CM036: Advanced Database
Lecture 3 [Self Study]
Relational Algebra and SQL
3 Structured Query Language – SQL

A standard language for working with relational databases; mixture
of DDL, DML and DCL constructs

It is a specific database language, not general-purpose
programming language; all its constructs are primarily for
manipulating tables, rows, columns, database schemes and users not for direct processing of the data
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There are several SQL standards; among them SQL-92 (SQL2) and
SQL-99 (SQL3) are the most widely used, and SQL-92 is still
regarded up-to-date; Different vendors implement them to certain
levels of compliance – for example, Oracle 8i is SQL2 compliant,
while Oracle 9i is SQL3 compliant

SQL is purely declarative; procedural extensions of SQL exist, but
they are vendor-specific (e.g. Oracle PL/SQL, Microsoft Transact
SQL, Informix 4GL, etc.)
CM036: Advanced Databases
Lecture 3: Relational Languages
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3.1 SQL DML
For querying and manipulating relational databases; its constructs are
recognised by the first keyword - SELECT, INSERT, UPDATE or DELETE
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The SELECT statements implement the relational algebra
operations; All relational operations can be expressed in a standard
SQL implementation using SELECT statements only
INSERT statements are used to add tuples to the relations, defined
by the relational schema
DELETE statements exclude tuples from the relations
UPDATE change some of the attributes of the existing tuples
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Lecture 3: Relational Languages
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3.2 SELECT- statement

The general form of this statement in SQL is
SELECT <list-of-columns>
FROM <list-of-tables>
WHERE <conditions-on-the-tables>
The result from executing the statement is directed to the system output by
default. It corresponds to the following form
 <algebraic expression>
Example: The following statement
SELECT e.name, a.address
FROM EMP e, ADDR a
WHERE a.no = e.no
corresponds to the algebraic expression

 name,address(EMP * ADDR)
CM036: Advanced Databases
Lecture 3: Relational Languages
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3.2 SELECT- statement …

In some cases (e.g. in Oracle extended SQL), the query
result can be stored
SELECT <list-of-columns>
INTO <storage-place>
FROM <list-of-tables>
WHERE <conditions-on-the-tables>
In this case, the result is stored into <storage-place>
and the statement corresponds to the following algebraic
expression
<relation>  <algebraic expression>
where <relation> is the relation calculated as a result of
the expression
CM036: Advanced Databases
Lecture 3: Relational Languages
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3.2 SELECT- statement …

There are variations of these templates, which support the
implementation of relational operations through varying of different
clauses in the statement:
 SELECT clause can explicitly point at the required columns;
alternatively, it can contain special symbol *, which projects full
rows without skip of any columns in them
 FROM clause can contain more then one table, which allows to
implement both unary and binary operations
 WHERE clause in the statement can be used to restrict the rows
to be selected using additional conditions on the columns
 INTO clause, when present, points to a data storage which should
store the result from the query; it should have the same structure,
as the expected result
CM036: Advanced Databases
Lecture 3: Relational Languages
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3.3 Simulating RA operations

All relational algebra operations are simulated in SQL using SELECT
statements only. For this purpose the following variations of different
parameters in the SELECT clauses can be used:
 The list of attributes to be selected in the SELECT clause
 The number of tables to be looked into in the FROM clause
 The conditions specified in the WHERE clause
 The resulting relation given INTO clause is present

There is no structural correspondence between the expressions of
relational algebra and the SQL expressions; in a single SQL statement
the following combinations are possible:
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single unary operator applied to one single relation
single binary operator applied to pair of relations
sequence of unary operators applied inner side out to one relation
and all the intermediate results
combinations of binary and unary operators applied to several
relations and the intermediate results according nesting rules
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Lecture 3: Relational Languages
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Restriction and Projection

The SELECT statements of SQL when applied to one table only correspond to three
possible combinations of the relational algebra operators s (RESTRICT) and 
(PROJECT)
Examples:
 List of all student ids, names and addresses
SELECT StudentId, Name, Address
FROM Student
 StudentId, Name, Address (STUDENT)

Full information about the students in Business Computing
SELECT * FROM Student
WHERE CourseName = ‘Business Computing’
s CourseName = ‘Business Computing’(STUDENT)

List of ids and names for students in Business Computing
SELECT StudentId, Name FROM Student
WHERE CourseName = ‘Business Computing’
 StudentId, Name (s CourseName = ‘Business Computing’(STUDENT))
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Lecture 3: Relational Languages
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Cartesian Product
When applied to two tables simultaneously without WHERE clause,
the SELECT statements correspond to combinations of the unary
relational algebra operator  with the binary operator 
Examples:
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Full information about students and courses
SELECT * FROM Student, Course
STUDENT  COURSE

List of ids for both students and lecturers
SELECT StudentId, LecturerId,
FROM Student, Lecturer
 StudentId, LecturerId (STUDENT  LECTURER)
Note: When more than one tables are in a single SELECT statement, to
avoid ambiguity when referring to columns with the same names we
precede them with the names of respective tables.
• Names of all students and lecturers
SELECT STUDENT.Name, LECTURER.Name
FROM STUDENT, LECTURER
CM036: Advanced Databases
Lecture 3: Relational Languages
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Inner Joins
When applied to two tables simultaneously, the SELECT statements
with WHERE clause correspond to combination of the two unary
relational algebra operators s (RESTRICT) and  (PROJECT) with
proper binary operators
Examples:
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Full information about the students and their courses
SELECT *
FROM
Student, Course
WHERE
Student.Course = Course.Name
OR
SELECT *
FROM
Student INNER JOIN Course
ON
Student.Course = Course.Name
STUDENT ⋈ Course = Name COURSE
 List of student names with their course leaders
SELECT StudentName, CourseLeader
FROM Student NATURAL JOIN Course
 StudentName, CourseLeader(STUDENT * COURSE)
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Lecture 3: Relational Languages
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
Full information about students from Business computing with
details about the course
SELECT *
FROM Student INNER JOIN Course
ON Student.Course = Course.Name
WHERE Course.CourseName = ‘Business Computing’
s CourseName = ‘Business Computing’
(STUDENT ⋈ Course = Name COURSE)
Note: In order to avoid ambiguity when referring to columns from
different tables which have the same names, we should qualify
them explicitly in the WHERE clause. This can be done through
preceding their names with aliases of the respective tables.

