From Relational Algebra to SQL CS 157B Enrique Tang

Topics Relational Algebra Definition Operations Translation to SQL

Relational Algebra Defined: Tuple An ordered set of data values. { a1, a2, a3, …, an }

Relational Algebra Defined: Relation A set of tuples. { { a1, a2, a3, …, an }, { b1, b2, b3, …, bn }, { c1, c2, c3, …, cn }, …………. }

Relational Algebra Defined: Algebra Any formal mathematical system consisting of a set of objects and operations on those objects. Based on operators and a domain of values Operators map arguments from domain into another domain value Example: x = 3.5 * y

Relational Algebra Defined: Relational Algebra An algebra whose objects are relations and whose operators transform relations into other relations. Domain: set of relations, i.e., result is another relation Basic operators: select, project, union, set difference, Cartesian product (or cross product)

Relational Algebra Defined: Where is it in DBMS? parser SQL Relational algebra expression Optimized Relational algebra expression Query optimizer Code generator Query execution plan Executable code DBMS

Operations (Unary): Selection, Projection Selection:  ( ) Picks tuples from the relation Projection:  ( ) Picks columns from the relation

Operations (Set): Union, Set Difference Union: ( ) U ( ) New relation contains all tuples from both relations, duplicate tuples eliminated. Set Difference: R – S Produces a relation with tuples that are in R but NOT in S.

Operations (Set): Cartesian Product, Intersect Cartesian Product: R x S Produces a relation that is concatenation of every tuple of R with every tuple of S The Above operations are the 5 fundamental operations of relational algebra. Intersection: R S All tuples that are in both R and S

Operations (Join): Theta Join, Natural Join Theta Join: R F S =  F (R x S) Select all tuples from the Cartesian product of the two relations, matching condition F When F contains only equality “=“, it is called Equijoin Natural Join: R S Equijoin with common attributes eliminated

Operations: Outer Join, Semi Join (left) Outer Join: R S Natural join relations while preserving all tuples from the “outer” side -> NULL values incurred. Semi Join: R F S =  A (R F S) Join two relations and only keeps the attributes seem in relation R There are Semi-Theta Join, Semi-Equijoin and Semi-Natural Join

Operations: Division Division: R ÷ S Produce a relation consist of the set of tuples from R that matches the combination of every tuple in S R S R÷S T1 ←  c (R) T2 ←  c ((SxT1)–R) T ← T1 – T2

Translation to SQL FROM clause produces Cartesian product (x) of listed tables WHERE clause assigns rows to C in sequence and produces table containing only rows satisfying condition ( sort of like  ) SELECT clause retains listed columns (  )

Translation to SQL (Cont.) SELECT C.CrsName FROM Course C, Teaching T WHERE C.CrsCode=T.CrsCode AND T.Sem=‘F2003’ List CS courses taught in F2003 Tuple variables clarify meaning. Join condition “C.CrsCode=T.CrsCode” eliminates garbage Selection condition “ T.Sem=‘F2003’ ” eliminates irrelevant rows Equivalent (using natural join) to:  CrsName(Course  Sem=‘F2003’ (Teaching) )  CrsName (  Sem=‘F2003’ (Course Teaching) )