Κεφάλαιο 4

YV - Relational Calculus, SQL, QBE 1

Κεφάλαιο 4

Η Γλώσσα SQL και Σχεσιακός Λογισμός


Relational Calculus: Introduction

The Relational Calculus (RC) is a non-procedural, formal language based on first-order predicate calculus

Queries in RC specify WHAT is to be retrieved (declarative) while the system takes care of HOW

Most commercial relational languages are based on relational calculus (QUEL, QBE, and SQL). Such languages emphasize ease and convenience of use.

In terms of expressiveness, RELATIONAL ALGEBRA and RELATIONAL CALCULUS are identical.


Relational Calculus: Introduction (2)

The Relational Calculus uses the notion of VARIABLE There are two flavors of the language:

– tuple calculusvariables refer to tuples from a specified relatione.g., t is a tuple variable referring to a tuple of r(R)

– domain calculusvariables refer to individual values from a specified domain e.g., d is a domain variable referring to the value which a tuple in r(R) has for attribute A (from domain D)


Tuple Calculus

A TUPLE CALCULUS EXPRESSION defines a new relation in terms of existing (base) relations.

An expression is constructed from the following elements:(1) tuple variables (e.g., t, v, w, t1, t2, t3, ... tn ), which are defined

to range over a specified relation instance r(R)Tuple variables may be restricted, where, t.A, with A an attribute of R, denotes the A-component of the value of t Example: t.Name

(2) conditions of the form x operator y, where-- x, y are restricted tuple variables or constant values -- operator

Examples: t.Name = ‘mary’, t.City v.City


Tuple Calculus Expressions

(3) Well-Formed Formulas (WFFs), defined as:a condition is a WFFif f is a WFF, so is (f) and (f) (where is the logical NOT)if f and g are WFFs, so are (f g) and (f g) (where are the logical AND, OR respectively)if f is a WFF with free variable t, so are t(f), t(f) (where , are the existential and universal quantifiers)

A tuple variable t is said to be bound in a formula f if it is one of the quantified variables in f. Otherwise, t is free in f.Example: t is free in f1 : (t.City = ‘london’) and is bound in f2

: (t ) (t.DNumber = v.Dno), while v is free in f2


Tuple Calculus Expressions

Examples of WFFs– t.City = v.City– (t.City = v.City)– (t.City = v.City)– (t.City v.City)– (t.City = v.City) (w.City = london)– t (t.City = v.City)– t (t.City = athens)

if f is a WFF, then a tuple calculus expression is any expression of the form:

{ ti.Aj | ti r(Rk) AND f }where Rk are relation schemes and Aj are attributes in Rk


Calculus Query Examples

Recall the sailors-boats database

SAILORS (Sid, SName, Rating)BOATS (Bid, BName, Color)RESERVE (Sid, Bid, Date)

QUERY1: Find the names of sailors whose id is greater than 10 and have rating ‘a’

RANGE of t is SAILORSt.SName where (t.Sid > 10) (t.Rating = ‘a’)This is an equivalent form of the pure RC query:{ t.SName | t r(SAILORS) (t.Sid > 10) (t.Rating = ‘a’)) }


Calculus Query Examples (2)

QUERY2: Find the names and ratings of sailors who have reserved boat number 3

RANGE of t is SAILORSRANGE of v is RESERVE t.SName, t.Rating where v ( (t.Sid = v.Sid) v.Bid = 3) )

QUERY3: Find the names sailors who have not reserved boat number 3

RANGE of t is SAILORSRANGE of v is RESERVE t.SName where ( v ( (t.Sid = v.Sid) v.Bid = 3) ) )


SQL - Introduction

SQL (Structured Query Language) has become the “standard” in query languages. It was first used in IBM’s prototype , called SYSTEM-R, developed at San Jose in the mid-seventies. SQL has gone over many evaluations.

