Updates from review of shacl12-rules/index.html

Co-authored-by: simon <simon.steyskal@siemens.com>

Author: afs

shacl12-rules/index.html

@@ -152,7 +152,7 @@ <h3>Terminology</h3>
         <p class="ednote">Connect to definitions in RDF 1.2 Concepts.</p>
 
         <p>
-          The following definitions from other specications are used in this document: @@
+          The following definitions from other specifications are used in this document: @@
         </p>
       </section>
 
@@ -190,7 +190,7 @@ <h3>Document Conventions</h3>
           </tr>
           <tr>
             <td><code>ex:</code></td>
-            <td><code>http://example.com/ns#</code></td>
+            <td><code>http://example.com/</code></td>
           </tr>
         </table>
         <p>
@@ -269,7 +269,7 @@ <h3>Basic Usage</h3>
 RULE { ?x :descendedFrom ?y } WHERE { ?x :childOf ?z . ?z :childOf ?y }
 </pre>
         </div>
-        <p>The above rules, applied ot the data, will conclude 
+        <p>The above rules, applied to the data, will conclude 
           that: `:X` is the `:childOf` `:A` and `:B`, and that `:X` is `:descendedFrom` `:C`.
         </p>
       </section>
@@ -320,7 +320,7 @@ <h2>Shape Rules Abstract Syntax</h2>
               <a>Expressions</a> are compatible with
               <a data-cite="shacl12-node-expr#dfn-list-parameter-function"
                  >SHACL list parameter functions</a>
-              and with <a data-cite="sparql12-query#expressions">SPARQL expressions</a>.
+              and with <a data-cite="sparql12-query#expressions">SPARQL expressions</a>.</p>
           </dd>
 
           <dt><dfn data-lt="data-block">data block</dfn></dt>
@@ -332,15 +332,17 @@ <h2>Shape Rules Abstract Syntax</h2>
           <dt><dfn>triple template</dfn></dt>
           <dd>
             A [=triple template=] is 3-tuple where each element is either
-            a variable or an RDF term (which might be a triple term).
+            a [=variable=] or an [=RDF term] (which might be a [=triple term=]).
+            The second element of the tuple must be an [=IRI=] or a [=variable=].
             [=Triple templates=] appear in the [=head=] of a [=rule=].
           </dd>
 
           <dt><dfn>triple pattern</dfn></dt>
           <dd>
             A [=triple pattern=] is 3-tuple where each element is either a
-            variable, or an RDF term  (which might be a triple term).
-            [=Triple  patterns=] appear in the [=body=] of a [=rule=].
+            [=variable=], or an [=RDF term=] (which might be a triple term).
+            The second element of the tuple must be an [=IRI=].
+            [=Triple patterns=] appear in the [=body=] of a [=rule=].
           </dd>
 
           <dt><dfn>condition expression</dfn></dt>
@@ -372,7 +374,7 @@ <h2>Shape Rules Abstract Syntax</h2>
 
           <dt><dfn data-lt="rule body element|rule element|element">rule body element</dfn></dt>
           <dd>
-            A [=rule body element=] (often just "rule element") is one of elements that 
+            A [=rule body element=] (often just "rule element") is any element that
             can appear in a [=rule body=];
             a [=triple pattern=],
             a [=condition expression=],
@@ -391,7 +393,7 @@ <h2>Shape Rules Abstract Syntax</h2>
             <dfn data-lt="rule body|body">rule body</dfn>
           </dt>
           <dd> 
-            A [=rule body=] is a sequence of [=rule body elements=].</dfn>
+            A [=rule body=] is a sequence of [=rule body elements=].
           </dd>
 
           <dt><dfn>rule</dfn></dt>
@@ -426,7 +428,7 @@ <h3>Stratification</h3>
             <dt><dfn data-lt="stratification layer|layer">stratification layer</dfn></dt>
             <dd>
               A stratification layer, usually, just "layer", is the set of rules 
-              with same straification labelling.
+              with same stratification labelling.
               <a>stratification layer</a>, <a>layer</a>
             </dd>
 
@@ -520,7 +522,7 @@ <h3>Well-formedness Conditions</h3>
 
     <section id="concrete-syntax">
       <h2>Concrete Syntax forms for Shapes Rules</h2>
-      <P>There are two concrete syntaxes.</p>
+      <p>There are two concrete syntaxes.</p>
       <ul>
         <li><a href="#shape-rules-syntax">Shape Rules Language syntax</a></li>
         <li><a href="#rdf-rules-syntax">RDF Rules syntax</a></li>
@@ -566,7 +568,7 @@ <h2>Concrete Syntax forms for Shapes Rules</h2>
       rdf:type shrl:Rule;
       shrl:head (
         [ shrl:subject [ shrl:var "x" ] ; shrl:predicate :bothPositive; shrl:object true ]
-      )
+      ) ;
       shrl:body (
         [ shrl:subject [ shrl:var "x" ]; shrl:predicate :p; shrl:object [ shrl:var "v1" ] ]
         [ shrl:expr [ sparql:greaterThan ( [ shrl:var "v1" ] 0 ) ] ]
@@ -578,7 +580,7 @@ <h2>Concrete Syntax forms for Shapes Rules</h2>
       rdf:type shrl:Rule;
       shrl:head (
         [ shrl:subject [ shrl:var "x" ] ; shrl:predicate :oneIsZero ; shrl:object true ]
-      )
+      ) ;
       shrl:body (
         [ shrl:subject [ shrl:var "x" ] ; shrl:predicate :p ; shrl:object [ shrl:var "v1" ] ]
         [ shrl:subject [ shrl:var "x" ] ; shrl:predicate :q ; shrl:object [ shrl:var "v2" ] ]
@@ -603,7 +605,7 @@ <h4>Shape Rules Language Abbreviations</h4>
           <p>Additional helpers (short-hand abbreviations):</p>
 
