Relational Calculus

**Relational calculus** consists of two calculi, the tuple relational calculus and the domain relational calculus, that are part of the relational model for databases and provide a declarative way to specify database queries. This in contrast to the relational algebra, which is also part of the relational model but provides a more procedural way for specifying queries.

The relational algebra might suggest these steps to retrieve the phone numbers and names of book stores that supply *Some Sample Book*:

- Join book stores and titles over the BookstoreID.
- Restrict the result of that join to tuples for the book
*Some Sample Book*. - Project the result of that restriction over StoreName and StorePhone.

The relational calculus would formulate a descriptive, declarative way:

- Get StoreName and StorePhone for book stores such that there exists a title BK with the same BookstoreID value and with a BookTitle value of
*Some Sample Book*.

The relational algebra and the relational calculus are essentially logically equivalent: for any algebraic expression, there is an equivalent expression in the calculus, and vice versa. This result is known as Codd's theorem.

- Date, Christopher J. (2004).
*An Introduction to Database Systems*(8th ed.). Addison Wesley. ISBN 0-321-19784-4.

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