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Chapter 3:  Relational Model ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example of a Relation
Basic Structure ,[object Object],[object Object],[object Object]
Attribute Types ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Relation Schema ,[object Object],[object Object],[object Object],[object Object],[object Object]
Relation Instance ,[object Object],[object Object],Jones Smith Curry Lindsay customer-name Main North North Park customer-street Harrison Rye Rye Pittsfield customer-city customer attributes (or columns) tuples (or rows)
Relations are Unordered ,[object Object],[object Object]
Database ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The  customer  Relation
The  depositor  Relation
E-R Diagram for the Banking Enterprise
Keys ,[object Object],[object Object],[object Object],[object Object],[object Object]
Determining Keys from E-R Sets ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Schema Diagram for the Banking Enterprise
Query Languages ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Relational Algebra ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Select Operation – Example ,[object Object],A B C D         1 5 12 23 7 7 3 10 ,[object Object],A B C D     1 23 7 10
Select Operation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Project Operation – Example ,[object Object],A B C     10 20 30 40 1 1 1 2 A C     1 1 1 2 = A C    1 1 2 ,[object Object]
Project Operation ,[object Object],[object Object],[object Object],[object Object],[object Object]
Union Operation – Example ,[object Object],r    s: A B    1 2 1 A B   2 3 r s A B     1 2 1 3
Union Operation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Set Difference Operation – Example ,[object Object],r – s : A B    1 2 1 A B   2 3 r s A B   1 1
Set Difference Operation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Cartesian-Product Operation-Example Relations  r, s : r  x  s : A B   1 2 A B         1 1 1 1 2 2 2 2 C D           10 10 20 10 10 10 20 10 E a a b b a a b b C D     10 10 20 10 E a a b b r s
Cartesian-Product Operation ,[object Object],[object Object],[object Object],[object Object],[object Object]
Composition of Operations ,[object Object],[object Object],[object Object],[object Object],A B         1 1 1 1 2 2 2 2 C D             10 10 20 10 10 10 20 10 E a a b b a a b b A B C D E    1 2 2    10 20 20 a a b
Rename Operation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Banking Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example Queries ,[object Object],[object Object],[object Object], amount   > 1200  ( loan )  loan-number  (  amount   > 1200  ( loan ))
Example Queries ,[object Object],[object Object],[object Object],[object Object],[object Object]
Example Queries ,[object Object],[object Object], customer-name  (  branch-name = “Perryridge” (  borrower.loan-number = loan.loan-number ( borrower x loan )))  –     customer-name ( depositor )  customer-name  (  branch-name=“Perryridge ” (  borrower.loan-number = loan.loan-number ( borrower x loan )))
Example Queries ,[object Object],[object Object],[object Object],[object Object]
Example Queries ,[object Object],[object Object],[object Object], balance (account)  -   account.balance (  account.balance < d.balance   ( account x   d  (account )))
Formal Definition ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Additional Operations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Set-Intersection Operation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Set-Intersection Operation - Example ,[object Object],[object Object],A  B    1 2 1 A  B   2 3 r s A  B    2
Natural-Join Operation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Natural Join Operation – Example ,[object Object],A B      1 2 4 1 2 C D      a a b a b B 1 3 1 2 3 D a a a b b E      r A B      1 1 1 1 2 C D      a a a a b E      s r  s
