Database Systems - Discussions

San77

Chapter05_accessible.pptx

Home >Computer Science homework help >Database Systems - Discussions

Fundamentals of Database Systems

Seventh Edition

Chapter 5

The Relational Data Model and Relational Database Constraints

If this PowerPoint presentation contains mathematical equations, you may need to check that your computer has the following installed:

1) MathType Plugin

2) Math Player (free versions available)

3) NVDA Reader (free versions available)

Learning Objectives

5.1 Relational Model Concepts

5.2 Relational Model Constraints and Relational Database Schemas

5.3 Update Operations and Dealing with Constraint Violations

Relational Model Concepts (1 of 2)

The relational Model of Data is based on the concept of a Relation

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

We review the essentials of the formal relational model in this chapter

In practice, there is a standard model based on S Q L – this is described in Chapters 6 and 7 as a language

Note: There are several important differences between the formal model and the practical model, as we shall see

Relational Model Concepts (2 of 2)

A Relation is a mathematical concept based on the ideas of sets

The model was first proposed by Dr. E.F. Codd of I B M Research in 1970 in the following paper:

“A Relational Model for Large Shared Data Banks,” Communications of the A C M, June 1970

The above paper caused a major revolution in the field of database management and earned Dr. Codd the coveted A C M Turing Award

Informal Definitions (1 of 2)

Informally, a relation looks like a table of values.

A relation typically contains a set of rows.

The data elements in each row represent certain facts that correspond to a real-world entity or relationship

In the formal model, rows are called tuples

Each column has a column header that gives an indication of the meaning of the data items in that column

In the formal model, the column header is called an attribute name (or just attribute)

Example of a Relation

Figure 5.1 The attributes and tuples of a relation STUDENT.

Informal Definitions (2 of 2)

Key of a Relation:

Each row has a value of a data item (or set of items) that uniquely identifies that row in the table

Called the key

In the STUDENT table, S S N is the key

Sometimes row-ids or sequential numbers are assigned as keys to identify the rows in a table

Called artificial key or surrogate key

Formal Definitions - Schema

The Schema (or description) of a Relation:

Denoted by

R is the name of the relation

The attributes of the relation are

Example:

CUSTOMER (Cust-id, Cust-name, Address, Phone #)

CUSTOMER is the relation name

Defined over the four attributes: Cust-id, Cust-name, Address, Phone #

Each attribute has a domain or a set of valid values.

For example, the domain of Cust-id is 6 digit numbers.

Formal Definitions - Tuple

A tuple is an ordered set of values (enclosed in angled brackets

Each value is derived from an appropriate domain.

A row in the CUSTOMER relation is a 4-tuple and would consist of four values, for example:

This is called a 4-tuple as it has 4 values

A tuple (row) in the CUSTOMER relation.

A relation is a set of such tuples (rows)

Formal Definitions - Domain

A domain has a logical definition:

Example: “U S A_phone_numbers” are the set of 10 digit phone numbers valid in the U.S.

A domain also has a data-type or a format defined for it.

The U S A_phone_numbers may have a format: (ddd)ddd-dddd where each d is a decimal digit.

Dates have various formats such as year, month, date formatted as yyyy-mm-dd, or as dd mm,yyyy etc.

The attribute name designates the role played by a domain in a relation:

Used to interpret the meaning of the data elements corresponding to that attribute

Example: The domain Date may be used to define two attributes named “Invoice-date” and “Payment-date” with different meanings

Formal Definitions - State

The relation state is a subset of the Cartesian product of the domains of its attributes

each domain contains the set of all possible values the attribute can take.

Example: attribute Cust-name is defined over the domain of character strings of maximum length 25

dom(Cust-name) is varchar(25)

The role these strings play in the CUSTOMER relation is that of the name of a customer.

Formal Definitions - Summary

Formally,

Given

is the schema of the relation

R is the name of the relation

are the attributes of the relation

r(R): a specific state (or "value" or “population”) of relation R – this is a set of tuples (rows)

where each ti is an n-tuple

where each vj element-of dom(Aj)

Formal Definitions - Example

Let R(A1, A2) be a relation schema:

Let dom(A1) = {0,1}

Let dom(A2) = {a,b,c}

Then:

is all possible combinations:

The relation state

For example: r(R) could be

this is one possible state (or “population” or “extension”) r of the relation R, defined over A1 and A2.

It has three 2-tuples:

Definition Summary

Informal Terms	Formal Terms
Table	Relation
Column Header	Attribute
All possible Column Values	Domain
Row	Tuple
Table Definition	Schema of a Relation
Populated Table	State of the Relation

Example – A Relation STUDENT

Figure 5.1 The attributes and tuples of a relation STUDENT.

