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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 without distinguished variables are called boolean conjunctive queries.Conjunctive queries where all variables are distinguished (and no variables are bound) are called equi-join queries, [1] because they are the equivalent, in the relational calculus, of the equi-join queries in the relational algebra (when selecting all columns of the result).
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.
A join clause in the Structured Query Language combines columns from one or more tables into a new table. The operation corresponds to a join operation in relational algebra. Informally, a join stitches two tables and puts on the same row records with matching fields : INNER, LEFT OUTER, RIGHT OUTER, FULL OUTER and CROSS.
The result of query rewriting may not be at the same abstraction level or application programming interface (API) as the original set of queries (though often is). For example, the input queries may be in relational algebra or SQL, and the rewritten queries may be closer to the physical representation of the data, e.g. array operations.
Whereas relational databases use a relational calculus or relational algebra, with relational operations, such as union, intersection, set difference and cartesian product to specify queries, Datalog uses logical connectives, such as if, or, and and not to define relations as part of the database itself.
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 ...
SELECT list is the list of columns or SQL expressions to be returned by the query. This is approximately the relational algebra projection operation. AS optionally provides an alias for each column or expression in the SELECT list. This is the relational algebra rename operation. FROM specifies from which table to get the data. [3]