DBMS Unit-2.pdf

UNIT-2
Course Name: Database Management System

04/18/22
Department of Computer Science &
Engineering
Course Outcome (CO): At the
ends of this course students will
have:
CO1: Awareness of database
management basics and different
models that we use for database.
CO2: Design and architecture of
relational model, relational
algebra and SQL queries.
CO3: Implement different form of
normalization.
CO4: Logical representation of
internet database.
CO5: Analysis and concepts of
transaction, concurrency and
recovery systems

Outline
• Relational Model concepts
• Integrity Constraints
• Relational Algebra
Unary Relational Operations
Relational Algebra Operations From Set Theory
Binary Relational Operations
Additional Relational Operations
• Relational Calculus
Tuple Relational Calculus
Domain Relational Calculus
• SQL

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

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
operation
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
operation
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

Relational Algebra
03/28/22
Engineering

43
Relational Algebra Overview
Relational algebra is the basic set of operations
for the relational model
These operations enable a user to specify basic retrieval
requests (or queries)
The result of an operation is a new relation,
which may have been formed from one or
more input relations
This property makes the algebra “closed” (all objects
in relational algebra are relations)

44
Relational Algebra Overview (continued)
The algebra operations thus produce new
relations
These can be further manipulated using operations of
the same algebra
A sequence of relational algebra operations
forms a relational algebra expression
The result of a relational algebra expression is also a
relation that represents the result of a database query (or
retrieval request)

45
Brief History of Origins of Algebra
Muhammad ibn Musa al-Khwarizmi (800-847 CE) wrote a book
titled al-jabr about arithmetic of variables
Book was translated into Latin.
Its title (al-jabr) gave Algebra its name.
Al-Khwarizmi called variables “shay”
“Shay” is Arabic for “thing”.
Spanish transliterated “shay” as “xay” (“x” was “sh” in Spain).
In time this word was abbreviated as x.
Where does the word Algorithm come from?
Algorithm originates from “al-Khwarizmi"
Reference: PBS (http://www.pbs.org/empires/islam/innoalgebra.html)

46
Relational Algebra Overview
Relational Algebra consists of several groups of operations
Unary Relational Operations
SELECT (symbol:  (sigma))
PROJECT (symbol:  (pi))
RENAME (symbol:  (rho))
Relational Algebra Operations From Set Theory
UNION (  ), INTERSECTION (  ), DIFFERENCE (or MINUS, – )
CARTESIAN PRODUCT ( x )
JOIN (several variations of JOIN exist)
DIVISION
Additional Relational Operations
OUTER JOINS, OUTER UNION
AGGREGATE FUNCTIONS (These compute summary of information: for
example, SUM, COUNT, AVG, MIN, MAX)

47
Database State for COMPANY
All examples discussed below refer to the COMPANY database shown here.

48
Unary Relational Operations: SELECT
The SELECT operation (denoted by  (sigma)) is used to select a subset of
the tuples from a relation based on a selection condition.
The selection condition acts as a filter
Keeps only those tuples that satisfy the qualifying condition
Tuples satisfying the condition are selected whereas the other
tuples are discarded (filtered out)
Examples:
Select the EMPLOYEE tuples whose department number is 4:
 DNO = 4 (EMPLOYEE)
Select the employee tuples whose salary is greater than $30,000:
 SALARY > 30,000 (EMPLOYEE)

49
Unary Relational Operations: SELECT
In general, the select operation is denoted by 
<selection condition>(R) where
the symbol  (sigma) is used to denote the select operator
the selection condition is a Boolean (conditional)
expression specified on the attributes of relation R
tuples that make the condition true are selected
appear in the result of the operation
tuples that make the condition false are filtered out
discarded from the result of the operation

50
Unary Relational Operations: SELECT (contd.)
SELECT Operation Properties
The SELECT operation  <selection condition>(R) produces a relation S that
has the same schema (same attributes) as R
SELECT  is commutative:
 <condition1>( < condition2> (R)) =  <condition2> ( < condition1> (R))
Because of commutativity property, a cascade (sequence) of SELECT
operations may be applied in any order:
<cond1>(<cond2> (<cond3> (R)) = <cond2> (<cond3> (<cond1> ( R)))
A cascade of SELECT operations may be replaced by a single
selection with a conjunction of all the conditions:
<cond1>(< cond2> (<cond3>(R)) =  <cond1> AND < cond2> AND < cond3>(R)))
The number of tuples in the result of a SELECT is less than (or
equal to) the number of tuples in the input relation R

51
The following query results refer to this database
state

52
Unary Relational Operations: PROJECT
PROJECT Operation is denoted by  (pi)
This operation keeps certain columns (attributes)
from a relation and discards the other columns.
PROJECT creates a vertical partitioning
The list of specified columns (attributes) is kept in each
tuple
The other attributes in each tuple are discarded
Example: To list each employee’s first and last
name and salary, the following is used:
LNAME, FNAME,SALARY(EMPLOYEE)

53
Unary Relational Operations: PROJECT (cont.)
The general form of the project operation is:
<attribute list>(R)
 (pi) is the symbol used to represent the project
operation
<attribute list> is the desired list of attributes from
relation R.
The project operation removes any duplicate
tuples
This is because the result of the project operation
must be a set of tuples
Mathematical sets do not allow duplicate elements.

54
Unary Relational Operations: PROJECT (contd.)
PROJECT Operation Properties
The number of tuples in the result of projection
<list>(R) is always less or equal to the number of
tuples in R
If the list of attributes includes a key of R, then the
number of tuples in the result of PROJECT is equal to
the number of tuples in R
PROJECT is not commutative
 <list1> ( <list2> (R) ) =  <list1> (R) as long as <list2>
contains the attributes in <list1>

55
Examples of applying SELECT and PROJECT
operations

56
Relational Algebra Expressions
We may want to apply several relational algebra
operations one after the other
Either we can write the operations as a single
relational algebra expression by nesting the
operations, or
We can apply one operation at a time and create
intermediate result relations.
In the latter case, we must give names to the
relations that hold the intermediate results.

