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INFS614, GMU The Relational Model The Relational Model Lecture 3 INFS614, Fall 2008
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The Relational ModelThe Relational Model
Lecture 3
INFS614, Fall 2008
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Relational ModelRelational Model Relational Model = Structure + Operations
– Structure: Relations (or Tables)– Operations: Relational Algebra, SQL.
Most widely implemented model.– Vendors: IBM DB2, Microsoft SQL Server, Oracle, etc.
Our design+implementation approach:Step 1: ER design (ERD)Step 2: Translate to Relational (Relational Schema)Step 3: Querying over the relational model
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Relational Database: Relational Database: DefinitionsDefinitions
Relational database: a set of relations
Relation: made up of 2 parts:– Instance : a table, with rows and columns.
#Rows = cardinality, #fields = degree / arity.– Schema : specifies name of relation, plus
name and type of each column. E.G. Students(sid: string, name: string, login:
string, age: integer, gpa: real).
We can think of a relation as a set of rows or tuples (i.e., all rows are distinct).
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Example: Instance of Example: Instance of Students RelationStudents Relation
sid name login age gpa
53666 Jones jones@cs 18 3.4
53688 Smith smith@eecs 18 3.2
53650 Smith smith@math 19 3.8
Cardinality = 3, degree = 5, all rows distinct;
Do all columns in a relation instance have to be distinct?
The order in which the rows are listed is not important;
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Another Example: Another Example: Employees RelationEmployees Relation
Employees Schema:Employees(ssn:integer,name:string,rank:char,salary:
float)
An instance of Employees:
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Example: Employees Relation Example: Employees Relation (Contd.)(Contd.)
An instanceinstance of Employees = { <633909767, Richard Boon, A,
75689.09>, <674627883,Adolfo Laurenti, B, 67890.00>, <193838904,Will Smith,C,50000.00>,…}Set of tuples
(or rows)
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Relational Database : Relational Database : DefinitionsDefinitions
InstanceInstance : a set of tuples of the relation
A tuple : < a1:d1, …,an:dn >, aj is an attribute name,dj is the value of the attribute aj , dj either belongs to Domain(aj ) or is NULLNULL
An instanceinstance of Employees = { <ssn:633909767,name:Richard Boon, rank:A,
salary:75689.09>,<ssn:674627883,name:Adolfo Laurenti, rank:B,
salary:67890.00>,<ssn:193838904,name:Will Smith, rank:C, salary:50000.00>,
… }
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Relational Database: Relational Database: DefinitionsDefinitions
Relational database: a set of relations;
Relational database schema: the collection of schemas for the relations in the database;
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Example: A Company Database Example: A Company Database SchemaSchema
A First Schema:
Employees(ssn:integer,name:string,rank:integer,sala
ry:float)Projects(pid:integer,pname:string,budget:float)Location(address:string,capacity:integer)Departments(did:integer,dname:string,budget:float)Manages(ssn:integer,did: integer,since:date)Reports_To(ssnSubordinate:integer,ssnSupervisor:
integer)Works_for(ssn:integer,pid: integer,hours:float)Works_in(ssn:integer,did: integer,address:string)
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Relational Query Relational Query LanguagesLanguages A major strength of the relational
model: supports simple, powerful querying of data.
Queries can be written intuitively, and the DBMS is responsible for efficient evaluation.– The key: precise semantics for relational
queries.– Allows the optimizer to extensively re-order
operations, and still ensure that the answer does not change.
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The SQL Query LanguageThe SQL Query Language
Developed by IBM (system R) in the 1970s
Need for a standard since it is used by many vendors
Standards: – SQL-86– SQL-89 (minor revision)– SQL-92 (major revision, current standard)– SQL-99 (major extensions)
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Creating Relations in SQLCreating Relations in SQL
Creates the Students relation. Observe that the type (domain) of each field is specified, and enforced by the DBMS whenever tuples are added or modified.
As another example, the Enrolled table holds information about courses that students take.
