Description
A database management system (DBMS) is a collection of programs that enables users to create and maintain a database. According to the ANSI/SPARC DBMS Report (1977), a DBMS should be envisioned as a multi-layered system
Database
Fundamentals
Robert J. Robbins
Johns Hopkins University
[email protected]
File: N_drive:\jhu\class\1995\db-fund.ppt
© 1994, 1995 Robert Robbins
Database Fundamentals: 1
What is a Database?
General:
• A database is any collection of related data.
Restrictive:
• A database is a persistent, logically coherent
collection of inherently meaningful data, relevant
to some aspects of the real world.
The portion of the real world relevant to the database is sometimes referred
to as the universe of discourse or as the database miniworld. Whatever it
is called, it must be well understood by the designers of the database.
File: N_drive:\jhu\class\1995\db-fund.ppt
© 1994, 1995 Robert Robbins
Database Fundamentals: 2
What is a Database Management System?
A database management system (DBMS) is a
collection of programs that enables users to create
and maintain a database.
According to the
ANSI/SPARC DBMS Report (1977), a DBMS
should be envisioned as a multi-layered system:
External Level
(individual user views)
Conceptual Level
(Enterprise-wide view\)
Internal Level
(storage view)
Storage Level
(physical storage)
File: N_drive:\jhu\class\1995\db-fund.ppt
External
View 1
•••••
External
View n
Conceptual
Schema
Internal
Schema
Physical
Database
© 1994, 1995 Robert Robbins
Database Fundamentals: 3
What Does a DBMS Do?
Database management systems provide several
functions in addition to simple file management:
•
allow concurrency
•
control security
•
maintain data integrity
•
provide for backup and recovery
•
control redundancy
•
allow data independence
•
provide non-procedural query language
•
perform automatic query optimization
File: N_drive:\jhu\class\1995\db-fund.ppt
© 1994, 1995 Robert Robbins
Database Fundamentals: 4
Who Interacts with a DBMS?
Many different individuals are involved with a
database management system over its life:
•
systems analysts
•
database designers
•
database administrators
•
application developers
•
users
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© 1994, 1995 Robert Robbins
Database Fundamentals: 5
Components of a Database System
Direct User
Queries
Application
Programs
Database
Administrator
DML
Processor
DDL
Compiler
Authorization
Tables
Database
Manager
Database
Description
Tables
Concurrent
Access
Tables
File
Manager
System
Catalog
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Physical
System
Database
© 1994, 1995 Robert Robbins
Metadata
Database
Database Fundamentals: 6
Relational Database Model
What is a relational database?
•
a database that treats all of its data as a
collection of relations
What is a relation?
•
a kind of set
•
a subset of a Cartesian product
•
an unordered set of ordered tuples
File: N_drive:\jhu\class\1995\db-fund.ppt
© 1994, 1995 Robert Robbins
Database Fundamentals: 7
Basic Set Concepts
SET
examples
CARTESIAN
PRODUCT
example
Note:
RELATION
example
Note:
any collection of distinct entities of any
sort.
A = { 1,2,3,4,5,6 }
B = { H,T }
C = { R,B }
D = { Grant, Sherman, Lee }
a set of ordered pairs, produced by
combining each element of one set with
each element of another set.
B x C = { ,,, }
Cartesian products may be generated by
multiplying any number of sets together.
The actual number of sets involved in a
particular case is said to be the “degree”
or “arity” of that Cartesian product.
a subset of a Cartesian product
Q = { , }
Relations may be of any degree (arity).
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© 1994, 1995 Robert Robbins
Database Fundamentals: 8
Basic Set Concepts
A set is usually indicated by including a commadelimited list of the names its members within a
pair of wavy brackets:
R = { 1,2,3,4,5,6 }
G = { Marshall, Eisenhower, Bradley }
The members of a set are unordered. Two sets
are considered equivalent if and only if they
contain exactly the same members, without regard
for the order in which the members are listed.
R = { 1,2,3,4,5,6 }
= { 3,2,1,6,4,5 }
G = { Marshall, Eisenhower, Bradley }
= { Bradley, Marshall, Eisenhower }
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© 1994, 1995 Robert Robbins
Database Fundamentals: 9
Basic Set Concepts
An ordered double (or triple or quadruple or ntuple) is usually indicated by including a commadelimited list of the names its members within a
pair of pointed brackets:
S = < 2,4 >
C = < Marshall, Eisenhower, Bradley >
Order must be maintained in ordered n-tuples.
Two tuples are considered different if they contain
the same members in a different order.
S = < 2,4 > ? < 4,2 >
C = < Marshall, Eisenhower, Bradley >
? < Bradley, Eisenhower, Marshall >
A set may consist of an unordered collection of
ordered tuples. For example, we could imagine
the set of all ordered pairs of integers, such that
the first element is the square root of the second
element.
R = { ,< 2,4 >, ... }
As this ellipsis indicates, sets can be
infinite in size. However, sets that
are actually represented in a database
must be finite.
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© 1994, 1995 Robert Robbins
Database Fundamentals: 10
Basic Set Concepts
LET
R be the set of possible outcomes when rolling
a single red die.
R = { 1,2,3,4,5,6 }
LET
B be the set of possible outcomes when rolling
a single blue die.
