Schedule Today: Next And then Relational Algebra. Read Chapter 5 to page 199. Next SQL Queries. Read Sections 6.1-6.2. And then Subqueries, Grouping and Aggregation. Read Sections 6.3-6.4. SCU Holliday - coen 178

Relational Algebra The relational algebra is a precise mathematical notation and set of rules for manipulating “relations”. SQL is basically a more human readable form of the relational algebra. SCU Holliday - coen 178

“Core” Relational Algebra A small set of operators that allow us to manipulate relations in limited but useful ways. The operators are: 1. Union, intersection, and difference: the usual set operators. But the relation schemas must be the same. 2. Selection: Picking certain rows from a relation. 3. Projection: Picking certain columns. 4. Products and joins: Composing relations in useful ways. 5. Renaming of relations and their attributes. SCU Holliday - coen 178

Relational Algebra  SELECT π PROJECT X CARTESIAN PRODUCT NATURAL JOIN SCU Holliday - coen 178

Selection Example R1 = C(R2) where C is a condition involving the attributes of relation R2. Example Relation Sells: JoeMenu = bar=Joe's(Sells) SCU Holliday - coen 178

Product R = R1  R2 pairs each tuple t1 of R1 with each tuple t2 of R2 and puts in R a tuple t1t2. SCU Holliday - coen 178

Natural-Join R = R1 R2 is equivalent to R = C(R1  R2) where c is the condition that the the values of the attributes that R1 and R2 have in common must match. SCU Holliday - coen 178

Example Sells = Bars = BarInfo = Sells Bars SCU Holliday - coen 178

Combining Operations Algebra = Universe or domain of objects Operators for constructing expressions. For relational algebra: Domain = variables standing for relations + finite, constant relations. Expressions constructed by applying one of the operators + parentheses. Query = expression of relational algebra. SCU Holliday - coen 178

Bag Semantics A relation (in SQL, at least) is really a bag or multiset. It may contain the same tuple more than once, although there is no specified order (unlike a list). Example: {1,2,1,3} is a bag and not a set. Select, project, and join work for bags as well as sets. Just work on a tuple-by-tuple basis, and don't eliminate duplicates. SCU Holliday - coen 178

Bag Union Bag Intersection Bag Difference Sum the times an element appears in the two bags. Example: {1,2,1}  {1,2,3,3} = {1,1,1,2,2,3,3}. Bag Intersection Take the minimum of the number of occurrences in each bag. Example: {1,2,1}  {1,2,3,3} = {1,2}. Bag Difference Proper-subtract the number of occurrences in the two bags. Example: {1,2,1} – {1,2,3,3} = {1}. SCU Holliday - coen 178

Duplicate Elimination (R) = relation with one copy of each tuple that appears one or more times in R. Example R = A B 1 2 3 4 (R) = SCU Holliday - coen 178

Bank Database Schema Branch = (branch-name, branch-city, assets) Customer = (customer-name, customer-street, customer-city) Account = (branch-name, account#, balance) Depositor = (customer-name, account#) Loan = (branch-name, loan#, amount) Borrower = (customer-name, loan#) SCU Holliday - coen 178

The Customer Table Customer-name C-Street C-city Bob 123 Third St San Jose Carol 456 Main St Santa Clara Ted 89 Blossom Ave Los Gatos Alice 64 Longwalk Dr Oakland SCU Holliday - coen 178

The Account Table Branch-name Account# Balance Oakland 101 2000 SJ-Main 205 7500 207 4500 Santa Clara 311 3100 SJ-West 251 850 SCU Holliday - coen 178

The Loan Table Branch-name loan# Amount Oakland 2301 5000 SJ-Main 5155 700 5709 9000 Santa Clara 1541 1800 SJ-West 4321 250 SCU Holliday - coen 178

The Depositor Table Customer-name Account# Bob 207 Carol 311 Ted 205 Alice 101 251 SCU Holliday - coen 178

Queries on the Loan Table Branch-name Oakland SJ-Main Santa Clara SJ-West Loan = (branch-name, loan#, amount) Find the names of all the branches in the Loan relation select branch-name from Loan (branch-name) (Loan) SCU Holliday - coen 178

More Queries on the Loan Table select * from Loan where amount > 3000   (amount>3000) (Loan) SCU Holliday - coen 178

where branch-name="Oakland" and amount>1200 Find the loan numbers for all loans made at the Oakland branch with loan amounts greater than 1200.  select loan# from Loan where branch-name="Oakland" and amount>1200 (loan#) (branch-name=“Oakland”^amount>1200) (Loan) SCU Holliday - coen 178

Cross Product Select A1, A2 from R1, R2 Result R = R1  R2 pairs each tuple t1 of R1 with each tuple t2 of R2 and puts in R a tuple t1t2. (A1, A2) (R1  R2) SCU Holliday - coen 178

Natural Join Find the name of customers with an account at the Oakland branch. select customer-name from Depositor, Account where Depositor.account# = Account.account# and branch-name = "Oakland" (cust-name) (b-name=“Oakland”) (Depositor Account) SCU Holliday - coen 178