1. The Relational Data Model
Database Systems
Chapter 5
The Relational Data Model
主講人:陳建源
研究室 :法401
日期:99/11/2

2. Outline 1.Relational Model Concepts
2.Relational Model Constraints and Relational Database Schemas
3.Update Operations and Dealing with Constraint Violations

3. 1. Relational Model Concepts
Basis of the model
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

4. 1. 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 in 1970
"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

5. 1. Relational Model Concepts
Informal Definitions
RELATION: A table of values
A relation may be thought of as a set of rows
A relation may alternately be though of as a set of columns
Each row of the relation may be given an identifier
Each column typically is called by its column name or column header or attribute name

6. 1. Relational Model Concepts
Formal Definitions
Domain D
Set of atomic values
Atomic
Each value indivisible
Specifying a domain
Data type specified for each domain

7. 1. Relational Model Concepts
Formal Definitions
The Schema of a Relation R (A1, A2, .....An)
Relation schema R is defined over attributes A1, A2, .....An
Each attribute Ai is the name of a role played by some domain D in the relation schema R
e.g., A relation schema
STUDENT(Name, SSN, HomePhone, Address, OfficePhone, Age, GPA)
Degree (or arity) of a relation
Number of attributes n of its relation schema

8. 1. Relational Model Concepts
A relation r(R) is a subset of the Cartesian product of the domains that define R
r(R)  (dom (A1)  dom (A2)  ....  dom(An))
e.g., Let S1 = {0,1}, S2 = {a,b,c}
r(R) = {<0, a>, <0, b>, <1, c>}
A relation may be regarded as a set of tuples (rows)
r = {t1, t2, . . ., tm}.
A tuple is an ordered set of values
t = <v1, v2, . . ., vn>

9. 1. Relational Model Concepts
Cardinality
Total number of values in domain
Current relation state
Relation state at a given time
Reflects only the valid tuples that represent a particular state of the real world
Attribute names
Indicate different roles, or interpretations, for the domain

10. 1. Relational Model Concepts
R is also called the intension of a relation
r is also called the extension of a relation
The degree of a relation is the number of attributes n of its relation schema

11. 1. Relational Model Concepts

12. 1. Relational Model Concepts
Definition summary
Informal Terms Formal Terms
Table Relation
Column Attribute/Domain
Row Tuple
Values in a column Domain
Table Definition Schema of Relation
Populated Table Extension

13. 1. Relational Model Concepts
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

14. 1. Relational Model Concepts
Characteristics of Relations
Ordering of attributes in a relation schema R
We will consider the attributes in R(A1, A2, ..., An)
and the values in t=<v1, v2, ..., vn> to be ordered
A more general alternative definition of relation
does not require this ordering

15. 1. Relational Model Concepts
Characteristics of Relations
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
e.g., OfficePhone for some students
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

16. 1. Relational Model Concepts
Relational Model Notation
Relation schema R of degree n
Denoted by R(A1, A2, ..., An)
Uppercase letters Q, R, S
Denote relation names
Lowercase letters q, r, s
Denote relation states
Letters t, u, v
Denote tuples

17. 1. Relational Model Concepts
Relational Model Notation
Name of a relation schema: STUDENT
Indicates the current set of tuples in that relation
Notation: STUDENT(Name, Ssn, ...)
Refers only to relation schema
Attribute A can be qualified with the relation name R to which it belongs
Using the dot notation R.A

18. 1. Relational Model Concepts
Relational Model Notation
n-tuple t in a relation r(R)
Denoted by t = <v1, v2, ..., vn>
vi is the value corresponding to attribute Ai
Component values of tuples:
t[Ai] and t.Ai refer to the value vi in t for attribute Ai
t[Au, Aw, ..., Az] and t.(Au, Aw, ..., Az) refer to the subtuple of values <vu, vw, ..., vz> from t corresponding to the attributes specified in the list

19. 2.Relational Model Constraints
Restrictions on the actual values in a database state
Derived from the rules in the miniworld that the database represents
Inherent model-based constraints or implicit constraints
Inherent in the data model

20. 2.Relational Model Constraints
Schema-based constraints or explicit constraints
Can be directly expressed in schemas of the data model
Application-based or semantic constraints or business rules
Cannot be directly expressed in schemas
Expressed and enforced by application program

21. 2.Relational Model Constraints
Domain Constraints
Typically include:
Numeric data types for integers and real numbers
Characters
Booleans
Fixed-length strings
Variable-length strings
Date, time, timestamp
Money
Other special data types

