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Relations

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Tuples Given a collection of types T i (i=1,2,….n), a tuple value on those types is a set of ordered triples of the form where Ai is attribute name Ti is type name vi is a value of type Ti and

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Tuples –The value n is the degree or arity of t – ordered triple is a component of t –The ordered pair is an attribute of t and identified by attribute name Ai –The complete set of attributes is the heading of t –The tuple type of t is determined by the heading of t; heading and tuple type both have the same attributes and the same degree as t does

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Tuples Tuple type name is TUPLE { A1 T1, A2 T2,…. An Tn} Example Degree : Heading Type MAJOR_PART_NUMBER : PART NUMBER MINOR_PART_NUMBER:P ART NUMBER QUANTITY : QUANTITY P2P47

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Tuples Properties of tuples –Each tuple contains exactly one value for each of its attributes –There is no left-to-right ordering to the components of a tuple. –Every subset of a tuple is a tuple –A tuple of degree n is said to be n-ary –Tuple of degree 0 is called nullary

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Tuples The TUPLE type generator: –General Form TUPLE { } Where each consists of an followed by a

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Tuples Example VAR ADDR TUPLE { STREET CHAR, CITY CHAR, STATE CHAR, ZIP CHAR } Tuple Selector operator TUPLE { STREET `14 Park View`, CITY `TVM`, STATE Kerala`, ZIP ` }

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Tuples Operators: –All operators of relational algebra –Candidate keys –Foreign keys –Functional and other dependencies –Tuple equality –Tuple type inference –WRAP and UNWRAP

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Tuples Tuple equality –Tuples t1 and t2 are equal if and only if they have the same set of attributes A1, A2, …An and for all i (i=1,2,..n) the value of v1 of Ai is equal to the value of v2 of Ai in t2 –t1 and t2 are duplicates of each other if and only if they are equal

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Tuples Tuple projection –ADDR { CITY, ZIP } WRAP and UNWRAP –Let TT1 = TUPLE {NAME NAME, ADDR TUPLE { STREET CHAR, CITY CHAR, STATE CHAR, ZIP CHAR} } TT2 = TUPLE {NAME NAME, ADDR TUPLE { STREET CHAR, CITY CHAR, STATE CHAR, ZIP CHAR} }

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Tuples Let –TT1 = TUPLE {NAME NAME, ADDR TUPLE { STREET CHAR, CITY CHAR, STATE CHAR, ZIP CHAR} } –TT1 = TUPLE {NAME NAME, STREET CHAR, CITY CHAR, STATE CHAR, ZIP CHAR} Let NADDR1 and NADDR2 be tuple variables of types TT1 and TT2

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Tuples NADDR1 := NADDR2 WRAP { STREET, CITY, STATE, ZIP } AS ADDR; NADDR1 UNWRAP ADDR NADDR2 := NADDR1 UNWRAP ADDR;

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Relation types Definition A relation value r consists of a heading and a body where : The heading of r is a tuple heading. relation r has the same attributes and the same degree as that heading has the body of r is a set of tuples, all having the same heading; cardinality of that set is said to be the cardinality of r.

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Relation types Relation type of r is determined by the heading of r Relation type name is RELATION { A1 T1, A2 T2,…An Tn } General form of relation selector is RELATION [ ] {tuple exp comalist>} is comalist of s enclosed in braces

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Relation values Relations are normalized There is no left-to-right ordering to atttributes There is no top-to-bottom ordering to the tuples There are no duplicate tuples

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Relation values RELATIONSTABLES Each heading involves a type name Type names are omitted Each component of a tuple has a type name and an attribute name Type names and attribute names are omitted Value is of applicable type Values are in abbreviated form

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No left-to-right ordering of attributes Have a left-to-right ordering No ordering of tuplesRows have a top-to- bottom ordering Does not contain duplicate tuples May contain duplicate rows RELATIONSTABLES

