relational algebra and relational calculus mca

8/7/2019 Relational Algebra and Relational Calculus MCA

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` Language in which user requests information fromthe database.

` Categories of languages

procedural

non-procedural` Pure languages:

Relational Algebra

Tuple Relational Calculus

Domain Relational Calculus` Pure languages form underlying basis of query

languages that people use.


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` Procedural language

` User has to specify what is required and what are

the steps to obtain the required output.

` The operators take one or more relations as inputs

and give a new relation as a result.

` Two types of relational operators-

Traditional Set operators

Special operators


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` Traditional set operators are:- Union

Intersection

Difference

Cartesian Product

` Union:-A union of two relations is a relation that contain all

data elements belonging to both relations while writing the

duplicate values only once.

In order to perform the union operation , both operand relations

must be union compatible i.e. they must have same no. of columns

drawn from same domain (i.e. must be of same data type).

It is represented by symbol U.


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Cust_name Cust_status

Sham Good

Rahul Excellent

Karan Bad


Sham Good

Rahul Excellent


Karan Bad

Sham Good

R S

R U S


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` Intersection of two relations consists of a third

relation with all rows that are common to both

relations.

` It is represented by symbol .

` Taking above example, R S is


Sham Good

R S


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` Difference of two relations consist of a thirdrelation which consists of elements which arepresent in one relation and not in another.

` It is represented using symbol -.

`

Minus is not associative.


Rahul Excellent


Karan Bad R-S S-R


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` Cartesian product of two relations include each row of

one relation is associated with each row of another

relation.

` It is denoted by cross (X).

A B

1

2

C D

10

20 11

24

A B C D

1 10

1 20

1 11

1 24

2 10

2 20

2 11

2 24

R

S

R X S


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` Four special relational operators are:-

Selection

Projection

Join

Division

` Selection:-Yields a horizontal subset of a given relation.

` Those tuples or rows of a table are selected which satisfy a

particular condition (predicate).` It is represented by Greek letter sigma .

` Notation: Wp (r)

` p is called the selection predicate.


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` E.g. Suppose from supplier table, we have to select

values where city is Mohali.

The query is like

` city= Mohali (Supplier)

Sno Sname Status City

S1 Suneet 20 Mohali

S2 Ankit 10 Amritsar

S3 Amit 30 Amritsar

S4 Raj 20 Chandigarh


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` Projection operation on a table simply forms another table by

copying specified columns from original table while eliminatingany duplicated rows.

` Projection is denoted by

` Consider the following employee table.

` Projections ofAge:- Age (employee)

Empno Ename Age Sal

E01 Smith 25 7500

E02 John 36 10000

E03 Allen 42 10000 Age

25

36

42


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` Notation:

A1, A2, , Ak (r)

whereA1,A2 are attribute names and r is a relation

name.

` The result is defined as the relation ofkcolumns

obtained by erasing the columns that are not listed

` Duplicate rows removed from result, since relations

are sets


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` An extension of the join operation that avoids loss of

information.` Computes the join and then adds tuples form one

relation that do not match tuples in the other relationto the result of the join.

` Uses nullvalues:

nullsignifies that the value is unknown or does notexist

All comparisons involving nullare (roughlyspeaking) false by definition.


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` Relation loan

Relation borrower

customer-name loan-number

Jones

Smith

Hayes

L-170

L-230

L-155

3000

4000

1700

loan-number amount

L-170

L-230

L-260

branch-name

Downtown

Redwood

Perryridge


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` Inner Joinloan Borrower

loan-number amount

L-170

L-230

3000

4000

customer-name

Jones

Smith

branch-name

Downtown

Redwood

JonesSmith

null

loan-number amount

L-170L-230

L-260

30004000

1700

customer-namebranch-name

DowntownRedwood

Perryridge

Left Outer Joinloan Borrower


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` Right Outer Joinloan borrower

loan borrower

Full Outer Join

loan-number amount

L-170

L-230

L-155

3000

4000

null

customer-name

Jones

Smith

Hayes

branch-name

Downtown

Redwood

null

loan-number amount

L-170L-230

L-260

L-155

30004000

1700

null

customer-name

JonesSmith

null

Hayes

branch-name

DowntownRedwood

Perryridge

null


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` Is used to divide a relation A of degree m+n (no. of

columns in a relation) by relation B of degree n, produces

a relation of degree m.

` It is denoted by z .


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sno pno

s1 p1

s1 p2

s1 p3s1 p4

s2 p1

s2 p2

s3 p2s4 p2

s4 p4

pno

p2

pno

p2

p4

pno

p1

p2

p4

sno

s1

s2s3

s4

snos1

s4

sno

s1

A

B1

B2

B3

A z B1 A z B2 A z B3


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` The result to the right of the n is assigned tothe relation variable on the left of the n.

` A n B

` Value of B is assigned to A.


