This document identifies problems with SPARQL EXISTS and describes two proposals.


Identified Issues

This section describes the issues identified by the Community group.
  1. Some uses of EXISTS are not defined during evaluation
  2. Substitution happens where definitions are only for variables
  3. Blank nodes substituted into BGPs act as variables
  4. Substitution can flip MINUS to its disjoint-domain case
  5. Substitution affects disconnected variables

Issue 1: Some uses of EXISTS are not defined during evaluation

The evaluation process in the specificiation is defined for graph patterns but there are situations where the evaluation is of an alegbra form not listed.

For example:

FILTER EXISTS { SELECT ?y { ?y :q :c . } }

The argument to exists is not explicitly listed as a "Graph Pattern" in the table of SPARQL algebra symbols in section 18.2 when the argument to EXISTS is a GroupGraphPattern containing just a subquery or just InlineData.

Issue 2: Substitution happens where definitions are only for variables

There are places in the SPARQL syntax and algebra where variables are allowed but not RDF terms (constant values).


FILTER EXISTS { BIND ( :e AS ?z ) { SELECT ?x { :b :p :c } } } }

Both positions "AS ?z" and "SELECT ?x" must be variables.

In the algebra, this affects

Issue 3: Blank nodes substituted into BGPs act as variables

In the evaluation of basic graph patterns (BGPs) blank nodes are replaced by RDF terms from the graph being matched and variables are replaced by a solution mapping from query variables to RDF terms so that the basic graph pattern is now a subgraph of the graph being matched.

Simply substituting a variable with a blank node in the EXISTS evaluation process does not cause the basic graph pattern to be to be restricted to subgraphs containing that blank node as an RDF term because it is mapped by an RDF instance mapping before checking that the BGP after mapping is a subgraph of the graph being queried.

Note that elsewhere in the evaluation of the SPARQL algebra, a solution mapping with a binding from variable to blank node, does treat blank nodes as RDF terms. They are not mapped by an RDF instance mapping.


    ?x :p :d .
    FILTER EXISTS { ?x :q :b . } }

against the graph { _:c :p :d , :e :q :b } the substitution for EXISTS produces BGP(_:c :q :b) which then matches against :e :q :b because the _:c can be mapped to :e by the RDF instance mapping that is part of pattern instance mappings in 18.3.1.

Issue 4: Substitution can flip MINUS to its disjoint-domain case

    ?x :p :c .
    FILTER EXISTS { ?x :p :c . MINUS { ?x :p :c . } } }
on the graph { :d :p :c }
the substitution from 18.6 ends up producing
  Minus( BGP( :d :p :c ), BGP( :d :p :c ) )
which produces a non-empty result because the two solution mappings for the
Minus have disjoint domains and 18.5 dictates that then the result is not

Issue 5: Substitution affects disconnected variables

    BIND ( :d AS ?x )
    FILTER EXISTS { BIND ( :e AS ?z )
                    SELECT ?y WHERE { ?x :p :c } } }
the substitution from 18.6 ends up producing
  Join ( Extend( BGP(), ?z :e ),
         ToMultiSet( Project( ToList( BGP( :d :p :c ) ), { ?y } ) ) )

Some, but not all, implementations diverge from the spec here.

Proposal B

A Deep-Binding Alternative to Substitution

All filtering in SPARQL is determining whether a solution mapping passes some condition. We call this solution mapping the current row in this description. We call the translation to the SPARQL algebra of "pattern", the EXISTS pattern.

Evaluation of the EXISTS function is defined by the process of substitution appiled to the EXISTS pattern, which is then evaluated. The EXISTS filter expression is true if the evaluation results in one or more solution mappings.

This is a section proposes an alternative mechanism. Rather than replace each variable by the value it is bound to in the current row, this alternative mechanism makes the whole of the current row available at any point in the evaluation of an EXISTS expression. It uses the current row to restrict the binding of variables at the points where variable bindings are created during evaluation of EXISTS to be those from the current row. It makes illegal syntactic constructs that could lead to an attempt to rebind a variable from the current row through using the AS syntax.

Section 2.2 describes how this alternative definition of EXISTS addresses each of the issues identified in Identifed Issues section.

