1. Chapter 71 The Relational Data Model, Relational Constraints & The Relational Algebra

2. Chapter 72 A relation schema R, denoted R(A 1, …, A n ), consists of a relation name R and a list of attributes A 1,…,A n eg. Course (CourseName, CourseNumber, InstructorName, StartTime, EndTime, Days) Each attribute A i is the name of a role played by domain dom (A i ). The number n of attributes is the degree of the relation schema. A data type is specified for each dom(A i ), eg., char, int, money,...

3. Chapter 73 A relation (or relation instance) r of the relation schema R(A 1,…A n ) is a set r={t 1,...,t n } where each t i is a n-tuple of the form s.t. each value r i  dom(A i ) or r i is a special null value. The value of attribute A i for tuple t j is denoted t j (A i ). Informally, a relation is a table of tuples.

4. Chapter 74 For the relation schema President (Name, YearStart, YearEnd) a relation is {, }* * The intension of schema is to assert facts from the miniworld - equivalently, it defines a “predicate” for relation tuples to satisfy. The tuples in a relation are unordered, and need not be a complete set satisfying the schema predicate; however, no duplicates.

5. Chapter 75 President

6. Chapter 76 A subset S of attributes of a relation schema R, s.t. NO two tuples in any relation instance r of R can have the same combination of values for attributes in S, is called a superkey. Thus, the values of the attributes in S uniquely identify a tuple. A superkey K, with the property that removing any attribute from K leaves a subset that is not a superkey, is called a key: it is a minimal superkey.

7. Chapter 77

8. 8 A relation schema may have more than one key. Each such key is called a candidate key. One candidate key is designated the primary key and is used to identify tuples in a relation. Attributes in a primary key are shown underlined in a relation schema. Car LicenseNumber EngineSerial Number Make Model Year Person Name Street City Zipcode PhoneNumber

9. Chapter 79 Constrains Domain Constraint: value of each attribute A must be an atomic value from dom(A). This means that the DBMS does type checking. Key Constraint: No two tuples can have the same combination of values for attributes in the primary key. This is also DBMS enforced

10. Chapter 710 Relational Database Schema A relational database schema is a set S = { R 1,..., R n } of relational schemas. A relation database instance I of S is a set I = {r 1,..., r n } of relational instances, s.t. each r i is an instance of R i.

11. Chapter 711

12. Chapter 712 Fig 7.6 1st 3 Tables

13. Chapter 713 Fig 7.6 2nd 3 Tables

14. Chapter 714 Referential Integrity Constraints The arrows on the next slide represent referential integrity constraints. The value of the attribute at the tail of the arrow (called foreign key) must, for each tuple, be either null or equal to the value of the attribute at the head of the arrow for some tuple

15. Chapter 715

16. Chapter 716 Maintenance Operations Insert: adds new tuples to a relation. Delete: removes tuples from a relation. Update: changes values of attributes of existing tuples in a relation.

17. Chapter 717 Relational Algebra Select :  ( ) Project :  ( )  (DNO =4 & SALARY>25000)OR(DNO=5 & SALARY.30000) (EMPLOYEE)  LNAME, FNAME, SALARY (EMPLOYEE),  SEX, SALARY (EMPLOYEE)* * Projection requires duplicate elimination.

18. Chapter 718 Fig 7.8

19. Chapter 719 Relational Algebra Expressions Query: Retrieve first name, last name, salary of employee in department number 5. (a)  FNAME,LNAME, SALARY (  DNO=5 (EMPLOYEE)) (b)TEMP <--   DNO=5 (EMPLOYEE) R(FIRSTNAME, LASTNAME, SALARY)* <--  FNAME, LNAME,SALARY(TEMP) * Attributes renamed.

20. Chapter 720

21. Chapter 721 Fig 7.11

22. Chapter 722 Fig 7.12

23. Chapter 723 Joins A Join is like a Cartesian Product except that it has a join condition in which an attribute(s) of one table are compared to those of another table.

