Relational Join

(Ported content:) Relational Join

Relational join ("dot join") combines two relations by seeking common values in the rightmost column and leftmost column of its arguments. More precisely, if \(A\) is arity \(N\) and \(B\) is arity \(M\), then the join of \(A\) with \(B\) is the \(N+M-2\)-ary relation:

\[{(a_1, ..., a_{N-1}, b_2, ..., b_M) | \;\exists x\; | (a_1, ..., a_{N-1}, x) \in A \text{ and } (x, b_2, ..., b_M) \in B}\]