There are 3 parts to the proposal:


Within sub-queries, variables with the same name can be used but do not appear in the overall results of the query if they do not occur in the projection in the sub-query. Such inner variables are not in-scope when they are not mentioned in the projection part of the inner SELECT expression.

    ?s :value ?v .
       {SELECT (count(*) AS ?C) {
            ?s :property ?w .
       FILTER ( ?C < ?v )

Here, the ?s is not mentioned in the projection in SELECT (count(*) AS ?C). Replacing ?s by, for example, ?V1234 in the sub-query does not change the overall results.

    ?s :value ?v .
       {SELECT (count(*) AS ?C) {
            ?V1234 :property ?w .
       FILTER ( ?C < ?v )

Such variable usages can be replaced with a variable of a different name, if that name is not used anywhere else in the query, and the same results are obtained in the sub-query. A sub-query always has a projection as its top-most algebra operator.

To preserve this, any such variables are renamed so they do not coincide with variables from the current row being filter by EXISTS.

The SPARQL algebra "project" operator has two components, an algebra expression and a set of variables for the projection.

Definition: Projection Expression Variable Remapping

For a projection algebra operation P with set of variables PV, define a partial mapping F from V, the set of all variables, to V where:

F(v) = v if v in PV
F(v) = v1 where v is a variable mentioned in the project expression, but not in PV, and v1 is a fresh variable
F(v) = v otherwise.

Define the Projection Expression Variable Remapping PrjMap(P,PV) to be the algebra expression P (and the subtree over which the projection is defined) with F applied to every variable of the algebra expression P over which P is evaluated.

This process is applied throughout the graph pattern of EXISTS:

Definition: Variable Remapping

For any algebra expression X define the Variable Remapping PrjMap(X):

PrjMap(X) = replace all project operations project(P PV) with project(PrjMap(P,PV) PV) for each projection in X.

This replacement is applied bottom-up when there are multiple project operations in the graph pattern of EXISTS.

Applying the renaming steps inside a sub-query does not change the solution mappings resulting from evaluating the sub-query. Remapping is only applied to variables not visible outside the sub-query. Renaming a variable in a SPARQL algebra expression causes the variable name used in bindings from evaluating the algebra expression to change. Since these are only variables that are not visible outside the sub-query, because they do not occur in the projection, the result of the sub-query is unchanged. SPARQL algebra expressions can not access the name of a variable nor introduce a variable except by remapping. Remapping is only applied to variables not visible outside the sub-query.

Limitations on Assignment

SPARQL syntactic forms that attempt to bind a variable through the use of AS that might already be in a solution mapping are forbidden in SPARQL: this is covered in the syntactic restrictions of 19.8 Grammar, notes 12 and 13.

This proposal adds the restriction that any variables in a current row, the set of variables in-scope of the FILTER containing EXISTS, can not be assigned with the extend algebra function linked to the AS syntax.

In addition, any use of VALUES in the EXISTS expression must not use a variable in the current row.

Restriction of Bindings

The proposal is to retain the variables from the current row, not substitute them for RDF terms, before evaluation, and also to restrict the binding of the solution to the RDF term of the current row. This occurs after renaming.

Binding for variables occur in several places in SPARQL:

Note that other places where solution mappings add variables are in extend function (connected to the AS syntax) and a multiset from VALUES syntax. Limitations on Assignment forbid this being of variables of the current row.

Restricting the RDF Terms for a variable binding is done using inline data that is joined with the evalaution of the basic graph pattern, property path or graph match.

Definition: Values Insertion

For solution mapping μ, define Table(μ) to be the multiset formed from μ.

Table(μ) = { μ }
Card[μ] = 1

Define the Values Insertion function Replace(X, μ) to replace each occurence Y of a Basic Graph Pattern, Property Path Expression, Graph(Var, pattern) in X with join(Y, Table(μ)).

Evaluation of EXISTS

The evaluation of EXISTS is defined as:

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 and only if eval(D(G), Replace(PrjMap(X), μ) is a non-empty solution sequence.
exists(X) = false otherwise


This section addresses each issue identified, given the proposal above.

Issue 1: Some uses of EXISTS are not defined during evaluation

This can be handled by handling solution sequences as graph patterns where needed by adding toMultiSet as is done for SubSelect in Translate Graph Patterns with a a correction to the text at the end of Section 18.2 introductory paragraph.