22. 2.Relational Model Constraints
Relational Integrity Constraints
Constraints are conditions that must hold on all valid relation instances
Three main types of constraints:
Key constraints
Entity integrity constraints
Referential integrity constraints

23. 2.Relational Model Constraints
Relational Integrity Constraints
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, i.e., for any distinct tuples t1 and t2 in r(R), t1[SK] <> t2[SK]
Key of R
A minimal superkey
A superkey K such that removal of any attribute from K results in a set of attributes that is not a superkey

24. 2.Relational Model Constraints
Relational Integrity Constraints
If a relation has several candidate keys, one is chosen arbitrarily to be the primary key
The primary key attributes are underlined
e.g,
CAR(State, Reg#, SerialNo, Make, Model, Year)
two keys, Key1 = {State, Reg#},
Key2 = {SerialNo}
{SerialNo, Make} is a superkey but not a key

25. 2.Relational Model Constraints
Relational Integrity Constraints

26. 2.Relational Model Constraints
Relational Integrity Constraints
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}
A relational database state DB of S
A set of relation states DB = {r1, r2, . . ., rm}
such that each ri is a state of Ri

27. Relational Integrity Constraints (cont.)

28. 2.Relational Model Constraints

29. 2.Relational Model Constraints

30. 2.Relational Model Constraints
Relational Integrity Constraints
Entity Integrity
The primary key attributes PK of each relation
schema R in S cannot have null values in any
tuple of r(R), i.e.,
t[PK] <> null for any tuple t in r(R)

31. 2.Relational Model Constraints
Relational Integrity Constraints
Referential Integrity
A constraint 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

32. 2.Relational Model Constraints
Relational Integrity Constraints
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
A foreign key can refer to its own relation
e.g., the attribute SUPERSSN in EMPLOYEE refers to the supervisor of an employee

33. 2.Relational Model Constraints

34. 2.Relational Model Constraints
Relational Integrity Constraints
Other types of constraints
Semantic integrity constraints
May have to be specified and enforced on a relational database
Use triggers and assertions
More common to check for these types of constraints within the application programs
e.g., the salary of an employee should not exceed the salary of the employee’s supervisor
Transition constraints
Used to deal with state changes in the database
e.g., the salary of an employee can only increase

35. 2.Relational Model Constraints
Relational Integrity Constraints
Other types of constraints
Functional dependency constraint
Establishes a functional relationship among two sets of attributes X and Y
Value of X determines a unique value of Y
State constraints
Define the constraints that a valid state of the database must satisfy

36. 3. Update Operations on Relations
Three basic update operations
INSERT a tuple
DELETE a tuple
MODIFY a tuple
Integrity constraints should not be violated by the update operations

37. 3. Update Operations on Relations
Insert
Insert can violate any of the four types of constraints
Insert <‘Cecilia’, ‘F’, ‘Kolonsky’, null, ‘ ’, ‘6357 Windy Lane, Katy, TX’, F, 28000, null, 4> into EMPLOYEE
violates the entity integrity constraint (null for the primary key SSN)
Insert <‘Alicia’, ‘J’, ‘Zelaya’, ‘ ’, ‘ ’, ‘6357 Windy Lane, Katy, TX’, F, 28000, ‘ ’, 4> into EMPLOYEE
violates the key constraint because ‘ ’ exists

38. 3. Update Operations on Relations
Delete
The Delete operation can violate only referential integrity, if the tuple being deleted is referenced by the foreign keys from other tuples in the database
Delete the EMPLOYEE tuple with SSN = ‘ ’
is not acceptable, because tuples in WORKS_ON refer to this tuple
Delete the EMPLOYEE tuple with SSN = ‘ ’
result in even worse referential integrity violations

39. 3. Update Operations on Relations
Delete
If tuple being deleted is referenced by foreign keys from other tuples
Restrict
Reject the deletion
Cascade
Propagate the deletion by deleting tuples that reference the tuple that is being deleted
Set null or set default
Modify the referencing attribute values that cause the violation

40. 3. Update Operations on Relations
Updating an attribute that is neither a primary key nor a foreign key usually causes no problems
Modifying a primary key value is similar to deleting one tuple and inserting another in its place
If a foreign key attribute is modified, the DBMS must make sure that the new value refers to an existing tuple in the referenced relation (or is null)

41. 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