57
Single expression versus sequence of relational
operations (Example)
To retrieve the first name, last name, and salary of all employees
who work in department number 5, we must apply a select and
a project operation
We can write a single relational algebra expression as follows:
FNAME, LNAME, SALARY( DNO=5(EMPLOYEE))
OR We can explicitly show the sequence of operations, giving a
name to each intermediate relation:
DEP5_EMPS   DNO=5(EMPLOYEE)
RESULT   FNAME, LNAME, SALARY (DEP5_EMPS)

58
Unary Relational Operations: RENAME
The RENAME operator is denoted by  (rho)
In some cases, we may want to rename the
attributes of a relation or the relation name or
both
Useful when a query requires multiple operations
Necessary in some cases (see JOIN operation later)

59
Unary Relational Operations: RENAME (contd.)
The general RENAME operation  can be
expressed by any of the following forms:
S (B1, B2, …, Bn )(R) changes both:
the relation name to S, and
the column (attribute) names to B1, B1, …..Bn
S(R) changes:
the relation name only to S
(B1, B2, …, Bn )(R) changes:
the column (attribute) names only to B1, B1, …..Bn

60
Unary Relational Operations: RENAME (contd.)
For convenience, we also use a shorthand for
renaming attributes in an intermediate relation:
If we write:
• RESULT   FNAME, LNAME, SALARY (DEP5_EMPS)
• RESULT will have the same attribute names as
DEP5_EMPS (same attributes as EMPLOYEE)
• If we write:
• RESULT (F, M, L, S, B, A, SX, SAL, SU, DNO)
 FNAME, LNAME, SALARY (DEP5_EMPS)
• The 10 attributes of DEP5_EMPS are renamed to F,
M, L, S, B, A, SX, SAL, SU, DNO, respectively

61
Example of applying multiple operations and
RENAME

62
Relational Algebra Operations from
Set Theory: UNION
UNION Operation
Binary operation, denoted by 
The result of R  S, is a relation that includes all
tuples that are either in R or in S or in both R and
S
Duplicate tuples are eliminated
The two operand relations R and S must be “type
compatible” (or UNION compatible)
R and S must have same number of attributes
Each pair of corresponding attributes must be type
compatible (have same or compatible domains)

63
Set Theory: UNION
Example:
To retrieve the social security numbers of all employees who either
work in department 5 (RESULT1 below) or directly supervise an
employee who works in department 5 (RESULT2 below)
We can use the UNION operation as follows:
DEP5_EMPS  DNO=5 (EMPLOYEE)
RESULT1   SSN(DEP5_EMPS)
RESULT2(SSN)  SUPERSSN(DEP5_EMPS)
RESULT  RESULT1  RESULT2
The union operation produces the tuples that are in either RESULT1
or RESULT2 or both

64
Example of the result of a UNION operation
UNION Example

65
Set Theory
Type Compatibility of operands is required for the binary set
operation UNION , (also for INTERSECTION , and SET
DIFFERENCE –, see next slides)
R1(A1, A2, ..., An) and R2(B1, B2, ..., Bn) are type compatible
if:
they have the same number of attributes, and
the domains of corresponding attributes are type compatible (i.e.
dom(Ai)=dom(Bi) for i=1, 2, ..., n).
The resulting relation for R1R2 (also for R1R2, or R1–R2,
see next slides) has the same attribute names as the first
operand relation R1 (by convention)

66
Relational Algebra Operations from Set Theory:
INTERSECTION
INTERSECTION is denoted by 
The result of the operation R  S, is a relation
that includes all tuples that are in both R and S
The attribute names in the result will be the same
as the attribute names in R
compatible”

67
SET DIFFERENCE (cont.)
SET DIFFERENCE (also called MINUS or
EXCEPT) is denoted by –
The result of R – S, is a relation that includes all
tuples that are in R but not in S
The attribute names in the result will be the same
as the attribute names in R
compatible”

68
Example to illustrate the result of UNION,
INTERSECT, and DIFFERENCE

69
Some properties of UNION, INTERSECT, and
DIFFERENCE
Notice that both union and intersection are commutative
operations; that is
R  S = S  R, and R  S = S  R
Both union and intersection can be treated as n-ary operations
applicable to any number of relations as both are associative
operations; that is
R  (S  T) = (R  S)  T
(R  S)  T = R  (S  T)
The minus operation is not commutative; that is, in general
R – S ≠ S – R

70
CARTESIAN PRODUCT
CARTESIAN (or CROSS) PRODUCT Operation
This operation is used to combine tuples from two relations in a
combinatorial fashion.
Denoted by R(A1, A2, . . ., An) x S(B1, B2, . . ., Bm)
Result is a relation Q with degree n + m attributes:
Q(A1, A2, . . ., An, B1, B2, . . ., Bm), in that order.
The resulting relation state has one tuple for each combination of
tuples—one from R and one from S.
Hence, if R has nR tuples (denoted as |R| = nR ), and S has nS tuples,
then R x S will have nR * nS tuples.
The two operands do NOT have to be "type compatible”

71
CARTESIAN PRODUCT (cont.)
Generally, CROSS PRODUCT is not a
meaningful operation
Can become meaningful when followed by other
operations
Example (not meaningful):
FEMALE_EMPS   SEX=’F’(EMPLOYEE)
EMPNAMES   FNAME, LNAME, SSN (FEMALE_EMPS)
EMP_DEPENDENTS  EMPNAMES x DEPENDENT
EMP_DEPENDENTS will contain every combination of
EMPNAMES and DEPENDENT
whether or not they are actually related

72
CARTESIAN PRODUCT (cont.)
To keep only combinations where the
DEPENDENT is related to the EMPLOYEE,
we add a SELECT operation as follows
Example (meaningful):
FEMALE_EMPS   SEX=’F’(EMPLOYEE)
EMPNAMES   FNAME, LNAME, SSN (FEMALE_EMPS)
EMP_DEPENDENTS  EMPNAMES x DEPENDENT
ACTUAL_DEPS   SSN=ESSN(EMP_DEPENDENTS)
RESULT   FNAME, LNAME, DEPENDENT_NAME (ACTUAL_DEPS)
RESULT will now contain the name of female employees and
their dependents

73
Example of applying CARTESIAN PRODUCT

74
Binary Relational Operations:
JOIN
JOIN Operation (denoted by )
The sequence of CARTESIAN PRODECT followed by SELECT is
used quite commonly to identify and select related tuples from
two relations
A special operation, called JOIN combines this sequence into a
single operation
This operation is very important for any relational database with
more than a single relation, because it allows us combine related
tuples from various relations
The general form of a join operation on two relations R(A1, A2, . .
., An) and S(B1, B2, . . ., Bm) is:
R <join condition>S
where R and S can be any relations that result from general
relational algebra expressions.

