Database Languages Chapter 7. The Relational Algebra.

Database Languages

Chapter 7

The Relational Algebra

The relational Algebra

The relational algebra is a complete set of operations on relations which allows to select data from a relational database.

Cartesian product Union , Intersection , Difference Projection -join Division

Sample database

R r1 r2 r3 S1 s1 s2

1 x 3 3 p4 x 3 4 q3 y 4 4 p2 z 7

S2 s1 s2

4 q2 m

Cartesian product

R x S2 r1 r2 r3 s1 s2

1 x 3 4 q4 x 3 4 q3 y 4 4 q2 z 7 4 q1 x 3 2 m4 x 3 2 m3 y 4 2 m2 z 7 2 m

Projection , -join

Projection R [ r2 , r3 ] r2 r3

x 3y 4z 7

-join R [ r3 > s1 ] S1

r1 r2 r3 s1 s2

3 y 4 3 p2 z 7 3 p2 z 7 4 q2 z 7 4 p

Left Outer-join

r1 r2 r3 s1 s2

1 x 3 3 p

4 x 3 3 p

3 y 4 4 q

3 y 4 4 p

2 z 7

R[r3 =ls1]S1

Union , Intersection , Difference

UNION S1 S2 s1 s23 p4 q4 p2 m

Intersection S1 S2 s1 s24 q

Difference S1 \ S2 s1 s23 p4 p

Division

S# P#

s1 p1s1 p2s1 p3s1 p4s1 p5s1 p6s2 p1s2 p2s3 p2s4 p2s4 p4s4 p5

Divide by ÷ Result DEND/DORDENDDOR 1 P#

p1

DOR 2

DOR 3

P#p2p4

P#p1p2p3p4p5p6

S#s1s2

S#s1s4

S#s1

Example

S S# Sname

1 Jones2 Duval3 Codd4 Carter

SP S# P#

1 111 152 123 15

1. Give all parts

2. Give names of suppliers supplying part 15

3. Give those suppliers that do not supply part 15

4. Give those suppliers that supply something else than part 15

5. Give those suppliers that supply something but not part 15

Solutions

1. SP [ P# ]

2. ( ( S [ S# = S# ]SP )[ P# ÷ 15] [15 ]) [ Sname ]

3.

Data Description Language

Sample Database

S S# SNAME STATUS CITY

S1 Smith 20 London

S2 Jones 10 Paris

S3 Blake 30 Paris

S4 Clark 20 London

S5 Adams 30 Athens

P P# PNAME COLOR WEIGHT CITYP1Nut Red 12 LondonP2Bolt Green 17 ParisP3Screw Blue 17 RomeP4Srew Red 14 LondonP5Cam Blue 19 LondonP6CogRed 19 London

SP S# P# QTYS1 P1 300S1 P2 200S1 P3 400S1 P5 200S1 P6 100S2 P1 300S2 P2 400S3 P2 200S4 P2 200S4 P4 300S4 P5 400

CREATE CREATE TABLE base-table-name ( base-table-element - commmalist )

where base-table-element is a column-definition

or a base-table-constraint-definition

column-definition:

column representation [ default definition ]

default definition:

NOT NULL, NULL, current-date, ....)

Create Table

Base-table-constraint

candidate key:

UNIQUE ( column-commalist ) primary key:

PRIMARY KEY ( column-commalist ) foreign key:

FOREIGN KEY ( column-commalist )

REFERENCE base-table [ ( column-commalist ) ]

[ ON DELETE option ]

[ ON UPDATE option ]

option: NO ACTION , CASCADE, SET DEFAULT, SET NULL check constraint:

CHECK ( conditional-expression )

CREATE table example

CREATE TABLE SP (S# S# NOT NULL, P# P# NOT NULL, QTY QTY NOT NULL,

PRIMARY KEY ( S# , P# )FOREIGN KEY ( S# ) REFERENCE S

ON DELETE CASCADEON UPDATE CASCADE,

FOREIGN KEY ( P# ) REFERENCE PON DELETE CASCADEON UPDATE CASCADE,

CHECK ( QTY > 0 AND QTY < 5001 ) ) ;

