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A relational database consists of named relation variables (relvars) for the purposes of updating the database in response to changes in the real world. An update to a single relvar causes the body of the relation assigned to that variable to be replaced by a different set of tuples.
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.
The relational model (RM) is an approach to managing data using a structure and language consistent with first-order predicate logic, first described in 1969 by English computer scientist Edgar F. Codd, [1] [2] where all data are represented in terms of tuples, grouped into relations.
The basic data structure of the relational model is the table, where information about a particular entity (say, an employee) is represented in rows (also called tuples) and columns. Thus, the "relation" in "relational database" refers to the various tables in the database; a relation is a set of tuples. The columns enumerate the various ...
The relational algebra uses set union, set difference, and Cartesian product from set theory, and adds additional constraints to these operators to create new ones.. For set union and set difference, the two relations involved must be union-compatible—that is, the two relations must have the same set of attributes.
An example of such a forbidden query is the query "select all tuples other than those occurring in relation R", where R is a relation in the database. Assuming different domains, i.e., sets of atomic data items from which tuples can be constructed, this query returns different results and thus is clearly not domain independent.
In the relational data model a superkey is any set of attributes that uniquely identifies each tuple of a relation. [1] [2] Because superkey values are unique, tuples with the same superkey value must also have the same non-key attribute values.
In relational database theory, a tuple-generating dependency (TGD) is a certain kind of constraint on a relational database. It is a subclass of the class of embedded dependencies (EDs). An algorithm known as the chase takes as input an instance that may or may not satisfy a set of TGDs (or more generally EDs) and, if it terminates (which is a ...