3.5

Chapter 3.5 Programming Paradigms

3.5 Introduction

3.5 (a) Programming Paradigms
Programming paradigms are simply methods of programming. Initially, computers
were programmed using binary. This was difficult and led to many errors that were
difficult to find. Programs written in binary are said to be written in machine code,
this is a very low-level programming paradigm.

To make programming easier, assembly languages were developed. These replaced
machine code functions with mnemonics and addresses with labels. Assembly
language programming is also a low-level paradigm although it is a second generation
paradigm. Figure 3.5.a.1 shows an assembly language program that adds together two
numbers and stores the result.

Label Function Address Comments
LDA X Load the accumulator with the value of X
ADD Y Add the value of Y to the accumulator
STA Z Store the result in Z
STOP Stop the program
X: 20 Value of X = 20
Y: 35 Value of Y = 35
Z: Location for result

Figure 3.5.a.1

Although this assembly language is an improvement over machine code, it is still
prone to errors and code is difficult to debug, correct and maintain.

The next advance was the development of procedural languages. These are third
generation languages and are also known as high-level languages. These languages
are problem oriented as they use terms appropriate to the type of problem being
solved. For example, COBOL (Common Business Oriented Language) uses the
language of business. It uses terms like file, move and copy.

FORTRAN (FORmula TRANslation) and ALGOL (ALGOrithmic Language) were
developed mainly for scientific and engineering problems. Although one of the ideas
behind the development of ALGOL was that it was an appropriate language to define
algorithms. BASIC (Beginners All purpose Symbolic Instruction Code) was
developed to enable more people to write programs. All these languages follow the
procedural paradigm. That is, they describe, step by step, exactly the procedure that
should be followed to solve a problem.

The problem with procedural languages is that it can be difficult to reuse code and to
modify solutions when better methods of solution are developed. In order to address
these problems, object-oriented languages (like Eiffel, Smalltalk and Java) were
developed. In these languages, data and methods of manipulating the data, are kept as

4.5 - 1

a single unit called an object. The only way that a user can access the data is via the
object's methods. This means that, once an object is fully working, it cannot be
corrupted by the user. It also means that the internal workings of an object may be
changed without affecting any code that uses the object.

A further advance was made when declarative programming paradigms were
developed. In these languages the computer is told what the problem is, not how to
solve the problem. Given a database the computer searches for a solution. The
computer is not given a procedure to follow as in the languages discussed so far.

3.5 (b) Programming Paradigms and examples.
Procedural languages specify, exactly, the steps required to solve a problem. These
languages use the constructs: sequence, selection and repetition (see Section 1.3 in the
AS text). For example, to find the area of a rectangle the steps are

1. Read the length
2. Read the breadth
3. Multiply the length by the breadth
4. Output the result

In C++ this can be coded as

cout << "Enter the length: ";
cin >> Length;
cout << "Enter the breadth: ";
cin >> Breadth;
Area = Length * Breadth;
cout << "The area is "
<< Area << endl;

Here each line of code is executed one after the other in sequence.

Most procedural languages have two methods of selection. These are the IF …
THEN … ELSE statement and the SWITCH or CASE statement. For example, in
C++, we have

IF (Number > 0)
cout << "The number is positive.";
ELSE
{
IF (Number = = 0)
cout << "The number is zero.";
ELSE
cout << "The number is negative.";
}

4.5 - 2

In C++ multiple selections can be programmed using the SWITCH statement. For
example, suppose a user enters a single letter and the output depends on that letter, a
typical piece of code could be

switch (UserChoice)
{
case 'A':
cout << "A is for Apple.";
break;
case 'B':
cout << "B is for Banana.";
break;
case 'C':
cout << "C is for Cat.";
break;
default:
cout << "I don't recognise that letter.";
}

Repetition (or iteration) is another standard construct. Most procedural languages
have many forms of this construct such as

FOR … NEXT
REPEAT … UNTIL …
WHILE … ENDWHILE

A typical use of a loop is to add a series of numbers. The following pieces of C++
code add the first ten positive integers.

//Using a FOR loop
Sum = 0;
FOR (int i = 1; i <= 10; i++)
{
Sum = Sum + i;
}
cout << "The sum is "
<< Sum;

//Using a WHILE loop
Sum = 0;
i = 1;
while (i <= 10)
{
Sum = Sum + i;
i++;
}
cout << "The sum is "
<< Sum;

4.5 - 3

In procedural languages is that the programmer has to specify exactly what the
computer is to do.

Another programming paradigm is the declarative one. Declarative languages tell the
computer what is wanted but do not provide the details of how to do it. These
languages are particularly useful when solving problems in artificial intelligence such
as medical diagnosis, fault finding in equipment and oil exploration. The method is
also used in robot control. An example of a declarative language is Prolog. The idea
behind declarative languages is shown in Fig. 3.5.b.1.

