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Papers > Miscellaneous > Relational Algebra
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Relational Algebra |
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... ) - A query language is a language in which a user requests information from the database - The formal languages: Relational algebra and Relational Calculus - The commercial languages: SQL and QBE Formal language Commercial (Informal) language DML Procedural (Relational Algebra) SQL (Structured Query Language) Non-procedural (Relational calculus) QBE (Query by Example) Relational Algebra - The relational algebra consists of a collection of high-level operators that operate on relations - Codd defined a very specific set of eight such operators, two groups of four each • The traditional set operation: Union, Intersection, Difference, and Cartesian Product • The special relational operation: Restrict (or Select), Project, Join, and Divide - Each such operator takes either one (Restrict and Project ) or two relations (the rest of eight) as its input and produces a new relation as its output - Union Compatibility • Two relations are union-compatible if and only if they have identical headings - meaning, precisely, that: 1) They have the same set of attribute name (note, therefore, that they must have a fortiori have the same degree) 2) Corresponding attributes (i. ... Depart_ID > DEPARTMENT Division (R1 R2) - Takes two relations, one binary and one unary, and builds a relation consisting of all values of one attribute of the binary relation that match (in the other attribute) all values in the unary relations A S# P# S1 P1 S1 P2 S1 P3 S1 P4 S1 P5 S1 P6 S2 P1 S2 P2 S3 P2 S4 P2 S4 P4 S4 P5 B P# P2 P4 C A B Closure - The output from each of the operations is another relation - Because the output of any operation is the same kind of object as the input, so the output from one operations can become input to another - In other words, it is possible to write nested relational expression Relational Calculus - The relational algebra and the relational calculus are alternative candidates as a forma basis for the manipulative part of the relational model - The difference is as follows: where the relational algebra provides a collection of explicit operations that can actually be used to tell the system how to build some desired relation from the given relations in the database, the calculus merely provides a notation for formulating the definition of that desired relation in terms of those given relations Codd’s Equivalence Theorem - Everything that can be retrieved using the Algebra can also be retrieved using the Calculus, and vice versa - The algebra and the calculus are precisely equivalent to one another. |
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Title: Relational Algebra
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