There are 4 basic commands:– select (not to be confused with SELECTION in algebra)– insert– update– delete

The result of any query on relations is again a relation


SQL - Informal Definition

Assume the EMPLOYEE relation and the following query: “Find the names of employees who earn more than 30000” This is expressed in SQL as:

select e.Namefrom EMPLOYEE ewhere (e.Salary > 30000)

– e is a tuple variable defined to range over the relation EMPLOYEE (in the from clause)

– e.Name, as a restricted tuple variable, specifies the value of e in attribute Name, and is the target list (specifies in the select clause the projections of columns)

– (e.Salary > 30000) is the qualification (specifies in the where clause all selections and joins)


SQL -- Formal Definition

A selection clause is a comparison between a restricted tuple variable x and a constant c of the form : x operator c where operator Example: t.Name = ‘mary’, t.Salary

A join clause is a comparison between two restricted tuple variables x and y of the form x operator y where x, y belong to different relations and

operator Example: t.Name = v.EName


SQL -- Formal Definition (2)

A qualification is a Boolean combination (i.e., with logical and, or, not) of selection and join clauses.)Example: (t.Name = v.EName) and (t.Salary > 30000)

QUALIFICATION SEMANTICSA qualification Q describes the subset of the Cartesian product of the ranges of its tuple variables that satisfy Q

Example: Consider relations: EMPLOYEE(SSN, DNumber), and DEPARTMENT(Dno, mgrSSN), with e and d tuple variables

Q = (e.DNumber = d.Dno) and (d.mgrSSN = 9876)

Semantics of Q: The set of e, d pairs that satisfy Q


SQL Qualification Semantics

.SSN DNumber1234 59998 49876 4

Dno MgrSSN5 33344 98761 8886

X =

SSN DNumber Dno mgrSSN1234 5 5 33441234 5 4 98761234 5 1 88869998 4 5 33449998 4 4 98769998 4 1 88869876 4 5 33449876 4 4 98769876 4 1 8886

SSN DNumber Dno mgrSSN9998 4 4 98769876 4 4 9876

Finally, after establishing the subsetof EMPLOYEE X DEPARTMENTthat satisfies the qualification Q, weget two tuples:

Cartesian Product

EMPLOYEE DEPARTMENT


SQL -- Complete Format

select [ distinct ] target_list from tuple_variable_list[ where qualification ][ group by grouping_attributes ][ having group_condition ][ order by target_list_subset ]

– A query is evaluated by first applying the WHERE clause, then GROUP-BY and HAVING (all optional), and finally the SELECT clause (target list) - ordering the resulting tuples if required in the ORDER BY clause (also optional).


SQL: Sailor Examples

Consider again the Sailors-Boats database:

SAILORS (Sid, SName, Rating)BOATS (Bid, BName, Color)RESERVE (Sid, Bid, Date)

SQUERY1: Find the names of sailors who have reserved boat number 2select s.SNamefrom SAILORS s, RESERVE rwhere s.Sid = r.Sid and r.Bid = 2


SQL Sailor Examples (2)

SQUERY2: Find the names of sailors who have reserved a red boatselect s.SNamefrom SAILORS s, BOATS b, RESERVE rwhere s.Sid = r.Sid and r.Bid = b.Bid and b.Color = “red”

SQUERY3: Find the colors of the boats reserved by eleniselect b.Colorfrom SAILORS s, BOATS b, RESERVE rwhere s.Sid = r.Sid and r.Bid =b.Bid and s.SName= “eleni”



SQUERY4: Find the names of the sailors who have reserved at least one boatselect s.SNamefrom SAILORS s, RESERVE rwhere s.Sid = r.Sid

SQUERY5: Find the names of sailors who have reserved a red or a green boatselect s.SName from SAILORS s, BOATS b, RESERVE rwhere s.Sid = r.Sid and r.Bid = b.Bid and

(b.Color = “red” or b.Color = “green”)



SQUERY6: Find the names of sailors who have reserved both a red and a green boat

select s.SName from SAILORS s, BOATS b1, RESERVE r1,

BOATS b2, RESERVE r2where s.Sid = r1.Sid and r1.Bid = b1.Bid and

b1.Color = “red” and s.Sid = r2.Sid and r2.Bid = b2.Bid and

b2.Color = “green”


SQL Elaboration: Examples from the COMPANY database

EMPLOYEE ( SSN, Name, BirthDate, Address, Sex, Salary, SupSSN, DNumber)

DEPARTMENT ( DNumber, DName, MgrSSN, MgrStartDate)

PROJECT ( PNumber, PName, Location, DNumber)

DEPT_LOCATION ( DNumber, DLocation)

WORKS_ON ( SSN, PNumber, HoursPW)

DEPENDENT ( SSN, DependName, Sex, BirthDate, Relationship)


SQL: Target List Examples (1)

TARGET LISTS: Each item in a target list can be as general as: attribute_name = expressionwhere expression is any arithmetic or string expression over restricted tuple variables and constants (also built-ins and aggregates.)

