relationa

Note

These slides have been edited (improved by adding slides, figures and symbols, and in minor

ways) by Dr. JDBrownsmith

Chapter 5

The Relational Data Model and Relational Database Constraints

Chapter 5-4

Chapter Outline

Relational Model ConceptsRelational Model Constraints and Relational Database

SchemasUpdate Operations and Dealing with Constraint

Violations

Chapter 5-5

5.1 Relational Model Concepts

The relational Model of Data is based on the mathematical concept of a relation (which is based on the ideas of sets).

The strength of the relational approach to data management comes from the formal foundation provided by the theory of relations.

We present the essentials of the relational approach in this chapter.

Chapter 5-6

The model was first proposed by Dr. E.F. Codd of IBM in 1970 in the following paper:"A Relational Model for Large Shared Data Banks," Communications of the ACM, June 1970.

The above paper caused a major revolution in the field of Database management and earned Ted Codd the coveted ACM Turing Award.

Relational Model Concepts

Chapter 5-7

INFORMAL DEFINITIONSRELATION: A table of values

– A relation may be thought of as a set of rows.– A relation may alternately be thought of as a set of columns.– Each row represents a fact that corresponds to a real-world entity or

relationship.– Each row has a value of an item or set of items that uniquely

identifies that row in the table.– Sometimes row-ids or sequential numbers are assigned to identify the

rows in the table.– Each column typically is called by its column name or column header

or attribute name.

Relational Model Concepts

Chapter 5-8

I'm not sure I got that. Please provide a lucid example or I'll shoot you with my finger.

Chapter 5-9

table

1. A relation is a table of values

row

The "ENum" column

column

relationtuple

Employee ENum EName Dept Hire_date

204 R. B. Jones E21 11/01/19991917 M. R. Brent E21 10/10/2003

TABLE **

Chapter 5-10

FORMAL DEFINITIONS

Each row in the EMPLOYEE table may be referred to as a tuple in the table and would consist of four values, e.g.:<1917, "M. R. Brent", "E21", "10/10/2003"> .

A relation (table) may be regarded as a set of tuples (rows).



"Tuple" rhymes with "couple". Got it.

Chapter 5-11

table

2. No two rows in a table can be the same (i.e., they can't have identical values)

relationtuple



The ROWS of a TABLE

Well why not?

row

Chapter 5-12

OK, to clarify, in the Relational Modelno two rows in a table can be the same.

In practice, using SQL, two rows can bethe same.

The ROWS of a TABLE

So, the theory is no good!

Chapter 5-13

The theory is excellent and should be yourfoundation/guide/mentor in practice. You need not implement according to the relational theory, but beware of poor designs, complexities, mistakes, and errors.

We will implement according to the theory.

The ROWS of a TABLE

OK for now, but I'll be watching.

Chapter 5-14

FORMAL DEFINITIONSA Relation may be defined in multiple ways.

The Schema of a Relation: R (A1, A2, .....An)Relation schema R is defined over attributes A1, A2, .....An

For Example -EMPLOYEE (ENum, EName, Dept, Hire_date)

Here, EMPLOYEE is a relation defined over the four attributes ENum, EName, Dept, and Hire_date, each of which has a domainor a set of valid values. For example, the domain of ENum is 4 digit integer numbers.

Chapter 5-15

Let's see if I've got that. Employee is a table with

attributes, each of which has a set of valid values. Sounds like a

data type to me. ZZZzzz.

Chapter 5-16

A row (tuple) is a set of values In relational theory this set can be ordered or unordered In practice the values are ordered within a row

A row (tuple) is a collection of related data values

"Tuple" rhymes with "supple". Got it.

The ROWS of a TABLE



Chapter 5-17

The second row states that an Employee has employee number (ENum) 1917, has name (EName) M.R. Brent, works in Department (Dept) E21, and was hired on (Hire_date) 10/10/2003.

The ROWS of a TABLE



Chapter 5-18

Notes

Chapter 5-19

The columns of a table are also called attributes of the relation.

The attribute help in interpreting the meaning of the valuesThe attribute names will be useful in searching the table.

For example: Find all EName where Dept=E21.



The COLUMNS of a TABLE

In plain English, that would be ________________________

Attributes

Chapter 5-20

A domain is a set of values.




... ... ... ... Domains

Attributesp. 127

Chapter 5-21

A domain is a set of values.