B = { 1,2,3,4,5,6 }
THEN
The Cartesian product R x B gives the set of
outcomes when the two dice are rolled
together:
R x B: {
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}
© 1994, 1995 Robert Robbins
Database Fundamentals: 11
Relation: Subset of a Cartesian Product
Set R
Set B
1
1
2
2
3
3
4
4
5
5
6
6
A Cartesian product of two sets
can be generated by combining
every member of one set with
every member of the other set.
This results in a complete set of
ordered pairs, consisting of
every possible combination of
one member of the first set
combined with one member of
the second set. The number of
elements in a Cartesian product
is equal to M x N, where M and
N give the number of members
in each set.
Starting two sets.
A Cartesian product of two sets,
shown as a list of ordered pairs.
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1
1
2
2
3
3
4
4
5
5
6
6
A Cartesian product of two sets,
shown as a connection diagram,
with each member of the first set
connected to each member of the
other set.
© 1994, 1995 Robert Robbins
Database Fundamentals: 12
Relation: Subset of a Cartesian Product
A Cartesian product pairs every
member of the first set with every
member of the second set.
A relation pairs some
members of the first set
with some members of
the second set.
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A relation, therefore, must always
be representable as a subset of some
Cartesian product.
© 1994, 1995 Robert Robbins
Database Fundamentals: 13
Relation: Set of Ordered Tuples
A binary relation is a set of ordered doubles, with one element a member of the
first set and one element a member of the second set. Generally, we could
represent a set of ordered doubles as below. S1 is the first set and S2 the second.
S1
x
S2
•
•
•
•
•
•
•
•
•
By adding sets, relations can be extended to include ordered triples, ordered
quadruples or, in general, any ordered n-tuple, as below. A relation with n
participating sets is said to be of degree n or to possess arity n.
S1 x
S2
x
S3
x
x
•••••••••
Sn
•••••••••
•••••••••
•••••••••
•••••••••
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•••••••••
•••••••••
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© 1994, 1995 Robert Robbins
Database Fundamentals: 14
Relations as a Database
An n-ary relation (i.e., a subset of a Cartesian product of n sets) could be be
represented in a computer system as an n-column tabular file, with one member
from the first set named in the first column of each record and one member of
the second set in the second column, etc.
S1 x
S2
x
S3
x
x
Sn
•••••••••
•••••••••
•••••••••
•••••••••
•••••••••
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•••••••••
•••••••••
Codd recognized that many of the files used in computerized information
systems were very similar in structured to tabularized relations.
Smith
Robert
L.
1154 Elm Street
Glendale
MD
21200
Smith
Judy
F.
1154 Elm Street
Glendale
MD
21200
Jones
Greg
G.
765 Cedar Lane
Towson
MD
21232
Harris
Lloyd
K.
2323 Maple Dr
Towson
MD
21232
•
•
•
•
•
•
Ziegler
•
•
•
Fred
File: N_drive:\jhu\class\1995\db-fund.ppt
•
•
•
K.
•
•
•
7272 Cherry Ln.
© 1994, 1995 Robert Robbins
•
•
•
Baltimore
•
•
•
MD
•
•
•
21208
Database Fundamentals: 15
Relations as a Database
The business data file resembles a relation in a number of ways. The tabular
file itself corresponds to a relation. Each column, or attribute, in the file
corresponds to a particular set and all of the values from a particular column
come from the same domain, or set. Each row, or record, in the file
corresponds to a tuple
Domains
(sets)
Name-L
Name-F
MI
address
city
state
zip
Smith
Robert
L.
1154 Elm Street
Glendale
MD
21200
Smith
Judy
F.
1154 Elm Street
Glendale
MD
21200
Jones
Greg
G.
765 Cedar Lane
Towson
MD
21232
Harris
Lloyd
K.
2323 Maple Dr
Towson
MD
21232
•
•
•
•
•
•
Ziegler
•
•
•
Fred
•
•
•
K.
•
•
•
7272 Cherry Ln.
•
•
•
Baltimore
•
•
•
MD
•
•
•
21208
If such a file is to be genuinely interchangeable with a relation, certain
contraints must be met:
• every tuple must be unique
• every attribute within a tuple must be single-valued
• in in all tuples, the values for the same attribute must come from the
same domain or set
• no attributes should be null
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© 1994, 1995 Robert Robbins
Database Fundamentals: 16
Relations as a Database
An essential attribute of a relation is that every tuple must be unique. This
means that the values present in some individual attribute (or set of attributes)
must always provide enough information to allow a unique identification of
every tuple in the relation. In a relational database, these identifying values
are known as key values or just as the key.
Sometimes more than one key could be defined for given table. For
example, in the table below (which represents, perhaps, a patient record file),
several columns might serve as a key. Either patient number (assigned by
the hospital) or social security number (brought with the patient) are
possibilities. In addition, one might argue that the combination of last name,
address, and birth date could collectively serve as a key.
