that is defined as follows.</p>
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<ul>
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<li>If <var>scalarvals</var> is defined for the argument "separator",
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then <var>sep</var> = <var>scalarvals</var>("separator").</li>
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<li>If <var>scalarvals</var> is undefined for the argument "separator",
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then <var>sep</var> is the "space" character (i.e., unicode codepoint U+0020).</li>
9801+
</ul>
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<p><var>GroupConcat</var>(<var>S</var>, <var>scalarvals</var>) =
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<var>GCList</var>(<var>L</var>, <var>sep</var>),</p>
9804+
<p>where <var>L</var> = Flatten(<var>S</var>) and
9805+
<var>GCList</var>(<var>L</var>, <var>sep</var>)
9806+
is defined recursively as follows.</p>
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<ul>
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<li>If <a href="#defn_Card">Card</a>(<var>L</var>) = 0, then
9809+
<var>GCList</var>(<var>L</var>, <var>sep</var>) = "".</li>
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<li>If <a href="#defn_Card">Card</a>(<var>L</var>) = 1, then
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<var>GCList</var>(<var>L</var>, <var>sep</var>) =
9812+
<a href="#func-concat"><code>CONCAT</code></a>("", <var>L</var><sub>1</sub>).</li>
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<li>If <a href="#defn_Card">Card</a>(<var>L</var>) > 1, then
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<var>GCList</var>(<var>L</var>, <var>sep</var>) =
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<a href="#func-concat"><code>CONCAT</code></a>(<var>L</var><sub>1</sub>, <var>sep</var>, <var>GCList</var>(<var>L</var><sub>2..n</sub>, <var>sep</var>)).</li>
9816+
</ul>
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<p>Note that <var>L</var><sub>1</sub> is the first element in
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<var>L</var>, and <var>L</var><sub>2..n</sub> is <var>L</var>
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without its first element.</p>
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</div>
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<p>For example, <var>GroupConcat</var>([("a"), ("b"), ("c")], {"separator" → "."})
9822+
= <var>GCList</var>( ("a", "b", "c"), "." )
9823+
= "a.b.c".</p>
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</section>
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<section id="aggSample">
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<h5>Sample</h5>

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