relational operators 1 lecture 7 relational operators

Relational operators

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Lecture 7

Relational Operators


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Relational data model

relational data objects

relational operators

relational data integrity


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preamble why do we need relational operators? what kind of operations do we need to perform? how many operators would we like to have? what do you think a “powerful set of operators” means?

procedural / declarative relational algebra / relational calculus


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Relational algebra operators

basic primitive 4 “set specific” operations 4 “relation specific” operations relational closure


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“Set specific” operators

specialised for relations type compatibility attribute name inheritance candidate key inheritance

they are union intersection difference Cartesian product exemplify them with a couple of relations of your choice


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“Relation specific” operators

restriction <relation name> WHERE <condition>

projection <relation name> [ <attr_1>, <attr_2>, …, <attr_n> ]

join <relation name> JOIN <relation name>

difference <relation name> DIVBY <relation name>


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Restriction

conditional expressions on atomic values primitive data types

• supported in SQL

• non-conditional scalar operators cannot be used in conditional expressions; however, they can be introduced via EXTEND

domains • no support provided in SQL

• PostgreSQL - extendable set of operators on atomic value

atomic / non-atomic conditions nested conditions logical expressions


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Join

natural join theta-join

can be expressed via a Cartesian product and a restriction; how?

properties commutative associative


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Join

Supplier SupplyCity TelephoneE-A Inc Coventry 01203 456678E & E Ltd London 0181 3994567H200 London 0171 1233456S-TV Tokyo 0081 3 11122233

PruductID ProductName Cost InStock SupplierPID23 Washing machine 289 2 E-A IncXX24A Dish dryer 399 0 H20000012 Power supply extension 14.99 15 E-A IncMM25y Television set 395 0 S-TVMM45x Television set 555 0 S-TV


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Join

PruductID ProductName Cost InStock Supplier SupplyCity TelephonePID23 Washing machine 289 2 E-A Inc Coventry 01203 456678XX24A Dish dryer 399 0 H200 London 0171 123345600012 Power supply extension 14.99 15 E-A Inc Coventry 01203 456678MM25y Television set 395 0 S-TV Tokyo 0081 3 11122233MM45x Television set 555 0 S-TV Tokyo 0081 3 11122233


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Division

Supplier PartS1 P1S1 P2S1 P3S1 P4S2 P2S2 P3S2 P5S3 P3S3 P5S4 P3

PartP1P2P3

Contracts Set1

PartP3P5

PartP5

Set3Set2


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Division

SupplierS2S3S4

Contracts DIVBY Set1

SupplierS2S3

SupplierS1

Contracts DIVBY Set2 Contracts DIVBY Set3


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Relational algebra operators

closure nested expressions

primitive set restriction, projection, Cartesian product, union, difference


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Examples

SName Age Address

Students

TName Position Salary

Tutors

SName MName TName MName

MName Type Level Credits Syllabus

Registrations Teaching

Modules


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Examples

get the name of the tutors who teach at least one module get the name position and salary of all the tutors who teach

at least one module get the name of the tutors who do not teach any module get the name and address of all the students who take level

one courses get the name of students who take all optional modules ... think of other queries and devise relational algebra

expressions for them


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Extensions

EXTEND you can think as allowing scalar computations in WHERE

clauses

SUMMARISE projections combined with the performance of summary

calculations


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Implementation

DML in SQL relational operators can be implemented via SELECT

statements SQL provides a richer set of operations than just the set of

basic relational algebra operations• e.g. sub-queries


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The optimiser

optimiser for a specific implementation, the module that ‘decides’ what

is the best strategy of evaluating an expression (a query)(note that evaluation record level operations)

example• get the addresses of all students who take the “AI” module

• 3000 students; 4 modules per student, on average; some 100 students for the AI module;

• ((Students JOIN Registration) WHERE Mname = “AI”) [Sname, Address]

• (Students JOIN (Registration WHERE Mname = “AI”)) [Sname, Address]


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Summary

relational algebra operators (set and relation specific) relational closure extensions implementation - SQL the optimiser

relational calculus

relational operators 1 lecture 7 relational operators

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