Characteristics of Relations (1 of 3)

Ordering of tuples in a relation r(R):

The tuples are not considered to be ordered, even though they appear to be in the tabular form.

Ordering of attributes in a relation schema R (and of values within each tuple):

We will consider the attributes in

and the values in

to be ordered.

(However, a more general alternative definition of relation does not require this ordering. It includes both the name and the value for each of the attributes).

This representation may be called as “self-describing”.

Same State as Previous Figure (but with Different Order of Tuples)

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

Characteristics of Relations (2 of 3)

Values in a tuple:

All values are considered atomic (indivisible).

Each value in a tuple must be from the domain of the attribute for that column

If tuple

is a tuple (row) in the relation state r of

Then each vi must be a value from dom (Ai)

A special null value is used to represent values that are unknown or not available or inapplicable in certain tuples.

Characteristics of Relations (3 of 3)

Notation:

We refer to component values of a tuple t by:

This is the value vi of attribute Ai for tuple t

Similarly,

refers to the subtuple of t containing the values of attributes

respectively in t

Constraints

Constraints determine which values are permissible and which are not in the database.

They are of three main types:

Inherent or Implicit Constraints: These are based on the data model itself. (E.g., relational model does not allow a list as a value for any attribute)

Schema-based or Explicit Constraints: They are expressed in the schema by using the facilities provided by the model. (E.g., max. cardinality ratio constraint in the E R model)

Application based or semantic constraints: These are beyond the expressive power of the model and must be specified and enforced by the application programs.

Relational Integrity Constraints

Constraints are conditions that must hold on all valid relation states.

There are three main types of (explicit schema-based) constraints that can be expressed in the relational model:

Key constraints

Entity integrity constraints

Referential integrity constraints

Another schema-based constraint is the domain constraint

Every value in a tuple must be from the domain of its attribute (or it could be null, if allowed for that attribute)

Key Constraints (1 of 3)

Superkey of R:

Is a set of attributes S K of R with the following condition:

No two tuples in any valid relation state r(R) will have the same value for S K

That is, for any distinct tuples t 1 and t 2 in r(R),

This condition must hold in any valid state r(R)

Key of R:

A "minimal" superkey

That is, a key is a superkey K such that removal of any attribute from K results in a set of attributes that is not a superkey (does not possess the superkey uniqueness property)

A Key is a Superkey but not vice versa

Key Constraints (2 of 3)

Example: Consider the CAR relation schema:

CAR ( State, Reg#, SerialNo, Make, Model, Year)

CAR has two keys:

Key1 = {State, Reg#}

Key2 = {SerialNo}

Both are also superkeys of CAR

{Serial No, Make} is a superkey but not a key.

In general:

Any key is a superkey (but not vice versa)

Any set of attributes that includes a key is a superkey

A minimal superkey is also a key

Key Constraints (3 of 3)

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

The primary key attributes are underlined.

Example: Consider the CAR relation schema:

CAR (State, Reg#, SerialNo, Make, Model, Year)

We chose SerialNo as the primary key

The primary key value is used to uniquely identify each tuple in a relation

Provides the tuple identity

Also used to reference the tuple from another tuple

General rule: Choose as primary key the smallest of the candidate keys (in terms of size)

Not always applicable – choice is sometimes subjective

Car Table with Two Candidate Keys – License Number Chosen as Primary Key

Figure 5.4 The CAR relation, with two candidate keys: License_number and Engine_serial_number.

Relational Database Schema

Relational Database Schema:

A set S of relation schemas that belong to the same database.

S is the name of the whole database schema

and a set I C of integrity constraints.

are the names of the individual relation schemas within the database S

Following slide shows a COMPANY database schema with 6 relation schemas

COMPANY Database Schema

Figure 5.5 Schema diagram for the COMPANY relational database schema.

Relational Database State

A relational database state D B of S is a set of relation states

such that each ri is a state of Ri and such that the ri relation states satisfy the integrity constraints specified in I C.

A relational database state is sometimes called a relational database snapshot or instance.

We will not use the term instance since it also applies to single tuples.

A database state that does not meet the constraints is an invalid state

Populated Database State

Each relation will have many tuples in its current relation state

The relational database state is a union of all the individual relation states

Whenever the database is changed, a new state arises

Basic operations for changing the database:

INSERT a new tuple in a relation

DELETE an existing tuple from a relation

MODIFY an attribute of an existing tuple

Next slide (Figure 5.6) shows an example state for the COMPANY database schema shown in Figure 5.5 (see slide 28).

Populated Database State for COMPANY

Figure 5.6 One possible database state for the COMPANY relational database schema.

