ndnbfgdfgdfgModel and Relational Database Constraints.ppt

1
Copyright © 2007 Ramez Elmasri and Shamkant B. Navathe

Chapter 5
The Relational Data Model and
Relational Database Constraints

3
Chapter Outline
 Relational Model Concepts
 Relational Model Constraints and Relational
Database Schemas
 Update Operations and Dealing with Constraint
Violations

4
Relational Model Concepts
 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 SQL –
this is described in Chapters 8 and 9
 Note: There are several important differences between
the formal model and the practical model, as we shall see

5
Relational Model Concepts
 A Relation is a mathematical concept based on
the ideas of sets
 The model was first proposed by Dr. E.F. Codd of
IBM Research 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 Dr.
Codd the coveted ACM Turing Award

6
Informal Definitions
 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)

7
Example of a Relation

8
Informal Definitions
 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, SSN 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

9
Formal Definitions - Schema
 The Schema (or description) of a Relation:
 Denoted by R(A1, A2, .....An)
 R is the name of the relation
 The attributes of the relation are A1, A2, ..., An
 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.

10
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:
 <632895, "John Smith", "101 Main St. Atlanta, GA 30332",
"(404) 894-2000">
 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)

11
Formal Definitions - Domain
 A domain has a logical definition:
 Example: “USA_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 USA_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

12
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.

13
Formal Definitions - Summary
 Formally,
 Given R(A1, A2, .........., An)
 r(R)  dom (A1) X dom (A2) X ....X dom(An)
 R(A1, A2, …, An) is the schema of the relation
 R is the name of the relation
 A1, A2, …, An 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)
 r(R) = {t1, t2, …, tn} where each ti is an n-tuple
 ti = <v1, v2, …, vn> where each vj element-of dom(Aj)

14
Formal Definitions - Example
 Let R(A1, A2) be a relation schema:
 Let dom(A1) = {0,1}
 Let dom(A2) = {a,b,c}
 Then: dom(A1) X dom(A2) is all possible combinations:
{<0,a> , <0,b> , <0,c>, <1,a>, <1,b>, <1,c> }
 The relation state r(R)  dom(A1) X dom(A2)
 For example: r(R) could be {<0,a> , <0,b> , <1,c> }
 this is one possible state (or “population” or “extension”) r of
the relation R, defined over A1 and A2.
 It has three 2-tuples: <0,a> , <0,b> , <1,c>

15
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

16
Example – A relation STUDENT

17
Characteristics Of Relations
 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 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).

18
Same state as previous Figure (but
with different order of tuples)

19
 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 t = <v1, v2, …, vn> is a tuple (row) in the
relation state r of R(A1, A2, …, An)

Then each vi must be a value from dom(Ai)
 A special null value is used to represent values
that are unknown or inapplicable to certain tuples.

20
 Notation:
 We refer to component values of a tuple t by:

t[Ai] or t.Ai

This is the value vi 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 in t

21
Relational Integrity Constraints
 Constraints are conditions that must hold on all valid
relation states.
 There are three main types of constraints in the relational
model:
 Key constraints
 Entity integrity constraints
 Referential integrity constraints
 Another implicit 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)

22
Key Constraints
 Superkey of R:
 Is a set of attributes SK of R with the following condition:

No two tuples in any valid relation state 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]

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)

23
Key Constraints (continued)
 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
 {SerialNo, 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

24
Key Constraints (continued)
 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

25
CAR table with two candidate keys –
LicenseNumber chosen as Primary Key

26
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
 S = {R1, R2, ..., Rn}
 R1, R2, …, Rn are the names of the individual
relation schemas within the database S
 Following slide shows a COMPANY database
schema with 6 relation schemas

27
COMPANY Database Schema

28
Entity Integrity
 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)

If PK 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.

29
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.

30
Referential Integrity
 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.

31
Referential Integrity (or foreign key)
Constraint
 Statement of the constraint
 The 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 a
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.

32
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 the primary key of the referenced relation
for clarity
 Next slide shows the COMPANY relational schema
diagram

33
Referential Integrity Constraints for COMPANY database

34
Other Types of Constraints
 Semantic Integrity Constraints:
 based on application semantics and cannot be
expressed by the model per se
 Example: “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
express for some of these

35
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 shows an example state for the COMPANY
database

36
Populated database state for COMPANY

37
Update Operations on Relations
 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.

38
Update Operations on Relations
 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

39
Possible violations for each operation
 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

40
 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 8 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

41
 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 (PK):

Similar to a DELETE followed by an INSERT

Need to specify similar options to DELETE
 Updating a foreign key (FK):

May violate referential integrity
 Updating an ordinary attribute (neither PK nor FK):

Can only violate domain constraints

42
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

43
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.

ndnbfgdfgdfgModel and Relational Database Constraints.ppt

More Related Content

Similar to ndnbfgdfgdfgModel and Relational Database Constraints.ppt (20)

More from WrushabhShirsat3 (20)

Recently uploaded (20)

ndnbfgdfgdfgModel and Relational Database Constraints.ppt