Any attribute or set of attributes that might possibly serve as a key is known
as a candidate key. Keys that involve only one attribute are known as
simple keys. Keys that involve more than one attribute are composite keys.
patient #
SS #
Last Name
address
birth date
P-64122
123-45-6789
Smith
123 Main Street
10 MAY 44
P-75642
001-32-6873
Pedersen
1700 Cedar Barn Way
31 MAR 59
P-70875
444-44-5555
Wilson
1321 North South St
7 AUG 90
P-79543
555-12-1212
Grant
808 Farragut Avenue
1 DEC 66
•
•
•
•
•
•
P-71536
•
•
•
888-88-8888
•
•
•
MacPherson
•
•
•
•
•
•
1617 Pennsylvania Ave
11 APR 60
In designing a database, one of the candidate keys for each relation must be
chosen to be the primary key for that table. Choosing primary keys is a
crucial task in database design. If keys need to be redesignated, the entire
system may have to be redone. Primary keys can never be null and should
never be changed. Sometimes none of the candidate keys for a relation are
likely to remain stable over time. Then, an arbitrary identifier might be created
to serve as a primary key. Such arbitrary keys are also known as surrogate
keys.
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© 1994, 1995 Robert Robbins
Database Fundamentals: 17
Relations as a Database
A binary relation (i.e., a subset of a Cartesian product of two sets) could be be
represented in a computer system as two-column tabular file, with one member
from the first set named in the first column of each record and one member of
the second set in the second column. For example, a binary relation could be
used to provide unique three-letter identifiers for academic departments.
Additional relations could be used to give more information about individual
departments or individual faculty members.
ZOL
Zoology
PSD
Political Science
CPS
Computer Science
HIS
History
•
•
•
•
•
•
ACC
•
•
•
Accounting
ZOL
Zoology
Room 203
Natural Science Bldg
355 4640
CPS
Computer Science
Room 714A
Wells Hall
355 5210
BSP
Biological Science
Room 141
Natural Science Bldg
353 4610
CEM
Chemistry
Room 320
Chemistry Bldg
355 9175
•
•
•
PSD
Room 303
Political Science
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
355 6590
South Kedzie Hall
999-99-9999
Johnson
William
F.
1533 Raleigh Dr.
Baltimore
MD
21211
888-88-8888
Johnson
William
F.
2842 Colony Ave.
Baltimore
MD
21201
777-77-7777
Brown
James
G.
99 W. East St.
Towson
MD
21232
666-66-6666
Brown
Gwen
K.
99 W. East St.
Towson
MD
21232
•
•
•
•
•
•
111-11-1111
•
•
•
Ziegler
File: N_drive:\jhu\class\1995\db-fund.ppt
•
•
•
Samual
•
•
•
L.
•
•
•
7272 Cherry Ln.
© 1994, 1995 Robert Robbins
•
•
•
Baltimore
•
•
•
MD
•
•
•
21208
Database Fundamentals: 18
Relations as a Database
Yet another relation could be used to show what faculty were members of what
departments. Notice that faculty member 999-99-9999 is a member of more
than one department and that, even on this short list, the department of zoology
has two members given.
999-99-9999
ZOL
888-88-8888
PSD
7777-77-7777
CPS
666-66-6666
ZOL
•
•
•
•
•
•
•
•
•
999-99-9999
BSP
Relations of this sort, that combine identifiers from two other relations, provide
the “glue” that holds a relational database together.
• • • other fields
Member-of Relation
è
SS Number
SS Number
Departments Relation
è
ç
Faculty Relation
Dept Code
Dept Code
other fields • • •
Whenever the values in an attribute column in one table “point to” primary keys
in another (or the same) table, the attribute column is said to be a foreign key.
Columns containing foreign keys are subject to an integrity constraint: any
value present as a foreign key must also be present as a primary key.
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© 1994, 1995 Robert Robbins
Database Fundamentals: 19
Relational Database Operators
Data models consist of data structures and
permitted operations on those data structures.
Part of Codd’s genius was to recognize that
many of the standard set operators that can take
relations as operands map nicely to real data
manipulation problems:
•
Cartesian product
•
union
•
intersection
•
difference
Codd devised some additional operators to
provide extra manipulatory power:
•
select
•
project
•
join
•
divide
The operators have now been extended to
include more useful manipulations:
•
outer join
•
outer union
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© 1994, 1995 Robert Robbins
Database Fundamentals: 20
Relational Database Normal Forms
Considerable study has been made of the properties of relations as they affect
the behavior of relational databases. The results of these studies are captured in
the definition of normal forms.
First Normal Form:
• A relation is in first normal form (1NF)
if and only if all underlying domains
contain atomic values only.
Second Normal Form:
• A relation is in second normal form
(2NF) if and only if it is in 1NF and
every non-key attribute is fully
dependent on the primary key.
Third Normal Form:
• A relation is in third normal form (3NF)
if and only if it is in 2 NF and the nonkey attributes are mutually
independent.
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© 1994, 1995 Robert Robbins
Database Fundamentals: 21
What is the E-R Data Model?
The Entity-Relationship (E-R) data model is a
semantically rich model that can be mapped to a
relational system.
• • • other fields
Member-of Relation
è
SS Number
SS Number
Departments Relation
è
ç
Faculty Relation
Dept Code
Dept Code
other fields • • •
The three files represented above are all relations in the formal sense. Chen
(1976) noted that different relations may play different roles in a database and
that being able to recognize and document those roles is a key part of database
design. The “faculty” and the “department” relations above both store
information about particular real-world entities. The “member-of” relation, on
the other hand, stores information about specific relationships involving
individual pairs of real-world entities.