User Search Engine Database

Fig. 3.5.b.1

Here the user inputs a query to the search engine, which then searches the database for
the answers and returns them to the user. For example, using Prolog, suppose the
database is

female(jane).
female(anne).
female(sandip).
male(charnjit).
male(jaz).
male(tom).

Note that in Prolog values start with a lowercase letter and variables start with an
uppercase letter. A user may want to know the names of all the males. The query

male(X).

will return

X = charnjit
X = jaz
X = tom

Notice that the user does not have to tell Prolog how to search for the values of X that
satisfy the query. This is fairly straightforward. However, suppose we now add to the
Prolog database the following data.

parent(jane,mary).
parent(jane, rajinder).
parent(charnjit, mary).
parent(charnjit, rajinder).
parent(sandip, atif).

4.5 - 4

parent(jaz, atif).

and suppose we wish to know the name of the mother of Atif. In Prolog we use the
query

parent(X, atif), female(X).

Prolog will output

X = sandip

Try writing a Visual Basic program to do this.

To get a list of all the fathers, we can simply write

parent(X, Y), male(X).

The result is

X = charnjit Y = mary
X = charnjit Y = rajinder
X = jaz Y = atif

If we only want a list of fathers we use the underscore and create the query

parent(X, _ ), male(X).
and the result is

X = charnjit
X = charnjit
X = jaz

3.5 (d) Standard Programming Techniques.

Let us consider how data can be input to a function or procedure. This is done by
means of parameters. The function below, written in Visual Basic, finds the perimeter
of a rectangle given its length and breadth. This is not the only way of finding the
perimeter and it probably is not the best way. However, it has been written like this in
order to illustrate certain programming points.

Public Function PerimeterOfRectangle(X As Integer, Y As Integer) As Integer

X=2*X
Y=2*Y
PerimeterOfRectangle = X + Y

End Function

4.5 - 5

In this function X and Y are integers the values of which must be passed to the
function before it can find the area of the rectangle. These variables are called formal
parameters. To use this function, another program will have to call it and provide the
values for X and Y. This can be done by means of a statement of the form

Perimeter = PerimeterOfRectangle(4, 6)

or we can use

A=3
B=4
Perimeter = PerimeterOfRectangle(A, B)

In both of these statements the variables inside the parentheses ( 4 and 6 in the first
example and A and B in the second) are called actual parameters.

Visual Basic is said to pass parameters by reference (or address) and C++ passes them
by value. It is interesting to see the effect of passing values by address. Here is the
function described above and a copy of the calling function in Visual Basic.

Public Function PerimeterOfRectangle(X As Integer, Y As Integer) As Integer

X=2*X
Y=2*Y

End Function

Private Sub cmdShow_Click()

Dim A As Integer
Dim B As Integer
Dim Perimeter As Integer

A=3
B=4

picResults.Print "Before call to Sub A = "; A; " and B = "; B
Perimeter = PerimeterOfRectangle(A, B)
picResults.Print "Perimeter = "; Perimeter
picResults.Print "After call to Sub A = "; A; " and B = "; B;

End Sub

Fig.3.5.d.3 shows the output when this program is run.

4.5 - 6

Fig.3.5.d.3

Notice that after the function has been run the values of A and B have changed. This
is because the addresses of A and B were passed not their actual values.

Visual Basic can pass parameters by value and C++ can pass parameters by reference.
In Visual Basic we have to use the ByVal key word if we want values to be passed by
value. Here is a modified form of the Visual Basic function together with the output
from running the modified program.

Public Function PerimeterOfRectangle(ByVal X As Integer, ByVal Y As
Integer) As Integer

X=2*X
Y=2*Y

End Function

Fig. 3.5.d.4

4.5 - 7

3.5 (f) Object-Oriented Programming (OOP)

Person Class name

name
Data
address

outputData( )
getName( ) Methods
getAddress( )

Fig. 3.5.f.2

Now suppose we want a class Employee that requires the same data and methods as
Person and also needs to store and output an employee's National Insurance number.
Clearly, we do not wish to rewrite the contents of the class person. We can do this by
creating a class called Employee that inherits all the details of the class Person and
adds on the extra data and methods needed. This is shown in Fig. 3.5.f.3 where the
arrow signifies that Employee inherits the data and methods provided by the class
Person. Person is called the super-class of Employee and Employee is the derived
class from Person. An object of type Employee can use the methods provided by
Employee and those provided by Person.

