Relational calculus

Relational calculus consists of two calculi, the tuple relational calculus

Tuple relational calculus

Tuple calculus is a calculus that was introduced by Edgar F. Codd as part of the relational model, in order to provide a declarative database-query language for this data model...

 and the domain relational calculus

Domain relational calculus

In computer science, domain relational calculus is a calculus that was introduced by Michel Lacroix and Alain Pirotte as a declarative database query language for the relational data model.In DRC, queries have the form:...

, that are part of the relational model

Relational model

The relational model for database management is a database model based on first-order predicate logic, first formulated and proposed in 1969 by Edgar F...

 for databases and provide a declarative way to specify database queries. This in contrast to the relational algebra

Relational algebra

Relational algebra, an offshoot of first-order logic , deals with a set of finitary relations that is closed under certain operators. These operators operate on one or more relations to yield a relation...

 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:

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

The relational calculus would formulate a descriptive, declarative way:

Get StoreName and StorePhone for supplies 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

Logical equivalence

In logic, statements p and q are logically equivalent if they have the same logical content.Syntactically, p and q are equivalent if each can be proved from the other...

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

Codd's theorem

Codd's theorem states that relational algebra and the domain-independent relational calculus queries, two well-known foundational query languages for the relational model, are precisely equivalent in expressive power. That is, a database query can be formulated in one language if and only if it can...

.