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

SQLRelationalalgebraexpression

OptimizedRelationalalgebraexpression

Query optimizer

Codegenerator

Queryexecutionplan

Executablecode

DBMS

Operations (Unary):

Selection, Projection

Selection: <condition(s)> (<relation>) Picks tuples from the relation

Projection: <attribute-list> (<relation>) Picks columns from the relation

Operations (Set):

Union, Set Difference

Union: (<relation>) U (<relation>) 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) )