The names of all unit leaders of current units together with the
names of the units themselves
SELECT l.Name, u.Name
FROM LECTURER l INNER JOIN UNIT u
ON u.Leader = l.Name WHERE u.Status = ‘Current’
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Lecture 3: Relational Languages
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Set Operations
The tuples returned as answers of two independent queries can be
combined in a single relation using the set operators  (UNION) - for the
union of two relations and  (DIFFERENCE or MINUS) - for the
difference between them
Examples: (using Oracle SQL Syntax)
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Full details for students in both Mathematics and Computing
SELECT * FROM Student
WHERE Course = ‘Computing’ UNION
SELECT * FROM Student
WHERE Course = ‘Mathematics’
s Course = ‘Computing’ (STUDENT)  s Course = ‘Mathematics’ (STUDENT)
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Full details for students in Computing after first year
SELECT * FROM Student
WHERE Course = ‘Computing’ MINUS
SELECT * FROM Student
WHERE Level = 1
s Course = ‘Computing’ (STUDENT)  s Level = 1 (STUDENT)
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Outer Joins (Oracle 8i)
Outer joins are not always directly expressible in the commercial
SQL implementations. But they can be modelled if needed
Examples: (using Oracle SQL syntax)
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List of unit leaders with their units, including leaders still without
assigned units
SELECT LecturerName, UnitName
FROM Lecturer, Unit
WHERE Lecturer.UnitName = Unit.UnitName (+)
LECTURER

UnitName = UnitName UNIT
List of units with their leaders, including units still without
appointed leaders
SELECT UnitName, LecturerName
FROM Lecturer, Unit
WHERE Lecturer.UnitName (+) = Unit.UnitName
LECTURER
CM036: Advanced Databases
UnitName = UnitName UNIT
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Combined list of units and leaders, including units without
leaders and leaders without units (full outer join)
SELECT Lecturer.UnitName, Unit.UnitName
FROM Lecturer, Unit
WHERE Lecturer.UnitName = Unit.UnitName(+) UNION
SELECT Lecturer.UnitName, Unit.UnitName
FROM Lecturer, Unit
WHERE Lecturer.UnitName (+) = Unit.UnitName
LECTURER
CM036: Advanced Databases
UnitName = UnitName UNIT
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Outer Joins (Oracle 9i)
Outer joins are not always directly expressible in the commercial
SQL implementations. But they can be modelled if needed
Examples: (using Oracle SQL syntax)


List of unit leaders with their units, including leaders still without
assigned units
SELECT LecturerName, UnitName
FROM Lecturer LEFT OUTER JOIN Unit
ON Lecturer.UnitName = Unit.UnitName
LECTURER

UnitName = UnitName UNIT
List of units with their leaders, including units still without
appointed leaders
SELECT UnitName, LecturerName
FROM Lecturer RIGHT OUTER JOIN Unit
WHERE Lecturer.UnitName = Unit.UnitName
LECTURER
CM036: Advanced Databases
UnitName = UnitName UNIT
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
Combined list of units and leaders, including units without
leaders and leaders without units (full outer join)
SELECT Lecturer.UnitName, Unit.UnitName
FROM Lecturer FULL OUTER JOIN Unit
ON Lecturer.UnitName = Unit.UnitName
LECTURER

UnitName = UnitName UNIT
When more than two tables are queried, the SQL operator
corresponds to combination of unary and binary operations
Examples: (using Oracle SQL syntax)

List of students in Computing after first year
SELECT StudentId, StudentName FROM Student
WHERE CourseName= ‘Computing’MINUS
SELECT StudentId, StudentName FROM Student
WHERE CourseLevel = 1
s CourseName = ‘Computing’ ( StudentId, StudentName (STUDENT))
 s CourseLevel = 1 ( StudentId, StudentName (STUDENT))
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Note: According to relational algebra theory, the relations do not
contain duplicated tuples. However, the result from an SQL query
could contain several identical rows. If we wish to have a true
relation as a result instead, the keyword DISTINCT should be
specified after SELECT to indicate eliminating of possible
duplications.

All units which have been subscribed by the students without
duplicates
SELECT DISTINCT e.Unit
FROM STUDENT s, ENROLMENT e
WHERE e.Student = s.Name
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Lecture 3: Relational Languages
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Summary
Relational Algebra
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Formal languages have unambiguous syntax and clear semantics,
which makes them good for specifications
Formal languages hide the details of implementation and can’t give
very deep insight into the real DBMS
Formal languages formalize adequately only part of the database
operations, which have semantics inherited from the relational
model; they do not cover DCL at al.
SQL
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SQL syntax is ambiguous about the order of operations, which
requires knowledge of the way it is interpreted
SQL is not a programming language, but language for
communication with DBMS and still can’t give very deep insight into
the real data processing
SQL as a mixture of DDL, DML and DCL is the ultimate choice for
practical relational databases
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Lecture 3: Relational Languages
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