Domain relational calculus

In computer science, domain relational calculus (DRC) is a calculus that was introduced by Michel Lacroix and Alain Pirotte as a declarative database query language for the relational data model. Computer science (or computing science) is the study and the Science of the theoretical foundations of Information and Computation and their In Computer science, Declarative programming is a Programming paradigm that attempts to minimize or eliminate side effects by describing what Query languages are Computer languages used to make queries into Databases and Information systems Broadly query languages can be classified The relational model for Database management is a Database model based on first-order predicate logic, first formulated and proposed in 1969 by Edgar ^[1]

In DRC, queries have the form:

< X 1, X 2,. . . . , X n > | p ( < X 1, X 2,. . . . , X n > )

where each X_i is either a domain variable or constant, and p(<X1, X2, . . . . , Xn>) denotes a DRC formula. The result of the query is the set of tuples X_i to X_n which makes the DRC formula true.

This language uses the same operators as tuple calculus; Logicial operators ∧ (and), ∨ (or) and ¬ (not). The Tuple Calculus is a calculus that was introduced by Edgar F The existential quantifier (∃) and the universal quantifier (∀) can be used to bind the variables. In Predicate logic, an existential quantification is the predication of a property or relation to at least one member of the domain In Predicate logic, universal quantification is an attempt to formalize the notion that something (a Logical predicate) is true for everything, or every

Its computational expresivity is equivalent to that of Relational algebra. Relational algebra, an offshoot of First-order logic (and of Algebra of sets) deals with a set of relations closed under Operators ^[2]

Examples

Let A, B, C mean Rank, Name, ID and D, E, F to mean Name, DeptName, ID

Find all captains of the starship USS Enterprise:

$\left\{ \ {\left\langle A, B, C \right\rangle} \ | \ {\left\langle A, B, C \right\rangle \in Enterprise \ \land \ A = \mathrm{Captain} } \ \right\}$

In this example, A, B, C denotes both the result set and a set in the table Enterprise. The USS Enterprise (NCC-1701 is a Starship in Star Trek, which chronicles the vessel's mission "to explore strange new worlds to

Find Names of Enterprise crewmembers who are in Stellar Cartography:

$\begin{align} {\left\langle B \right\rangle} \ & | \ {\exists A, C \ \left\langle A, B, C \right\rangle \in Enterprise } \\ & \land \ {\exists D, E, F \ \left\langle D, E, F \right\rangle \in Departments } \\ & \land \ F = C \ \land \ E = \mathrm{Stellar \ Cartography} \\ \end{align}$

In this example, we're only looking for the name, and that's B. F = C is a requirement, because we need to find Enterprise crew members AND they are in the Stellar Cartography Department.

An alternate representation of the previous example would be:

$\left\{ \ {\left\langle B \right\rangle} \ | \ {\exists A, C \ \left\langle A, B, C \right\rangle \in Enterprise } \ \land \ {\exists D \ \left\langle D, \mathrm{Stellar \ Cartography}, C \right\rangle \in Departments } \ \right\}$

In this example, the value of the requested F domain is directly placed in the formula and the C domain variable is re-used in the query for the existence of a department, since it already holds a crew member's id.

References

^ Michel Lacroix, Alain Pirotte: Domain-Oriented Relational Languages. Relational algebra, an offshoot of First-order logic (and of Algebra of sets) deals with a set of relations closed under Operators Relational calculus consist of two calculi the Tuple relational calculus and the Domain relational calculus, that are part of the Relational model The Tuple Calculus is a calculus that was introduced by Edgar F VLDB 1977: 370-378
^ E. F. Codd: Relational Completeness of Data Base Sub-languages. Edgar Frank "Ted" Codd ( August 23, 1923 – April 18, 2003) was a British computer scientist who while working In R. Rustin, editor, Data Base Systems. Prentice Hall, 1972

Examples

See also

References