The relational calculus consists of two calculi, the tuple relational calculus and the domain relational calculus, that is part of the relational model for databases and provide a declarative way to specify database queries. The raison d'être of relational calculus is the formalization of query optimization, which is finding more efficient manners to execute the same query in a database.
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 that 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 expression are meant to be executed from left-to-right and inside-out following their nesting.
Per Codd's theorem, the relational algebra and the domain-independent relational calculus are logically equivalent.
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.
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.
The raison d'être of the relational calculus is the formalization of query optimization. Query optimization consists in determining from a query the most efficient manner (or manners) to execute it.
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In database theory, relational algebra is a theory that uses algebraic structures for modeling data, and defining queries on it with a well founded semantics. The theory was introduced by Edgar F. Codd. The main application of relational algebra is to provide a theoretical foundation for relational databases, particularly query languages for such databases, chief among which is SQL. Relational databases store tabular data represented as relations. Queries over relational databases often likewise return tabular data represented as relations.
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 tuples, grouped into relations. A database organized in terms of the relational model is a relational database.
A relational database is a (most commonly digital) database based on the relational model of data, as proposed by E. F. Codd in 1970. A system used to maintain relational databases is a relational database management system (RDBMS). Many relational database systems are equipped with the option of using SQL (Structured Query Language) for querying and updating the database. The term "relational database" was first defined by E. F. Codd at IBM in 1970. Codd introduced the term in his research paper "A Relational Model of Data for Large Shared Data Banks".
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