Relational calculus is another mathematical model that is dual to relational algebra: if you have one representation you can always get the other. Relational a

Relational calculus is another mathematical model that is dual to relational algebra: if you have one representation you can always get the other. Relational algebra describes a fairly direct set of manipulations of database rows that can be implemented efficiently. Relational calculus operations are more abstract, but have useful identity transformations you can use to optimize query plans. So, when you ask a database system to perform a query, you ask it in relational algebra terms because they’re easy to understand. It then transforms your query into a relational calculus-like form to shuffle things around, and then back to a different, but equivalent, algebraic form to actually execute.