CQUERY1: List, increased by 10000 the salary of employees who have worked on two different projects more than 25 hours select e.Name, Salary = e.Salary + 10000from EMPLOYEE e, WORKS_ON w1, WORKS_ON w2where e.SSN = w1.SSN and e.SSN = w2.SSN and

w1.HoursPW > 25 and w2.HoursPW > 25 and w1.PNumber != w2.PNumber



TARGET Lists may also contain the keyword DISTINCT– Since SQL does not treat relations as sets, duplicate tuples may

appear, therefore DISTINCT is used to eliminate the duplicates

CQUERY2: Show all distinct (different values) salaries that employees earn

select distinct e.Salary from EMPLOYEE e

The above query also shows that the WHERE clause is optional (with missing WHERE, all tuples qualify)



The TARGET List may contain the wild character: “*”When a * is used, it implies that all attributes from the relation(s) should be retrieved

CQUERY3: Show all employees in department number 4

select * from EMPLOYEE ewhere e.Dnumber = 4


SQL: Use of Tuple Variables

Relation names can be used instead of tuple variables Tuple variables can be implicit if the system can figure

out which relation each attribute belongs to.

CQUERY4: For every project located in Athens, list the project name, the controlling department number and the department’s manager name

select PName, DEPARTMENT.DNumber, Name from EMPLOYEE, DEPARTMENT, PROJECTwhere PROJECT.DNumber = DEPARTMENT.DNumber

and MgrSSN = SSN and Location = “athens”


SQL Qualification Examples -1

QUALIFICATIONS: Each item in a qualification can be as general as: expression = expression

CQUERY5: Find the names of employees whose salary is more than double the salary of some other employee (also show their name)

select Name1 = e1.Name, Name2 = e1.Namefrom EMPLOYEE e1, EMPLOYEE e2 where 2 * e1.Salary < e2.Salary



SQL provides direct support of several SET operations, like:– union– minus– intersect

CQUERY6: Find the names of employees who work in department number 4 and earn at most 40000

(select Name from EMPLOYEE where DNumber = 4 ) minus

(select Name from EMPLOYEE where Salary > 40000 )



CQUERY7: List all project names for projects that involve an employee whose name is “jenny” as a worker or as a manager of the department that controls the project

(select PName from EMPLOYEE, PROJECT, DEPARTMENT where EMPLOYEE.DNumber=DEPARTMENT.DNumber and MgrSSN = SSN and Name = “jenny” ) union (select PName from EMPLOYEE, PROJECT, WORKS_ON where PROJECT.PNumber = WORKS_ON.PNumber and WORKS_ON.SSN=EMPLOYEE.SSN and Name = “jenny” )


SQL Qualification Examples-4

NESTING OF SQL QUERIES: A complete SELECT query (called the nested query) can be specified in the qualification of another query (called the outer query)

CQUERY8: List all employees that work in the research departmentselect Name from EMPLOYEE where DNumber in

(select DNumber from DEPARTMENT where DName = “research” )



CORRELATED NESTED Queries: If a condition in the qualification of a nested query references an attribute in the outer query, the two are said to be CORRELATEDThe result of the nested query is different for each tuple of the relation(s) in the outer query

CQUERY9: List the name of each employee who has a dependent with the same sex as the employee

select Name from EMPLOYEE e where e.SSN in

(select d.SSN from DEPENDENT d where d.SSN = e.SSN and d.Sex = e.Sex )



Any query that uses the IN comparison operator (tests for set membership) can always be expressed as a single block query (flat query)

CQUERY9a: List the name of each employee who has a dependent with the same sex as the employee

select Name from EMPLOYEE e, DEPENDENT d where e.SSN = d.SSN and d.Sex = e.Sex )



Similar connectives to IN are:not in (tests for set non-membership)

OP any (OP relationship with some tuple in a set)OP all (OP relationship with all tuples in a set)where OP

CQUERY10: List all employees that earn more than everybody in the research department

select Name fromEMPLOYEE

where Salary > all (select Salary from EMPLOYEE e, DEPARTMENT d where e.DNumber = d.DNumber and DName = “research” )