Person

name
address

outputData( )
getName( )
getAddress( )

Employee

NINumber

outputData( )
getNINumber( )

Fig. 3.5.f.3

4.5 - 8

Notice that we now have two methods with the same name. How does the program
determine which one to use? If myPerson is an instantiation of the Person class, then

myPerson.outputData( );

will use the outputData( ) method from the Person class. The statement

myEmp.outputData( );

will use the method outputData( ) from the Employee class if myEmp is an
instantiation of the Employee class.
The concept of a method having two different meanings is called polymorphism.
Now suppose we have two types of employee; one is hourly paid and the other is paid
a salary. Both of these require the data and methods of the classes Person and
Employee but they also need different data to one another. This is shown in Fig.
3.5.f.4.

Person

name
address

outputData( )
getName( )
getAddress( )

Employee

NINumber

outputData( )
getNINumber( )

HourlyPaidEmp SalariedEmp

hourlyRate salary

outputData( ) outputData( )
getHourlyRate( ) 4.5 - 9 getSalary( )

How can an object of type Employee output the name and address as well as the N.I.
number? The outputData( ) method in class Employee can refer to the outputData( )
method of its superclass. This is done by writing a method, in class Employee, of the
form

void outputData( ) {
super.outputData( );
System.out.println("The N.I. number is " + NINumber);
}//end of outputData method.

Here super. outputData( ) calls the outputData( ) method of the super-class and then
outputs the N.I. number. Similarly, the other derived classes can call the methods of
their super classes.
Definitions

Data encapsulation is the combining together of the variables and the methods that
can operate on the variables so that the methods are the only ways of using the
variables..

A class describes the variables and methods appropriate to some real-world entity.

An object is an instance of a class and is an actual real-world entity.

Inheritance is the ability of a class to use the variables and methods of a class from
which the new class is derived.

3.5 (g) Declarative Languages
In Section 4.5.1, we saw that, in declarative languages, the programmer can simply
state what is wanted having declared a set of facts and rules. We now look at how
this works using examples of Prolog scripts. In order to do this, we shall use the
following facts.

female(jane).
female(anne).
female(sandip).
male(charnjit).
male(jaz).
male(tom).
parent(jane,mary).

4.5 - 10

parent(jaz, atif).

Remember that variables must start with an uppercase letter; constants start with a
lowercase letter.

Suppose we ask
male(X).

Prolog starts searching the database and finds male(charnjit) matches male(X) if X is
given the value charnjit. We say that X is instantiated to charnjit. Prolog now
outputs

X = charnjit

Prolog then goes back to the database and continues its search. It finds male(jaz) so
outputs

X = jaz

and again continues its search. It continues in this way until the whole database has
been searched. The complete output is

X = charnjit
X = jaz
X = tom
No

The last line means that there are no more solutions.

The query male(X) is known as a goal to be tested. That is, the goal is to find all X
that satisfy male(X). If Prolog finds a match, we say that the search has succeeded
and the goal is true. When the goal is true, Prolog outputs the corresponding values of
the variables.

Now we shall add the rule

father(X, Y) :- parent(X, Y), male(X).

This rule states that X is father of Y if (the :- symbol) X is a parent of Y AND (the
comma) X is male.

The database now looks like this.

female(jane).
female(anne).
female(sandip).
male(charnjit).
male(jaz).
male(tom).
parent(jane,mary).

4.5 - 11

parent(jaz, atif).

Suppose our goal is to find the father of rajinder. That is, our goal is to find all X that
satisfy

father(X, rajinder).

In the database and the rule the components female, male, parent and father are called
predicates and the values inside the parentheses are called arguments. Prolog now
looks for the predicate father and finds the rule


In this rule Y is instantiated to rajinder and Prolog starts to search the data base for

parent(X, rajinder)

This is the new goal. Prolog finds the match

parent(jane, rajinder)

if X is instantiated to jane. Prolog now uses the second part of the rule

male(X)

with X = jane. That is, Prolog's new goal is male(jane) which fails. Prolog does not
give up at this stage but backtracks to the match

parent(jane, rajinder)

and starts again, from this point in the database, to try to match the goal

parent(X, rajinder)

This time Prolog finds the match

parent(charnjit, rajinder)

with X instantiated to charnjit. The next step is to try to satisfy the goal

male(charnjit)

This is successful so

parent(charnjit, rajinder) and male(charnjit)

4.5 - 12

are true. Thus father(charnjit, rajinder) is true and Prolog returns

X = charnjit

Prolog continues to see if there are any more matches. There are no more matches so
Prolog outputs

No

Definitions: Instantiation is giving a variable in a statement a value.

Predicate logic is a branch of mathematics that manipulates logical statements that
can be either True or False.

A goal is a statement that we are trying to prove whether or not it is True or False.

3.5 (i) Third and Fourth Generation Languages
Third generation languages are those that use a structured syntax such as C, C++ and
Pascal. Early versions of Fortran and BASIC were not structured and are usually
treated as second generation languages. However, Visual Basic is structured and can
be treated as a third generation language.

