Lecture_3_-_Relational_algebra_and_calculus

# Lecture_3_-_Relational_algebra_and_calculus - CSCI 507...

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1 1 Lecture 3 Relational Algebra and Relational Calculus CSCI 507 Database Theory 2 Learning Objectives Meaning of the term relational completeness. How to form queries in relational algebra. How to form queries in tuple relational calculus. How to form queries in domain relational calculus. Categories of relational DML.

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2 3 Introduction Relational algebra and relational calculus are formal languages associated with the relational model. Informally, relational algebra is a (high-level) procedural language and relational calculus a non-procedural language. However, formally both are equivalent to one another. A language that produces a relation that can be derived using relational calculus is relationally complete . 4 Relational Algebra Relational algebra operations work on one or more relations to define another relation without changing the original relations. Both operands and results are relations, so output from one operation can become input to another operation. Allows expressions to be nested, just as in arithmetic. This property is called closure .
3 5 Relational Algebra Five basic operations in relational algebra: Selection, Projection, Cartesian product, Union, and Set Difference. These perform most of the data retrieval operations needed. Also have Join, Intersection, and Division operations, which can be expressed in terms of 5 basic operations. 6 Relational Algebra Operations

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4 7 Relational Algebra Operations 8 Selection (or Restriction) σ predicate (R) Works on a single relation R and defines a relation that contains only those tuples (rows) of R that satisfy the specified condition ( predicate ).
5 9 Example - Selection (or Restriction) List all staff with a salary greater than \$10,000. σ salary > 10000 (Staff) 10 Projection Π col1, . . . , coln (R) Works on a single relation R and defines a relation that contains a vertical subset of R, extracting the values of specified attributes and eliminating duplicates.

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6 11 Example - Projection Produce a list of salaries for all staff, showing only staffNo, fName, lName, and salary details. Π staffNo, fName, lName, salary (Staff) 12 Union R S Union of two relations R and S defines a relation that contains all the tuples of R, or S, or both R and S, duplicate tuples being eliminated. R and S must be union-compatible. If R and S have I and J tuples, respectively, union is obtained by concatenating them into one relation with a maximum of ( I + J ) tuples.
13 Example - Union List all cities where there is either a branch office or a property for rent. Π city (Branch) ∪ Π city (PropertyForRent) 14 Set Difference R – S Defines a relation consisting of the tuples that are in relation R, but not in S. R and S must be union-compatible.

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Lecture_3_-_Relational_algebra_and_calculus - CSCI 507...

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