DDL - table modification

ALTER table ALTER TABLE base-name-table ADD column-name data-type ;

( “not null” is not permitted )

DROP table

DROP TABLE base-table-name

DDL - Indexes

CREATE index

CREATE [ UNIQUE ] INDEX index-name ON base-table-name ( column-name [ ORDER ] [ , column-name [ ORDER ] ... )

DROP index

DROP INDEX index-name ;

Data Manipulation Language

DML - Data Manipulation Language

SELECT [ DISTINCT ] field(s)

FROM table(s)

[ WHERE predicate ]

[ GROUP BY field(s) [ HAVING predicate ] ]

[ ORDER BY field(s) ] ;

SQL

Simple Retrieval - SQL

Get part numbers for all parts supplied

SELECT P#FROM SP ;

SELECT DISTINCT P#FROM SP ;

P#P1P2P3P4P5P6P1P2P2P2P4P5

P#P1P2P3P4P5P6

Simple retrieval - QBE

Get part numbers for all parts supplied

SP S# P# QTY

P._PX

SP S# P# QTY

P.ALL._PX

Retrieval of expressions For all parts get the part number and the weight in grams ( in the table weights are in pounds ).

SELECT P.p# , P.weight*454FROM P ;

P P# Pname Color weight City

P._PX P.Weight *454

P# P1 5448P2 7718P3 7718P4 6356P5 5448P6 8626

OUTPUT

Simple retrieval of table

Get full details of all suppliers

SELECT *FROM S ;

S S# Sname Status City

P._SX P._SN P._ST P._SC


P.

SQL

QBE

Qualified retrieval 1

Get supplier numbers for suppliers located in Paris or with status greater than 20.

SELECT S#FROM SWHERE City = ‘PARIS’ OR Status > 20 ;

S S# Sname Status CityP._SX > 20P._SY Paris

Qualified retrieval - 2

Get supplier numbers for suppliers located in Paris with status greater than 20.

SELECT S#FROM SWHERE City = ‘PARIS’ AND Status > 20 ;

S S# Sname Status CityP._SX > 20 Paris

Qualified retrieval with ordering

Get supplier numbers and status for suppliers in Parisin descending order of status

SELECT S# , StatusFROM S

WHERE City = ‘Paris’ORDER BY Status DESC ;


P._SX P.DO._ST Paris

Simple Equi-join

Get all combinations of supplier and part information such thatthe supplier and part in question are located in the same city

SELECT S.* , P.*FROM S , PWHERE S.City = P.City ;


P. _X

P.


_X

SQL

QBE

Greater-than join

Get all combinations of supplier and part information such thatthe supplier city follows the part city in alphabetical order.

SELECT S.* , P.*FROM S , PWHERE S.City > P.City


P. > _X

P.


_X

SQL

QBE

Join with additional condition

Get all combinations of supplier and part information such thatthe supplier and part are colocated , but omitting supplierswith status > 20 .

SELECT S.* , P.*FROM S , PWHERE S.City = P.City AND S.Status NOT > 20 ;


P. NOT > 20 _X

P.


_X

SQL

QBE

Retrieving specified fields from a join

Get all part-number / supplier-number combinations such thatsupplier and part are colocated

SELECT S.S# , P.P#FROM S , PWHERE S.City = P.City


P._SX _X

P._PX


_X

SQL

QBE

Join of three tables

Get all pairs of city names such that a supplier located in the first city supplies a part stored in the second city

SELECT DISTINCT S.City , P.CityFROM S , P , SPWHERE S.S# = SP.S# AND SP.P# = P.P# ;


_X P._CS

_Y


P._PC

SQL

QBE

SP S# P# QTY

_X _Y

Function in a select clause

Get the total number of suppliers

SQL

QBE

SELECT count ( * )FROM S ;


P.COUNT._SX

Function in select clause with predicate

Get the total number of suppliers supplying part 2.

