Relational algebra

Relational algebra, first described by E.F. Codd while at IBM, is a family of algebras with a well-founded semantics used for modelling the data stored in relational databases, and defining queries on it.

The main application of relational algebra is providing a theoretical foundation for relational databases, particularly query languages for such databases, chief among which is SQL.

Introduction

Relational algebra received little attention outside of pure mathematics until the publication of E.F. Codd's relational model of data in 1970. Codd proposed such an algebra as a basis for database query languages. (See section Implementations.)

Five primitive operators of Codd's algebra are the selection, the projection, the Cartesian product (also called the cross product or cross join), the set union, and the set difference.

Set operators

The relational algebra uses set union, set difference, and Cartesian product from set theory, but adds additional constraints to these operators.

Join (SQL)

A SQL join clause combines records from two or more tables in a relational database. It creates a set that can be saved as a table or used as it is. A JOIN is a means for combining fields from two tables (or more) by using values common to each. ANSI-standard SQL specifies five types of JOIN: INNER, LEFT OUTER, RIGHT OUTER, FULL OUTER and CROSS. As a special case, a table (base table, view, or joined table) can JOIN to itself in a self-join.

A programmer writes a JOIN statement to identify records for joining. If the evaluated predicate is true, the combined record is then produced in the expected format, a record set or a temporary table.

Sample tables

Relational databases are usually normalized to eliminate duplication of information such as when objects have one-to-many relationships. For example, a Department may be associated with a number of Employees. Joining separate tables for Department and Employee effectively creates another table which combines the information from both tables. This is at some expense in terms of the time it takes to compute the join. While it is also possible to simply maintain a denormalized table if speed is important, duplicate information may take extra space, and add the expense and complexity of maintaining data integrity if data which is duplicated later changes.