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# lec05 - Relational Algebra Chapter 4 EECS 484 Database...

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1 1/23/11 EECS 484: Database Management Systems, Kristen LeFevre 1 Relational Algebra Chapter 4 1/23/11 EECS 484: Database Management Systems, Kristen LeFevre 2 “Formal” Query Languages Foundation for commercial query languages like SQL Two types Declarative: Relational Calculus Describe what a user wants, rather than how to compute it. Inspired SQL Procedural : Relational Algebra Operations very useful for understanding how DB executes queries. Query Languages != programming languages! QLs not expected to be “Turing complete”. QLs not intended to be used for complex calculations. QLs support easy, efficient access to large data sets. Understanding Relational Algebra and Calculus is important to understanding SQL and query processing!

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2 1/23/11 EECS 484: Database Management Systems, Kristen LeFevre 3 Relational Algebra Preliminaries Query: Input: Relational instances Output: Relational instances! Specified using the schema May produce different results for different instances But schema of the result is fixed Relational Algebra is “closed” 1/23/11 EECS 484: Database Management Systems, Kristen LeFevre 4 Relational Algebra Basic operations: Selection ( ) Selects a subset of rows from relation. Projection ( ) Deletes unwanted columns from relation. Cross-product ( ) Allows us to combine two relations. Set-difference ( ) Tuples in reln. 1, but not in reln. 2. Union ( ) Tuples in reln. 1 and in reln. 2. Additional operations (constructed from basic ops): Intersection, Join , Division, Renaming Not essential, but (very!) useful. Because algebra is closed, we can compose operators ! ! ! ! U
3 1/23/11 EECS 484: Database Management Systems, Kristen LeFevre 5 Selection Retrieve rows that satisfy a logical condition Conditions are boolean combinations ( ∧, V, ¬ ) of terms Each term has one of the

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