• A domain for Enum is all positive integers greater than 0 and less than 10000.• A domain for EName is all stings less than 26 characters.• A domain for Dept is ______________• A domain for Hire_date is _________________

Example domains

Domains are established in accordance with business rules.

Chapter 5-22

A domain has a name, data type, and a format. It also has constraints and a set of permissible operators




Consider the Hire_date column of the Employee table:The domain name is denoted dom(Hire_date) and is the set of all valid hire dates.The domain data type is, say, character stringThe domain format is mm/dd/yyyy

Chapter 5-23

A domain is a set of values and has a name, logical definition, data type, and a format.

It also has constraints and a set of permissible operators




Consider the Hire_date attribute of the Employee table:The domain name for this attribute is, say, date_of_hire.The attribute, Hire_date, indicates the role played by the domainThe logical definition is: the set of all valid hire dates.The domain data type is, say, character string The domain format is mm/dd/yyyy

Revised

Chapter 5-24


Consider the Hire_date column of the Employee table:The domain name is denoted dom(Hire_date)The domain data type is, say, character stringThe domain format is mm/dd/yyyy

• This is the representation that the user sees. • There is another representation that is physically stored.• These representations need not match.

• e.g., user may see hot, warm, cold and the database storesan integer value (representing degrees centigrade).

A domain has a name, data type, and a format.

Chapter 5-25




Data type: A set of rules describing a specific set of information, including the allowed range and operations, and how information is stored. (not from Elmasri text)

Data types in SQL include INT, FLOAT, CHAR(n), andBIT, and DATE (see p. 212-213)

Chapter 5-26



• There are constraints that may be in effect (e.g., yyyy must be greater than 1900).

• There is a set of valid operators for each data type (e.g., * and / are not valid, but > and < are).


Chapter 5-27

A domain is a set of atomic values.Atomic means that each value is indivisible as far as the

relational model is concerned




Now, there you go again. You mean I can't search on a hire date of 1999 or find all

Brents?

Chapter 5-28




In general, when you define a table with attributes, you will know the data type and the operators that are in effect.This will provide the answer to that question.

We are discussing the definitions of the relational theoryand atomic attribute values.This question goes to database operation (practice).

Note: Using SQL, you can do what "angry man" wants.

Chapter 5-29

Concept Review: Domain

A domain has a logical definition: e.g.,“USA_phone_numbers” are the set of 10 digit phone numbers valid in the U.S.

A domain may have a data-type or a format defined for it. The USA_phone_numbers may have a format: (ddd)-ddd-dddd where each d is a decimal digit. E.g., Dates have various formats such as monthname, date, year or yyyy-mm-dd, or dd mm,yyyy etc.

An attribute designates the role played by the domain. E.g., the domain Date may be used to define attributes “Invoice-date” and “Payment-date”.

p. 127

Chapter 5-30

Notes

Write the answer to Question 5.1 (p 144) here:

domain

attribute

n-tuple

degree of a relation

set

*

Chapter 5-31

I can't bear to watch

Chapter 5-32

FORMAL DEFINITIONS

The relation is formed over the cartesian product of the sets; each set has values from a domain; that domain is used in a specific role which is conveyed by the attribute name.

For example, attribute EName is defined over the domain of strings of 25 characters. The role these strings play in the EMPLOYEE relation is that of the name of employees.

Formally,

Given R(A1, A2, .........., An) r(R) dom (A1) X dom (A2) X ....X dom(An)

R: schema of the relation r of R: a specific "value" or population of R.R is also called the intension of a relation r is also called the extension of a relation page 129

Chapter 5-33

Example

Let S1 = {0,1}Let S2 = {a,b,c}

Let R S1 X S2

Then for example: r(R) = {<0,a> , <0,b> , <1,c> }

is one possible “state” or “population” or “extension” r of the relation R, defined over domains S1 and S2. It has three tuples.

Chapter 5-34

Let's see if I've got that. A populated table is

created from the domain values of each attribute.

ZZZzzz.

Chapter 5-35

DEFINITION SUMMARY

Informal Terms Formal Terms

Table Relation

Column Attribute/Domain

Row Tuple

Values in a column Domain

Table Definition Schema of a Relation

Populated Table Extension

Chapter 5-36

Tell them we're working on populating our table. Waiter, more

Java and croissants please.

Chapter 5-37

To reiterate...

Chapter 5-38

Figure 5.1 The attributes and tuples of a relation STUDENT.