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© 1994, 1995 Robert Robbins
Database Fundamentals: 22
The E-R Data Model
Different needs for access and use of the
database can be supported through different
user views
External
View 1
External
View n
•••••
Logical data independence
occurs here.
Conceptual
Database
Physical data independence
occurs here.
Physical
Database
Definition and mapping
written in data definition
language
Implemented on physical
devices, using a commercial
database product
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© 1994, 1995 Robert Robbins
Database Fundamentals: 23
The E-R Data Model
Layers may be added to a conceptual design in
order to increase the semantic richness available
at the top design level.
External
View 1
•••••
Conceptual
Database
(E-R)
Although the E-R approach
does not require an underlying relational model, most
E-R models can be converted
to relational models fairly
easily.
Conceptual
Database
(relational)
Physical
Database
File: N_drive:\jhu\class\1995\db-fund.ppt
© 1994, 1995 Robert Robbins
External
View n
The
entity-relationship
approach (Chen, 1976)
improved the mapping
between the semantics of a
database design and that
portion of the real world
being modeled with the
data.
Codd’s relational model
(1970) provided the first
formal basis for database
design.
Database Fundamentals: 24
The E-R Data Model
If layered conceptual models are used, the layering may be perceived differently
by the system’s users and developers. Users often see the database only in terms
of the views that they employ. System analysts and designers may think
primarily about the E-R schema, whereas the database administrator is likely to
deal primarily with the relational schema and the physical system.
External
View 1
Moving between conceptual
models can be difficult,
especially if automated
tools to facilitate the move
are not available.
•••••
Conceptual
Database
(E-R)
Conceptual
Database
(relational)
If a commercial RDBMS is
used, a relational conceptual
model provides a basis for
designing and implementing
an underlying physical
database.
File: N_drive:\jhu\class\1995\db-fund.ppt
External
View n
A different conceptual model
may be necessary to capture
the semantics of the database
domain.
If a commercial relational
database system is used,
mapping from a relational
conceptual model to the
physical database should be
relatively straightforward.
Physical
Database
© 1994, 1995 Robert Robbins
Database Fundamentals: 25
E-R Data Model: Graphical Conventions
Sets of real-world entities are represented with
named rectangles:
Faculty
Departments
Students
Classrooms
Courses
Relationships between members of entity sets
are represented with named diamonds that are
connected to the rectangles of the participating
entity sets with directed arcs:
Departments
4,n
majors
in
1,2
Students
Arcs are drawn with an orientation that “points” from foreign keys to primary
keys. The min:max participation cardinality can be indicated by placing
pairs of numbers on each arc. Here, “4,n” means that every department is
required to have at least four student majors, but can have many more; “1,2”
means that each student is required to have at least one major and is permitted
to have no more than two majors. Sometimes only the maximum participation
cardinalities are shown.
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© 1994, 1995 Robert Robbins
Database Fundamentals: 26
E-R Data Model: Graphical Conventions
Many different cardinalities are possible.
Documenting the cardinalities is an essential
part of database analysis and design.
One-to-one:
Entity Set A
Many-to-one:
Entity Set A
1
n
Relates
Relates
1
1
Entity Set B
Entity Set B
One-to-many:
Entity Set A
1
n
Entity Set B
Relates
m
Entity Set B
Relates
1:n
Entity Set B
Relates
0:n
Entity Set B
Relates
Many-to-many:
Entity Set A
One-to-many:
(mandatory)
Entity Set A
One-to-many:
(optional)
Entity Set A
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n
1:1
1:1
© 1994, 1995 Robert Robbins
Database Fundamentals: 27
E-R Data Model: Examples
Faculty and departments entities could be
related by a many-to-many “member-of”
relationship:
Departments
m
member
of
n
Faculty
They could also be related by a one-to-one
“chairman-of” relationship:
Departments
1,1
chairman
of
0,1
Faculty
The “1,1” cardinality for departments means that every department must have
one and only one chairman. The “0,1” cardinality for faculty means that not all
faculty participate in the chairman-of relationship and that no faculty member
may participate more than once. That is, not all faculty are chairmen and no one
faculty member may serve as chairman of more than one department.
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Database Fundamentals: 28
E-R Data Model: Graphical Conventions
Combining these two relationships into a single
diagram, we would have:
Departments
m
member
of
n
1,1
chairman
of
0,1
Faculty
A database design derived from the figure above
would allow a faculty member to chair a
department of which he/she was not a member.
To indicate an integrity constraint that requires
membership in a department in order to chair the
department, the E-R diagram would be modified
as below:
Departments
m
member
of
n
Faculty
0,1
1,1
File: N_drive:\jhu\class\1995\db-fund.ppt
chairman
of
© 1994, 1995 Robert Robbins
Database Fundamentals: 29
E-R Data Model: Graphical Conventions
Class hierarchies (“ISA” hierarchies) can be
indicated as below:
Person
1:n
ISA
1:n
1:n
1:n
Faculty
1:n
Staff
Student
1:n
1:n
ISA
ISA
1:n
1:n
Tenured
1:n
Untenured
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1:n
1:n
1:n
Temporary
Graduate
© 1994, 1995 Robert Robbins
1:n
Undergraduate
1:n
Nondegree
Database Fundamentals: 30
E-R Data Model: Graphical Conventions
Relationships may be recursive. Here, this E-R
figure represents all possible mother-child
relationships among all humans.
mother:child
This cardinality indicates that
not all persons participate in the
relationship as mothers, but that
those who do participate may
participate one or more times.