75
Binary Relational Operations: JOIN (cont.)
Example: Suppose that we want to retrieve the name of the
manager of each department.
To get the manager’s name, we need to combine each
DEPARTMENT tuple with the EMPLOYEE tuple whose SSN
value matches the MGRSSN value in the department tuple.
We do this by using the join operation.
DEPT_MGR  DEPARTMENT MGRSSN=SSN EMPLOYEE
MGRSSN=SSN is the join condition
Combines each department record with the employee who manages
the department
The join condition can also be specified as
DEPARTMENT.MGRSSN= EMPLOYEE.SSN

76
Example of applying the JOIN operation

77
Some properties of JOIN
Consider the following JOIN operation:
R(A1, A2, . . ., An) S(B1, B2, . . ., Bm)
R.Ai=S.Bj
Result is a relation Q with degree n + m attributes:
Q(A1, A2, . . ., An, B1, B2, . . ., Bm), in that order.
The resulting relation state has one tuple for each combination of
tuples—r from R and s from S, but only if they satisfy the join
condition r[Ai]=s[Bj]
Hence, if R has nR tuples, and S has nS tuples, then the join result
will generally have less than nR * nS tuples.
Only related tuples (based on the join condition) will appear in the
result

78
Some properties of JOIN
The general case of JOIN operation is called a
Theta-join: R S
theta
The join condition is called theta
Theta can be any general boolean expression on
the attributes of R and S; for example:
R.Ai<S.Bj AND (R.Ak=S.Bl OR R.Ap<S.Bq)
Most join conditions involve one or more
equality conditions “AND”ed together; for
example:
R.Ai=S.Bj AND R.Ak=S.Bl AND R.Ap=S.Bq

79
Binary Relational Operations: EQUIJOIN
EQUIJOIN Operation
The most common use of join involves join
conditions with equality comparisons only
Such a join, where the only comparison operator
used is =, is called an EQUIJOIN.
In the result of an EQUIJOIN we always have one or
more pairs of attributes (whose names need not be
identical) that have identical values in every tuple.
The JOIN seen in the previous example was an
EQUIJOIN.

80
Binary Relational Operations:
NATURAL JOIN Operation
NATURAL JOIN Operation
Another variation of JOIN called NATURAL JOIN — denoted by
* — was created to get rid of the second (superfluous) attribute
in an EQUIJOIN condition.
because one of each pair of attributes with identical values is
superfluous
The standard definition of natural join requires that the two join
attributes, or each pair of corresponding join attributes, have
the same name in both relations
If this is not the case, a renaming operation is applied first.

81
NATURAL JOIN (contd.)
Example: To apply a natural join on the DNUMBER attributes of
DEPARTMENT and DEPT_LOCATIONS, it is sufficient to write:
DEPT_LOCS  DEPARTMENT * DEPT_LOCATIONS
Only attribute with the same name is DNUMBER
An implicit join condition is created based on this attribute:
DEPARTMENT.DNUMBER=DEPT_LOCATIONS.DNUMBER
Another example: Q  R(A,B,C,D) * S(C,D,E)
The implicit join condition includes each pair of attributes with the same
name, “AND”ed together:
R.C=S.C AND R.D.S.D
Result keeps only one attribute of each such pair:
Q(A,B,C,D,E)

82
Example of NATURAL JOIN operation

83
Complete Set of Relational Operations
The set of operations including SELECT ,
PROJECT  , UNION , DIFFERENCE - ,
RENAME , and CARTESIAN PRODUCT X
is called a complete set because any other
relational algebra expression can be expressed
by a combination of these five operations.
For example:
R  S = (R  S ) – ((R - S)  (S - R))
R <join condition>S =  <join condition> (R X S)

84
Binary Relational Operations: DIVISION
DIVISION Operation
The division operation is applied to two relations
R(Z)  S(X), where X subset Z. Let Y = Z - X (and hence Z = X
 Y); that is, let Y be the set of attributes of R that are not
attributes of S.
The result of DIVISION is a relation T(Y) that includes a tuple t if
tuples tR appear in R with tR [Y] = t, and with
tR [X] = ts for every tuple ts in S.
For a tuple t to appear in the result T of the DIVISION, the values
in t must appear in R in combination with every tuple in S.

85
Example of DIVISION

86
Recap of Relational Algebra Operations

87
Additional Relational Operations: Aggregate
Functions and Grouping
A type of request that cannot be expressed in the basic relational
algebra is to specify mathematical aggregate functions on
collections of values from the database.
Examples of such functions include retrieving the average or total
salary of all employees or the total number of employee tuples.
These functions are used in simple statistical queries that
summarize information from the database tuples.
Common functions applied to collections of numeric values
include
SUM, AVERAGE, MAXIMUM, and MINIMUM.
The COUNT function is used for counting tuples or values.

88
Aggregate Function Operation
Use of the Aggregate Functional operation ℱ
ℱMAX Salary (EMPLOYEE) retrieves the maximum salary value from
the EMPLOYEE relation
ℱMIN Salary (EMPLOYEE) retrieves the minimum Salary value from
the EMPLOYEE relation
ℱSUM Salary (EMPLOYEE) retrieves the sum of the Salary from the
EMPLOYEE relation
ℱCOUNT SSN, AVERAGE Salary (EMPLOYEE) computes the count
(number) of employees and their average salary
Note: count just counts the number of rows, without removing
duplicates

89
Using Grouping with Aggregation
The previous examples all summarized one or more attributes for
a set of tuples
Maximum Salary or Count (number of) Ssn
Grouping can be combined with Aggregate Functions
Example: For each department, retrieve the DNO, COUNT SSN,
and AVERAGE SALARY
A variation of aggregate operation ℱ allows this:
Grouping attribute placed to left of symbol
Aggregate functions to right of symbol
DNO ℱCOUNT SSN, AVERAGE Salary (EMPLOYEE)
Above operation groups employees by DNO (department
number) and computes the count of employees and average
salary per department

90
Examples of applying aggregate functions and
grouping

91
Illustrating aggregate functions and grouping

92
Additional Relational Operations (cont.)
Recursive Closure Operations
Another type of operation that, in general, cannot be
specified in the basic original relational algebra is
recursive closure.
This operation is applied to a recursive relationship.
An example of a recursive operation is to retrieve all
SUPERVISEES of an EMPLOYEE e at all levels
— that is, all EMPLOYEE e’ directly supervised
by e; all employees e’’ directly supervised by each
employee e’; all employees e’’’ directly supervised
by each employee e’’; and so on.