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`

Aggregation function takes a collection of values and returnsa single value as a result.

avg: average valuemin: minimum valuemax: maximum value

sum: sum of valuescount: number of values

` Aggregate operation in relational algebra

G1, G2, , Gn g F1( A1), F2( A2),, Fn( An) (E)

E is any relational-algebra expression

G1, G2 , Gn is a list of attributes on which to group (can beempty)

Each Fi is an aggregate function

Each Ai is an attribute name


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` Relation r: A B

C

g sum(c) (r)sum-C

27


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` Relation account grouped by branch-name:

branch-name

gsum(balance)

(account)

branch-name account-number balance

Perryridge

PerryridgeBrighton

Brighton

Redwood

A-102

A-201A-217

A-215

A-222

400

900750

750

700

branch-name balance

Perryridge

Brighton

Redwood

1300

1500

700


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` Result of aggregation does not have a name Can use rename operation to give it a name

For convenience, we permit renaming as part ofaggregate operation

branch-name g sum(balance) as sum-balance (account)


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Tuple oriented relational calculus

Domain Oriented relational calculus


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` Non procedural language

`

User is not concerned with the procedure to obtain the results, he/she just tell theresults and output is available without knowing the method of retrieval.

` A query is expressed as a formula consisting of a no. of variables and an

expression involving these variables.

` It is up to DBMS to transform these non procedural queries into procedural

queries.

` This concept was first proposed by Codd.

` It is based on predicate calculus.

` Propositions specifying a property consist of an expression that names an

individual object and another expression called the predicate stand for the property

that object possesses.

` E.g. MCA is a class ObjectMCA, India

India is a country. Predicate- Class, Country


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` A convenient method of writing the statements is to place the

predicate first and follow it with the object enclosed in parenthesis.

` E.g. MCA is a class can be written asis a class (MCA) or

Class (MCA)

` Finally, if we use symbols for both the predicate and the object, we

can rewrite the statement as P(X) where P is the predicate and X is theobject.

` These are known as one place predicate.

` Two place predicate-require two objects.

` E.g. Naresh is taller than RajeshABC is intelligent than XYZ

These can be written as

TALLER_THAN (Naresh, Rajesh)

INTELLIGENT_THAN (ABC,XYZ)


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` A predicate followed by its arguments is called an Atomic Formula.

` E.g. CLASS(MCA)

TALLER_THAN (Naresh ,Rajesh)

` Atomic formulas can also be combined using logical connectors

such as

NOT or Negation

OR V

AND ^

IMPLICATION

` E.g. oracle is a DBMS and ABC is a company

Can be written in atomic formula as

DBMS (oracle) COMPANY(ABC)


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` Based on specifying a number of tuple variables.

` A nonprocedural query language, where each query is of the form{t|P(t) }

` It is the set of all tuples tsuch that predicate Pis true fort

` tis a tuple variable, t[A] denotes the value of tuple ton attribute A

` t rdenotes that tuple tis in relation r

` Pis a formulasimilar to that of the predicate calculus.` E.g. {t | Book (t) and t. Price>100}

Will get you all books whose price is greater than 100.It retrievesattributes for each selected value.

` To retrieve only some of the attributes say TITLE,AUTHOR,PRICE,

Query is like

{ t.TITLE, t. AUTHOR, t. PRICE|BOOK (t) and t. PRICE>200}


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` Thus in a tuple calculus, we need

A condition to select the required tuples from the relation. A set of attributes to be retrieved.

` WFF (Well Formed Formula)

Every condition is a WFF.A WFF is constructed fromconditions, Boolean operations (AND,OR,NOT) and

quantifiers like for all ()

and there exists().y tr (Q(t))|there exists a tuple in t in relation r

such that predicate Q(t) is true

y tr (Q(t)) |Qis true for all tuples tin relation r


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`

In Domain Calculus the variables range over singlevalues from domains of attributes rather than rangingover tuples.

` An expression of domain calculus is

{ x1,x2, ,xn " |P(x1, x2, ,xn)}

x1, x2, ,xn represent domain variables Prepresents a formula similar to that of the predicate calculus

` E.g. Get emp no in relation emp

EX where emp (empno: EX)

` Get emp no for job ClerkEX where emp (empno: Ex, job=Clerk)


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RELATIONALALGEBRA RELATIONAL CALCULUS

1. It is a procedural method of

solving the queries.

2. The solution is obtained by

stating what is required and what

are the steps to obtain that

information.

3. It is used as a vehicle for

implementation of Relational

Calculus.

4.Two types operators -

Traditionalset operators, Special operators.

1. It is a non procedural method of

solving the queries.

2. The solution is obtained by stating

what is required and letting the

system find the answer.

3. Relational Calculus queries are

converted into equivalent

relational algebra format using

codds Reduction algorithm and

than it is implemented using

relational operators.

4. Two types calculus- Tuple oriented

, Domain oriented.

relational algebra and relational calculus mca

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