0:n
1:1
This cardinality indicates that
all persons participate in the
relationship as child and that no
child may have more than one
mother.
All Persons
Recursive relationships are particularly useful for representing any data
structure that could also be represented as a directed graph. Entries in the entity
table represent nodes of the graph and entries in the relationship table represent
arcs.
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© 1994, 1995 Robert Robbins
Database Fundamentals: 31
doc_895529353.pdf
A database management system (DBMS) is a collection of programs that enables users to create and maintain a database. According to the ANSI/SPARC DBMS Report (1977), a DBMS should be envisioned as a multi-layered system
Database
Fundamentals
Robert J. Robbins
Johns Hopkins University
[email protected]
File: N_drive:\jhu\class\1995\db-fund.ppt
© 1994, 1995 Robert Robbins
Database Fundamentals: 1
What is a Database?
General:
• A database is any collection of related data.
Restrictive:
• A database is a persistent, logically coherent
collection of inherently meaningful data, relevant
to some aspects of the real world.
The portion of the real world relevant to the database is sometimes referred
to as the universe of discourse or as the database miniworld. Whatever it
is called, it must be well understood by the designers of the database.
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Database Fundamentals: 2
What is a Database Management System?
A database management system (DBMS) is a
collection of programs that enables users to create
and maintain a database.
According to the
ANSI/SPARC DBMS Report (1977), a DBMS
should be envisioned as a multi-layered system:
External Level
(individual user views)
Conceptual Level
(Enterprise-wide view\)
Internal Level
(storage view)
Storage Level
(physical storage)
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External
View 1
•••••
External
View n
Conceptual
Schema
Internal
Schema
Physical
Database
© 1994, 1995 Robert Robbins
Database Fundamentals: 3
What Does a DBMS Do?
Database management systems provide several
functions in addition to simple file management:
•
allow concurrency
•
control security
•
maintain data integrity
•
provide for backup and recovery
•
control redundancy
•
allow data independence
•
provide non-procedural query language
•
perform automatic query optimization
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© 1994, 1995 Robert Robbins
Database Fundamentals: 4
Who Interacts with a DBMS?
Many different individuals are involved with a
database management system over its life:
•
systems analysts
•
database designers
•
database administrators
•
application developers
•
users
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Database Fundamentals: 5
Components of a Database System
Direct User
Queries
Application
Programs
Database
Administrator
DML
Processor
DDL
Compiler
Authorization
Tables
Database
Manager
Database
Description
Tables
Concurrent
Access
Tables
File
Manager
System
Catalog
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Physical
System
Database
© 1994, 1995 Robert Robbins
Metadata
Database
Database Fundamentals: 6
Relational Database Model
What is a relational database?
•
a database that treats all of its data as a
collection of relations
What is a relation?
•
a kind of set
•
a subset of a Cartesian product
•
an unordered set of ordered tuples
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Database Fundamentals: 7
Basic Set Concepts
SET
examples
CARTESIAN
PRODUCT
example
Note:
RELATION
example
Note:
any collection of distinct entities of any
sort.
A = { 1,2,3,4,5,6 }
B = { H,T }
C = { R,B }
D = { Grant, Sherman, Lee }
a set of ordered pairs, produced by
combining each element of one set with
each element of another set.
B x C = { ,,, }
Cartesian products may be generated by
multiplying any number of sets together.
The actual number of sets involved in a
particular case is said to be the “degree”
or “arity” of that Cartesian product.
a subset of a Cartesian product
Q = { , }
Relations may be of any degree (arity).
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Database Fundamentals: 8
Basic Set Concepts
A set is usually indicated by including a commadelimited list of the names its members within a
pair of wavy brackets:
R = { 1,2,3,4,5,6 }
G = { Marshall, Eisenhower, Bradley }
The members of a set are unordered. Two sets
are considered equivalent if and only if they
contain exactly the same members, without regard
for the order in which the members are listed.
R = { 1,2,3,4,5,6 }
= { 3,2,1,6,4,5 }
G = { Marshall, Eisenhower, Bradley }
= { Bradley, Marshall, Eisenhower }
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Database Fundamentals: 9
Basic Set Concepts
An ordered double (or triple or quadruple or ntuple) is usually indicated by including a commadelimited list of the names its members within a
pair of pointed brackets:
S = < 2,4 >
C = < Marshall, Eisenhower, Bradley >
Order must be maintained in ordered n-tuples.
Two tuples are considered different if they contain
the same members in a different order.
S = < 2,4 > ? < 4,2 >
C = < Marshall, Eisenhower, Bradley >
? < Bradley, Eisenhower, Marshall >
A set may consist of an unordered collection of
ordered tuples. For example, we could imagine
the set of all ordered pairs of integers, such that
the first element is the square root of the second
element.
R = { ,< 2,4 >, ... }
As this ellipsis indicates, sets can be
infinite in size. However, sets that
are actually represented in a database
must be finite.
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Database Fundamentals: 10
Basic Set Concepts
LET
R be the set of possible outcomes when rolling
a single red die.