CREATE TABLE Students
(sid CHAR(20), name CHAR(20), login CHAR(10),
age INTEGER, gpa REAL)
CREATE TABLE Enrolled
(sid CHAR(20), cid CHAR(20), grade CHAR(2))
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Adding and Deleting Adding and Deleting TuplesTuples We can insert a single tuple using:
INSERT
INTO Students (sid, name, login, age, gpa)VALUES (53688, ‘Smith’, ‘smith@ee’, 18, 3.2)
Can delete all tuples satisfying some condition (e.g., name = Smith):
DELETE FROM Students SWHERE S.name = ‘Smith’
Powerful variants of these commands are available; more later!
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Querying Relational DataQuerying Relational Data
To find all 18 year old students, we can write:
SELECT *FROM Students SWHERE S.age=18
sid name login age gpa
53666 Jones jones@cs 18 3.4
53688 Smith smith@eecs 18 3.2
53650 Smith smith@math 19 3.8
Instance of Students:
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Querying Relational Data Querying Relational Data (Contd.)(Contd.)
The result is:
SELECT *FROM Students SWHERE S.age=18
•To find just names and logins, replace the first line:
SELECT S.name, S.login
sid name login age gpa
53666 Jones jones@cs 18 3.4
53688 Smith smith@ee 18 3.2
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Updating TuplesUpdating Tuples
Can update tuples using:
UPDATE Students S SET S.age = S.age + 1, S.gpa = S.gpa -1WHERE S.sid = 53688
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Querying Multiple Querying Multiple RelationsRelations
What does the following query compute?
SELECT S.name, E.cidFROM Students S, Enrolled EWHERE S.sid=E.sid AND E.grade=“A”
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Querying Multiple Querying Multiple RelationsRelations
S.name E.cid
Smith Topology112
sid cid grade53831 Carnatic101 C53831 Reggae203 B53650 Topology112 A53666 History105 B
we get:
sid name login age gpa
53666 Jones jones@cs 18 3.4
53688 Smith smith@eecs 18 3.2
53650 Smith smith@math 19 3.8
Instance ofStudents:
Instance ofEnrolled:
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Destroying and Altering Destroying and Altering RelationsRelations
Destroys the relation Students. The schema information and the tuples are deleted.
DROP TABLE Students
The schema of Students is altered by adding a new field; every tuple in the current instance is extended with a null value in the new field.
ALTER TABLE Students ADD COLUMN firstYear: INTEGER
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Integrity Constraints (ICs)Integrity Constraints (ICs)
IC: condition that must be true for any instance of the database; e.g., domain constraints.– ICs are specified when schema is defined.– ICs are checked when relations are modified.
A legal instance of a relation is one that satisfies all specified ICs. – DBMS should not allow illegal instances.
If the DBMS checks ICs, stored data is more faithful to real-world meaning.– Avoids data entry errors, too!
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Primary Key ConstraintsPrimary Key Constraints
A set of fields is a (candidate) key for a relation if :1. No two distinct tuples can have same values in all
key fields, and2. This is not true for any subset of the key.– Part 2 false? A superkey.– If there’s >1 candidate keys for a relation, one of the
keys is chosen (by DBA) to be the primary key. E.g., sid is a key for Students. (What about
name?) The set {sid, gpa} is a superkey.
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Primary and Candidate Primary and Candidate Keys in SQLKeys in SQL
Possibly many candidate keys (specified using UNIQUE), one of which is chosen as the primary key.
CREATE TABLE Enrolled (sid CHAR(20) cid CHAR(20), grade CHAR(2), PRIMARY KEY (sid,cid) )
“For a given student and course, there is a single grade.” vs. “Students can take only one course, and receive a single grade for that course; further, no two students in a course receive the same grade.”
Used carelessly, an IC can prevent the storage of database instances that arise in practice!
CREATE TABLE Enrolled (sid CHAR(20) cid CHAR(20), grade CHAR(2), PRIMARY KEY (sid), UNIQUE (cid, grade) )
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Foreign Keys, Referential Foreign Keys, Referential IntegrityIntegrity
In addition to Students we have a second relation: Enrolled(sid: string, cid: string, grade: string)
Only students listed in the Students relation should be allowed to enroll for courses.
sid name login age gpa
53666 Jones jones@cs 18 3.453688 Smith smith@eecs 18 3.253650 Smith smith@math 19 3.8
sid cid grade53666 Carnatic101 C53666 Reggae203 B53650 Topology112 A53666 History105 B
EnrolledStudents
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Foreign Keys, Referential Foreign Keys, Referential IntegrityIntegrity
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’.