"Section 18.2 Translation to the SPARQL Algebra" intro (end):

ToMultiSet can be used where a graph pattern is mentioned below because the
outcome of evaluating a graph pattern is a multiset.

Multisets of solution mappings are elements of the SPARQL algebra.  Multisets
of solution mappings count as graph patterns.

Issue 2: Substitution happens where definitions are only for variables

Rather then replace a varialbe by its value in the current row, the new mechanism makes the binding of variable to value available. The variable remains in the graph pattern of EXISTS and the evaluation.

Issue 3: Blank nodes substituted into BGPs act as variables

By making the current row, which can include blank nodes, available, and not modifying the BGP by substitution, no blank nodes are introduced into the evalaution of the BGP. Instead, the possible solutions is restricted by the current row.

Issue 4: Substitution can flip MINUS to its disjoint-domain case

Issue 4 is addressed because variablea re not removed from the domain of MINUS. This propsoal does not preserve all uses MINUS expressions; the problem identified in issue 4 is considered to be a bug in the original SPARQL specification.

Issue 5: Substitution affects disconnected variables

Issue 5 is addressed by noting that variables inside sub-queries which are not projected can be renamed without affecting the sub-query results. Whether to preserve that invariant or allow the variables to be set by the current row is a choice point - this design preserves the independence of disconnected variables.


The proposal described in this document does not cover use of variables from the current row in a HAVING clause.

Proposal A

A Shallow-Binding Alternative to Substitution

This proposal for EXISTS emphasizes simplicity and the SPARQL notions of variable scoping and bottom-up evaluation of sub-queries over maximum compatability with the current SPARQL definition for EXISTS. Its basic idea is to inject values for the variables in-scope just outside a FILTER expression at the beginning of the pattern argument to EXISTS almost as if a VALUES construct was injected there.

  1. Modify the scoping rules so that variables in-scope at a FILTER are in-scope at the beginning of the pattern argument to any EXISTS in the FILTER expression. (This is independent of the change to a mapping-based definition but fixes an error that affects EXISTS.) The additional scoping rule could be written as:
    In FILTER ... EXISTS { P } ... with P not a sub-select, if v is in-scope from the preceeding elements in the group graph pattern in which the FILTER is used then v is in-scope for an empty BGP that is considered to be inserted just before P.
  2. Add a new construct, Initial, to the SPARQL syntax and algebra. Initial will be used to set up the initial multiset of solution mappings inside an EXISTS. It will work much like VALUES except that it will transfer solution mappings through the EXISTS instead of setting up a constant solution mapping.
  3. When collecting FILTER elements replace EXISTS P in the filter expression with exists(Initial(t),translate(Initial(t) P')) where t is a fresh token, and similarly for NOT EXISTS {P}. If P is a SubSelect then P' is {P} otherwise P' is just P.
  4. Translate Initial(t) as itself.
  5. Change the definition of the exists function to:
    Let μ be the current solution mapping for a filter, t a token, and P a graph pattern: The value exists(Initial(t),P) given D(G) is true iff eval(D(G),P') is a non-empty multiset of solution bindings, where P' is P with Initial(t) replaced by {μ}.


The same solution as for Proposal B can be used here to solve Issue 1.

There is no substitution of variables by values (including blank nodes) thus solving Issues 2, 3, and 4.

As the value-injection is done only at the beginning of the argument to EXISTS it will not affect disconnected variables, such solving Issue 5.

Other errata

This section records other possible errata discovered by the community group.

Translation of VALUES

Near the end of section " Translate Graph" the translation of inline data should result in a ToMultiSet(data).

Translation of a trailing VALUES already uses this form.

For each DataBlock, form a solution mapping from the variable in the corresponding position in list of variables (or single variable), omitting a binding if the BindingValue is the word UNDEF.

Combine each solution mappings into a solution sequence S, and apply ToMultiSet.

The result is ToMultiset(S)

The text in then needs to be aligned: ToMultiSet(data) becomes translate(data).

Security and Privacy Considerations

This proposal does not introduce any additional security or privacy considerations to SPARQL 1.1.