R = { 1,2,3,4,5,6 }
LET
B be the set of possible outcomes when rolling
a single blue die.
B = { 1,2,3,4,5,6 }
THEN
The Cartesian product R x B gives the set of
outcomes when the two dice are rolled
together:
R x B: {
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}
© 1994, 1995 Robert Robbins
Database Fundamentals: 11
Relation: Subset of a Cartesian Product
Set R
Set B
1
1
2
2
3
3
4
4
5
5
6
6
A Cartesian product of two sets
can be generated by combining
every member of one set with
every member of the other set.
This results in a complete set of
ordered pairs, consisting of
every possible combination of
one member of the first set
combined with one member of
the second set. The number of
elements in a Cartesian product
is equal to M x N, where M and
N give the number of members
in each set.
Starting two sets.
A Cartesian product of two sets,
shown as a list of ordered pairs.
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1
1
2
2
3
3
4
4
5
5
6
6
A Cartesian product of two sets,
shown as a connection diagram,
with each member of the first set
connected to each member of the
other set.
© 1994, 1995 Robert Robbins
Database Fundamentals: 12
Relation: Subset of a Cartesian Product
A Cartesian product pairs every
member of the first set with every
member of the second set.
A relation pairs some
members of the first set
with some members of
the second set.
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A relation, therefore, must always
be representable as a subset of some
Cartesian product.
© 1994, 1995 Robert Robbins
Database Fundamentals: 13
Relation: Set of Ordered Tuples
A binary relation is a set of ordered doubles, with one element a member of the
first set and one element a member of the second set. Generally, we could
represent a set of ordered doubles as below. S1 is the first set and S2 the second.
S1
x
S2
•
•
•
•
•
•
•
•
•
By adding sets, relations can be extended to include ordered triples, ordered
quadruples or, in general, any ordered n-tuple, as below. A relation with n
participating sets is said to be of degree n or to possess arity n.
S1 x
S2
x
S3
x
x
•••••••••
Sn
•••••••••
•••••••••
•••••••••
•••••••••
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•••••••••
•••••••••
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Database Fundamentals: 14
Relations as a Database
An n-ary relation (i.e., a subset of a Cartesian product of n sets) could be be
represented in a computer system as an n-column tabular file, with one member
from the first set named in the first column of each record and one member of
the second set in the second column, etc.
S1 x
S2
x
S3
x
x
Sn
•••••••••
•••••••••
•••••••••
•••••••••
•••••••••
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•••••••••
•••••••••
Codd recognized that many of the files used in computerized information
systems were very similar in structured to tabularized relations.
Smith
Robert
L.
1154 Elm Street
Glendale
MD
21200
Smith
Judy
F.
1154 Elm Street
Glendale
MD
21200
Jones
Greg
G.
765 Cedar Lane
Towson
MD
21232
Harris
Lloyd
K.
2323 Maple Dr
Towson
MD
21232
•
•
•
•
•
•
Ziegler
•
•
•
Fred
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•
•
•
K.
•
•
•
7272 Cherry Ln.
© 1994, 1995 Robert Robbins
•
•
•
Baltimore
•
•
•
MD
•
•
•
21208
Database Fundamentals: 15
Relations as a Database
The business data file resembles a relation in a number of ways. The tabular
file itself corresponds to a relation. Each column, or attribute, in the file
corresponds to a particular set and all of the values from a particular column
come from the same domain, or set. Each row, or record, in the file
corresponds to a tuple
Domains
(sets)
Name-L
Name-F
MI
address
city
state
zip
Smith
Robert
L.
1154 Elm Street
Glendale
MD
21200
Smith
Judy
F.
1154 Elm Street
Glendale
MD
21200
Jones
Greg
G.
765 Cedar Lane
Towson
MD
21232
Harris
Lloyd
K.
2323 Maple Dr
Towson
MD
21232
•
•
•
•
•
•
Ziegler
•
•
•
Fred
•
•
•
K.
•
•
•
7272 Cherry Ln.
•
•
•
Baltimore
•
•
•
MD
•
•
•
21208
If such a file is to be genuinely interchangeable with a relation, certain
contraints must be met:
• every tuple must be unique
• every attribute within a tuple must be single-valued
• in in all tuples, the values for the same attribute must come from the
same domain or set
• no attributes should be null
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Database Fundamentals: 16
Relations as a Database
An essential attribute of a relation is that every tuple must be unique. This
means that the values present in some individual attribute (or set of attributes)
must always provide enough information to allow a unique identification of
every tuple in the relation. In a relational database, these identifying values
are known as key values or just as the key.
Sometimes more than one key could be defined for given table. For
example, in the table below (which represents, perhaps, a patient record file),
several columns might serve as a key. Either patient number (assigned by
the hospital) or social security number (brought with the patient) are
possibilities. In addition, one might argue that the combination of last name,
address, and birth date could collectively serve as a key.