E.g. sid is a foreign key referring to Students:– Enrolled(sid: string, cid: string, grade: string)– If all foreign key constraints are enforced,
referential integrity is achieved, i.e., no dangling references.
– Can you name a data model w/o referential integrity?
Links in HTML!
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Foreign Keys, Referential IntegrityForeign Keys, Referential Integrity
Another Example :– Only employees in the Employees Relation
should be allowed to be managers: ssn is a Foreign Key respect to
Employees– Only projects in the Project Relation should
be allowed to be managed : pid is a Foreign Key respect to Projects
Employees Managers Projects
ssn pid hours 534559257 1 2 123456789 1 56 231896598 53 8 193838902 18 36 354681756 18 46
pid pname pbudget 1 XA011 5000000.00 53 Y 7560000.00 18 X 250000.00
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Foreign Keys in SQLForeign Keys in SQL
Only students listed in the Students relation should be allowed to enroll for courses.
CREATE TABLE Enrolled (sid CHAR(20), cid CHAR(20), grade CHAR(2), PRIMARY KEY (sid,cid), FOREIGN KEY (sid) REFERENCES Students )
sid name login age gpa
53666 Jones jones@cs 18 3.453688 Smith smith@eecs 18 3.253650 Smith smith@math 19 3.8
sid cid grade53666 Carnatic101 C53666 Reggae203 B53650 Topology112 A53666 History105 B
EnrolledStudents
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Foreign Keys, Referential Foreign Keys, Referential IntegrityIntegrity A Foreign KeyForeign Key must correspond to the primary
key of the referenced relation A Foreign KeyForeign Key states a ReferentialReferential ICIC
between two relations : a tuple in one relation that refers to another must refer to an existing tuple in that relation.
Referential Integrity ConstraintsReferential Integrity Constraints is used to maintain the consistency among tuples of two related relations
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Enforcing Referential Enforcing Referential IntegrityIntegrity
Consider Students and Enrolled; sid in Enrolled is a foreign key that references Students.
What should be done if an Enrolled tuple with a non-existent student id is inserted? (Reject it!)
What should be done if a Students tuple is deleted?– Also delete all Enrolled tuples that refer to it.– Disallow deletion of a Students tuple that is referred to.– Set sid in Enrolled tuples that refer to it to a default sid.– (In SQL, also: Set sid in Enrolled tuples that refer to it to a
special value null, denoting `unknown’ or `inapplicable’.) Similarly if primary key value of a Students tuple is
updated.
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Referential Integrity in Referential Integrity in SQL/92SQL/92
SQL/92 supports all 4 options on deletes and updates.– Default is NO ACTION
(delete/update is rejected)
– CASCADE (also delete all tuples that refer to deleted tuple)
– SET NULL / SET DEFAULT (sets foreign key value of referencing tuple)
CREATE TABLE Enrolled (sid CHAR(20), cid CHAR(20), grade CHAR(2), PRIMARY KEY (sid,cid), FOREIGN KEY (sid) REFERENCES Students
ON DELETE CASCADE
ON UPDATE NO ACTION )
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Where do ICs Come From?Where do ICs Come From? ICs are based upon the semantics of the real-
world enterprise that is being described in the database relations.
We can check a database instance to see if an IC is violated, but we can NEVER infer that an IC is true by looking at an instance.– An IC is a statement about all possible instances!– From example, we know name is not a key, but the
assertion that sid is a key is given to us.
Key and foreign key ICs are the most common; more general ICs supported too.
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Logical DB Design: ER to Logical DB Design: ER to RelationalRelational
Entity sets to tables.
CREATE TABLE
Employees (ssn CHAR(11), name CHAR(20), lot INTEGER, PRIMARY KEY (ssn))
Employees
ssnname
lot
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Relationship Sets to Relationship Sets to TablesTables
In translating a relationship set to a relation, attributes of the relation must include:
– Keys for each participating entity set (as foreign keys).
This set of attributes forms a superkey for the relation.
