Initial values-insertion draft

Author: afs

spec/index.html

@@ -10369,7 +10369,151 @@ Evaluation Semantics
 eval(D(G), Slice(L, start, length)) = Slice(eval(D(G), L), start, length)
             
           
+
+          
+          
+            Value Insertion and `EXISTS`
+            The following sections contain draft of material for a revised
+              "`exists`" operation.
+            
+            Background:
+            
+              SPARQL CG SEP-0007
+            
+
+            
+              Syntax Restriction
+              Additional [[[#sparqlGrammar]]] note:
+                
+                Any variable that is assigned to in the graph pattern of `EXISTS`/`NOT EXISTS` must not be in-scope.
+                This applies to `BIND`, variables introduced by `AS` in a `SELECT` clause, variables in a `VALUES`
+                clause, and variables intrucded by `AS` in `GROUP BY`.
+              
+              Extend the "in-scope" rules to include the variables in-scope from the current row:
+              10394+                10395+                  10396+                    Syntax Form10397+                    In-scope variables10398+                  10399+                  10400+                    `EXISTS` and `NOT EXISTS` filters 10401+                    v is in-scope if it is in-scope for pattern to which the `FILTER` is applied.10402+                    10403+                  10404+                10405+              
+                
+                  
+                    
+                    
+                  
+                  
+                    
+                    
+                    
+                  
+                
+              
+              
+                This restriction means that values inserted
+                do not conflict with values assigned to varibales with the pattern.
+              
+            
+
+            
+              Remapping
+              
+                Remapping ensures that a variable name used inside a project expression,
+                but which is not part of the results of the evaluation of the project expression,
+                does not coincide with a variable mentioned anywhere else in the
+                algebra expression of a query.
+              
+              
+                Renaming these variables does not change the results of evalauting
+                the project expresssion.
+              
+
+                Definition: Projection Expression Variable Remapping
+                
+                  For a projection algebra operation #sparqlProjection `Project(A, PV)` acting on algreg express `A` and with set of variables `PV`, define
+                  a partial mapping `F` from
+                  `V`,
+                  the set of all variables, to `V` where:
+                
+                F(v) = v1 if v is in PV, where v1 is a fresh variable
+F(v) = v if v is not in PV
+                
+                Define the Projection Expression Variable Remapping `ProjectMap(P,PV)`
+                
+                ProjectMap(Project(A, PV)) = Project(A1, PV) 
+                                where A1 is the result of applying F
+                                to every variable mentioned in A.
+                
+                
+                  The Projection Expression Variable Remapping yields an algrebra expression that
+                  evalautes to the same results as the Project argument. No variable of `ProjectMap(Project(A, PV))`
+                  that is not in `PV` is mentioned anywhere else in the algebra expression for the query.
+                
+              
+            
+              This process is applied throughout the graph pattern of EXISTS:
+
+
+                Definition: Variable Remapping
+                
+                  For any algebra expression `X`, define the Variable Remapping `PrjMap(X)`of algebra expression `X`:
+                
+                  PrjMap(X) = replace all project operations Project(P, PV) 
+                with ProjectMap(P,PV) for each projection in X.
+              
+              
+                The outcome of `PrjMap` is independent of the order of replacement
+                (e.g. bottom-up or top-down).
+                Replacements may happen several times, depending on recusive order
+                but each time a replacement is made, the variable not used anywhere else.
+              
+        
+              
+                A variable inside a project expression that is not in the variables projected
+                is not affected by value insertion because it is renamed apart.
+              
+            
+
+            
+              Values Insertion
+
+
+                  Definition: Values Insertion
+                  
+                    Define the Values Insertion function `ValuesInsert(X, μ)`
+                  
+                  Let Table(μ) = { μ } and multiplicity( μ | Table(μ) = { μ } ) = 1
+
+Replace each occurence of `Y` in X where `Y` is one of
+          Basic Graph Pattern,
+          Property Path Expression,
+          `Graph(Var, pattern)`
+        with `join(Y, Table(μ))`.
+
+                
+                @@ rename as ???correllate
+              
+
+
+                
+                  Examples
+                
+              
+            
+
+            
+              Evaluation of EXISTS
+
+                Definition: Evaluation of Exists
+                
+                  Let `μ` be the current solution mapping for a filter, and `X` a graph pattern,
+                      define the Evaluation of Exists `exists(X)`
+                
+                exists(X) = true 
+                  if eval( D(G), ValuesInsert(PrjMap(X), μ) )
+                  is a non-empty solution sequence.
+  exists(X) = false otherwise
+              
+            
+          
+          
+
         
+
         
           Extending SPARQL Basic Graph Matching
           The overall SPARQL design can be used for queries which assume a more elaborate form of