1. CS 405G: Introduction to Database Systems Lecture 4: Relational Model Instructor: Chen Qian

2. 7/2/20152 Review A data model is a group of concepts for describing data. What are the two terms used by ER model to describe a miniworld? Entity Relationship What makes a good conceptual database design 10101 11101 ? 27/2/2015

3. 3 Today’s Outline Relational Model Relational Model and Relational Database Schemas Informal definition, not so formal, and formal Relational Model Constraints

4. 7/2/20154 Why Study the Relational Model? Most widely used model. “Legacy systems” in older models e.g., IBM’s IMS Object-oriented concepts merged in “Object-Relational” model Early work done in POSTGRES research project at Berkeley XML features in most relational systems Can export XML interfaces Can embed XML inside relational fields

5. 7/2/20155 Historically The model was first proposed by Dr. E.F. Codd of IBM in 1970 in the following paper: "A Relational Model for Large Shared Data Banks," Communications of the ACM, June 1970. The above paper caused a major revolution in the field of Database management and earned Ted Codd the coveted ACM Turing Award. The picture is from wikipedia

6. 7/2/20156 Database Design

7. 7/2/20157 Relational Model Concepts Relational database: a set of relations. Relation: made up of 2 parts: Schema : specifies name of relation, plus the name and type of each attribute. E.g. Students(sid: string, name: string, login: string, age: integer, gpa: real) Instance : a table, with rows and columns. #rows = cardinality #fields = degree / arity

8. 7/2/20158 Relation RELATION: A table of values A relation may be thought of as a set of rows (table view). Each row represents a fact that corresponds to a real- world entity or relationship. Each row has a value of an item or set of items that uniquely identifies that row in the table.

9. 7/2/20159 Relation Sometimes row-ids or sequential numbers are assigned to identify the rows in the table. A relation may alternately be thought of as a set of columns (schema view). Each column typically is called by its column name or column header or attribute name.

10. 7/2/201510 A (Slightly) Formal Definition A database is a collection of relations (or tables) Each relation is identified by a name and a list of attributes (or columns) Each attribute has a name and a domain (or type) Such as SID:string Set-valued attributes not allowed Simplicity is a virtue!

11. Schemas 11 Relation schema = relation name + attributes + types of attributes in order Example: Beers(name, manf) or Beers(name: string, manf: string) Database = collection of relations. Database schema = set of all relation schemas in the database.

12. 7/2/201512 Schema versus instance Schema (metadata) Students(sid: string, name: string, login: string, age: integer, gpa: real) Specification of how data is to be structured logically Defined at set-up; Rarely changes Instance Content Changes rapidly, but always conforms to the schema  Compare to type and objects of type in a programming language  Entity and entity type?

13. 7/2/201513 Example Schema Student (SID integer, name string, age integer, GPA float) Course (CID string, title string) Enroll (SID integer, CID integer) Instance { 142, Amy, 20, 3.3, 123, Bob, 22, 3.1,...} { CS405G, Intro. to Database Systems,...} { 142, CS405G, 142, CS314,...}

14. 7/2/201514 Formal Definition (Set Theory) Formally, given sets D 1, D 2, …. D n a relation r is a subset of D 1 x D 2 x … x D n x: Cartesian product For sets A and B, the Cartesian product A × B is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B. Thus, a relation is a set of n-tuples (a 1, a 2, …, a n ) where each a i  D i

15. 7/2/201515 Example Example: If customer_name = {Jones, Smith, Curry, Lindsay, …} customer_street = {Main, North, Park, …} customer_city = {Harrison, Rye, Pittsfield, …} Then r = { (Jones, Main, Harrison), (Smith, North, Rye), (Curry, North, Rye), (Lindsay, Park, Pittsfield) } is a relation over customer_name × customer_street × customer_city

