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YV - Relational Calculus, SQL, QBE 1
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Η Γλώσσα SQL και Σχεσιακός Λογισμός
YV - Relational Calculus, SQL, QBE 2
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.
YV - Relational Calculus, SQL, QBE 3
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)
YV - Relational Calculus, SQL, QBE 4
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
YV - Relational Calculus, SQL, QBE 5
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
YV - Relational Calculus, SQL, QBE 6
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
YV - Relational Calculus, SQL, QBE 7
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’)) }
YV - Relational Calculus, SQL, QBE 8
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) ) )
YV - Relational Calculus, SQL, QBE 9
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
YV - Relational Calculus, SQL, QBE 10
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)
YV - Relational Calculus, SQL, QBE 11
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
YV - Relational Calculus, SQL, QBE 12
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
YV - Relational Calculus, SQL, QBE 13
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
YV - Relational Calculus, SQL, QBE 14
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).
YV - Relational Calculus, SQL, QBE 15
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
YV - Relational Calculus, SQL, QBE 16
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”
YV - Relational Calculus, SQL, QBE 17
SQL Sailor Examples (3)
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”)
YV - Relational Calculus, SQL, QBE 18
SQL Sailor Examples (4)
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”
YV - Relational Calculus, SQL, QBE 19
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)
YV - Relational Calculus, SQL, QBE 20
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
YV - Relational Calculus, SQL, QBE 21
SQL: Target List Examples (2)
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)
YV - Relational Calculus, SQL, QBE 22
SQL: Target List Examples (3)
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
YV - Relational Calculus, SQL, QBE 23
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”
YV - Relational Calculus, SQL, QBE 24
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
YV - Relational Calculus, SQL, QBE 25
SQL Qualification Examples -2
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 )
YV - Relational Calculus, SQL, QBE 26
SQL Qualification Examples -3
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” )
YV - Relational Calculus, SQL, QBE 27
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” )
YV - Relational Calculus, SQL, QBE 28
SQL Qualification Examples-5
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 )
YV - Relational Calculus, SQL, QBE 29
SQL Qualification Examples-6
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 )
YV - Relational Calculus, SQL, QBE 30
SQL Qualification Examples-7
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” )
YV - Relational Calculus, SQL, QBE 31
SQL Qualification Examples-8
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)
YV - Relational Calculus, SQL, QBE 32
SQL Qualification Examples-9
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 )
YV - Relational Calculus, SQL, QBE 33
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
YV - Relational Calculus, SQL, QBE 34
SQL Aggregates and Groups-2
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
YV - Relational Calculus, SQL, QBE 35
SQL Aggregates and Groups-3
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
YV - Relational Calculus, SQL, QBE 36
SQL Aggregates and Groups-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
YV - Relational Calculus, SQL, QBE 37
SQL Aggregates and Groups-5
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.
YV - Relational Calculus, SQL, QBE 38
SQL Aggregates and Groups-6
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
YV - Relational Calculus, SQL, QBE 39
SQL Aggregates and Groups-6
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 )
YV - Relational Calculus, SQL, QBE 40
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”)
YV - Relational Calculus, SQL, QBE 41
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
YV - Relational Calculus, SQL, QBE 42
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”)
YV - Relational Calculus, SQL, QBE 43
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”)