RelationalModel

�Arelationschemeisa�nitesequenceofuniqueattributenames.For

example,

EMPLOYEES

=

(EMPID,

ENAME,

ADDRESS,

SALARY)

isarelationschemewithfourattributenames.

�Adomainisasetofvalues.Witheachattributename,A,adomain,

dom(A),isassociated.Thisdomainincludesaspecialvaluecallednull.

Forexample,dom(EMPID)couldbethesetofallpossibleintegers

between1000and9999andthespecialnullvalue.

�GivenarelationschemeR

=

A1,

...,

An,arelationronthe

schemeRisde�nedasany�nitesubsetoftheCartesianproduct

dom(A1)

x

...

x

dom(An).

1

�AssumingappropriatedomainsfortheEMPLOYEESrelationscheme,a

samplerelationunderthisschemecouldbe

{

(1111,'Jones','111

Ash

St.',20000),

(2222,'Smith','123

Elm

St.',25000),

(3333,'Brown','234

Oak

St.',30000)

}

�Eachoftheelementsofarelationisalsoreferredtoasatuple.

�Arelationaldatabasescheme,D,isa�nitesetofrelationschemes,

fR1,

...,

Rmg.

�ArelationaldatabaseonschemeDisasetofrelations

fr1,

...

rmg

whereeachriisarelationonthecorrespondingschemeRi.

2

KeyConstraint

�AsuperkeyforarelationschemeRisanysubset,KofRthatsatis�es

thepropertythatineveryvalidrelationundertheschemeR,itisnot

possibletohavetwodi�erenttupleswiththesamevaluesunderK.

�AcandidatekeyforRisanykeyforRsuchthatnoneofitsproper

subsetsisalsoakey.

�TheprimarykeyforarelationschemeRisoneofthecandidatekeys

chosenbythedesignerofthedatabase.

�Theprimarykeyattributesarerequiredtosatisfythenot

null

constraint,i.e.,notuplecanhaveanullvalueundertheprimarykey

attributes.

3

ReferentialIntegrity/ForeignKeyConstraint

�Duringthedesignofarelationaldatabase,thedesignermaycreatea

relationschemeRwhichincludestheprimarykeyattributesofanother

relationscheme,sayS.

�Insuchasituation,thereferentialintegrityconstraintspeci�esthe

conditionthatthevaluesthatappearundertheprimarykeyattributes

inanyvalidrelationunderschemeRm

u

st

alsoappearintherelation

underschemeS.

�TheattributesintheschemeRthatcorrespondtotheprimarykey

attributesofschemeScollectivelyarereferredtoasaforeignkeyin

schemeR.

�Unliketheprimarykeyattributes,theforeignkeyattributesdonot

havetosatisfythenot

nullconstraint.

4

NotNullconstraint

�

Thisconstraintspeci�estheconditionthattuplevaluesundercertain

attributes(speci�edtobenotnull)cannotbenull.

�

Thisconditionisusuallyalwaysimposedontheprimarykeyattributes.

InOracle,primarykeyattributesareautomaticallyconstrainedtobe

notnull.

�

Otherattributesmayalsobeconstrainedtobenotnulliftheneed

arises.

5

Gradebookdatabase

CATALOG(CNO,ctitle)

STUDENTS(SID,fname,lname,minit)

COURSES(TERM,LINENO,cno,a,b,c,d)

COMPONENTS(TERM,LINENO,COMPNAME,maxpoints,weight)

ENROLLS(SID,TERM,LINENO)

SCORES(SID,TERM,LINENO,COMPNAME,points)