Any attribute or set of attributes that might possibly serve as a key is known
as a candidate key. Keys that involve only one attribute are known as
simple keys. Keys that involve more than one attribute are composite keys.
patient #
SS #
Last Name
address
birth date
P-64122
123-45-6789
Smith
123 Main Street
10 MAY 44
P-75642
001-32-6873
Pedersen
1700 Cedar Barn Way
31 MAR 59
P-70875
444-44-5555
Wilson
1321 North South St
7 AUG 90
P-79543
555-12-1212
Grant
808 Farragut Avenue
1 DEC 66
•
•
•
•
•
•
P-71536
•
•
•
888-88-8888
•
•
•
MacPherson
•
•
•
•
•
•
1617 Pennsylvania Ave
11 APR 60
In designing a database, one of the candidate keys for each relation must be
chosen to be the primary key for that table. Choosing primary keys is a
crucial task in database design. If keys need to be redesignated, the entire
system may have to be redone. Primary keys can never be null and should
never be changed. Sometimes none of the candidate keys for a relation are
likely to remain stable over time. Then, an arbitrary identifier might be created
to serve as a primary key. Such arbitrary keys are also known as surrogate
keys.
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Database Fundamentals: 17
Relations as a Database
A binary relation (i.e., a subset of a Cartesian product of two sets) could be be
represented in a computer system as two-column tabular file, with one member
from the first set named in the first column of each record and one member of
the second set in the second column. For example, a binary relation could be
used to provide unique three-letter identifiers for academic departments.
Additional relations could be used to give more information about individual
departments or individual faculty members.
ZOL
Zoology
PSD
Political Science
CPS
Computer Science
HIS
History
•
•
•
•
•
•
ACC
•
•
•
Accounting
ZOL
Zoology
Room 203
Natural Science Bldg
355 4640
CPS
Computer Science
Room 714A
Wells Hall
355 5210
BSP
Biological Science
Room 141
Natural Science Bldg
353 4610
CEM
Chemistry
Room 320
Chemistry Bldg
355 9175
•
•
•
PSD
Room 303
Political Science
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
355 6590
South Kedzie Hall
999-99-9999
Johnson
William
F.
1533 Raleigh Dr.
Baltimore
MD
21211
888-88-8888
Johnson
William
F.
2842 Colony Ave.
Baltimore
MD
21201
777-77-7777
Brown
James
G.
99 W. East St.
Towson
MD
21232
666-66-6666
Brown
Gwen
K.
99 W. East St.
Towson
MD
21232
•
•
•
•
•
•
111-11-1111
•
•
•
Ziegler
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•
•
•
Samual
•
•
•
L.
•
•
•
7272 Cherry Ln.
© 1994, 1995 Robert Robbins
•
•
•
Baltimore
•
•
•
MD
•
•
•
21208
Database Fundamentals: 18
Relations as a Database
Yet another relation could be used to show what faculty were members of what
departments. Notice that faculty member 999-99-9999 is a member of more
than one department and that, even on this short list, the department of zoology
has two members given.
999-99-9999
ZOL
888-88-8888
PSD
7777-77-7777
CPS
666-66-6666
ZOL
•
•
•
•
•
•
•
•
•
999-99-9999
BSP
Relations of this sort, that combine identifiers from two other relations, provide
the “glue” that holds a relational database together.
• • • other fields
Member-of Relation
è
SS Number
SS Number
Departments Relation
è
ç
Faculty Relation
Dept Code
Dept Code
other fields • • •
Whenever the values in an attribute column in one table “point to” primary keys
in another (or the same) table, the attribute column is said to be a foreign key.
Columns containing foreign keys are subject to an integrity constraint: any
value present as a foreign key must also be present as a primary key.
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Database Fundamentals: 19
Relational Database Operators
Data models consist of data structures and
permitted operations on those data structures.
Part of Codd’s genius was to recognize that
many of the standard set operators that can take
relations as operands map nicely to real data
manipulation problems:
•
Cartesian product
•
union
•
intersection
•
difference
Codd devised some additional operators to
provide extra manipulatory power:
•
select
•
project
•
join
•
divide
The operators have now been extended to
include more useful manipulations:
•
outer join
•
outer union
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Database Fundamentals: 20
Relational Database Normal Forms
Considerable study has been made of the properties of relations as they affect
the behavior of relational databases. The results of these studies are captured in
the definition of normal forms.
First Normal Form:
• A relation is in first normal form (1NF)
if and only if all underlying domains
contain atomic values only.
Second Normal Form:
• A relation is in second normal form
(2NF) if and only if it is in 1NF and
every non-key attribute is fully
dependent on the primary key.
Third Normal Form:
• A relation is in third normal form (3NF)
if and only if it is in 2 NF and the nonkey attributes are mutually
independent.
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Database Fundamentals: 21
What is the E-R Data Model?
The Entity-Relationship (E-R) data model is a
semantically rich model that can be mapped to a
relational system.
• • • other fields
Member-of Relation
è
SS Number
SS Number
Departments Relation
è
ç
Faculty Relation
Dept Code
Dept Code
other fields • • •
The three files represented above are all relations in the formal sense. Chen
(1976) noted that different relations may play different roles in a database and
that being able to recognize and document those roles is a key part of database
design. The “faculty” and the “department” relations above both store
information about particular real-world entities. The “member-of” relation, on
the other hand, stores information about specific relationships involving
individual pairs of real-world entities.
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Database Fundamentals: 22
The E-R Data Model
Different needs for access and use of the
database can be supported through different
user views
External
View 1
External
View n
•••••
Logical data independence
occurs here.
Conceptual
Database
Physical data independence
occurs here.
