Domain relational calculus explained

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 X₁ to X_n that make 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) in the Enterprise relation

and let (D, E, F) mean (Name, DeptName, ID) in the Department relation

All captains of the starship USS Enterprise:$$\backslash left\backslash$$

In this example, A, B, C denotes both the result set and a set in the table Enterprise.

Names of Enterprise crew members who are in Stellar Cartography:$$\backslash begin\backslash \; \backslash \backslash \backslash end$$

In this example, we're only looking for the name, and that's B. The condition F = C is a requirement that describes the intersection of Enterprise crew members AND members of the Stellar Cartography Department.

An alternate representation of the previous example would be:$$\backslash begin\backslash \; \backslash \backslash \backslash end$$

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.

Both of them written in SQL will be like:SELECT BFROM EnterpriseJOIN Department ON F = C AND E = 'Stellar Cartography';

See also

• Relational calculus

External links

• DES – An educational tool for working with Domain Relational Calculus and other formal languages
• WinRDBI – An educational tool for working with Domain Relational Calculus and other formal languages

Notes and References

1. Michel Lacroix, Alain Pirotte: Domain-Oriented Relational Languages. VLDB 1977: 370-378
2. [E. F. Codd]