6

catalog

CNO

CTITLE

csc226IntroductiontoProgrammingI

csc227IntroductiontoProgrammingII

csc343AssemblyProgramming

csc481AutomataandFormalLanguages

csc498IntroductiontoDatabaseSystems

csc880DeductiveDatabasesandLogicProgramming

7

students

SID

FNAME

LNAME

MINIT

1111Nandita

RajshekharK

2222Sydney

Corn

A

3333Susan

Williams

B

4444Naveen

RajshekharB

5555Elad

Yam

G

6666Lincoln

Herring

F

8

courses

TERM

LINENO

CNO

A

B

C

D

f96

1031

csc22690806550

f96

1032

csc22690806550

sp97

1031

csc22790806550

components

TERM

LINENO

COMPNAME

MAXPOINTSWEIGHT

f96

1031

exam1

100

30

f96

1031

quizzes

80

20

f96

1031

�nal

100

50

f96

1032

programs

400

40

f96

1032

midterm

100

20

f96

1032

�nal

100

40

sp97

1031

paper

100

50

sp97

1031

project

100

50

9

enrolls

SID

TERM

LINENO

1111f96

1031

2222f96

1031

4444f96

1031

1111f96

1032

2222f96

1032

3333f96

1032

5555sp97

1031

6666sp97

1031

10

scores

SID

TERM

LINENO

COMPNAME

POINTS

1111f96

1031

exam1

90

1111f96

1031

quizzes

75

1111f96

1031

�nal

95

2222f96

1031

exam1

70

2222f96

1031

quizzes

40

2222f96

1031

�nal

82

4444f96

1031

exam1

83

4444f96

1031

quizzes

71

4444f96

1031

�nal

74

11

Mailorderdatabase

EMPLOYEES(ENO,ename,zip,hdate)

PARTS(PNO,pname,qoh,price,level)

CUSTOMERS(CNO,cname,street,zip,phone)

ORDERS(ONO,CNO,ENO,received,shipped)

ODETAILS(ONO,PNO,qty)

ZIPCODES(ZIP,city)

12

employees

ENO

ENAME

ZIP

HDATE

1000

Jones

6722612-DEC-95

1001

Smith

6060601-JAN-92

1002

Brown

5030201-SEP-94

parts

PNO

PNAME

QOH

PRICE

LEVEL

10506LandBeforeTimeI

200

19.99

20

10507LandBeforeTimeII

156

19.99

20

10508LandBeforeTimeIII

190

19.99

20

10509LandBeforeTimeIV

60

19.99

20

10601SleepingBeauty

300

24.99

20

10701WhenHarryMetSally120

19.99

30

10800DirtyHarry

140

14.99

30

10900Dr.Zhivago

100

24.99

30

13

customers

CNO

CNAME

STREET

ZIP

PHONE

1111

Charles

123MainSt.

67226316-636-5555

2222

Bertram

237AshAvenue67226316-689-5555

3333

Barbara

111InwoodSt.

60606316-111-1234

orders

ONO

CNO

ENO

RECEIVED

SHIPPED

1020

1111

1000

10-DEC-94

12-DEC-94

1021

1111

1000

12-JAN-95

15-JAN-95

1022

2222

1001

13-FEB-95

20-FEB-95

1023

3333

1000

20-JUN-97

null

14

odetails

ONO

PNO

QTY

1020

105061

1020

105071

1020

105082

1020

105093

1021

106014

1022

106011

1022

107011

1023

108001

1023

109001

zipcodes

ZIP

CITY

67226Wichita

60606FortDodge

50302KansasCity

54444Columbia

66002Liberal

61111FortHays

15

RelationalAlgebra-Set-theoreticoperations

�

Tworelationsareunion-compatibleiftheyhavethesamenumber

ofattributesandthedomainsofthecorrespondingattributesinthe

tworelationsarethesame.

�

Considertworelationsr

ands

thatareunion-compatible.

Union:r

[s

=ftjt

2r

ort

2sg.

Di�erence:r

�s

=ftjt

2r

andt

62sg

Intersection:r

\s

=ftjt

2r

andt

2sg

�CartesianProduct:Letr

ands

beanytworelations.

r

�s

=ft1:t2jt12r

andt22sg,

where,t1:t2istheconcatenationoftuplest1andt2toformalarger

tuple.

16

Example:Set-theoreticOperators

r

A

B

a

b

a

c

b

d

s

A

B

a

c

a

e

r

[s

A

B

a

b

a

c

b

d

a

e

r

�s

A

B

a

b

b

d

r

�s

r.A

r.B

s.A

s.B

a

b

a

c

a

b

a

e

a

c

a

c

a

c

a

e

b

d

a

c

b

d

a

e

r

\s

A

B

a

c

17

Relation-theoreticoperations

Rename:Therenameoperatortakesasinputarelationandreturnsthe

samerelationasoutput,butunderadi�erentname.Thesymbolic

notationfortherenameoperatoris�s (r),whereristheinputrelation

andsisthenewname.

Select:Symbolically,theselectoperatoriswrittenas�F(r),whereFisthe

selectioncriterionandristheinputrelationandisde�nedasfollows:

�F(r)=ftjt2randtsatis�esFg.

