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The Relational Data Model

Properties of Relations

Keys and Constraints

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Relational Data Base

• The data base is a collection of relations or tables.

• Data organisation is based on the relational data model.

• A relation is actually a set of tuples – but we can visualise it as a table with columns and rows.

• Each tuple in a relation has the same number and type of attributes.

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Relational Model

• A data model is a collection of constructs used to organise data.

• The Relational Model is based on a simple and uniform construct – the relation (Codd, 1970).

• A relation is a mathematical concept based on the idea of sets.

• The strength of the relational model comes from the formal foundation provided by the theory of relations.

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Relational Concepts – Relations

• A relation consists of a relation scheme and a relation instance.

• The relation scheme can be thought of as a heading for the table.

• It consists of the relation name, and a set of pairs (attribute name and domain), where

• A domain represents the set of (atomic) values that the attribute can take.

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Relations – cont…

• e.g. Student (Name: string, RegNo: string,

Address: string, PhoneNo: string, Age: integer, AvgeMark: real)

• A relation instance can be visualised as the “body” of a table.

• It consists of a set of rows (tuples) each containing values corresponding to the various attributes in the relation scheme.

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Relations – cont…• Student Table

• Alternative terminologies for the relational modelInformal Terms Formal TermsTable RelationColumn Attribute/DomainRow TupleValues in a column DomainTable Definition Relation SchemePopulated Table Relation Instance/Extension

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Properties of Relations

• No duplicate tuples in a relation– because a relation is a set of tuples

• The tuples in a relation have no order– ditto

• No duplicate attributes– because the relation scheme contains a set of attributes

• The attributes have no order– they are identified by name, not position

• Every tuple must have attribute values drawn from each of the domains of the relation scheme (or alternatively the special “value” NULL)

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Tuples are unordered

A1 A4 A3 A2 A1 A4 A3 A2

A1 A4 A3 A2A1 A2 A3 A4

Attributes areunordered

If you change the place of a row in a table, the meaning of the data remains the same.

If you change the place of a column in a table, the meaning of the data remains the same.

Position is Not Important

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Mathematical Relations

Mathematical definition of a relation:• Consider two sets, Cars and Colours.

– Cars = {NissanMicra, FordEscort}– Colours = {Red, Blue, Silver} (the notation { … } denotes a set)

• Let’s find all combinations of elements: first element from Cars, and second from Colours.

– {(NissanMicra, Red), (NissanMicra, Blue), (NissanMicra, Silver), (FordEscort, Red), (FordEscort, Blue), (FordEscort, Silver)}

• Mathematically, this set is called the Cartesian Product of Cars and Colours.

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Mathematical Relations – cont…

A relation is a sub-set of the Cartesian Product of its domains, e.g. BlueCars = {(NissanMicra, Blue), (FordEscort, Blue)}

The above set can be written mathematically using conditions as: {(x, y) such that x belongs to Cars

and y belongs to Colours and y = Blue}

Cars = {NissanMicra, FordEscort}

Colours = {Red, Blue, Silver}

BlueCars = {(NissanMicra, Blue), (FordEscort, Blue)}

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Mathematical Relations – cont…

Consider another set for models: Years = {2008, 2009, 2006, 2007}

Let’s define a relation for LatestBlueCars: {(x, y, z) such that x belongs to Cars

and y belongs to Colours and y = Blueand z belongs to Years and z > 2007}

So we can write: LatestBlueCars = {(NissanMicra, Blue, 2008),

(NissanMicra, Blue, 2009), (FordEscort, Blue, 2008), (FordEscort, Blue, 2009)}

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Relational Concepts – Domains

• A domain is a set of atomic values, e.g. – Gender = {“Male”, “Female”}– DepartmentCodes = {“CG”, “EN”, “BE”, …}– NationalPhoneNums = {“0191-227 3521”,

“0161-275 6138”, …}

• An atomic value is indivisible.– A data item is treated as a whole for simplicity.– Although “0191-227-3521” can be divided into

0191, 227, and 3521, in the relational model it is considered as one atomic value.

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Domains – cont…

• A data type may be used to define a domain, e.g. integer, real.

• A format can be defined to specify the pattern of the legal values, e.g.

– NationalPhoneNums: dddd-ddd dddd– Date: MM/DD/YYYY (where MM = {01, 02, …,

12}, DD = {01, 02, …, 31}, YYYY = {0000, 0001, …, 1999, 2000, 2001, …, 9999})

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Relational Constrains

Constraints are conditions that must hold on all relation instances.• Domain Constraint.

– Values of attributes must belong to the appropriate domain.

• Key Constraint.– A sub-set (Primary Key) of the attributes of a relation should

identify each tuple uniquely.

• Entity Integrity Constraint.– No Primary Key value can be null.

• Referential Integrity Constraint.– Specifies data dependencies between relations.

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Domain Constraint

• The value of each attribute A must be an atomic value drawn from the domain of A.

• E.g. if a Person relation has a Sex attribute defined on the Gender domain, the only allowable values are “Male” and “Female”.

• Each domain has an associated data type.• Standard data types include INT(EGER),

DECIMAL, DATE, CHAR, VARCHAR, etc.

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Key Constraint

• Since a relation is a set, all tuples must be unique (no duplicates).

• No two tuples can have the same combinations of values for all of their attributes.

• The Key Constraint makes sure that all tuples in a relation are unique.

• A sub-set of the attributes of a relation may be used to guarantee that no two tuples have the same values for these attributes.