– All descriptive attributes.
CREATE TABLE Works_In( ssn CHAR(11), did INTEGER, since DATE, PRIMARY KEY (ssn, did), FOREIGN KEY (ssn) REFERENCES Employees, FOREIGN KEY (did) REFERENCES Departments)
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Translating Ternary Relationship Translating Ternary Relationship SetSet
Works_In0(ssn:integer,did:integer,address:string)
CREATE TABLE Works_In0(ssn CHAR(11),
did INTEGER, address CHAR(60), PRIMARY KEY (ssn, did, address),FOREIGN KEY (ssn) REFERENCES Employees,FOREIGN KEY (did) REFERENCES Departments,FOREIGN KEY (address) REFERENCES Locations)
Works-In0 Departments
dnamedid
Locationsaddress Capacity
dbudget
Employees
salaryname
ssnrank
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Review: Key ConstraintsReview: Key Constraints
Each dept has at most one manager, according to the key constraint on Manages.
Translation to relational model?
Many-to-Many1-to-1 1-to Many Many-to-1
dname
budgetdid
since
lot
name
ssn
ManagesEmployees Departments
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Translating ER Diagrams with Key Translating ER Diagrams with Key ConstraintsConstraints
Map relationship to a table:– Note that did is the
key now!– Separate tables for
Employees and Departments.
Since each department has a unique manager, we could instead combine Manages and Departments.
CREATE TABLE Manages( ssn CHAR(11), did INTEGER, since DATE, PRIMARY KEY (did), FOREIGN KEY (ssn) REFERENCES Employees, FOREIGN KEY (did) REFERENCES Departments)
CREATE TABLE Dept_Mgr( did INTEGER, dname CHAR(20), budget REAL, ssn CHAR(11), since DATE, PRIMARY KEY (did), FOREIGN KEY (ssn) REFERENCES Employees)
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Review: Participation Review: Participation ConstraintsConstraints
Does every department have a manager?– If so, this is a participation constraint: the participation of
Departments in Manages is said to be total (vs. partial). Every did value in Departments table must appear in a row
of the Manages table (with a non-null ssn value!)
lot
name dnamebudgetdid
sincename dname
budgetdid
since
Manages
since
DepartmentsEmployees
ssn
Works_In
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Participation Constraints Participation Constraints in SQLin SQL
We can capture participation constraints involving one entity set in a binary relationship, but little else (without resorting to CHECK constraints).
CREATE TABLE Dept_Mgr( did INTEGER,
dname CHAR(20), budget REAL, ssn CHAR(11) NOT NULL, since DATE, PRIMARY KEY (did), FOREIGN KEY (ssn) REFERENCES Employees, ON DELETE NO ACTION)
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Participation ConstraintsParticipation Constraints Is it possible to express this participation constraint using
only key and foreign key constraints?
Works_for( ssn: integer, pid: integer, hours: float)
Works_For Projects
pid pnamehours
Employees
salary
name
ssn
rank
CREATE TABLE Works_for(ssn INTEGER, pid INTEGER, hours float,PRIMARY KEY (ssn,pid),FOREIGN KEY (ssn) REFERENCES Employees,FOREIGN KEY (pid) REFERENCES Projects)
NO
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Review: Weak EntitiesReview: Weak Entities A weak entity can be identified uniquely only by
considering the primary key of another (owner) entity.– Owner entity set and weak entity set must
participate in a one-to-many relationship set (1 owner, many weak entities).
– Weak entity set must have total participation in this identifying relationship set.
lot
name
agepname
DependentsEmployees
ssn
Policy
cost
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Translating Weak Entity Translating Weak Entity SetsSets
Weak entity set and identifying relationship set are translated into a single table.– When the owner entity is deleted, all owned
weak entities must also be deleted.
CREATE TABLE Dep_Policy ( pname CHAR(20), age INTEGER, cost REAL, ssn CHAR(11), PRIMARY KEY (pname, ssn), FOREIGN KEY (ssn) REFERENCES Employees, ON DELETE CASCADE)
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Review: ISA HierarchiesReview: ISA Hierarchies
Contract_Emps
namessn
Employees
lot
hourly_wages
ISA
Hourly_Emps
contractid
hours_worked
As in C++, or other PLs, attributes are inherited.If we declare A ISA B, every A entity is also considered to be a B entity.