Project:Symbolically,theprojectoperatoriswrittenas�A(r),whereAis

asub-listoftheattributesofr,andisde�nedasfollows:

�A(r)=ft[A]jt2rg

wheret[A]isatupleconstructedfromtbykeepingthevaluesthat

correspondtotheattributesinAanddiscardingothervalues.

18

Relation-theoreticoperations-Continued

NaturalJoin:Symbolically,thenaturaljoiniswrittenasr./s,wherer

isarelationonschemeRandsisarelationonschemeS,andis

de�nedasfollows:

r./s=ftj(9u2r)(9v2s)(t[R]=uandt[S]=v)g

Division:Symbolically,thedivisionoperationiswrittenasr�sandis

de�nedasfollows:

r�s=ftj(8u2s)(t:u2r)g

wheret:uistheconcatenationoftupletwithtupleu.

19

Example:Relation-theoreticoperations

r

A

C

D

a

c

d

a

e

f

a

g

h

b

c

d

b

g

h

c

c

d

c

e

f

s

C

D

c

d

e

f

t

B

C

D

b

c

d

b

e

f

�A=0b0

orC=0c0(r)

A

C

D

a

c

d

b

c

d

b

g

h

c

c

d

�A(r)

Aabc

r

./

t

A

C

D

B

a

c

d

b

a

e

f

b

b

c

d

b

c

c

d

b

c

e

f

b

r

�

s

Aac

20

BasicOperations

Basicsetofoperations:rename,select,project,cartesianproduct,

union,di�erence.Otheroperationscanbeexpressedintermsofthese

six.

Intersection:

r\

s=r�

(r�

s)

NaturalJoin:

r./s=�R\

S(�F(r�

s))

whereF

isaselectionconditionwhichindicatesthatthetuple

valuesunderthecommonattributesofrandsareequal.

Division:

r�

s=�R�

S(r)�

�R�

S((�R�

S(r)�

s)�

r)

Eventhoughrelationschemesarede�nedassequences,theyaretreated

assetsintheseequalitiesforsimplicity.

21

Queryingusingrelationalalgebra

Gradebookdatabasequeries

Q1GetthenamesofstudentsenrolledintheAssemblyProgramming

classinthef96term.

t1:=�

CTITLE=0AssemblyProgramming

0(catalog)

t2:=�TERM=0f960(courses)

t3:=t1./t2./enrolls./students

result:=�FNAME;LNAME;MINIT(t3)

Q2GettheSIDvaluesofstudentswhodidnotenrollinanyclassduring

thef96term.

�SID(students)�

�SID(�TERM=0f960(enrolls))

22

Gradebookdatabasequeriescontinued

Q3GettheSIDvaluesofstudentswhohaveenrolledincsc226and

csc227,

t1:=�SID(enrolls./�CNO=0csc2260(courses))

t2:=�SID(enrolls./�CNO=0csc2270(courses))

result:=t1\

t2

Q4GettheSIDvaluesofstudentswhohaveenrolledincsc226orcsc227,

t1:=�SID(enrolls./�CNO=0csc2260(courses))

t2:=�SID(enrolls./�CNO=0csc2270(courses))

result:=t1[

t2

Q5GettheSIDvaluesofstudentswhohaveenrolledinallthecoursesin

thecatalog.

�SID;CNO(courses./enrolls)�

�CNO(catalog)

23

Mailorderdatabasequeries

Q6Getpartnamesofpartsthatcostlessthan20.00.

�PNAME(�PRICE<2

0

:0

0 (parts))

Q7GetpairsofCNOvaluesofcustomerswhohavethethesamezipcode.

t1:=�c1 (customers)�

�c2 (customers)

t2:=�c1

:ZIP=

c2

:ZIP

andc1

:CNO<c2

:CNO(t1)

result:=�c1

:CNO;c2

:CNO(t2)

Q8Getthenamesofcustomerswhohaveorderedpartsfromemployees

livinginWichita.

t1:=�ENO(employees./�CITY=

0Wichita0(zipcodes))

result:=�CNAME(customers./orders./t1)

24

Mailorderdatabasequeriescontinued

Q9GetCNOvaluesofcustomerswhohaveorderedpartsonlyfrom

employeeslivinginWichita.

t1:=�ENO(employees./�CITY6=0Wichita0(zipcodes))

result:=�CNO(orders)�

�CNO(orders./t1))

Q10GetCNOvaluesofcustomerswhohaveorderedpartsfromall

employeeslivinginWichita.

t1:=�ENO(employees./�CITY=

0Wichita0(zipcodes))

result:=�CNO;ENO(orders)�

t1

25