ARQ - Lateral Join

Lateral joins using the keyword LATERAL were introduced in Apache Jena 4.7.0.

A LATERAL join is like a foreach loop, looping on the results from the left-hand side (LHS), the pattern before the LATERAL keyword, and executing the right-hand side (RHS) query pattern once for each row, with the variables from the input LHS in-scope during each RHS evaluation.

A regular join only executes the RHS once, and the variables from the LHS are used for the join condition after evaluation of the left and right sub-patterns.

Another way to think of a lateral join is as a flatmap.

Examples:

## Get exactly one label for each subject with type `:T`
SELECT * {
   ?s rdf:type :T
   LATERAL {
     SELECT * { ?s rdfs:label ?label } LIMIT 1
   }
}
## Get zero or one labels for each subject.
SELECT * {
   ?s ?p ?o
   LATERAL { OPTIONAL { SELECT * ?s rdfs:label ?label } LIMIT 1}
   }
}

Syntax

The LATERAL keyword which takes the graph pattern so far in the group, from the { starting of the current block, and a { } block afterwards.

Evaluation

Substituting variables from the LHS into the RHS (with the same restrictions), then executing the pattern, gives the evaluation of LATERAL.

Variable assignment

There needs to be a new syntax restriction: there can no variable introduced by AS (BIND, or sub-query) or VALUES in-scope at the top level of the LATERAL RHS, that is the same name as any in-scope variable from the LHS.

Such a variable assignment would conflict with the variable being set in variables of the row being joined.

## ** Illegal **
SELECT * {
   ?s ?p ?o
   LATERAL { BIND( 123 AS ?o) }
}

See SPARQL Grammar note 12.

In ARQ, LET would work. LET for a variable that is bound acts like a filter.

Variable Scopes

In looping on the input, a lateral join makes the bindings of variables in the current row available to the right hand side pattern, setting their value from the top down.

In SPARQL, it is possible to have variables of the same name which are not exposed within a sub-select. These are not lateral-joined to a variable of the same name from the LHS.

This is not speciifc to lateral joins. In

SELECT * {
  ?s rdf:type :T 
  { SELECT ?label { ?s rdfs:label ?label } }

the inner ?s can be replaced by ?z without changing the results because the inner ?s is not joined to the outer ?s but instead is hidden by the SELECT ?label.

SELECT * {
  ?s rdf:type :T 
  { SELECT ?label { ?z rdfs:label ?label } }

The same rule applies to lateral joins.

SELECT * {
   ?s rdf:type :T 
   LATERAL {
     SELECT ?label { ?s rdfs:label ?label } LIMIT 1
   }
}

The inner ?s in the SELECT ?label is not the outer ?s because the SELECT ?label does not pass out ?s. As a sub-query the ?s could be any name except ?label for the same results.

Notes

There is a similarity to filter NOT EXISTS/EXISTS expressed as the non-legal FILTER ( ASK { pattern } ) where the variables of the row being filtered are available to “pattern”. This is similar to an SQL correlated subquery.

SPARQL Specification Additional Material

Syntax

LATERAL is added to the SPARQL grammar at rule [[56] GraphPatternNotTriples](https://www.w3.org/TR/sparql11-query/#rGraphPatternNotTriples). As a syntax form, it is similar to OPTIONAL.

[56]  	GraphPatternNotTriples	  ::=  	GroupOrUnionGraphPattern | OptionalGraphPattern | LateralGraphPattern | ...
[57]  	OptionalGraphPattern	  ::=  	'OPTIONAL' GroupGraphPattern
[  ]  	LateralGraphPattern	  ::=  	'LATERAL' GroupGraphPattern

Algebra

The new algebra operator is lateral which takes two expressions

  SELECT * {
    ?s  ?p  ?o
    LATERAL
      { ?a  ?b  ?c }
}

is translated to:

  (lateral
    (bgp (triple ?s ?p ?o))
    (bgp (triple ?a ?b ?c)))

Evaluation

To evaluate lateral:

  • Evaluate the first argument (left-hand side from syntax) to get a multiset of solution mappings.
  • For each solution mapping (“row”), inject variable bindings into the second argument Evaluate this pattern Add to results

Outline:

Definition: Lateral

Let Ω be a multiset of solution mappings. We define:

Lateral(Ω, P) = { μ | union of Ω1 where 
           foreach μ1 in Ω:
               pattern2 = inject(pattern, μ1)
               Ω1 = eval(D(G), pattern2)
	       result Ω1
	   }

where inject is the corrected substitute operation.

An alternative style is to define Lateral more like “evaluate P such that μ is in-scope” in some way, rather than rely on inject which is a mechanism.

Definition: Evaluation of Lateral

eval(D(G), Lateral(P1, P2) = Lateral(eval(D(G), P1), P2)