Domain relational calculus

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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.[1]

In DRC, queries have the form:

< X1,X2,....,Xn > | p( < X1,X2,....,Xn > )

where each Xi 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 Xi to Xn which makes the DRC formula true.

This language uses the same operators as tuple calculus; Logicial operators ∧ (and), ∨ (or) and ¬ (not). The existential quantifier (∃) and the universal quantifier (∀) can be used to bind the variables.

Its computational expresivity is equivalent to that of Relational algebra.[2]

[edit] 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.

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.

[edit] See also


  • Aldat Relational Algebra
  • Domain algebra

[edit] References

  1. ^ Michel Lacroix, Alain Pirotte: Domain-Oriented Relational Languages. VLDB 1977: 370-378
  2. ^ E. F. Codd: Relational Completeness of Data Base Sub-languages. In R. Rustin, editor, Data Base Systems. Prentice Hall, 1972
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