removes inconsistencies in how the cardinality of a sequence/list is denoted

Author: hartig

spec/index.html

@@ -9474,9 +9474,10 @@ <h4>Aggregate Algebra</h4>
             </ol>
 
             <p><b>Special Case:</b> when <code>COUNT</code> is used with the expression
-              <code>*</code> the value of F will be the cardinality of the group solution sequence,
-              <code>card[Ψ]</code>, or <code>card[Dedup(Ψ)]</code> if the <code>DISTINCT</code>
-              keyword is present.</p>
+              <code>*</code>, then F(Ψ) is the cardinality of the group solution sequence,
+              i.e., F(Ψ)&nbsp;=&nbsp;<a href="#defn_Card">Card</a>(Ψ),
+              or F(Ψ)&nbsp;=&nbsp;<a href="#defn_Card">Card</a>(Dedup(Ψ))
+              if the <code>DISTINCT</code> keyword is present.</p>
           </div>
           <p><i>scalarvals</i> are used to pass values to the underlying set function, bypassing
             the mechanics of the grouping. For example, the aggregate expression
@@ -9537,6 +9538,11 @@ <h4>Aggregate Algebra</h4>
             <p>The Flatten(S) function takes a sequence of lists, S = [(L<sub>1</sub>, L<sub>2</sub>,
               ...), ...], and returns the list ( x | L in S and x in L ).</p>
           </div>
+          <p>Card is a function that returns the cardinality of a sequence or a list of elements (which may be solution mappings or other types of elements, depending on the context).
+          <div class="defn">
+            <p><b>Definition: <span id="defn_Card">Card</span></b></p>
+            <p>Given a sequence or a list |L|, Card(|L|) is the cardinality of |L|.</p>
+          </div>
           <section id="setFunctions">
             <h5>Set Functions</h5>
             <p>The set functions which underlie SPARQL aggregates all have a common signature:
@@ -9568,7 +9574,7 @@ <h5>Count</h5>
               <pre class="code nohighlight">xsd:integer Count(sequence S)</pre>
               <p>L = Flatten(S)</p>
               <p>remove error elements from L</p>
-              <p>Count(S) = card[L]</p>
+              <p>Count(S) = <a href="#defn_Card">Card</a>(L)</p>
             </div>
           </section>
           <section id="aggSum">
@@ -9583,10 +9589,10 @@ <h5>Sum</h5>
               <pre class="code nohighlight">numeric Sum(sequence S)</pre>
               <p>L = Flatten(S)</p>
               <p>Sum(S) = Sum(L)</p>
-              <p>Sum(L) = op:numeric-add(L<sub>1</sub>, Sum(L<sub>2..n</sub>)) when card[L] &gt;
+              <p>Sum(L) = op:numeric-add(L<sub>1</sub>, Sum(L<sub>2..n</sub>)) when <a href="#defn_Card">Card</a>(L) &gt;
                 1<br>
-                Sum(L) = op:numeric-add(L<sub>1</sub>, 0) when card[L] = 1<br>
-                Sum(L) = "0"^^xsd:integer when card[L] = 0</p>
+                Sum(L) = op:numeric-add(L<sub>1</sub>, 0) when <a href="#defn_Card">Card</a>(L) = 1<br>
+                Sum(L) = "0"^^xsd:integer when <a href="#defn_Card">Card</a>(L) = 0</p>
               <p>In this way, Sum( (1, 2, 3) ) = op:numeric-add(1, op:numeric-add(2,
                 op:numeric-add(3, 0))).</p>
             </div>
@@ -9615,8 +9621,8 @@ <h5>Min</h5>
               <p>L = Flatten(S)</p>
               <p>Min(S) = Min(L)</p>
               <p>The flattened list L of values is ordered as per the <code>ORDER BY ASC</code> clause.</p>
-              <p>Min(L) = L<sub>0</sub> if card[L] > 0<br>
-                Min(L) = error if card[L] = 0</p>
+              <p>Min(L) = L<sub>0</sub> if <a href="#defn_Card">Card</a>(L) > 0<br>
+                Min(L) = error if <a href="#defn_Card">Card</a>(L) = 0</p>
             </div>
           </section>
           <section id="aggMax">
@@ -9631,8 +9637,8 @@ <h5>Max</h5>
               <p>L = Flatten(S)</p>
               <p>Max(S) = Max(L)</p>
               <p>The flattened list L of values is ordered as per the <code>ORDER BY DESC</code> clause.</p>
-              <p>Max(L) = L<sub>0</sub> if card[L] > 0<br>
-                Max(L) = error if card[L] = 0</p>
+              <p>Max(L) = L<sub>0</sub> if <a href="#defn_Card">Card</a>(L) > 0<br>
+                Max(L) = error if <a href="#defn_Card">Card</a>(L) = 0</p>
             </div>
           </section>
           <section id="aggGroupConcat">
@@ -9648,12 +9654,11 @@ <h5>GroupConcat</h5>
                 be the "space" character, unicode codepoint U+0020.</p>
               <p>L = Flatten(S)</p>
               <p>GroupConcat(S, scalarvals) = GroupConcat(L, scalarvals("separator"))</p>
-              <p>GroupConcat(L, sep) = "", where <span style=
-                                                       "font-size: 140%">|</span>L<span style="font-size: 140%">|</span> = 0</p>
+              <p>GroupConcat(L, sep) = "", where <a href="#defn_Card">Card</a>(L) = 0</p>
               <p>GroupConcat(L, sep) = CONCAT("", L<sub>0</sub>), where 
-                <span style="font-size: 140%">|</span>L<span style="font-size: 140%">|</span> = 1</p>
+                <a href="#defn_Card">Card</a>(L) = 1</p>
               <p>GroupConcat(L, sep) = CONCAT(L<sub>0</sub>, sep, GroupConcat(L<sub>1..n-1</sub>,
-                sep)), where <span style="font-size: 140%">|</span>L<span style="font-size: 140%">|</span> &gt; 1</p>
+                sep)), where <a href="#defn_Card">Card</a>(L) &gt; 1</p>
             </div>
             <p>For example, GroupConcat([("a"), ("b"), ("c")], {"separator" → "."}) = "a.b.c".</p>
           </section>