Entity Integrity

The primary key attributes P K 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.

for any tuple t in r(R)

If P K has several attributes, null is not allowed in any of these attributes

Note: Other attributes of R may be constrained to disallow null values, even though they are not members of the primary key.

Referential Integrity (1 of 2)

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.

Referential Integrity (2 of 2)

Tuples in the referencing relation R1 have attributes F K (called foreign key attributes) that reference the primary key attributes P K of the referenced relation R2.

A tuple t1 in R1 is said to reference a tuple t2 in R2

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

Referential Integrity (or Foreign Key) Constraint

Statement of the constraint

The value in the foreign key column (or columns) F K of the referencing relation R1 can be either:

(1) a value of an existing primary key value of a corresponding primary key P K in the referenced relation R2, or

(2) a null.

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

Displaying a Relational Database Schema and Its Constraints

Each relation schema can be displayed as a row of attribute names

The name of the relation is written above the attribute names

The primary key attribute (or attributes) will be underlined

A foreign key (referential integrity) constraints is displayed as a directed arc (arrow) from the foreign key attributes to the referenced table

Can also point the primary key of the referenced relation for clarity

Next slide shows the COMPANY relational schema diagram with referential integrity constraints

Referential Integrity Constraints for COMPANY Database

Figure 5.7 Referential integrity constraints displayed on the COMPANY relational database schema.

Other Types of Constraints

Semantic Integrity Constraints:

based on application semantics and cannot be expressed by the model per se

Example: “the maximum number of hours per employee for all projects he or she works on is 56 hours per week”

A constraint specification language may have to be used to express these

S Q L – 99 allows CREATE TRIGGER and CREATE ASSERTION to express some of these semantic constraints

Keys, Permissibility of Null values, Candidate Keys (Unique in S Q L), Foreign Keys, Referential Integrity etc. are expressed by the CREATE TABLE statement in S Q L.

Update Operations on Relations (1 of 2)

INSERT a tuple.

DELETE a tuple.

MODIFY a tuple.

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.

Update Operations on Relations (2 of 2)

In case of integrity violation, several actions can be taken:

Cancel the operation that causes the violation (RESTRICT or 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

Possible Violations for Each Operation (1 of 3)

INSERT may violate any of the constraints:

Domain constraint:

if one of the attribute values provided for the new tuple is not of the specified attribute domain

Key constraint:

if the value of a key attribute in the new tuple already exists in another tuple in the relation

Referential integrity:

if a foreign key value in the new tuple references a primary key value that does not exist in the referenced relation

Entity integrity:

if the primary key value is null in the new tuple

Possible Violations for Each Operation (2 of 3)

DELETE may violate only referential integrity:

If the primary key value of the tuple being deleted is referenced from other tuples in the database

Can be remedied by several actions: RESTRICT, CASCADE, SET NULL (see Chapter 6 for more details)

RESTRICT option: reject the deletion

CASCADE option: propagate the new primary key value into the foreign keys of the referencing tuples

SET NULL option: set the foreign keys of the referencing tuples to NULL

One of the above options must be specified during database design for each foreign key constraint

Possible Violations for Each Operation (3 of 3)

UPDATE may violate domain constraint and NOT NULL constraint on an attribute being modified

Any of the other constraints may also be violated, depending on the attribute being updated:

Updating the primary key (P K):

Similar to a DELETE followed by an INSERT

Need to specify similar options to DELETE

Updating a foreign key (F K):

May violate referential integrity

Updating an ordinary attribute (neither P K nor F K):

Can only violate domain constraints

Summary

Presented Relational Model Concepts

Definitions

Characteristics of relations

Discussed Relational Model Constraints and Relational Database Schemas

Domain constraints

Key constraints

Entity integrity

Referential integrity

Described the Relational Update Operations and Dealing with Constraint Violations

In-Class Exercise

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

STUDENT (S S N, Name, Major, Bdate)

COURSE (Course#, Cname, Dept)

ENROLL (S S N, Course#, Quarter, Grade)

BOOK_ADOPTION (Course#, Quarter, Book_I S B N)

TEXT (Book _I S B N, Book_Title, Publisher, Author)

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

‘’

)

…

()Ì()()

)

´´

(

rRAAA

dom dom .... dom

tvvv

,, …,

(

)

()

domdom

ΑA

<><><><><<>

{}

0,a , 0,b , 0,c, 1,a, 1,b, 1,c

(

)

())

(

domdom

ΑA

{

}

<><><>

0,a , 0,b , 1,c

<><><>

0,a , 0,b , 1,c

tvvv

,, ...,

=<>

,, ,

= <¼>

tvvv

[][]

SKSK

[]

PKnull