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.^[1]

In DRC, queries have the form:

$\{\langle X_1, X_2, ...., X_n \rangle \mid p(\langle X_1, X_2, ...., X_n\rangle) \}$

where each X_i is either a domain variable or constant, and $p(\langle X_1, X_2, ...., X_n \rangle)$ 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, the logical connectives ∧ (and), ∨ (or) and ¬ (not). The existential quantifier (∃) and the universal quantifier (∀) can be used to bind the variables.

Its computational expressiveness is equivalent to that of Relational algebra.^[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:

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

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:

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

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:

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

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.

See also

• Relational algebra
• Relational calculus
  • Tuple relational calculus (TRC)
• Aldat Relational Algebra
• Domain algebra

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