93
Although it is possible to retrieve employees at
each level and then take their union, we
cannot, in general, specify a query such as
“retrieve the supervisees of ‘James Borg’ at all
levels” without utilizing a looping mechanism.
The SQL3 standard includes syntax for recursive
closure.

94

95
The OUTER JOIN Operation
In NATURAL JOIN and EQUIJOIN, tuples without a matching (or
related) tuple are eliminated from the join result
Tuples with null in the join attributes are also eliminated
This amounts to loss of information.
A set of operations, called OUTER joins, can be used when we
want to keep all the tuples in R, or all those in S, or all those in
both relations in the result of the join, regardless of whether or
not they have matching tuples in the other relation.

96
The left outer join operation keeps every tuple in
the first or left relation R in R S; if no
matching tuple is found in S, then the
attributes of S in the join result are filled or
“padded” with null values.
A similar operation, right outer join, keeps every
tuple in the second or right relation S in the
result of R S.
A third operation, full outer join, denoted by
keeps all tuples in both the left and the right
relations when no matching tuples are found,

97

98
OUTER UNION Operations
The outer union operation was developed to take the
union of tuples from two relations if the relations
are not type compatible.
This operation will take the union of tuples in two
relations R(X, Y) and S(X, Z) that are partially
compatible, meaning that only some of their
attributes, say X, are type compatible.
The attributes that are type compatible are
represented only once in the result, and those
attributes that are not type compatible from either
relation are also kept in the result relation T(X, Y,
Z).

99
Example: An outer union can be applied to two relations whose
schemas are STUDENT(Name, SSN, Department, Advisor)
and INSTRUCTOR(Name, SSN, Department, Rank).
Tuples from the two relations are matched based on having the same
combination of values of the shared attributes— Name, SSN,
Department.
If a student is also an instructor, both Advisor and Rank will have a
value; otherwise, one of these two attributes will be null.
The result relation STUDENT_OR_INSTRUCTOR will have the
following attributes:
STUDENT_OR_INSTRUCTOR (Name, SSN, Department,
Advisor, Rank)

100
Examples of Queries in Relational Algebra
n Q1: Retrieve the name and address of all employees who work for the
‘Research’ department.
RESEARCH_DEPT   DNAME=’Research’ (DEPARTMENT)
RESEARCH_EMPS  (RESEARCH_DEPT DNUMBER= DNOEMPLOYEEEMPLOYEE)
RESULT   FNAME, LNAME, ADDRESS (RESEARCH_EMPS)
n Q6: Retrieve the names of employees who have no dependents.
ALL_EMPS   SSN(EMPLOYEE)
EMPS_WITH_DEPS(SSN)   ESSN(DEPENDENT)
EMPS_WITHOUT_DEPS  (ALL_EMPS - EMPS_WITH_DEPS)
RESULT   LNAME, FNAME (EMPS_WITHOUT_DEPS * EMPLOYEE)

03/28/22
Engineering
Relational Calculus

102
Relational Calculus
A relational calculus expression creates a new
relation, which is specified in terms of
variables that range over rows of the stored
database relations (in tuple calculus) or over
columns of the stored relations (in domain
calculus).
In a calculus expression, there is no order of
operations to specify how to retrieve the query
result—a calculus expression specifies only
what information the result should contain.
This is the main distinguishing feature between

103
Relational Calculus
Relational calculus is considered to be a
nonprocedural language.
This differs from relational algebra, where we
must write a sequence of operations to specify
a retrieval request; hence relational algebra can
be considered as a procedural way of stating a
query.

104
The tuple relational calculus is based on specifying a number of
tuple variables.
Each tuple variable usually ranges over a particular database
relation, meaning that the variable may take as its value any
individual tuple from that relation.
A simple tuple relational calculus query is of the form
{t | COND(t)}
where t is a tuple variable and COND (t) is a conditional expression
involving t.
The result of such a query is the set of all tuples t that satisfy
COND (t).

105
Example: To find the first and last names of all employees whose
salary is above $50,000, we can write the following tuple
calculus expression:
{t.FNAME, t.LNAME | EMPLOYEE(t) AND
t.SALARY>50000}
The condition EMPLOYEE(t) specifies that the range relation
of tuple variable t is EMPLOYEE.
The first and last name (PROJECTION FNAME, LNAME) of each
EMPLOYEE tuple t that satisfies the condition
t.SALARY>50000 (SELECTION  SALARY >50000) will be
retrieved.

106
The Existential and Universal Quantifiers
Two special symbols called quantifiers can appear in formulas;
these are the universal quantifier () and the existential
quantifier ().
Informally, a tuple variable t is bound if it is quantified, meaning
that it appears in an ( t) or ( t) clause; otherwise, it is free.
If F is a formula, then so are ( t)(F) and ( t)(F), where t is a
tuple variable.
The formula ( t)(F) is true if the formula F evaluates to true for
some (at least one) tuple assigned to free occurrences of t in F;
otherwise ( t)(F) is false.
The formula ( t)(F) is true if the formula F evaluates to true for
every tuple (in the universe) assigned to free occurrences of t in
F; otherwise ( t)(F) is false.

107
The Existential and Universal Quantifiers
 is called the universal or “for all” quantifier
because every tuple in “the universe of” tuples
must make F true to make the quantified
formula true.
 is called the existential or “there exists”
quantifier because any tuple that exists in “the
universe of” tuples may make F true to make
the quantified formula true.

108
Example Query Using Existential Quantifier
Retrieve the name and address of all employees who work for the ‘Research’
department. The query can be expressed as :
{t.FNAME, t.LNAME, t.ADDRESS | EMPLOYEE(t) and ( d)
(DEPARTMENT(d) and d.DNAME=‘Research’ and
d.DNUMBER=t.DNO) }
The only free tuple variables in a relational calculus expression should be
those that appear to the left of the bar ( | ).
In above query, t is the only free variable; it is then bound successively to
each tuple.
If a tuple satisfies the conditions specified in the query, the attributes FNAME,
LNAME, and ADDRESS are retrieved for each such tuple.
The conditions EMPLOYEE (t) and DEPARTMENT(d) specify the range
relations for t and d.
The condition d.DNAME = ‘Research’ is a selection condition and
corresponds to a SELECT operation in the relational algebra, whereas
the condition d.DNUMBER = t.DNO is a JOIN condition.