Overlap constraints: Can Joe be an Hourly_Emps as well as a Contract_Emps entity? (Allowed/disallowed)
Covering constraints: Does every Employees entity also have to be an Hourly_Emps or a Contract_Emps entity? (Yes/no)
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Translating ISA Hierarchies Translating ISA Hierarchies to Relationsto Relations
General approach:– 3 relations: Employees, Hourly_Emps and Contract_Emps.
Hourly_Emps: Every employee is recorded in Employees. For hourly emps, extra info recorded in Hourly_Emps (hourly_wages, hours_worked, ssn); must delete Hourly_Emps tuple if referenced Employees tuple is deleted).
Queries involving all employees easy, those involving just Hourly_Emps require a join to get some attributes.
Alternative: Just Hourly_Emps and Contract_Emps.– Hourly_Emps: ssn, name, lot, hourly_wages, hours_worked.– Each employee must be in one of these two subclasses.
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Translating ISA Hierarchies Translating ISA Hierarchies to Relationsto Relations
General approach:
CREATE TABLE Hourly_Emps ( hourly_wages REAL, hours_worked REAL, ssn CHAR(11), PRIMARY KEY (ssn), FOREIGN KEY (ssn) REFERENCES Employees, ON DELETE CASCADE)
Similarly for Contract_Emps TABLE
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Translating AggregationsTranslating Aggregations
Monitors until
SponsorsDepartments
dbudget
Projects
dname
did pid pnamesince
Employees
salary
name
ssn
rank
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Translating AggregationsTranslating Aggregations
Sponsors(did, pid, since)
Monitors(ssn, did, pid,until)
CREATE TABLE Sponsors(did INTEGER,
pid INTEGER,since DATE,
PRIMARY KEY (did,pid),FOREIGN KEY (did) REFERENCES Departments,FOREIGN KEY (pid) REFERENCES Projects)
CREATE TABLE Monitors(ssn INTEGER,did INTEGER,
pid INTEGER,until DATE,
PRIMARY KEY (ssn, did, pid),FOREIGN KEY (did,pid) REFERENCES Sponsors,FOREIGN KEY (ssn) REFERENCES Employees)
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Translating AggregationsTranslating Aggregations
If: Every sponsored project has a monitor, and
the attribute “since” is not required for Sponsors ….
Every possible instance of the Sponsors relationship is obtained by looking at the set of pairs <pid,did> in the relation Monitors
Therefore, we can omit the Sponsors relationrelation
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Review: Binary vs. Review: Binary vs. Ternary RelationshipsTernary Relationships
If each policy is owned by just 1 employee:– Key constraint
on Policies would mean policy can only cover 1 dependent!
What are the additional constraints in the 2nd diagram?
agepname
DependentsCovers
name
Employees
ssn lot
Policies
policyid cost
Beneficiary
agepname
Dependents
policyid cost
Policies
Purchaser
name
Employees
ssn lot
Bad design
Better design
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Binary vs. Ternary Binary vs. Ternary Relationships (Contd.)Relationships (Contd.)
The key constraints allow us to combine Purchaser with Policies and Beneficiary with Dependents.
Participation constraints lead to NOT NULL constraints.
CREATE TABLE Policies ( policyid INTEGER, cost REAL, ssn CHAR(11) NOT NULL, PRIMARY KEY (policyid), FOREIGN KEY (ssn) REFERENCES Employees, ON DELETE CASCADE)
CREATE TABLE Dependents ( pname CHAR(20), age INTEGER, policyid INTEGER, PRIMARY KEY (pname, policyid), FOREIGN KEY (policyid) REFERENCES Policies, ON DELETE CASCADE)
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Relational Model: Relational Model: SummarySummary
A tabular representation of data. Simple and intuitive, currently the most widely
used. Integrity constraints can be specified by the
DBA, based on application semantics. DBMS checks for violations. – Two important ICs: primary and foreign keys– In addition, we always have domain constraints.
Powerful and natural query languages exist. Rules to translate ER to relational model
