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Erschienen in:
2014 | OriginalPaper | Buchkapitel
5. Extensions of Relational Codd’s Algebra and DB Category
verfasst von : Zoran Majkić
Erschienen in: Big Data Integration Theory
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Abstract
In Chap. 5, we consider the extensions of Codd’s SPRJU relational algebra Σ
R
and their relationships with the internal algebra of the category DB. Then we show that the computational power of the DB category (used as denotational semantics for database-mapping programs) is equivalent to the Σ
RE
relational algebra, which extends the Σ
R
algebra with all update operations for relations, and which is implemented as SQL statements in the software programming. We introduce an “action” category RA where each tree-term of the Σ
RE
relational algebra is equivalently represented by a single path term (an arrow in this category) which, applied to its source object, returns its target object. The arrows of this action category will be represented as the Application Plans in the abstract categorical RDB machines, in Chap. 5, during the executions of the embedded SQL statements.