109
Example Query Using Universal Quantifier
Find the names of employees who work on all the projects controlled by department
number 5. The query can be:
{e.LNAME, e.FNAME | EMPLOYEE(e) and ( ( x)(not(PROJECT(x)) or
not(x.DNUM=5)
OR ( ( w)(WORKS_ON(w) and w.ESSN=e.SSN and x.PNUMBER=w.PNO))))}
Exclude from the universal quantification all tuples that we are not interested in by
making the condition true for all such tuples.
The first tuples to exclude (by making them evaluate automatically to true) are those
that are not in the relation R of interest.
In query above, using the expression not(PROJECT(x)) inside the universally
quantified formula evaluates to true all tuples x that are not in the PROJECT
relation.
Then we exclude the tuples we are not interested in from R itself. The expression
not(x.DNUM=5) evaluates to true all tuples x that are in the project relation but are
not controlled by department 5.
Finally, we specify a condition that must hold on all the remaining tuples in R.
( ( w)(WORKS_ON(w) and w.ESSN=e.SSN and x.PNUMBER=w.PNO)

110
Languages Based on Tuple Relational Calculus
The language SQL is based on tuple calculus. It uses the basic
block structure to express the queries in tuple calculus:
SELECT <list of attributes>
FROM <list of relations>
WHERE <conditions>
SELECT clause mentions the attributes being projected, the
FROM clause mentions the relations needed in the query, and
the WHERE clause mentions the selection as well as the join
conditions.
SQL syntax is expanded further to accommodate other operations.
(See Chapter 8).

111
Languages Based on Tuple Relational Calculus
Another language which is based on tuple
calculus is QUEL which actually uses the
range variables as in tuple calculus. Its syntax
includes:
RANGE OF <variable name> IS <relation name>
Then it uses
RETRIEVE <list of attributes from range variables>
WHERE <conditions>
This language was proposed in the relational
DBMS INGRES.

112
The Domain Relational Calculus
Another variation of relational calculus called the domain relational calculus,
or simply, domain calculus is equivalent to tuple calculus and to relational
algebra.
The language called QBE (Query-By-Example) that is related to domain
calculus was developed almost concurrently to SQL at IBM Research,
Yorktown Heights, New York.
Domain calculus was thought of as a way to explain what QBE does.
Domain calculus differs from tuple calculus in the type of variables used in
formulas:
Rather than having variables range over tuples, the variables range over
single values from domains of attributes.
To form a relation of degree n for a query result, we must have n of these
domain variables— one for each attribute.

113
The Domain Relational Calculus
An expression of the domain calculus is of the
form
{ x1, x2, . . ., xn |
COND(x1, x2, . . ., xn, xn+1, xn+2, . . ., xn+m)}
where x1, x2, . . ., xn, xn+1, xn+2, . . ., xn+m are domain
variables that range over domains (of attributes)
and COND is a condition or formula of the domain
relational calculus.

• Six basic operators
– select: 
– project: 
– union: 
– set difference: –
– Cartesian product: x
– rename: 

03/28/22
Engineering
SQL

History
• IBM Sequel language developed as part of System R project at the IBM
San Jose Research Laboratory
• Renamed Structured Query Language (SQL)
• ANSI and ISO standard SQL:
– SQL-86
– SQL-89
– SQL-92
– SQL:1999 (language name became Y2K compliant!)
– SQL:2003
• Commercial systems offer most, if not all, SQL-92 features, plus varying
feature sets from later standards and special proprietary features.
– Not all examples here may work on your particular system.

Data Definition Language
• The schema for each relation.
• The domain of values associated with each attribute.
• Integrity constraints
• And as we will see later, also other information such as
– The set of indices to be maintained for each relations.
– Security and authorization information for each relation.
– The physical storage structure of each relation on disk.
The SQL data-definition language (DDL) allows the specification
of information about relations, including:

Domain Types in SQL
• char(n). Fixed length character string, with user-specified length n.
• varchar(n). Variable length character strings, with user-specified
maximum length n.
• int. Integer (a finite subset of the integers that is machine-dependent).
• smallint. Small integer (a machine-dependent subset of the integer
domain type).
• numeric(p,d). Fixed point number, with user-specified precision of p
digits, with d digits to the right of decimal point. (ex., numeric(3,1),
allows 44.5 to be stores exactly, but not 444.5 or 0.32)
• real, double precision. Floating point and double-precision floating
point numbers, with machine-dependent precision.
• float(n). Floating point number, with user-specified precision of at
least n digits.
• More are covered in Chapter 4.

Create Table Construct
• An SQL relation is defined using the create table command:
create table r (A1 D1, A2 D2, ..., An Dn,
(integrity-constraint1),
...,
(integrity-constraintk))
– r is the name of the relation
– each Ai is an attribute name in the schema of relation r
– Di is the data type of values in the domain of attribute Ai
• Example:
create table instructor (
ID char(5),
name varchar(20),
dept_name varchar(20),
salary numeric(8,2))

Integrity Constraints in Create
Table
• not null
• primary key (A1, ..., An )
• foreign key (Am, ..., An ) references r
Example:
create table instructor (
ID char(5),
name varchar(20) not null,
salary numeric(8,2),
primary key (ID),
foreign key (dept_name) references department);
primary key declaration on an attribute automatically ensures not null

And a Few More Relation
Definitions
• create table student (
ID varchar(5),
name varchar(20) not null,
tot_cred numeric(3,0),
primary key (ID),
foreign key (dept_name) references department);
• create table takes (
ID varchar(5),
course_id varchar(8),
sec_id varchar(8),
semester varchar(6),
year numeric(4,0),
grade varchar(2),
primary key (ID, course_id, sec_id, semester, year) ,
foreign key (ID) references student,
foreign key (course_id, sec_id, semester, year) references section);
– Note: sec_id can be dropped from primary key above, to ensure a student
cannot be registered for two sections of the same course in the same semester

And more still
• create table course (
course_id varchar(8),
title varchar(50),
credits numeric(2,0),
primary key (course_id),
foreign key (dept_name) references
department);

Updates to tables
• Insert
– insert into instructor values (‘10211’, ’Smith’, ’Biology’, 66000);
• Delete
– Remove all tuples from the student relation
• delete from student
• Drop Table
– drop table r
• Alter
– alter table r add A D
• where A is the name of the attribute to be added to relation r and D is the
domain of A.
• All exiting tuples in the relation are assigned null as the value for the new
attribute.
– alter table r drop A
• where A is the name of an attribute of relation r
• Dropping of attributes not supported by many databases.