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Relational Keys

Superkey• A set of attributes (one or more) that uniquely

identifies a tuple within a relation.• Every relation must have at least one superkey:

the set of all its attributes.Key

• A minimum set of attributes that guarantees uniqueness of each tuple within a relation. (No proper sub-set of the key does so).

E.g. RegNo is a key of the Student relation.

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Relational Keys – cont…

Candidate Key• A relation may have more than one key. Each such key is

called a Candidate Key.Primary Key

• A Candidate Key chosen to identify each tuple in a relation uniquely – usually underlined.

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Entity Integrity Constraint

NULL• Represents a value for an attribute that is

currently unknown or is not applicable for this tuple.

• Deals with incomplete or exceptional data.• Represents the absence of a value and is not the

same as zero or spaces, which are values.

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Entity Integrity Constraint

• No Primary Key (PK) attribute can be NULL.

• A NULL PK would mean that a tuple cannot be identified, which is against the concept of PK, i.e. to identify tuples uniquely.

• If two tuples had NULLs in the PK, there would be no way of distinguishing them.

• Non-key attributes may or may not allow null values.

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Single attribute key

Multi-attribute key (composite key)

Every value in this column is defined to be different from all other values in that column.

Every combination of values in these columns is defined to be different from all other combined values in these columns.

Relational Keys – cont…

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Referential Integrity Constraint

• A constraint involving two relations: the referencing relation and the referenced relation (other constraints involve just a single relation).

• Tuples in the referencing relation R1 have attributes FK (called foreign key attributes) that reference the primary key attributes PK of the referenced relation R2.

• A tuple t1 in R1 is said to reference a tuple t2 in R2 if t1[FK] = t2[PK].

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Referential Integrity – cont…

Foreign Key• A set of attributes in a relation that exactly

“matches” a Primary Key in another relation.• The names of the attributes don’t have to be the

same, but they must be of the same domain.• A Foreign Key in a relation A, matching a

Primary Key in a relation B, represents a relationship between A and B.

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Referential Integrity – cont…

Primary Keyvalue here

These values are all the same Foreign key values here

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Referential Integrity – cont…

For example, consider two relations:

Student (Name, RegNo, Address, …, TutorId)

Lecturer (Name, IdNo, RoomNo, …)

Student [TutorId] is a FK referencing Lecturer [SSN], the PK of Lecturer.

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Referential Integrity – cont…

Referential Integrity says• A FK value cannot reference a non-existent PK.• Therefore we cannot delete a tuple from

Lecturer whilst a tuple in Student has a FK value the same as the PK of that tuple.

But a FK can be NULL• If a Lecturer tuple is deleted, the TutorId values

of all his / her tutees can be set to NULL, meaning that those students have no Tutor.

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Referential Integrity – cont.

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Relational Schemas

A relational data base usually contains many relations.A relational schema S contains many relation schemes

and a set of integrity constraints IC:• S = {R1, R2, …, Rm}

A relational data base state DB over S is a set of the relation instances:• DB = {r1, r2, …, rm}• Each relation instance in DB satisfies the

integrity constraints defined in IC.

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Company Data Base Schema

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Company Data Base Schema – Constraints

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Company Database State

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Relational Data Model Implementation

• The Relational Data Model is a formalism and an abstract structure for data organisation.

• A particular DBMS provides implementation of the Relational Data Model in general.

• SQL (Structured Query Language) is the standard for commercial DBMSs.

• It is composed of three sub-languages.– DDL: Data Definition Language.– DML: Data Manipulation Language.– DCL: Data Control Language.

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Data Definition in DDL

• DDL is used to specify relations (as tables) and the various types of constraints.

• We will use the SQL2 standard, a version of SQL proposed in 1992.

• Before SQL2, all tables were considered to be part of one global schema.

• A schema is defined using the CREATE SCHEMA command.

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Data Definition in DDL

• For the Company data base, the schema might be created by:

CREATE SCHEMA Company AUTHORIZATION NEliot;

• NEliot is the authorisation identifier of the user.• Not implemented in Oracle!

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Data Definition in DDL – cont.• SQL2 provides data types for string, numeric, date, and time

data.–CHAR, VARCHAR–INT(EGER), NUMERIC or DEC(IMAL)–FLOAT or REAL–DATE, TIME, TIMESTAMP, INTERVAL

• Domains can be defined using CREATE DOMAIN.– Suppose we want to define a domain for the RegNo attribute of

Student:

CREATE DOMAIN RegNoType AS CHAR(8);

–CHAR(8) means a string of 8 characters.– Oracle doesn’t implement domains!

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Data Definition in DDL – cont.

Defining relations.• A relation becomes a TABLE.• Relations are defined using CREATE TABLE.• CREATE TABLE specifies both Attributes and

Constraints.• Each attribute is given a name, a data type or domain,

and may have constraints specified, e.g. NOT NULL.• Constraints on the whole table, e.g. composite

Primary and Foreign Keys, are specified after all of the attributes have been defined.

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Data Definition in DDL – cont.

Creating Employee TableEMPLOYEE (FNAME, MINIT, LNAME, SSN,

BDATE, ADDRESS, SEX, SALARY, SUPERSSN*, DNO*)

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Data Definition in DDL – cont.

Alternative, specifying default values and referential actions:

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SummaryDBMS requires structured data.

• Structure is recorded in the Relation Scheme.• Structure depends on the kind of data model.• A Relational DBMS uses the Relational Model.• A Relation is a mathematically defined concept.• A Relation is visualised as a table with special

properties.Data model implementation using SQL DDL.

• Relations become Tables.• Relations, attributes, and constraints are defined

using CREATE TABLE.