Write down five things you know about this table:

Chapter 5-39

5.1.2 CHARACTERISTICS OF RELATIONS

Ordering of tuples in a relation r(R): The tuples (rows) are not considered to be ordered, even though they appear to be ordered in the tabular form.

Ordering of attributes in a relation schema R (and of values within each tuple): We will consider the attributes in R(A1, A2, ..., An) and the values in t=<v1, v2, ..., vn> to be ordered .(However, a more general alternative definition of relation does not require this ordering).

Values in a tuple: All values are considered atomic (indivisible). A special null value is used to represent values that are unknown or inapplicable to certain tuples.

p. 129

**

Chapter 5-40

CHARACTERISTICS OF RELATIONS

Notation:- We refer to component values of a tuple t by t[Ai] = vi

(the value of attribute Ai for tuple t).

Similarly, t[Au, Av, ..., Aw] refers to the subtuple of t containing the values of attributes Au, Av, ..., Aw, respectively.

Chapter 5-41

Figure 5.2 The relation STUDENT fromFigure 5.1 with a different order of tuples

Figure 5.1

Chapter 5-42

Figure 5.3 Two identical tuples when the order of attributes and values is not part of

relation definition.

Chapter 5-43

And then he showed us this totally cool example with two identical

tuples when the order of attributes and values is not part of the relation

definition.

Chapter 5-44

Notes

Write the answer to Question 5.2 (p 144) here: Why arethe tuples in a relation not ordered?

Write the answer to Question 5.3 (p 144) here: Why areduplicate tuples not allowed in a relation?

Chapter 5-45

5.2 Relational Integrity Constraints

Constraints are conditions that must hold on all valid relation instances. There are three main types of constraints:

1. Key constraints

2. Entity integrity constraints

3. Referential integrity constraints

Chapter 5-46

Key Constraints

Superkey of R:

A set of attributes SK of R such that no two tuples in any valid relation instance r(R) will have the same value for SK. That is, for any distinct tuples t1 and t2 in r(R), t1[SK] t2[SK].



What's the superkey of Employee?

Chapter 5-47

Key Constraints


204 R. B. Jones E21 11/01/1999 204 R. B. Jones E21 11/01/1999

Hey, what if I have a table that doesn't have a superkey? Now what?

Chapter 5-48

Key Constraints Superkey of R: A set of attributes SK of R such that no

two tuples in any valid relation instance r(R) will have the same value for SK. That is, for any distinct tuples t1 and t2 in r(R), t1[SK] t2[SK].

SuperKeys of CAR: 1. LN, ESN, Make, Model, Year;2. LN, Year; 3. ESN, Model, Year; 4. ESN; ...

Note: Year is not a superkey of CAR since more than one tuplehas the same value for year.

Chapter 5-49

You're telling me about superkeys? SUPERKEYS?! Ralph, there's nothing new here. It just means that no two rows can be the same

for the set of superkey attributes. Call me back

when you have something new.

Chapter 5-50

Key Constraints

Key of R: A "minimal" superkey; that is, a superkey K such that removal of any attribute from K results in a set of attributes that is not a superkey.

Example: The CAR relation schema:CAR(State, Reg#, SerialNo, Make, Model, Year)has two keys Key1 = {State, Reg#}, Key2 = {SerialNo}, which are

also superkeys. {SerialNo, Make} is a superkey but not a key.

If a relation has several candidate keys, one is chosen arbitrarily to be the primary key. The primary key attributes are underlined.

Chapter 5-51

Key Constraints

Coffees Name Supplier Price Sales

Colombian 101 7.99 9FR Roast 49 8.99 4

Hey, what if I have a table that doesn't have a key? Now what?

Colombian 49 7.99 9

Chapter 5-52

Key Constraints Key of R: A "minimal" superkey; that is, a superkey K

such that removal of any attribute from K results in a set of attributes that is not a superkey.

What are the candidate keys of the CAR relation? _____________

Chapter 5-53

Figure 5.4 The CAR relation, with two candidate keys: LicenseNumber and EngineSerialNumber

Key Constraints

Chapter 5-54

I tell you Mike, a primary key is a minimal superkey. Simple as that.

Say, where did everybody go?

Chapter 5-55



1. KeyKey constraints constraints

2. Entity integrity constraints


Chapter 5-56

Entity Integrity

Relational Database Schema: A set S of relation schemas that belong to the same database. S is the name of the database.