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Relation values Relations with no attributes –A relation can have an empty set of attributes or in other words no attribute at all –Such a relation can have atmost one tuple 0-tuple –Thus there are two relations of degree 0 One which contains one tuple (TABLE_DEE) That contains no tuples at all (TABLE_DUM) DEE means TRUE and DUM means false

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Relation values Relation selector RELATION { } { TUPLE { } } RELATION { } { }

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Relation values Operators on relations –Relational comparison Relation comp op = equals not equals subset of proper subset of superset of proper superset of

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Relation values To find if a relation is equal to an empty relation –IS_EMPTY ( ) To find whether a given tuple is found in a relation r or not –t r

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Relation variables Base Relvar Definition VAR BASE [ ]; takes the form RELATION { }

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Relation variables Example VAR SUPPLIERS BASE RELATION { SUP_NUMBER SUPPLIER_NUMBER, SUP_NAME NAME, STATUS INTEGER, CITYCHAR } PRIMARY KEY { SUP_NUMBER} ;

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Relation variables Explanation 1)The base relation has the type RELATION { SUP_NUMBER SUPPLIER_NUMBER, SUP_NAME NAME, STATUS INTEGER, CITY CHAR} 2)The terms heading, body, attribute, tuple, degree applies to relvars also 3)All possible values of any given relvar are of the same relation type and hence have the same heading

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Relational Algebra

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Introduction Original eight operators: –Union –Intersection –Difference –Cartesian product –Select –Project –Join –divide

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Closure Relational closure property –The output from any relational operation is another relation To achieve closure property, all relations should have proper attribute names in order to use those attributes in the subsequent operations

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Closure RENAME operator –To rename attributes within a specified relation –Eg: SUPPLIERS RENAME CITY AS SCITY Gives the same heading and body as the relation that is the current value of SUPPLIERS except that the city attribute is named SCITY instead of city Multiple renaming PARTS RENAME (PART_NAME AS PN, WEIGHT AS WT

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Relational Operators Union –Special type of mathematical union in which both the relations should be of the same type –This is referred to as union compatibility –Given two relations a and b of the same type, the union of those two relations a union b, is a relation of the same type, with the body consisting of all tuples t such that t appears in a or b or both

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Relational Operators Intersect –Given two relations a and b of the same type, the intersection of those two relations a INTERSECT b, is a relation of the same type, with the body consisting of all tuples t such that t appears in both a and b

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Relational Operators Difference –Given two relations a and b of the same type, the difference of those two relations a MINUS b, is a relation of the same type, with the body consisting of all tuples t such that t appears in a and not b –A MINUS B is not the same as B MINUS A

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Relational Operators Supplier_numberSupplier_nameStatusCity S1Sarala20Mumbai S4Priya20Mumbai Supplier_numberSupplier_nameStatusCity S1Sarala20Mumbai S2Uma10Chennai A B

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Relational Operators Product –The cartesian product of two relations a and b, a TIMES b, where a and b have no common attribute names, to be a relation with a heading that is the union of the headings of a and b and with a body consisting of the set of all tuples t such that t is the union of a tuple appearing in a and a tuple appearing in b

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Relational Operators Given the tuples {A1 a1, A2 a2,….Am am} And {B1 b1, B2 b2, …Bn bn} The union of the two is the single tuple {A1 a1, A2 a2,….Am am,B1 b1, B2 b2, …Bn bn }

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Relational Operators Select Used to select a subset of tuples in a relation that satisfy a selection condition Denoted by σ ( ) σ – SELECT operator Selection Condition – boolean expression specified on relation attributes using the comparison operators { =,, >=, }

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Relational Operators(Select) is applied to each tuple t in relation R specified by If condition is satisfied,tuple t is SELECTED Boolean operators AND, OR, NOT can be used to connect the conditions

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Relational Operators(Select) Is applied on a single relation Degree of relation resulting from SELECT is the same as the original relation Fraction of tuples selected is called as selectivity of the condition Is commutative

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Relational Operators(Project) Selects certain columns from the relation General Form π ( ) π – project operator Degree is equal to the number of attributes in

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Relational Operators(Project) Π x, y,….z(A) is a relation with –A heading derived from the heading of a by removing all attributes not mentioned in the set {X, Y, …., Z } –A body consisting of all tuples{X x,Y y,…, Z z} such that a tuple appears in a with X value x, Y value y, … and Z value z.