24. Chapter 724 Joins (con’t) There are three types of joins. – Equijoin Join. Where the attributes are equal and the result has both of them in it. – Natural Join. Where the attributes are both equal and have the same name. Result has that name only once. –Theta Join. The General Condition where a comparison is made between selected attributes of two or more tables.

25. Chapter 725 Joins (con’t) Join: |> Query: Retrieve the name of each department manager. DEPT_MGR  DEPARTMENT|><| MGRSSN=SSN EMPLOYEE

26. Chapter 726

27. Chapter 727 Connect_AC

28. Chapter 728 Fig 7.14

29. Chapter 729 Division If r is an instance of R(Z) and S is an instance of S(X) and X  then r  s is an instance of T(Y), where Y= Z-X and s.t. a tuple is in r  s iff its values appear in r in combination with every tuple in S

30. Chapter 730 Fig 7.15

31. Chapter 731 Aggregate (or Set) Functions F ( ) Valid Aggregate Functions –Count –Average –Maximum –Minimum

32. Chapter 732 Fig 7.16

33. Chapter 733 ER to Relational Mapping Step 1: For each regular entity type E in the ER schema, create a relation R that includes all the simple attributes of E. Include on the simple component attributes of a composite attribute. Choose one of the key attributes of E as primary key for R. If the chosen key of E is composite, the set of simple attributes that form it will together form the primary key of R.

34. Chapter 734 ER to Relational Mapping(con’t) Step 2: For each weak entity type W in the ER Schema with owner entity type E, create a relation R, and include all simple attributes (or simple components of composite attributes of W as attributes of R. In addition, include as foreign key attributes of R the primary key attribute(s) of the relation(s) that correspond to the owner entity type(s).

35. Chapter 735 ER to Relational Mapping(con’t) Step 3: For each binary 1:1 relationship type R in the ER schema, identify the relations S and T that correspond to the entity types participating in R. Choose one of the relations-S, say- and include as foreign key in S the primary key of T. It is better to choose an entity type with total participation in R in the role of S. Include the simple attributes of the 1:1 relationship type R as attributes of S.

36. Chapter 736 ER to Relational Mapping(con’t) Step 4: For each regular (non-weak) binary 1:N relationship type R, identify the relation S that represents the participating entity type at the N-side of the relationship type. Include as foreign key in S the primary key of the relations T that represents the other entity type participating in R. Include an simple attributes of the 1:n relationship type as attributes of S.

37. Chapter 737 ER to Relational Mapping(con’t) Step 5: For each binary M:N relationship type R, create a new relation S to represent R. Include as foreign key attributes in S the primary keys of the relations that represent the participating entity types; their combination will form the primary key of S. Also, include any simple attributes of the M:N relationship type as attributes of S.

38. Chapter 738 ER to Relational Mapping(con’t) Step 6: For each multivalued attribute A, create a new relation R that includes an attribute corresponding to A plus the primary key attribute K(as a foreign key in R) of the relation that represents the entity type or relationship type that has A as an attribute. The primary key of R is the combination of A and K. If a multivalued attribute is composite, we include its components.

39. Chapter 739 ER to Relational Mapping(con’t) Step 7: For each n-ary relationship type R, n>2, create a new relation S to represent R. Include as foreign key attributes in the S the primary keys of the relations that represent the participating entity types. Also include any simple attributes of the n-ary relationship types as attributes of S. The primary key for S is usually a combination of all the foreign keys that reference the relations representing the participating entity types. However, if

40. Chapter 740 Step 7 (con’t) The participation constraint (min,max) of one of the entity types E participating in the R has max =1, then the primary key of S can be the single foreign key attribute that references the relation E’ corresponding to E; this is because, in this case, each entity e in E will participate in at most one relationship instance of R and hence can uniquely identify that relationship instance.