Basic Query Structure
• A typical SQL query has the form:
select A1, A2, ..., An
from r1, r2, ..., rm
where P
– Ai represents an attribute
– Ri represents a relation
– P is a predicate.
• The result of an SQL query is a relation.

The select Clause
• The select clause lists the attributes desired in the
result of a query
– corresponds to the projection operation of the relational
algebra
• Example: find the names of all instructors:
select name
from instructor
• NOTE: SQL names are case insensitive (i.e., you
may use upper- or lower-case letters.)
– E.g., Name ≡ NAME ≡ name
– Some people use upper case wherever we use bold font.

The select Clause (Cont.)
• SQL allows duplicates in relations as well
as in query results.
• To force the elimination of duplicates,
insert the keyword distinct after select.
• Find the department names of all
instructors, and remove duplicates
select distinct dept_name
from instructor
• The keyword all specifies that duplicates
should not be removed.

• An asterisk in the select clause denotes “all
attributes”
select *
from instructor
• An attribute can be a literal with no from
clause
select ‘437’
– Results is a table with one column and a single
row with value “437”
– Can give the column a name using:
select ‘437’ as FOO

• The select clause can contain arithmetic
expressions involving the operation, +, –, , and /,
and operating on constants or attributes of tuples.
– The query:
select ID, name, salary/12
from instructor
would return a relation that is the same as the instructor
relation, except that the value of the attribute salary is
divided by 12.
– Can rename “salary/12” using the as clause:
select ID, name, salary/12 as monthly_salary

The where Clause
• The where clause specifies conditions that the result must satisfy
– Corresponds to the selection predicate of the relational algebra.
• To find all instructors in Comp. Sci. dept
select name
from instructor
where dept_name = ‘Comp. Sci.'
• Comparison results can be combined using the logical connectives
and, or, and not
– To find all instructors in Comp. Sci. dept with salary > 80000
select name
from instructor
where dept_name = ‘Comp. Sci.' and salary > 80000
• Comparisons can be applied to results of arithmetic expressions.

The from Clause
• The from clause lists the relations involved in the query
– Corresponds to the Cartesian product operation of the relational
algebra.
• Find the Cartesian product instructor X teaches
select 
from instructor, teaches
– generates every possible instructor – teaches pair, with all
attributes from both relations.
– For common attributes (e.g., ID), the attributes in the resulting
table are renamed using the relation name (e.g., instructor.ID)
• Cartesian product not very useful directly, but useful
combined with where-clause condition (selection operation
in relational algebra).

Cartesian Product
instructor teaches

Examples
• Find the names of all instructors who have taught
some course and the course_id
– select name, course_id
from instructor , teaches
where instructor.ID = teaches.ID
• Find the names of all instructors in the Art
department who have taught some course and the
course_id
from instructor , teaches
where instructor.ID = teaches.ID and instructor.
dept_name = ‘Art’

The Rename Operation
• The SQL allows renaming relations and
attributes using the as clause:
old-name as new-name
• Find the names of all instructors who have a
higher salary than
some instructor in ‘Comp. Sci’.
– select distinct T.name
from instructor as T, instructor as S
where T.salary > S.salary and S.dept_name =
‘Comp. Sci.’

Self Join Example
n Relation emp-super
n Find the supervisor of “Bob”
n Find the supervisor of the supervisor of “Bob”
n Find ALL the supervisors (direct and indirect) of “Bob
person supervisor
Bob Alice
Mary Susan
Alice David
David Mary

String Operations
• SQL includes a string-matching operator for comparisons
on character strings. The operator like uses patterns that
are described using two special characters:
– percent ( % ). The % character matches any substring.
– underscore ( _ ). The _ character matches any character.
• Find the names of all instructors whose name includes the
substring “dar”.
select name
from instructor
where name like '%dar%'
• Match the string “100%”
like ‘100 %' escape ''
in that above we use backslash () as the escape character.

String Operations (Cont.)
• Patterns are case sensitive.
• Pattern matching examples:
– ‘Intro%’ matches any string beginning with “Intro”.
– ‘%Comp%’ matches any string containing “Comp” as a substring.
– ‘_ _ _’ matches any string of exactly three characters.
– ‘_ _ _ %’ matches any string of at least three characters.
• SQL supports a variety of string operations such as
– concatenation (using “||”)
– converting from upper to lower case (and vice versa)
– finding string length, extracting substrings, etc.

Ordering the Display of Tuples
• List in alphabetic order the names of all
instructors
select distinct name
from instructor
order by name
• We may specify desc for descending order
or asc for ascending order, for each
attribute; ascending order is the default.
– Example: order by name desc
• Can sort on multiple attributes
– Example: order by dept_name, name

Where Clause Predicates
• SQL includes a between comparison operator
• Example: Find the names of all instructors with
salary between $90,000 and $100,000 (that is, 
$90,000 and  $100,000)
– select name
from instructor
where salary between 90000 and 100000
• Tuple comparison
from instructor, teaches
where (instructor.ID, dept_name) = (teaches.ID,
’Biology’);

Duplicates
• In relations with duplicates, SQL can define how many
copies of tuples appear in the result.
• Multiset versions of some of the relational algebra
operators – given multiset relations r1 and r2:
1.  (r1): If there are c1 copies of tuple t1 in r1, and t1 satisfies
selections ,, then there are c1 copies of t1 in  (r1).
2. A (r ): For each copy of tuple t1 in r1, there is a copy of tuple
A (t1) in A (r1) where A (t1) denotes the projection of the single
tuple t1.
3. r1 x r2: If there are c1 copies of tuple t1 in r1 and c2 copies of
tuple t2 in r2, there are c1 x c2 copies of the tuple t1. t2 in r1 x r2

Duplicates (Cont.)
• Example: Suppose multiset relations r1 (A, B) and r2
(C) are as follows:
r1 = {(1, a) (2,a)} r2 = {(2), (3), (3)}
• Then B(r1) would be {(a), (a)}, while B(r1) x r2
would be
{(a,2), (a,2), (a,3), (a,3), (a,3), (a,3)}
• SQL duplicate semantics:
select A1,, A2, ..., An
where P
is equivalent to the multiset version of the
expression:
))
(
( 2
1
,
,
, 2
1 m
P
A
A
A r
r
r
n



 
 