Division Operation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],r     s
Division Operation – Example Relations  r, s : r      s : A B   1 2 A B            1 2 3 1 1 1 3 4 6 1 2 r s
Another Division Example A B         a a a a a a a a C D         a a b a b a b b E 1 1 1 1 3 1 1 1 Relations  r, s : r      s : D a b E 1 1 A B   a a C   r s
Division Operation (Cont.) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Assignment Operation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example Queries ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],Example Queries  customer-name, branch-name   ( depositor   account )     branch-name  (  branch-city  = “Brooklyn”  ( branch ))
Extended Relational-Algebra-Operations ,[object Object],[object Object],[object Object]
Generalized Projection ,[object Object],[object Object],[object Object],[object Object],[object Object]
Aggregate Functions and Operations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Aggregate Operation – Example ,[object Object],A B         C 7 7 3 10 g   sum(c)   (r) sum-C 27
Aggregate Operation – Example ,[object Object],branch-name   g  sum(balance)  ( account ) branch-name account-number balance Perryridge Perryridge Brighton Brighton Redwood A-102 A-201 A-217 A-215 A-222 400 900 750 750 700 branch-name balance Perryridge Brighton Redwood 1300 1500 700
Aggregate Functions (Cont.) ,[object Object],[object Object],[object Object],branch-name   g  sum (balance)  as  sum-balance  ( account )
Outer Join ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Outer Join – Example ,[object Object],[object Object],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
Outer Join – Example ,[object Object],loan-number amount L-170 L-230 3000 4000 customer-name Jones Smith branch-name Downtown Redwood Jones Smith null loan-number amount L-170 L-230 L-260 3000 4000 1700 customer-name branch-name Downtown Redwood Perryridge ,[object Object],[object Object]
Outer Join – Example ,[object Object],[object Object],loan  borrower ,[object Object],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-170 L-230 L-260 L-155 3000 4000 1700 null customer-name Jones Smith null Hayes branch-name Downtown Redwood Perryridge null
Null Values ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Null Values ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Modification of the Database ,[object Object],[object Object],[object Object],[object Object],[object Object]
Deletion ,[object Object],[object Object],[object Object],[object Object],[object Object]
Deletion Examples ,[object Object],[object Object],[object Object],loan     loan  –    amount   0  and amount    50  ( loan ) account     account  –   branch-name = “Perryridge”  (account) r 1        branch-city = “Needham”   (account  branch) r 2      branch-name, account-number, balance  ( r 1 ) r 3        customer-name, account-number   ( r 2   depositor) account    account –  r 2 depositor    depositor –  r 3
Insertion ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Insertion Examples ,[object Object],[object Object],account     account     {(“Perryridge”, A-973, 1200)} depositor     depositor     {(“Smith”, A-973)} r 1     (  branch-name = “Perryridge”  (borrower  loan )) account     account       branch-name, account-number,200   (r 1 ) depositor     depositor      customer-name, loan-number (r 1 )
Updating ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Update Examples ,[object Object],[object Object],account         AN, BN, BAL  * 1.06   (    BAL    10000   (account ))       AN, BN, BAL *  1.05   (  BAL    10000   (account)) account        AN, BN, BAL  * 1.05   ( account ) where  AN ,  BN   and  BAL   stand for  account-number ,  branch-name  and  balance , respectively.