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Relational Operators(Project) PROJECT implicitly removes any duplicate tuples Whenever there are two identical tuples, only one is kept in the result.This is called duplicate elimination Commutativity does not hold on PROJECT

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Relational Operators(Join) Denoted by Combine related tuples from two relations General form R S The resultant relation Q has one tuple for each combination of tuples whenever the combination satisfies the join condition

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Relational Operators(Join) common join – joins with equality condition. A join where only the = comparison is used is called Equi Join Equi join always have one or more pairs of attributes that have identical values. To get rid of the second attribute, natural join is used

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Relational Operator(Divide) Let relations a and b have attributes X1, X2, …..Xm and Y1,Y2,….Yn Division of a by b a divideby b is a relation with heading {X} and body consisting of all tuples {X x} appearing in a such that a tuple {X x, Y y} appears in c for all tuples {Y y} appearing in b.

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Integrity

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Integrity An integrity constraint is a boolean expression that is associated with some database and is required to evaluate at all times to TRUE. Constraints should be formally declared to the DBMS and DBMS enforces these constraints

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Internal Vs External Predicates Internal predicates: what the data means to the system External predicates: What the data means to the user A given internal predicate is the systems approximation to the corresponding external predicate

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Internal Vs External Predicates External predicate for a given relvar is basically what the relvar means to the user –The EMPLOYEE with the specified employee number(EMPNO) has the specified name(ENAME), is working for the department with the specified number (DNO), and gets a salary specified(SALARY) S is a tuple of the form (EMPNO, ENAME, DNO, SALARY)

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A given tuple appears in a given relvar at a given time if and only if that tuple makes that relvars external predicate evaluate to TRUE at that time.

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Keys Candidate Key Primary Key and Alternate Key Foreign Key

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Candidate Key The set of all attributes of R having the uniqueness property Let K be a set of attributes of relvar R. Then K is a candidate key for R if and only if it has both of the following properties –Uniqueness: No legal value of R ever contains two distinct tuples with the same value for K –Irreducibility: No proper subset of K has the uniqueness property

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Primary Keys and alternate keys One of the candidate key is chosen as the Primary Key Others are Alternate Keys If there is only one candidate key, then that is chosen as the primary key.

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Foreign Key A set of attributes FK in relation Schema R1 is a foreign key of R1 that references R2 if it satisfies the following rules –The attributes in FK have the same domain as the primary key attributes PK of R2; the attributes of FK are said to refer to the relation R2 –A value of FK in a tuple t1 of the current state r1(R1) either occurs as a value of PK for some tuple t2 in the current state r2(R2) or is null. In the former case t1[FK]= t2[FK]

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Foreign key Let R1 be a relvar. Then a foreign key in R2 is a set of attributes ofR2, say FK such that –There exists a relvar R1 with a candidate key CK –It is possible to rename some subset of the attributes of FK, such that FK becomes FK and FK and CK are of the same type. –For all time, each value of FK in the current value of R2 yields a value for FK that is identical to the value of CK in some tuple in the current value of R1

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Foreign key Every value of FK must appear as a value of CK, but the converse is not a requirement; i.e., R1 might contain a CK value that does not currently appear as an FK value in R2 FK can be simple or composite The constraint that values of FK must match values of CK is known as the referential constraint.

