1. 603 Database Systems Senior Lecturer: Laurie Webster II, M.S.S.E.,M.S.E.E., M.S.BME, Ph.D., P.E. Lecture 11 A First Course in Database Systems

2. Relational Algebra Chapter 5 SELECTION  : Movie title yearlength inColor studioName producerC# Star Wars1977124 yes Fox 12345 Mighty Duck1971104 yes Disney 67890 Suppose we want the Set of tuples in the relation Movie(title, year, length, inColor, studioName, producerC#) that represent Fox movies at least 100 minutes long.  c (R) =  length  100 AND studioName = ‘Fox’ (Movie)

3. Relational Algebra  c (R) =  length  100 AND studioName = ‘Fox’ (Movie) ==> Result title yearlengthinColorstudioNameproducerC# Star Wars1977124YesFox12345

4. Relational Algebra Chapter 5 PROJECTION  :  Attribute list (R) Movie titleyearlength inColor studioName producerC# Star Wars1977124 yes Fox 12345 Mighty Duck1991104 yes Disney 67890 Wayne’s W.1992 95 yes Paramount 99999  title, year, length (Movie)

5. Relational Algebra Chapter 5 PROJECTION  :  title, year, length (Movie) Movie titleyearlength Star Wars1977124 Mighty Duck1991104 Wayne’s W.1992 95

6. Relational Algebra Chapter 5 SET THEORETIC OPERATIONS: Retrieve SSN of all employees who either work in DEP5 or directly supervise an employee who works in DEP5. Solution: Use union operation on Result1 and Result2 DEP5_EMPS   DNO = 5 (EMPLOYEE) RESULT1   SSN (DEP5_EMPS ) RESULT2(SSN)   SUPPERSSN (DEP5_EMPS ) RESULT  RESULT1  RESULT2

7. Relational Algebra QUERY RESULT: RESULT1SSN 123456789 333445555 666884444 453453453 RESULT2SSN 333445555 888665555 RESULTSSN 123456789 333445555 666884444 453453453 888666555 Query result after the UNION operation: RESULT1  RESULT2

8. Relational Algebra Set Theoretic Operations: UNION, INTERSECTION, and SET DIFFERENCE ==> These operations are adapted to relational databases where the two relations on which they apply must have the same types of tuples; ==> UNION compatible

9. Relational Algebra Chapter 5 Set Theoretic Operations: R(A 1, A 2, …., A n ) and S(B 1, B 2, …, B n ) is UNION compatible if dom(A i ) = dom(B i ) for 1  i  n. ==> two relations have the same number of attributes and that each pair of corresponding attributes have the same domain.

10. Relational Algebra Chapter 5 JOIN Operation: EMP_DEPENDENTS  EMPNAMES  DEPENDENT ACTUAL_DEPENDENTS   ssn = essn (EMP_DEPENDENTS) replaced with single JOIN operation: ACTUAL_DEPENDENTS  EMPNAMES  SSN = ESSN DEPENDENT

11. Relational Algebra Chapter 5 Examples of Queries in Relational Algebra: Query 1 Retrieve the name and address of all employees who work for the ‘Research’ department. RESEARCH_DEPT   DNAME = ‘RESEARCH’ (DEPARTMENT) RESEARCH_EMP  (RESEARCH_DEPT  DNUMBER = DNO EMPLOYEE) RESULT  FNAME, LNAME, ADDRESS (RESEARCH_EMPS)

12. Relational Algebra Chapter 5 Examples of Queries in Relational Algebra: Query 2 For every project located in ‘Stafford’, list the project number, the controlling department number, and the department manager’s last name, address, and birthdate. STAFFORD_PROJS   PLOCATION = ‘Stafford’ (DEPARTMENT) CONTR_DEPT  (STAFFORD_PROJS  DNUM = DNUMBER DEPARTMENT) PROJ_DEPT_MGR  (CONTR_DEPT  MGRSSN = SSN EMPLOYEE) RESULT  PNUMBER, DNUM, LNAME, ADDRESS, BDATE (PROJ_DEPT_MGR)

13. Relational Algebra Chapter 5 Relational Calculus: Relational calculus is a formal query language where we write on declarative expression to specify a retrieval request and hence there is no description of how to evaluate a query!! A calculus expression specifies WHAT is to be retrieved rather than HOW to retrieve it. Declarative Language Procedural Language

14. Relational Algebra Chapter 5 Relational Calculus: ==> nonprocedural language (Declarative Language) Relational Algebra: ==> Procedural Language

15. Relational Algebra Chapter 5 Relational Algebra ==> Procedural where we must write a sequence of operations to specify a retrieval request (HOW process). Relational Calculus ==> Declarative we express WHAT is to be retrieved without specifying HOW to retrieve it.

16. Relational Algebra Chapter 5 Expressive Power of the Two Languages: Any retrieval that can be specified in relational algebra can also be specified in the relational calculus, and vice versa => expressive power of two languages is identical

17. Relational Algebra Expressive Power of the Two Languages: Any retrieval that can be specified in relational algebra can also be specified in the relational calculus, and vice versa => expressive power of two languages is identical ==> led to the definition of the concept of relationally complete language.

18. Relational Algebra Complete Set of Relational Algebra Operations: All the operations discussed so far can be described as a sequence of only the operations SELECT, PROJECT, UNION, SET, DIFFERENCE, and CARTESIAN PRODUCT. Hence, the set { , , , -,  } is called a complete set of relational algebra operations.

19. Relational Calculus A relational query language L is considered relationally complete if we can express in L any query that can be expressed in relational calculus. Relational completeness has become an important basis for comparing the expressive power of high- level query languages.

20. Relational Calculus Tuple Variables and Range Relations The tuple relational calculus is based on specifying a number of tuple variables. Each tuple variable usually ranges over a particular database relation, meaning that the variable may take as its value any individual tuple from that relation.

21. Relational Calculus Tuple Relational Calculus Query: { t | COND (t) } where t is a tuple variable and COND(t) is a conditional expression involving t. The result of such a query is the set of all tuples t that satisfy COND( t ).

22. Relational Calculus Relational Calculus Query Example: Find all employees whose salary is above $50000. { t | EMPLOYEE (t) and t.SALARY > 50000}

23. Relational Calculus Relational Calculus Query Example: Find all employees whose salary is above $50000. { t | EMPLOYEE (t) and t.SALARY > 50000} ==> EMPLOYEE(t) => specifies that the range relation of tuple variable t is EMPLOYEE. Each EMPLOYEE tuple t that satisfies the condition t.SALARY > 50000 will be retrieved.

24. Relational Calculus NOTE: t.SALARY references attribute SALARY of tuple variable t; ==> this notation resembles how attribute names are qualified with relation names or aliases in SQL. t.SALARY  t[SALARY]

25. Relational Calculus NEXT LECTURE Relational Calculus