           <p class=note>
-            These allow for well-known rul epatterns and also specialised implementations in basic engines
+            These allow for well-known rule patterns and also specialised implementations in basic engines
           </p>
 
           <ul>
@@ -690,7 +692,7 @@ <h4>Evaluation Definitions</h4>
           <dt><dfn data-lt="solution|sparql12-query#defn_sparqlSolutionMapping">solution mapping</dfn></dt>
           <dd> 
             A <a data-lt="sparql12-query#defn_sparqlSolutionMapping">solution mapping</a>, 
-            <var>μ</var>, is a partial function <code><var>μ</var> : V → T</code>, 
+            <var>μ</var>, is a partial function <code><var>μ</var> : <var>V</var> → <var>T</var></code>, 
             where <var>V</var> is the set of all variables and <var>T</var> is the set of all RDF terms.
             The domain of <var>μ</var> is denoted by <code><var>dom</var>(<var>μ</var>)</code>,
             and it is the subset of <var>V</var> for which <var>μ</var> is defined.
@@ -767,13 +769,18 @@ <h4>Evaluation Definitions</h4>
             that maps variables of each solution to the [=RDF term=]
             from one or other of the solutions. 
             <div class="def">
-              Let S1 and S2 be solution sequences.
+              Let <var>μ</var><sub>1</sub>, <var>μ</var><sub>2</sub>
+              be solution mappings, and S1 and S2 be solution sequences.
               <pre>
+merge(<var>μ</var><sub>1</sub>, <var>μ</var><sub>2</sub>) = { <var>μ</var> |
+                    μ(v) = μ1(v) if v in dom(μ1)
+                    μ(v) = μ2(v) otherwise }</pre>
+
+<pre>
 merge(S1, S2) = { <var>μ</var> |
                     <var>μ</var><sub>1</sub> in S1, <var>μ</var><sub>2</sub> in S2
                     and compatible(<var>μ</var><sub>1</sub>, <var>μ</var><sub>2</sub>)
-                        μ(v) = μ1(v) if v in dom(μ1)
-                        μ(v) = μ2(v) if v in dom(μ2) }</pre>
+                    μ(v) = merge(<var>μ</var><sub>1</sub>, <var>μ</var><sub>2</sub>)</pre>
             </div>
             <div class="ednote">
               <p>
@@ -842,14 +849,13 @@ <h4>Evaluation of a Rule</h4>
 variable that does not occur in the rule body.
 
 # Evaluate rule body
-for each rule element rElt in B
-    let S1 = { }
 
+for each rule element rElt in B
     if rElt is a triple pattern TP:
         X = graphMatch(G, TP)
-        SEQ1 = { <var>μ</var><sub>0</sub> }
+        SEQ1 = {}
         for each <var>μ</var><sub>1</sub> in X:
-            for each <var>μ</var><sub>2</sub> in T:
+            for each <var>μ</var><sub>2</sub> in SEQ:
               if compatible(<var>μ</var><sub>1</sub>, <var>μ</var><sub>2</sub>)
                 <var>μ</var><sub>3</sub> = merge(<var>μ</var>1, <var>μ</var><sub>2</sub>)
                 add <var>μ</var><sub>3</sub> to SEQ1
@@ -870,7 +876,7 @@ <h4>Evaluation of a Rule</h4>
     if rElt is an assignment(V, expr)
         SEQ1 = {}
         for each solution S in SEQ:
-            let x = eval(expr, <var>μ</var>)
+            let x = eval(expr, S)
             add(V, x) to S
             add S to SEQ1
             endfor
@@ -887,18 +893,18 @@ <h4>Evaluation of a Rule</h4>
 
 # Evaluate rule head
 let H = empty set
-for each <var>μ</var> in T:
-    Let S = {}
+for each <var>μ</var> in SEQ:
+    let S = {}
     for each triple template TT in head
-        Let triple = subst(<var>μ</var>, TT)
+        let triple = subst(<var>μ</var>, TT)
         Add triple to S
     H = H union S
     endfor
 
 result eval(R, G) is H
 
 </pre>
-      <p>Note that `H` may contain triples that are also in the data grapoh.</p>
+      <p>Note that `H` may contain triples that are also in the data graph.</p>
       </section>
 
       <section id="eval-rule-set">
@@ -907,24 +913,23 @@ <h4>Evaluation of a Rule Set</h4>
         <p class=ednote>Sketch</p>
 
 <pre class="algorithm">
-Let G0 be the input RDF graph.
-Let GI be the set of triples generated by evaluation
-Let RS be a rule set
+let G0 be the input RDF graph.
+let RS be the rule set
 Apply stratification to RS
-Let L be the sequence of layers after stratification
+let L be the sequence of layers after stratification
 
-for each layer in L
-    Let finished = false
+let GI = G0
+for each layer in L:
+    let finished = false
     while !finished:
         finished = true
-        foreach rule in RS
-            let GI = G0 &cup; GI
+        for each rule in layer:
             let X = eval(rule, GI)
-            let Y = those triples in X that are not in G0
+            let Y = { t &isinv; X | t &notin; in GI }
             if Y is not empty:
                 finished = false
                 endif
-            let GI = Y &cup; GI
+            let GI = Y &cups; GI
             endfor
         endwhile
     endfor