SQL also provides SET COMPARATORS:– contains, not contains (a set (not) being a superset)– exists, not exists (a set (not) being empty)

CQUERY11: List all employees who work on all projects controlled by department number 4select Name from EMPLOYEE ewhere (select w.PNumber from

WORKS_ON where w.SSN = e.SSN) contains (select PNumber from PROJECT where DNumber = 4)



CQUERY9b: List the name of each employee who has a dependent with the same sex as the employee select Name from

EMPLOYEE e whereexists (select * fromDEPENDENT d where d.SSN=e.SSN and d.Sex = e.Sex)

CQUERY12: List the employees with no dependents select Name from

EMPLOYEE e where not exists (select * from DEPENDENT d where d.SSN=e.SSN )


SQL Aggregates and Groups-1

SQL supports FIVE AGGREGATE FUNCTIONS (can be applied to any attribute X of a relation):

count ( [DISTINCT] X) :number of unique values in Xsum ( [DISTINCT] X) :sum of unique values in X

avg ( [DISTINCT] X) :average of unique values in Xmax (X) :maximum value in Xmin (X) :minimum value in X

Aggregates return a single value



Some SQL implementations do not allow more than one value in the target list

CQUERY13: List the maximum salary, the minimum salary, and the average salary among all employees

select max(Salary), min(Salary), avg(Salary from EMPLOYEE

QUERY14: Find the number of employees

select count(*) from EMPLOYEE



Qualified Aggregates: The set on which aggregates apply can be restricted by the where-clause

CQUERY15: Find the average salary of employees in department with number 4

select avg(Salary)from EMPLOYEEwhere DNumber = 4



Aggregate Functions: Aggregates or groups of tuples are computed using the GROUP BY clause

CQUERY16: In each department, find the minimum age of employees who earn more than 40000

select DNumber, max(BirthDate)from EMPLOYEEwhere Salary > 40000group by DNumber

– Note that the grouping attributes MUST ALSO appear in the select clause



CQUERY17: For each project, retrieve the project number, project name, and the number of employees that work on that project

select p.PNumber, p.PName, count(*)from PROJECT p, WORKS_ON wwhere p.PNumber = w.PNumbergroup by PNumber, PName

In the above query, the grouping and functions are applied after joining the relations PROJECT and WORKS_ON.



HAVING CLAUSE: Qualifications that have to be satisfied by each group formed by the group by- clause are put in a HAVING clause

CQUERY18: Find the average salary of employees born after 1950 for each department with more than 10 such employees

select DNumber, avg(Salary)from EMPLOYEEwhere BirthDate > “1.1.51”group by DNumberhaving count(*) > 10



CQUERY19: Find the average salary of employees born after 1950 for each department with more than 10 employees

select e1.DNumber, avg(e1.Salary)from EMPLOYEE e1where e1.BirthDate > “1.1.51”group by e1.DNumberhaving 10 < any

(select count(e2.SSN) from EMPLOYEE e2 where e2.DNumber = e1.DNumber )


SQL Updates (1)

INSERT command

insert into relation_name select-statementor

insert into relation_name values (value_list)

CUPDATE1: Insert a new department

insert into DEPARTMENT values (6, “inventory”, 9879, “30.5.45”)


SQL Updates (2)

Suppose we have a relation DEPT_INFO as in:DEPT_INFO ( DeptName, NoOfEmpl, TotalSalary)

We can insert tuples in this relation with (CUPDATE2):

insert into DEPT_INFO select d.DName, count(*), sum(e.Salary)

from DEPARTMENT d, EMPLOYEE e where d.DNumber=e.DNumber

group by d.DName


SQL Updates (3)

DELETE command

delete from relation_name where-qualification

SEMANTICS:-- Execute the corresponding SELECT command and then

remove the resulting tuples from relation_name

CUPDATE3:

delete from EMPLOYEEwhere DNumber in (select DNumber

from DEPARTMENT where DName = “admin”)


SQL Updates (4)

UPDATE commandupdate relation_name set target_listwhere qualification

SEMANTICS:-- Execute the two corresponding SELECT commands, then

remove the old tuples from relation, then insert the new ones

CUPDATE4: update EMPLOYEEset Salary = Salary * 1.14where DNumber in (select DNumber

from DEPARTMENT where DName = “admin”)

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