S = {R1, R2, ..., Rn}Entity Integrity: The primary key attributes PK of each

relation schema R in S cannot have null values in any tuple of r(R). This is because primary key values are used to identify the individual tuples.

t[PK] null for any tuple t in r(R) Note: Other attributes of R may be similarly constrained

to disallow null values, even though they are not members of the primary key.

Chapter 5-57

Entity IntegrityRelational Database Schema: A set S of relation schemas

that belong to the same database. S is the name of the database.

S = {R1, R2, ..., Rn}

Schema S = ...

Chapter 5-58

Entity Integrity

STUDENT key = ___________ COURSE key = ______________

Entity Integrity: The primary key attributes PK of each relation schema R in S cannot have null values in any tuple of r(R). This is because primary key values are used to identify the individual tuples. t[PK] null for any tuple t in r(R)

Chapter 5-59

Entity Integrity

STUDENT key = ___________ COURSE key = ______________

Entity Integrity: The primary key attributes PK of each relation schema R in S cannot have null values in any tuple of r(R). This is because primary key values are used to identify the individual tuples. t[PK] null for any tuple t in r(R)

Thesevalues are constrained

Chapter 5-60

Notes

Chapter 5-61



1. KeyKey constraints constraints

2. Entity integrityEntity integrity constraints constraints


Chapter 5-62

Referential Integrity

A constraint involving two relations (the previous constraints involve a single relation).

Used to specify a relationship among tuples in two relations: the referencing relation and the referenced 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].

A referential integrity constraint can be displayed in a relational database schema as a directed arc from R1.FK to R2.

Chapter 5-63


foreign keyforeign key

referencing relationreferencing relation

referenced relationreferenced relation referential integrity constraintreferential integrity constraint

Chapter 5-64

Referential Integrity Constraint

Statement of the constraintThe value in the foreign key column (or

columns) FK of the the referencing relation R1 can be either: (1) a value of an existing primary key value of the corresponding primary key PK in the referenced relation R2,, or..

(2) a null.

In case (2), the FK in R1 should not be a part of its own primary key.

Chapter 5-65


foreign keyforeign key

referencing relationreferencing relation

referenced relationreferenced relation referential integrity constraintreferential integrity constraint

Thesevalues are constrained

Chapter 5-66

Chapter 5-67

Other Types of Constraints

Semantic Integrity Constraints:- based on application semantics and cannot be

expressed by the model per se- E.g., “the max. no. of hours per employee for all

projects he or she works on is 56 hrs per week”- A constraint specification language may have

to be used to express these- SQL-99 allows triggers and ASSERTIONS to

allow for some of these

Chapter 5-68

Figure 5.5 Schema diagram for the COMPANY relational database schema

Chapter 5-69

Figure 5.6One possible

database state for the COMPANY database schema

p. 137

Chapter 5-70

Righttttttt...

Chapter 5-71

Figure 5.7 Referential integrity constraints displayed on the COMPANY relational database

schema.

p. 139

Chapter 5-72

Rightttttttagain.

Chapter 5-73

5.3 Update Operations on Relations

The update operations are:

INSERT a tuple.DELETE a tuple.MODIFY a tuple.

Chapter 5-74

Integrity constraints should not be violated by the update operations.

Several update operations may have to be grouped together.

Updates may propagate to cause other updates automatically. This may be necessary to maintain integrity constraints.

Chapter 5-75

Update Operations on Relations

In case of integrity violation, several actions can be taken:– Cancel the operation that causes the violation (REJECT

option)

– Perform the operation but inform the user of the violation

– Trigger additional updates so the violation is corrected (CASCADE option, SET NULL option)

– Execute a user-specified error-correction routine

Chapter 5-76

In-Class Exercise(Taken from Exercise 5.15)

Consider the following relations for a database that keeps track of student enrollment in courses and the books adopted for each course:

STUDENT(SSN, Name, Major, Bdate)

COURSE(Course#, Cname, Dept)

ENROLL(SSN, Course#, Quarter, Grade)

BOOK_ADOPTION(Course#, Quarter, Book_ISBN)

TEXT(Book_ISBN, Book_Title, Publisher, Author)

Draw a relational schema diagram specifying the foreign keys for this schema.

Chapter 5-77

Figure 5.8The

AIRLINE relational database schema.

Chapter 5-78

Notes

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