9th December 2014 Birkbeck College, U. London 1

Introduction to Computer Systems

Lecturer: Steve Maybank

Department of Computer Science and Information Systemssjmaybank@dcs.bbk.ac.uk

Autumn 2014

Week 11a: Relational Operations

9th December 2014 Brookshear, Section 9.2 2

Database Queries

Show all orders for plate. Show all order numbers and the associated

products. Show all order numbers and the associated

company names.

In the relational model the answers are always relations, ie. tables.

Can the answers to database queries be found in asystematic way?

9th December 2014 Brookshear, Section 9.2 3

Relational Operations The answers to database queries

are obtained using the relational operations

SELECT PROJECT JOIN These operations produce new

relations from old ones.

9th December 2014 Birkbeck College 4

Relational Database

37 102 £1000 1.7.06 Plate

43 103 £2000 5.5.06 Case

20 54 £3400 2.4.06 Panel

102 Sperry 1 The Lane

103 Univac 15 Retail Road

54 Honeywell

205 North Street

Num CNum

Price

Due date

Product

O C Num Name Address

O: relation containing ordersC: relation containing details of customers

9th December 2014 Brookshear, Section 9.2 5

List of Tuples of Orders for Plate

37 102 £1000

1.7.06

Plate

43 103 £2000

5.5.06

Case

20 54 £3400

2.4.06

Panel

Num CNum

Price

Due date

Product

37 102 £1000

1.7.06

Plate

O SELECT: take all tuplesfor which the productis Plate, to give …

Num CNum

Price

Due date

Product

ANS1

ANS1<- SELECT from O where Product=Plate

9th December 2016 Brookshear, Section 9.2 6

List of Order Numbers and Products

37 102 £1000

1.7.06

Plate

43 103 £2000

5.5.06

Case

20 54 £3400

2.4.06

Panel

Num

CNum

Price

Due date

Product

37 Plate

43 Case

20 Panel

O PROJECT: remove attributes CNum, Price and Due date to leave…

Num Product

ANS2

ANS2 <- PROJECT Num, Product from O

9th December 2014 Brookshear, Section 9.2 7

Example of a JOIN

a 1

b 2m 5

n 2

A.V A.W

Relation A Relation B

B.X B.Y

a 1 m 5

a 1 n 2

b 2 m 5

B 2 n 2

A.V A.W B.X B.Y

C <- JOIN A and B

9th December 2014 Brookshear, Section 9.2 8

Definition of JOIN

Let A, B, C be relations such that C=JOIN(A,B).

Let a be any tuple from A and let b be any tuple from B. The tuples in C are obtained by merging pairs of tuples (a, b).

All possible pairs (a, b) are used to construct the tuples in C.

9th December 2014 Brookshear, Section 9.2 9

Relation Containing O.Num and C.Name

37 102 £1000 1.7.06 Plate

43 103 £2000 5.5.06 Case

20 54 £3400 2.4.06 Panel

102 Sperry 1 The Lane

103 Univac 15 Retail Road

54 Honeywell

205 North Street

Num CNum

Price

Due date

Product

O CNum Name Address

JOIN: combine tuples in O and C. Then use PROJECT toremove all attributes except O.Num and C.Name.

9th December 2014 Brookshear, Section 9.2 10

JOIN and then PROJECT

37 102 £1000 1.7.06

Plate 102 Sperry 1 The Lane

43 103 £2000 5.5.06

Case 103 Univac

15 Retail Road

20 54 £3400 2.4.06

Panel

54 Honeywell

205 North Street

O.Num

O.CNum

O.Prc O.D O.Prd C.Num

C.Name C.A

37 Sperry

43 Univac

20 Honeywell

TEMP <- JOIN O and C where O.CNum=C.Num

ANS3

O.Num C.Name

ANS3<-PROJECT O.Num, C.Name from TEMP

9th December 2014 Brookshear, Section 9.2 11

SELECT The original relation is R1, the new

relation created by SELECT is R2 and the conditions on the attribute values in R2 are c1,…cn.

R2 <- SELECT from R1 where c1,…, cn.

Example:ANS1 <- SELECT from O where O.Product=‘Plate’

9th December 2014 Brookshear, Section 9.2 12

PROJECT The original relation is R1, the new

relation created by PROJECT is R2 and the attributes projected to R2 are att1,…, attn.

R2 <- PROJECT att1,…attn from R1 Example:

ANS2 <- PROJECT O.Num, O.Product from O

9th December 2014 Brookshear, Section 9.2 13

JOIN

The original relations are R1, R2, the new relation created by JOIN is R3 and the conditions on the attribute values in R3 are c1,…cn.

R3 <- JOIN R1 and R2 where c1,…, cn Example:

Temp <- JOIN O, C where O.CNum=C.Num

9th December 2014 Brookshear, Section 9.2 14

Second Example of JOIN R3 <- JOIN O and C where O.Price>£1500

and O.CNum=C.Num

43 103 £2000 5.5.06

Case 103 Univac

15 Retail Road

20 54 £3400 2.4.06

Panel 54 Honeywell

205 North Street

O.Num

O.CNum

O.Prc

O.D

O.Prd

C.Num

C.Name

C.A

R3

9th December 2014 15

Join and Keys

34 16 D1

28 22 D2

key foreign key

data key data

16 DB1

22 DB2

BA

C <- JOIN A and B where A.foreign key=B.key

34 16 D1 16 DB1

28 22 D2 22 DB2

A.key

A.Foreign key

A.data B.key B.data

C

9th December 2014 cf. Brookshear, Section 9.2 16

Symmetries A relation does not specify the order of

the attributes or the order of the tuples.

102

Sperry 1 The Lane

103

Univac 15 Retail Road

54 Honeywell

205 North Street

is thesame as

102

1 The Lane

Sperry

54 205 North Street

Honeywell

103

15 Retail Road

Univac

C C

9th December 2014 cf. Brookshear, Section 9.2 17

Repeated Tuples

A relation cannot have repeated tuples

102 Sperry 1 The Lane

103 Univac 15 Retail Road

54 Honeywell 205 North Street

54 Honeywell 205 North Street

Not a relation in arelational database.

9th December 2014 Birkbeck College 18

Attributes in Different Relations

An attribute of a given relation is not an attribute of any other relation.

E.g. O.CNum is a different attribute fromC.Num.

Structured Query Language

9th December 2014 19Brookshear, Section 9.2

9th December 2014 20

SQL Statement

select O.Num, C.Namefrom O, Cwhere O.CNum=C.Num

Interpretation: JOIN O and C, SELECT those tuples forwhich O.CNum=C.Num, then PROJECT, retaining theattributes O.Num and C.Name.

9th December 2014 Brookshear Ch. 9, problem 12 21

Problem

3 J

4 K

In terms of the relations shown below, what is the appearance of therelation RESULT after executing each of these instructions?

X relationU V W

A Z 5

B D 3

C O 5

Y relation R S

a. RESULT <- PROJECT W from Xb. RESULT <- SELECT from X where W=5c. RESULT <- PROJECT S from Yd. RESULT <- JOIN X and Y where X.W>= Y.R.