- The paper 'An Overview of TQuel' from 1993 explores temporal relational algebra, extending Quel for Ingres, and provides algebraic identities for temporal operators useful for query planning in Postgres.
- TQuel represents valid-time as sets of chronons (multiranges) per attribute rather than intervals per tuple, which complicates but is representable in Postgres via multiranges.
- Snapshot reducibility allows temporal operators to be evaluated by first taking snapshots of base tables, enabling efficient query optimization for queries focused on a single time point.
- Theorem 13 shows that Cartesian product does not distribute over difference in temporal algebra, as demonstrated by counterexamples using TQuel, rangetypes, and multiranges.
- Retaining input valid-times in temporal operators breaks certain algebraic identities, while dropping them preserves the algebra, suggesting valid-time should be treated as a qualifier, not a regular attribute.
- The author developed a Racket library 'relsim' to simulate temporal operators and find counterexamples, highlighting the need for dedicated executor nodes and optimizer transformations in Postgres.