The relational calculus consists of two calculi, the
tuple relational calculus and the
domain relational calculus, that are part of the
relational model
The relational model (RM) is an approach to managing data using a structure and language consistent with first-order predicate logic, first described in 1969 by English computer scientist Edgar F. Codd, where all data is represented in terms of tu ...
for databases and provide a declarative way to specify database queries. The raison d'être of the relational calculus is the formalization of
query optimization
Query optimization is a feature of many relational database management systems and other databases such as NoSQL and graph databases. The query optimizer attempts to determine the most efficient way to execute a given query by considering the po ...
, which is finding more efficient manners to execute the same query.
The relational calculus is similar to the
relational algebra, which is also part of the relational model: While the relational calculus is meant as a declarative language which prescribes no execution order on the subexpressions of a relational calculus expression, the
relational algebra is meant as an imperative language: the sub-expressions of a relational algebraic expressions are meant to be executed from left-to-right and inside-out following their nesting.
Per
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 ...
, the relational algebra and the
domain-independent relational calculus are
logically equivalent.
Example
A
relational algebra expression might prescribe the following 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.
A relational calculus expression would formulate this query in the following descriptive or declarative manner:
: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''.
Mathematical properties
The relational algebra and the
domain-independent relational calculus are
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
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 ...
.
Purpose
The raison d'être of the relational calculus is the formalization of
query optimization
Query optimization is a feature of many relational database management systems and other databases such as NoSQL and graph databases. The query optimizer attempts to determine the most efficient way to execute a given query by considering the po ...
.
Query optimization
Query optimization is a feature of many relational database management systems and other databases such as NoSQL and graph databases. The query optimizer attempts to determine the most efficient way to execute a given query by considering the po ...
consists in determining from a query the most efficient manner (or manners) to execute it. Query optimization can be formalized as translating a relational calculus expression delivering an answer A into efficient relational algebraic expressions delivering the same answer A.
See also
*
Calculus of relations
In mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with free variables.
What is now usually called classical algebraic logic focuses on the identification and algebraic description of models appropriate for ...
References
*
Logical calculi
Relational model
{{database-stub