1. Query Languages Language in which user requests information from the database. Categories of languages Procedural Non-procedural, or declarative “Pure” languages: Relational algebra Tuple relational calculus Domain relational calculus

2. Relational Algebra It is a Procedural language It consist of set of operation which takes one or two relation as input and produce relation as output. Six basic operators select:  - unary project:  - unary rename:  - unary union:  - binary set difference: – - binary Cartesian product: x- binary The operators take one or two relations as inputs and produce a new relation as a result.

3. Additional Operations We define additional operations that do not add any power to the relational algebra, but that simplify common queries. Set intersection Natural join Division Assignment

4. Select Operation Notation:  p (r) p is called the selection predicate Defined as: Each term is one of: op or where op is one of: =, , >, . <.  Each term is connected by:  (and),  (or),  (not) Example of selection:  branch_name=“Perryridge” (account)

5. Select Operation – Example Relation r ABCD   1 5 12 23 7 3 10   A=B ^ D > 5 (r) ABCD   1 23 7 10

6. Project Operation Notation: where A 1, A 2 are attribute names and r is a relation name. The result is defined as the relation of k columns obtained by erasing the columns that are not listed Duplicate rows removed from result, since relations are sets Example: To eliminate the branch_name attribute of account  account_number, balance (account)

7. Project Operation – Example Relation r: ABC  10 20 30 40 11121112 AC  11121112 = AC  112112  A,C (r)

8. Find those customers who live in “xyz” :  customer_name (  cutomer-city = “xyz” (account)) Composition of Operations

9. Union Operation Notation: r  s Defined as: r  s = {t | t  r or t  s} For r  s to be valid. 1. r, s must have the same arity (same number of attributes) 2. The attribute domains must be compatible (example: 2 nd column of r deals with the same type of values as does the 2 nd column of s) Example: to find all customers with either an account or a loan  customer_name (depositor)   customer_name (borrower)

10. Union Operation – Example Relations r, s: r  s: AB  121121 AB  2323 r s AB  12131213

11. Set Difference Operation Notation r – s Defined as: r – s = {t | t  r and t  s} Set differences must be taken between compatible relations. r and s must have the same arity attribute domains of r and s must be compatible

12. Set Difference Operation – Example Relations r, s: r – s: AB  121121 AB  2323 r s AB  1111

13. Cartesian-Product Operation Notation r x s Defined as: r x s = {t q | t  r and q  s} Assume that attributes of r(R) and s(S) are disjoint. (That is, R  S =  ). If attributes of r(R) and s(S) are not disjoint, then renaming must be used.

14. Cartesian-Product Operation – Example Relations r, s: r x s: AB  1212 AB  1111222211112222 CD  10 20 10 20 10 E aabbaabbaabbaabb CD  20 10 E aabbaabb r s

15. Composition of Operations Can build expressions using multiple operations Example:  A=C (r x s) r x s  A=C (r x s) AB  1111222211112222 CD  10 20 10 20 10 E aabbaabbaabbaabb ABCDE  122122  20 aabaab

16. Rename Operation Allows us to name, and therefore to refer to, the results of relational-algebra expressions. Allows us to refer to a relation by more than one name. Example:  x (E) returns the expression E under the name X If a relational-algebra expression E has arity n, then returns the result of expression E under the name X, and with the attributes renamed to A 1, A 2, …., A n.

17. Banking Example branch (branch_name, branch_city, assets) customer (customer_name, customer_street, customer_city) account (account_number, branch_name, balance) loan (loan_number, branch_name, amount) depositor (customer_name, account_number) borrower (customer_name, loan_number)

18. Example Queries Find all loans of over $1200 Find the loan number for each loan of an amount greater than $1200  amount > 1200 (loan)  loan_number (  amount > 1200 (loan)) Find the names of all customers who have a loan, an account, or both, from the bank  customer_name (borrower)   customer_name (depositor)

19. Example Queries Find the names of all customers who have a loan at the Perryridge branch. Query 1  customer_name (  branch_name = “Perryridge” (  borrower.loan_number = loan.loan_number (borrower x loan)))

20. Example Queries Find the names of all customers who have a loan at the Perryridge branch but do not have an account at any branch of the bank.  customer-name (  branch-name = “Perryridge” (  borrower.loan-number = loan.loan-number ( borrower x loan ))) –  customer-name ( depositor )

21. Formal Definition A basic expression in the relational algebra consists of either one of the following: A relation in the database A constant relation Let E 1 and E 2 be relational-algebra expressions; the following are all relational-algebra expressions: E 1  E 2 E 1 – E 2 E 1 x E 2  p (E 1 ), P is a predicate on attributes in E 1  s (E 1 ), S is a list consisting of some of the attributes in E 1  x (E 1 ), x is the new name for the result of E 1