Set Operations
• Find courses that ran in Fall 2009 or in
Spring 2010
n Find courses that ran in Fall 2009 but not in Spring 2010
(select course_id from section where sem = ‘Fall’ and year = 2009)
union
(select course_id from section where sem = ‘Spring’ and year = 2010)
n Find courses that ran in Fall 2009 and in Spring 2010
intersect
except

Set Operations (Cont.)
• Find the salaries of all instructors that are less than the largest
salary.
– select distinct T.salary
where T.salary < S.salary
• Find all the salaries of all instructors
– select distinct salary
from instructor
• Find the largest salary of all instructors.
– (select “second query” )
except
(select “first query”)

Set Operations (Cont.)
• Set operations union, intersect, and except
– Each of the above operations automatically
eliminates duplicates
nTo retain all duplicates use the
corresponding multiset versions union all,
intersect all and except all.
nSuppose a tuple occurs m times in r and n
times in s, then, it occurs:
– m + n times in r union all s
– min(m,n) times in r intersect all s

Null Values
• It is possible for tuples to have a null value, denoted
by null, for some of their attributes
• null signifies an unknown value or that a value does
not exist.
• The result of any arithmetic expression involving null
is null
– Example: 5 + null returns null
• The predicate is null can be used to check for null
values.
– Example: Find all instructors whose salary is null.
select name
from instructor
where salary is null

Null Values and Three Valued
Logic
• Three values – true, false, unknown
• Any comparison with null returns unknown
– Example: 5 < null or null <> null or null = null
• Three-valued logic using the value unknown:
– OR: (unknown or true) = true,
(unknown or false) = unknown
(unknown or unknown) = unknown
– AND: (true and unknown) = unknown,
(false and unknown) = false,
(unknown and unknown) = unknown
– NOT: (not unknown) = unknown
– “P is unknown” evaluates to true if predicate P evaluates to unknown
• Result of where clause predicate is treated as false if it evaluates to
unknown

Aggregate Functions
• These functions operate on the multiset
of values of a column of a relation, and
return a value
avg: average value
min: minimum value
max: maximum value
sum: sum of values
count: number of values

Aggregate Functions (Cont.)
• Find the average salary of instructors in the
Computer Science department
– select avg (salary)
from instructor
where dept_name= ’Comp. Sci.’;
• Find the total number of instructors who teach a
course in the Spring 2010 semester
– select count (distinct ID)
from teaches
where semester = ’Spring’ and year = 2010;
• Find the number of tuples in the course relation
– select count (*)
from course;

Aggregate Functions – Group By
• Find the average salary of instructors in each
department
– select dept_name, avg (salary) as avg_salary
from instructor
group by dept_name; avg_salary

Aggregation (Cont.)
• Attributes in select clause outside of aggregate
functions must appear in group by list
– /* erroneous query */
select dept_name, ID, avg (salary)
from instructor
group by dept_name;

Aggregate Functions – Having
Clause
• Find the names and average salaries of all departments
whose average salary is greater than 42000
Note: predicates in the having clause are applied after the
formation of groups whereas predicates in the where
clause are applied before forming groups
select dept_name, avg (salary)
from instructor
group by dept_name
having avg (salary) > 42000;

Null Values and Aggregates
• Total all salaries
select sum (salary )
from instructor
– Above statement ignores null amounts
– Result is null if there is no non-null amount
• All aggregate operations except count(*) ignore
tuples with null values on the aggregated attributes
• What if collection has only null values?
– count returns 0
– all other aggregates return null

Nested Subqueries
• SQL provides a mechanism for the nesting of subqueries. A subquery
is a select-from-where expression that is nested within another query.
• The nesting can be done in the following SQL query
select A1, A2, ..., An
where P
as follows:
– Ai can be replaced be a subquery that generates a single value.
– ri can be replaced by any valid subquery
– P can be replaced with an expression of the form:
B <operation> (subquery)
Where B is an attribute and <operation> to be defined later.

Subqueries in the Where Clause

Subqueries in the Where Clause
• A common use of subqueries is to
perform tests:
– For set membership
– For set comparisons
– For set cardinality.

Set Membership
• Find courses offered in Fall 2009 and in Spring 2010
n Find courses offered in Fall 2009 but not in Spring 2010
select distinct course_id
from section
where semester = ’Fall’ and year= 2009 and
course_id in (select course_id
from section
where semester = ’Spring’ and year= 2010);
select distinct course_id
from section
where semester = ’Fall’ and year= 2009 and
course_id not in (select course_id
from section
where semester = ’Spring’ and year= 2010);

Set Membership (Cont.)
• Find the total number of (distinct) students who have taken course
sections taught by the instructor with ID 10101
n Note: Above query can be written in a much simpler manner.
The formulation above is simply to illustrate SQL features.
select count (distinct ID)
from takes
where (course_id, sec_id, semester, year) in
(select course_id, sec_id, semester, year
from teaches
where teaches.ID= 10101);

Set Comparison – “some” Clause
• Find names of instructors with salary greater than that of
some (at least one) instructor in the Biology department.
n Same query using > some clause
select name
from instructor
where salary > some (select salary
from instructor
where dept name = ’Biology’);
select distinct T.name
where T.salary > S.salary and S.dept name = ’Biology’;

Definition of “some” Clause
• F <comp> some r   t  r such that (F <comp>
t )
Where <comp> can be:     
0
5
6
(5 < some ) = true
0
5
0
) = false
5
0
5
(5  some ) = true (since 0  5)
(read: 5 < some tuple in the relation)
(5 < some
) = true
(5 = some
(= some)  in
However, ( some)  not in

Set Comparison – “all” Clause
• Find the names of all instructors whose salary is greater than the
salary of all instructors in the Biology department.
select name
from instructor
where salary > all (select salary
from instructor
where dept name = ’Biology’);

Definition of “all” Clause
• F <comp> all r   t  r (F <comp> t)
0
5
6
(5 < all ) = false
6
10
4
) = true
5
4
6
(5  all ) = true (since 5  4 and 5  6)
(5 < all
) = false
(5 = all
( all)  not in
However, (= all)  in

Test for Empty Relations
• The exists construct returns the value
true if the argument subquery is
nonempty.
• exists r  r  Ø
• not exists r  r = Ø

