Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

Relational Algebra

  • Val TannenEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_967


The operators of the relational algebra were already described in Codd’s pioneering paper [2]. In [3] he introduced the term relational algebra and showed its equivalence with the tuple relational calculus.

This entry details the definition of the relational algebra in the unnamed perspective [1], with selection, projection, cartesian product, union and difference operators. It also describes some operators of the named perspective [1] such as join.

The flagship property of the relational algebra is that it is equivalent to the (undecidable!) set of domain independent relational calculus queries thus providing a standard for relational completeness.

Key Points

Fix a countably infinite set ⅅ of constants over which Σ-instances are defined for a relational schema Σ.

The relational algebra is a many-sorted algebra, where the sorts are the natural numbers. The idea is that the elements of sort n are finite n-ary relations. The carrier of sort nof the algebra is the set of...

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Recommended Reading

  1. 1.
    Abiteboul S, Hull R, Vianu V. Foundations of databases: the logical level. Reading: Addison Wesley; 1994.Google Scholar
  2. 2.
    Codd EF. A relational model of data for large shared data banks. Commun ACM. 1970;13(6):377–87.zbMATHCrossRefGoogle Scholar
  3. 3.
    Codd EF. Relational completeness of database sublanguages. In: Rustin R, editor. Courant computer science symposium 6: data base systems. Englewood Cliffs: Prentice-Hall; 1972. p. 65–98.Google Scholar
  4. 4.
    Ramakrishnan R, Gehrke J. Database management systems. 3rd ed. New York: McGraw-Hill; 2003.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer and Information ScienceUniversity of PennsylvaniaPhiladelphiaUSA

Section editors and affiliations

  • Val Tannen
    • 1
  1. 1.Dept. of Computer and Inf. ScienceUniv. of PennsylvaniaPhiladelphiaUSA