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Lecture Notes: Relational Algebra – A quick tutorial to adapt SQL queries into relational algebra; Relational – A graphic implementation of the relational algebra; Query Optimization This paper is an introduction into the use of the relational algebra in optimizing queries, and includes numerous citations for more in-depth study.
Conjunctive queries also correspond to select-project-join queries in relational algebra (i.e., relational algebra queries that do not use the operations union or difference) and to select-from-where queries in SQL in which the where-condition uses exclusively conjunctions of atomic equality conditions, i.e. conditions constructed from column ...
Codd's theorem states that relational algebra and the domain-independent relational calculus queries, two well-known foundational query languages for the relational model, are precisely equivalent in expressive power. That is, a database query can be formulated in one language if and only if it can be expressed in the other.
Queries made against the relational database, and the derived relvars in the database are expressed in a relational calculus or a relational algebra. In his original relational algebra, Codd introduced eight relational operators in two groups of four operators each. The first four operators were based on the traditional mathematical set operations:
The purpose of the relational model is to provide a declarative method for specifying data and queries: users directly state what information the database contains and what information they want from it, and let the database management system software take care of describing data structures for storing the data and retrieval procedures for ...
Since the calculus is a query language for relational databases we first have to define a relational database. The basic relational building block is the domain (somewhat similar, but not equal to, a data type). A tuple is a finite sequence of attributes, which are ordered pairs of domains and values. A relation is a set of (compatible) tuples ...
The result of the query is the set of tuples X 1 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.
extending the relational language with hierarchy manipulations, such as in the nested relational algebra. extending the relational language with transitive closure, such as SQL's CONNECT statement; this allows a parent-child relation to be used, but execution remains expensive; the queries can be expressed in a language that supports iteration ...