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Foreign Key The problem of ensuring that the database does not include any invalid foreign key values is the referential integrity problem Referential integrity rule: The database must not contain any unmatched foreign key values

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Data Definition (DDL) CREATE – specify a new relation ALTER – change the definition of a table DROP – delete a table

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CREATE TABLE Specifies a new relation by giving it a name and specifying the attributes and initial constraints Attributes have : name data type constraints such as NOT NULL

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CREATE TABLE CREATE TABLE table_name( field1 data type [NOT NULL], field2 datatype [NOT NULL] PRIMARY KEY ( ) UNIQUE ( ) FOREIGN KEY ( ) REFERENCES [ column name commalist] [ON DELETE ] [ON UPDATE ] CHECK ( IS NOT NULL) )

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Attribute data types Numeric –Integer number s of various sizes INTEGER or INT, SMALLINT –Floating point numbers FLOAT, REAL and DOUBLE PRECISION

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Attribute data types Character- string –Fixed lengthCHAR(n) or CHARACTER(n) –Varying length VARCHAR(n) String is placed within single quotes

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Attribute data types Bit-String –Fixed length – BIT(n) or variable length BITVARYING(n) n – max. number of bits Boolean –TRUE or FALSE

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Attribute data types DATE –Ten positions – YEAR, MONTH and DAY –Format : YYYY-MM-DD TIME –Atleast 8 positions HOUR, MINUTE, SECOND –Format HH:MM:SS

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Attribute data types TimeStamp –Includes both date and time fields –Plus minimum of 6 positions for decimal fraction of seconds –Eg: TIMESTAMP :12:

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Attribute constraints NOT NULL DEFAULT CHECK Primary key, foreign key constraint

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DELETE command Removes tuples from a relation Tuples are deleted from only one table at a time Missing WHERE clause deletes all tuples

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DELETE command DELETE FROM EMPLOYEE where name = Brown Delete from employee where DNO in (select dnumber from department where dname = Research) DELETE FROM Employee

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UPDATE command Used to modify values of one or more selected values UPDATE "table_name" SET "column_1" = [new value] WHERE {condition} SET – specifies attributes to be modified and their new values

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UPDATE command+ UPDATE PROJECT SET PLOC = DELHI, DNUM = 5 WHERE PNUM = 10

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Referential Actions CASCADE: operations will cascade to delete all matching tuples RESTRICT : operations are restricted to the case where there are no matching keys. NO ACTION : Delete is performed exactly as requested

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ALTER TABLE To change the definition of the database table Possible actions –Adding or dropping a column –Changing a column definition –Adding or dropping table constraints

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ALTER Table To add an attribute JOB in EMPLOYEE, ALTER TABLE EMPLOYEE ADD JOB VARCHAR(15); NOT NULL constraint is not allowed

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ALTER TABLE To drop we must choose either CASCADE or RESTRICT ALTER TABLE EMPLOYEE DROP ADDRESS CASCADE

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ALTER TABLE Dropping an existing default clause or defining new clause ALTER TABLE DEPARTMENT ALTER MGRSSN DROP DEFAULT; ALTER TABLE DEPARTMENT ALTER MGRSSN SET DEFAULT ;

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ALTER TABLE Adding or dropping a constraint ALTER TABLE EMPLOYEE DROP CONSTRAINT EMPSUPERPK CASCADE

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Update statements Modifying the data base –INSERT –DELETE –UPDATE

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INSERT command Used to add a single tuple to a relation Values should be listed in the same order in which they are placed in the CREATE TABLE command INSERT INTO tablename VALUES (list of attribute values)

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Triggers Triggered procedures are precompiled procedures that are stored along with the database and invoked automatically whenever some specified event occurs To design a trigger mechanism, we must: –Specify the conditions under which the trigger is to be executed. –Specify the actions to be taken when the trigger executes.

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Triggers create table general_comments ( …. modified_date date not null, …..); create trigger general_comments_modified before insert or update on general_comments for each row begin :new.modified_date := sysdate; end;

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