Physical
Database
Definition and mapping
written in data definition
language
Implemented on physical
devices, using a commercial
database product
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Database Fundamentals: 23
The E-R Data Model
Layers may be added to a conceptual design in
order to increase the semantic richness available
at the top design level.
External
View 1
•••••
Conceptual
Database
(E-R)
Although the E-R approach
does not require an underlying relational model, most
E-R models can be converted
to relational models fairly
easily.
Conceptual
Database
(relational)
Physical
Database
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External
View n
The
entity-relationship
approach (Chen, 1976)
improved the mapping
between the semantics of a
database design and that
portion of the real world
being modeled with the
data.
Codd’s relational model
(1970) provided the first
formal basis for database
design.
Database Fundamentals: 24
The E-R Data Model
If layered conceptual models are used, the layering may be perceived differently
by the system’s users and developers. Users often see the database only in terms
of the views that they employ. System analysts and designers may think
primarily about the E-R schema, whereas the database administrator is likely to
deal primarily with the relational schema and the physical system.
External
View 1
Moving between conceptual
models can be difficult,
especially if automated
tools to facilitate the move
are not available.
•••••
Conceptual
Database
(E-R)
Conceptual
Database
(relational)
If a commercial RDBMS is
used, a relational conceptual
model provides a basis for
designing and implementing
an underlying physical
database.
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External
View n
A different conceptual model
may be necessary to capture
the semantics of the database
domain.
If a commercial relational
database system is used,
mapping from a relational
conceptual model to the
physical database should be
relatively straightforward.
Physical
Database
© 1994, 1995 Robert Robbins
Database Fundamentals: 25
E-R Data Model: Graphical Conventions
Sets of real-world entities are represented with
named rectangles:
Faculty
Departments
Students
Classrooms
Courses
Relationships between members of entity sets
are represented with named diamonds that are
connected to the rectangles of the participating
entity sets with directed arcs:
Departments
4,n
majors
in
1,2
Students
Arcs are drawn with an orientation that “points” from foreign keys to primary
keys. The min:max participation cardinality can be indicated by placing
pairs of numbers on each arc. Here, “4,n” means that every department is
required to have at least four student majors, but can have many more; “1,2”
means that each student is required to have at least one major and is permitted
to have no more than two majors. Sometimes only the maximum participation
cardinalities are shown.
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Database Fundamentals: 26
E-R Data Model: Graphical Conventions
Many different cardinalities are possible.
Documenting the cardinalities is an essential
part of database analysis and design.
One-to-one:
Entity Set A
Many-to-one:
Entity Set A
1
n
Relates
Relates
1
1
Entity Set B
Entity Set B
One-to-many:
Entity Set A
1
n
Entity Set B
Relates
m
Entity Set B
Relates
1:n
Entity Set B
Relates
0:n
Entity Set B
Relates
Many-to-many:
Entity Set A
One-to-many:
(mandatory)
Entity Set A
One-to-many:
(optional)
Entity Set A
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n
1:1
1:1
© 1994, 1995 Robert Robbins
Database Fundamentals: 27
E-R Data Model: Examples
Faculty and departments entities could be
related by a many-to-many “member-of”
relationship:
Departments
m
member
of
n
Faculty
They could also be related by a one-to-one
“chairman-of” relationship:
Departments
1,1
chairman
of
0,1
Faculty
The “1,1” cardinality for departments means that every department must have
one and only one chairman. The “0,1” cardinality for faculty means that not all
faculty participate in the chairman-of relationship and that no faculty member
may participate more than once. That is, not all faculty are chairmen and no one
faculty member may serve as chairman of more than one department.
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Database Fundamentals: 28
E-R Data Model: Graphical Conventions
Combining these two relationships into a single
diagram, we would have:
Departments
m
member
of
n
1,1
chairman
of
0,1
Faculty
A database design derived from the figure above
would allow a faculty member to chair a
department of which he/she was not a member.
To indicate an integrity constraint that requires
membership in a department in order to chair the
department, the E-R diagram would be modified
as below:
Departments
m
member
of
n
Faculty
0,1
1,1
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chairman
of
© 1994, 1995 Robert Robbins
Database Fundamentals: 29
E-R Data Model: Graphical Conventions
Class hierarchies (“ISA” hierarchies) can be
indicated as below:
Person
1:n
ISA
1:n
1:n
1:n
Faculty
1:n
Staff
Student
1:n
1:n
ISA
ISA
1:n
1:n
Tenured
1:n
Untenured
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1:n
1:n
1:n
Temporary
Graduate
© 1994, 1995 Robert Robbins
1:n
Undergraduate
1:n
Nondegree
Database Fundamentals: 30
E-R Data Model: Graphical Conventions
Relationships may be recursive. Here, this E-R
figure represents all possible mother-child
relationships among all humans.
mother:child
This cardinality indicates that
not all persons participate in the
relationship as mothers, but that
those who do participate may
participate one or more times.
0:n
1:1
This cardinality indicates that
all persons participate in the
relationship as child and that no
child may have more than one
mother.
All Persons
Recursive relationships are particularly useful for representing any data
structure that could also be represented as a directed graph. Entries in the entity
table represent nodes of the graph and entries in the relationship table represent
arcs.
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Database Fundamentals: 31
doc_895529353.pdf