SQL

QBE

SELECT count ( * )FROM SPWHERE P# = ‘P2’ ;

SP S# P# QTY

P.CNT.ALL._SX P2

Join of table with itself

Get all pairs of supplier numbers such that the two suppliersare colocated .

SELECT FIRST.S# , SECOND.S#FROM S FIRST , S SECOND

WHERE FIRST.City = SECOND.City AND FIRST.S# < SECOND.S# ;


_SX_SY

_CZ_CZ

Conditions

_SX < _SY

RESULT FIRST SECOND

P. _SX _SY

Use of GROUP BY

For each part supplied , get the part number and the total shipment quantity for that part

SQL

QBE

SELECT P# , SUM(QTY) FROM SPGROUP BY P# ;

SP S# P# QTY

P.G._PX P.SUM.ALL._QX

Use of HAVINGGet part numbers for all parts supplied by more than one supplier.

SQL

QBE

SELECT P# FROM SPGROUP BY P#HAVING COUNT(*) > 1 ;

SP S# P# QTY

_SX P._PXNOT._SX _PX

or

SP S# P# QTY

CNT.ALL._SX> 1 P.G._PX

Retrieval involving a subquery

Get supplier names for suppliers who supply part P2 .

SELECT UNIQUE SNAME FROM S , SPWHERE S.S# = SP.S# AND SP.P# = ‘P2’ ;

SELECT UNIQUE SnameFROM SWHERE S# IN (SELECT S# FROM SP WHERE P# = ‘P2’) ;

SELECT SnameFROM SWHERE ‘P2’ IN (SELECT P# FROM SP WHERE S#= S.S#) ;

SP S# P# QTY


_X P._SN

_X P2

Single-record Update

Change color of part P2 to yellow

SQL: Update distinct PSet color = “yellow”where P# = P2 ;

QBE: P p# pname color weight city

p2 U.yellow

Multiple Update

Double the status of all suppliers in London

SQL Update SSet status = status * 2where City = “London” ;

QBES S# sname status city

_SX _ST LondonU. _SX 2 * _ST

Update involving sub-query

Set quantity to zero for all suppliers in London

SQL Update SPSet qty = 0where “London” =

( select city from S where s# = SP.s# ) ;

QBESP s# p# qty

U. _SX 0

S s# sname status city

_SX London

Views

CREATE VIEW name

AS SELECT statement ;

Example:

CREATE VIEW good-suppliers

AS SELECT s# , status , city

FROM S

WHERE status = 15 ;

The VIEW-definition is stored in the directory

but the select is not performed

VIEWS - 2

Example:

CREATE VIEW PQ ( P# , sumqty )

AS SELECT p# , SUM(qty)

FROM SP

GROUP BY p# ;

Views can be defined in terms of other views Some views are updateble Views can be dropped

VIEWS - usage

VIEWS can be used just like base tables

CREATE VIEW LONDON-SUPPLIERS AS SELECT s, sname , status FROM S WHERE city = ‘London’ ;

Two formulations with the same result

SELECT * SELECT s# , sname , statusFROM LONDON-SUPPLIERS FROM SWHERE status < 50 WHERE status < 50ORDER by s# ; AND city = ‘London’ ORDER BY s# ;

SQL System Catalog

The system catalog is also a relational database

SYSTABLES ( name , creator , colcount , ... ) SYSCOLUMNS ( name , tbname , coltype , ... ) SYSINDEX ( name , tbname , creator , ... )

SELECT tbnameFROM SYSCOLUMNSWHERE name = ‘s#’ ;

SELECT name FROM SYSCOLUMNSWHERE tbname = ‘S’ ;

Examples:

Updating the catalog is not possible

QBE dictionary

Retrieval of table names : Get all tables known to the system

P.

Creation of new table

I. S S# Sname Status City

I. S S# Sname Status City

domain S# Sname Status Citytype char 5 char 20 fixed char 15key Y U.N U.N U.Ninvers Y U.N U.N U.N

Database Languages Chapter 7. The Relational Algebra.

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