Views ,[object Object],[object Object],[object Object],[object Object]
View Definition ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
View Examples ,[object Object],[object Object], branch-name   (  branch-name   =  “Perryridge”   ( all-customer )) create view  all-customer  as  branch-name, customer-name   (depositor  account)     branch-name, customer-name   ( borrower   loan )
Updates Through View ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Updates Through Views (Cont.) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Views Defined Using Other Views ,[object Object],[object Object],[object Object],[object Object]
View Expansion ,[object Object],[object Object],[object Object],[object Object],[object Object]
Tuple Relational Calculus ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Predicate Calculus Formula ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Banking Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example Queries ,[object Object],[object Object],Notice that a relation on schema [ loan-number ] is implicitly defined by the query { t |    s   loan ( t [ loan-number ] =  s [ loan-number ]     s  [ amount ]    1200)} { t  |  t      loan      t  [ amount ]    1200}
Example Queries ,[object Object],{ t |   s     borrower( t [ customer-name ] =  s [ customer-name ])       u     depositor (  t [ customer-name ] =  u [ customer-name ]) ,[object Object],{ t |   s     borrower( t [ customer-name ] =  s [ customer-name ])       u     depositor (  t [ customer-name ] =  u [ customer-name ])
Example Queries ,[object Object],{ t |   s     borrower( t [ customer-name ] =  s [customer-name]       u     loan ( u [ branch-name ] = “Perryridge”      u [ loan-number ] =  s [loan- number ]))      not    v     depositor  ( v [ customer-name ] =    t [customer-name]) } ,[object Object],{ t |   s     borrower(t [ customer-name ] =  s [ customer-name ]        u     loan ( u [ branch-name ] = “Perryridge”      u [ loan-number ] =  s [ loan-number ]))}
Example Queries ,[object Object],{ t |   s     loan(s [ branch-name ] = “Perryridge”       u     borrower (u [ loan-number ] =  s [ loan-number ]      t  [ customer-name ] =  u [ customer-name ])        v     customer (u [ customer-name ] =  v [ customer-name ]      t [ customer-city ] =  v [ customer-city ])))}
Example Queries ,[object Object],{ t |    c    customer ( t [customer.name] = c[customer-name])        s     branch(s [ branch-city ] = “Brooklyn”          u     account ( s [ branch-name ] =  u [branch-name]        s     depositor (  t [ customer-name ] =  s [customer-name]      s [ account-number ] =  u [account-number] )) )}
Safety of Expressions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Domain Relational Calculus ,[object Object],[object Object],[object Object],[object Object],[object Object]
Example Queries ,[object Object],{    c, a     |     l  (    c, l         borrower      b (    l, b, a        loan      b  = “Perryridge”))} or {    c, a     |     l  (    c, l         borrower        l, “ Perryridge ”, a        loan )} ,[object Object],{    c     |     l, b, a  (    c, l        borrower        l, b, a        loan      a  > 1200)} ,[object Object],{    l ,  b, a    |     l ,  b, a        loan      a  > 1200}
Example Queries ,[object Object],{    c     |    s,  n  (    c, s, n        customer)      x,y,z (    x, y, z        branch      y  = “Brooklyn”)        a,b (    x, y, z        account         c,a         depositor )}  ,[object Object],{    c     |     l  ({    c, l         borrower          b,a (    l, b, a        loan      b  = “Perryridge”))         a (    c, a         depositor         b,n (    a, b, n        account      b  = “Perryridge”))}
Safety of Expressions ,[object Object],[object Object],[object Object],[object Object],[object Object]
End of Chapter 3
Result of     branch-name =  “Perryridge”  ( loan )
Loan Number and the Amount of the Loan
Names of All Customers Who Have Either a Loan or an Account
Customers With An Account But No Loan
Result of  borrower     loan
Result of    branch-name =  “Perryridge”  ( borrower     loan)
Result of   customer-name
Result of the Subexpression
Largest Account Balance in the Bank
Customers Who Live on the Same Street and In the Same City as Smith
Customers With Both an Account and a Loan at the Bank
Result of   customer-name, loan-number, amount   ( borrower  loan)
Result of   branch-name (  customer-city =  “Harrison” ( customer   account  depositor))
Result of   branch-name (  branch-city =  “Brooklyn” (branch))
Result of   customer-name, branch-name ( depositor  account)
The  credit-info  Relation
Result of   customer-name, (limit – credit-balance)  as  credit-available (credit-info).
The  pt-works  Relation
The  pt-works  Relation After Grouping
Result of  branch-name     sum (salary)  (pt-works)
Result of  branch-name     sum  salary,  max( salary ) as  max-salary  (pt-works)
The  employee  and  ft-works  Relations
The Result of  employee  ft-works
The Result of  employee   ft-works
Result of  employee  ft-works
Result of  employee  ft-works
Tuples Inserted Into  loan  and  borrower
Names of All Customers Who Have a Loan at the Perryridge Branch
E-R Diagram
The  branch  Relation
The  loan  Relation
The  borrower  Relation

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