16. 7/2/201516 Attribute Types Each attribute of a relation has a name, designating the role of the attribute The set of allowed values for each attribute is called the domain of the attribute Attribute values (domain members) are required to be atomic; that is, indivisible E.g. the value of an attribute can be an account number, but cannot be a set of account numbers Domain is said to be atomic if all its members are atomic The special value null is a member of every domain

17. 7/2/201517 Relation Schema A 1, A 2, …, A n are attributes R = (A 1, A 2, …, A n ) is a relation schema Example: Customer_schema = (customer_name, customer_street, customer_city) r(R) denotes a relation r on the relation schema R Example: customer (Customer_schema)

18. 7/2/201518 Relation Instance The current values (relation instance) of a relation are specified by a table An element t of r is a tuple, represented by a row in a table Jones Smith Curry Lindsay customer_name Main North Park customer_street Harrison Rye Pittsfield customer_city customer attributes (or columns) tuples (or rows)

19. 7/2/201519 Definition Summary Informal TermsFormal Terms TableRelation ColumnAttribute/Domain RowTuple Values in a columnDomain Table DefinitionSchema of a Relation Populated TableExtension

20. 7/2/201520 Characteristics of Relation The tuples in a ration r(R) are not considered to be ordered, even though they appear to be in the tabular form. We consider the attributes in R(A 1, A 2,..., A n ) and the values in t= to be ordered. All values are considered atomic (indivisible). A special null value is used to represent values that are unknown or inapplicable to certain tuples.

21. 7/2/201521 Characteristics of Relation Notation: we refer to component values of a tuple t by t[A i ] = v i (the value of attribute A i for tuple t). Similarly, t[A u, A v,..., A w ] refers to the subtuple of t containing the values of attributes A u, A v,..., A w, respectively.

22. 7/2/201522 Relational Integrity Constraints Integrity Constraints are conditions that must hold on all valid relation instances. There are four main types of constraints: 1. Domain constraints 1. The value of a attribute must come from its domain 2. Key constraints 3. Entity integrity constraints 4. Referential integrity constraints

23. Primary Key Constraints A set of fields is a candidate key (abbreviated as key) for a relation if : 1. No two distinct tuples can have same values in all key fields, and 2. Property 1 is not true for any subset of the key. What if Part 2 is false? A super key: a set of fields that contains a key. If there are multiple keys for a relation, one of the keys is chosen (by DBA) to be the primary key.

24. 7/2/201524 Key Example E.g., given a schema Student(sid: string, name: string, gpa: float) we have: sid is a key for Students. (What about name?) The set {sid, gpa} is a superkey. CAR (licence_num: string, Engine_serial_num: string, make: string, model: string, year: integer) What is the candidate key(s) Which one you may use as a primary key What are the super keys

25. 7/2/201525 Entity Integrity Entity Integrity: The primary key attributes (PK) of each relation schema R cannot have null values in any tuple of r(R). Other attributes of R may be similarly constrained to disallow null values, even though they are not members of the primary key.

26. Foreign Keys, Referential Integrity Foreign key : Set of fields in one relation that is used to `refer’ to a tuple in another relation. (Must correspond to primary key of the second relation.) Like a `logical pointer’. Foreign key constraint: The foreign key in the referencing relation must match the primary key of the referenced relation. E.g. sid is a foreign key referring to Students : Student(sid: string, name: string, gpa: float) Enrolled(sid: string, cid: string, grade: string) If all foreign key constraints are enforced, referential integrity is achieved, i.e., no dangling references.

27. Foreign Key constraints Only students listed in the Students relation should be allowed to enroll for courses. Enrolled Students Possible violation: Add to Enrolled. Possible violation: delete from Students.

28. 7/2/201528 Other Types of Constraints Semantic Integrity Constraints: based on application semantics and cannot be expressed by the model per se e.g., “the max. no. of hours per employee for all projects he or she works on is 56 hrs per week” A constraint specification language may have to be used to express these SQL-99 allows triggers and ASSERTIONS to allow for some of these

29. Next class Logical design of databases using the relational model. 7/2/201529

30. Home work 1, due 2/6 7/2/201530