A left outer join duplicates the tuple on the LHS for each tuple on the RHS. It's almost exclusively used for grouping operations, so then you need to group the

A left outer join duplicates the tuple on the LHS for each tuple on the RHS. It's almost exclusively used for grouping operations, so then you need to group the LHS tuples back into a single tuple and aggregate the RHS. But that's just weird -- in a normal programming language you would never duplicate the tuples and make this mess; you would keep a single tuple on the LHS and group the RHS into a set (or array/list). Then you'd aggregate the set on the RHS. That model is simple because an empty set is a value with known semantics (sum of an empty set is zero), whereas a half-NULL row is just a hack. Before someone asks, this has nothing to do with declarative/imperative, and nothing to do with some purity of the relational model. You can still have a declarative relational model with values that happen to be sets (or even relations).