Use of “exists” Clause
• Yet another way of specifying the query “Find all courses
taught in both the Fall 2009 semester and in the Spring 2010
semester”
select course_id
from section as S
where semester = ’Fall’ and year = 2009 and
exists (select *
from section as T
where semester = ’Spring’ and year= 2010
and S.course_id = T.course_id);
• Correlation name – variable S in the outer query
• Correlated subquery – the inner query

Use of “not exists” Clause
• Find all students who have taken all
courses offered in the Biology department.
select distinct S.ID, S.name
from student as S
where not exists ( (select course_id
from course
where dept_name = ’Biology’)
except
(select T.course_id
from takes as T
where S.ID = T.ID));
• First nested query lists all courses offered in Biology
• Second nested query lists all courses a particular student took
n Note that X – Y = Ø  X  Y
n Note: Cannot write this query using = all and its variants

Test for Absence of Duplicate
Tuples
• The unique construct tests whether a subquery has
any duplicate tuples in its result.
• The unique construct evaluates to “true” if a given
subquery contains no duplicates .
• Find all courses that were offered at most once in
2009
select T.course_id
from course as T
where unique (select R.course_id
from section as R
where T.course_id= R.course_id
and R.year = 2009);

Subqueries in the From Clause
• SQL allows a subquery expression to be used in the from clause
• Find the average instructors’ salaries of those departments where the
average salary is greater than $42,000.”
select dept_name, avg_salary
from (select dept_name, avg (salary) as avg_salary
from instructor
group by dept_name)
where avg_salary > 42000;
• Note that we do not need to use the having clause
• Another way to write above query
select dept_name, avg_salary
from (select dept_name, avg (salary)
from instructor
group by dept_name) as dept_avg (dept_name, avg_salary)
where avg_salary > 42000;

With Clause
• The with clause provides a way of defining a temporary
relation whose definition is available only to the query
in which the with clause occurs.
• Find all departments with the maximum budget
with max_budget (value) as
(select max(budget)
from department)
select department.name
from department, max_budget
where department.budget = max_budget.value;

Complex Queries using With
Clause
• Find all departments where the total salary is greater than the average
of the total salary at all departments
with dept _total (dept_name, value) as
(select dept_name, sum(salary)
from instructor
group by dept_name),
dept_total_avg(value) as
(select avg(value)
from dept_total)
select dept_name
from dept_total, dept_total_avg
where dept_total.value > dept_total_avg.value;

Scalar Subquery
• Scalar subquery is one which is used where a single value is expected
• List all departments along with the number of instructors in each
department
select dept_name,
(select count(*)
from instructor
where department.dept_name = instructor.dept_name)
as num_instructors
from department;
• Runtime error if subquery returns more than one result tuple

Modification of the Database
• Deletion of tuples from a given relation.
• Insertion of new tuples into a given relation
• Updating of values in some tuples in a
given relation

Deletion
• Delete all instructors
delete from instructor
• Delete all instructors from the Finance department
where dept_name= ’Finance’;
• Delete all tuples in the instructor relation for those instructors
associated with a department located in the Watson building.
where dept name in (select dept name
from department
where building = ’Watson’);

Deletion (Cont.)
• Delete all instructors whose salary is less than the
average salary of instructors
where salary < (select avg (salary)
from instructor);
 Problem: as we delete tuples from deposit, the average salary
changes
 Solution used in SQL:
1. First, compute avg (salary) and find all tuples to delete
2. Next, delete all tuples found above (without
recomputing avg or retesting the tuples)

Insertion
• Add a new tuple to course
insert into course
values (’CS-437’, ’Database
Systems’, ’Comp. Sci.’, 4);
• or equivalently
insert into course (course_id, title,
dept_name, credits)
values (’CS-437’, ’Database
Systems’, ’Comp. Sci.’, 4);

Insertion (Cont.)
• Add all instructors to the student relation with tot_creds set
to 0
insert into student
select ID, name, dept_name, 0
from instructor
• The select from where statement is evaluated fully before
any of its results are inserted into the relation.
Otherwise queries like
insert into table1 select * from table1
would cause problem

Updates
• Increase salaries of instructors whose salary
is over $100,000 by 3%, and all others by a
5%
– Write two update statements:
update instructor
set salary = salary * 1.03
where salary > 100000;
update instructor
set salary = salary * 1.05
where salary <= 100000;
– The order is important
– Can be done better using the case statement
(next slide)

Case Statement for Conditional
Updates
• Same query as before but with case statement
update instructor
set salary = case
when salary <=
100000 then salary * 1.05
else salary * 1.03
end

Updates with Scalar Subqueries
• Recompute and update tot_creds value for all students
update student S
set tot_cred = (select sum(credits)
from takes, course
where takes.course_id = course.course_id and
S.ID= takes.ID.and
takes.grade <> ’F’ and
takes.grade is not null);
• Sets tot_creds to null for students who have not taken any course
• Instead of sum(credits), use:
case
when sum(credits) is not null then sum(credits)
else 0
end

Engineering
A view is nothing more than a SQL statement that is stored in the
database with an associated name. A view is actually a composition of a
table in the form of a predefined SQL query.
A view can contain all rows of a table or select rows from a table. A view
can be created from one or many tables which depends on the written
SQL query to create a view.
Views, which are a type of virtual tables allow users to do the following −
Structure data in a way that users or classes of users find natural or
intuitive.
Restrict access to the data in such a way that a user can see and
(sometimes) modify exactly what they need and no more.
Summarize data from various tables which can be used to generate
reports.
Views

Engineering
Database views are created using the CREATE VIEW statement.
Views can be created from a single table, multiple tables or another
view.
To create a view, a user must have the appropriate system privilege
according to the specific implementation.
The basic CREATE VIEW syntax is as follows −
CREATE VIEW view_name AS SELECT column1,
column2..... FROM table_name WHERE [condition];
Consider the CUSTOMERS table having the following records −
ID | NAME | AGE | ADDRESS | SALARY | +----+----------+-----+-----------+----------+ |
1 | Ramesh | 32 | Ahmedabad | 2000.00 |
2 | Khilan | 25 | Delhi | 1500.00 | |
3 | kaushik | 23 | Kota | 2000.00 | |
Following is an example to create a view from the CUSTOMERS table. This view would be used to have customer
name and age from the CUSTOMERS table.
SQL > CREATE VIEW CUSTOMERS_VIEW AS SELECT name, age FROM CUSTOMERS;
Now, you can query CUSTOMERS_VIEW in a similar way as you query an actual table. Following is an example for
the same.
SQL > SELECT * FROM CUSTOMERS_VIEW;

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