Third generation languages need the user to specify clearly all the steps that need to
be taken to solve a problem. Fourth generation languages do not do this. Languages
that accompany modern database, word processing and spreadsheet packages do not
need the user to do this. The users of these packages tell the application what they
want to do not how to do it. An example is mail merge . Here all the user has to do is
tell the software what table or database to use and the mail merge will take place.
Databases often use query by example (QBE). Here the user simply states what is
required and the software will do the task. For example, Microsoft Access lets a user
specify conditions such as DOB < 01/01/90 and the necessary coding will be done. In
fact Access uses the Structured Query Language (SQL) to create the queries.
Consider the following table called Students.

name height weight
Alan 150 31.2
Brenda 140 27.8
Charnjit 148 30.7
Dalvinder 152 32.8
Elmira 143 28.1
Frank 158 33.4
Georgina 151 28.2
Now suppose we wish to find the names of all those students who have a height
greater than 150. In Access we could simply create a query with columns for name
and height and in the height column we would write

> 150

4.5 - 13

for the criteria. We could also specify, by means of a check box, that only the name
should be printed. The result would be

Dalvinder
Frank
Georgina

In fact, we can write the query in SQL as

SELECT name
FROM Students
WHERE height > 150;

This is what Access does.

Notice that we do not have to give the steps needed to check each entry in the table
Students. A more complicated query is

SELECT name
FROM Students
WHERE height > 145
AND
weight > 32;

Again, we do not tell the computer exactly how to find the answer required as we
would with a third generation language.

The development of fourth generation languages has meant that people who are not
programmers can produce useful results.

3.5 (j) Backus Naur Form and Syntax Diagrams
Since all programming languages have to be translated to machine code by means of a
computer, they must be clearly defined. Each statement must be of a prescribed form.
An example of the start of a FOR loop in Visual Basic is

For count = 1 To 10

but C++ expects

for (count = 1, count <= 10, count++)

A Visual Basic compiler would not understand the C++ syntax and vice versa. We
therefore need, for each language, a set of rules that specify precisely every part of the
language. These rules are specified using Backus Naur Form (BNF) or syntax
diagrams.

All languages use integers, so we shall start with the definition of an integer. An
integer is a sequence of the digits 0, 1, 2, … , 9. Now the number of digits in an

4.5 - 14

integer is arbitrary. That is, it can be any number. A particular compiler will restrict
the number of digits only because of the storage space set aside for an integer. But a
computer language does not restrict the number of digits. Thus the following are all
valid integers.

0
2
415
3040513002976
0000000123

Thus, an integer can be a single digit. We can write this as

<integer> ::= <digit>

This is read 'an integer is defined to be (::=) a digit'.

But we must now define a digit. A digit is 0 or 1 or 2 or … or 9 and we write this as

<digit> ::= 0|1|2|3|4|5|6|7|8|9

where the vertical line is read as OR. Notice that all the digits have to be specified and
that they are not inside angle brackets (< and >) like <integer> and <digit>. This is
because integer and digit have definitions elsewhere; the digits 0, 1, 2, … , 9 do not.

Our full definition of a single digit integer is

<integer> ::= <digit>
<digit> ::= 0|1|2|3|4|5|6|7|8|9

This is called Backus Naur Form (BNF).
But how are we going to specify integers of any length? Consider the integer

147

This is a single digit integer ( 1 ) followed by the integer 47. But 47 is a single digit
integer ( 4 ) followed by a single digit integer ( 7 ). Thus, all integers of more than
one digit start with a single digit and are followed by an integer. Eventually the final
integer is a single digit integer. Thus, an indefinitely long integer is defined as

<integer> ::= <digit><integer>

This is a recursive definition as integer is defined in terms of itself. Applying this
definition several times produces the sequence

<integer> ::= <digit><integer>

=<digit><digit><integer>

4.5 - 15

=<digit><digit><digit><integer>

To stop this we use the fact that, eventually, <integer> is a single digit and write

<integer> ::= <digit>|<digit><integer>

That is, <integer> is a <digit> OR a <digit> followed by an <integer>. This means
that at any time <integer> can be replaced by <digit> and the recursion stops. Strictly
speaking we have defined an unsigned integer as we have not allowed a leading plus
sign ( + ) or minus sign ( - ). This will be dealt with later. We now have the full
definition of an unsigned integer which, in BNF, is

<unsigned integer> ::= <digit>|<digit><unsigned integer>
<digit> ::= 0|1|2|3|4|5|6|7|8|9

This definition of an unsigned integer can also be described by means of syntax
diagrams as shown in Fig. 3.5.k.1.

integer digit
digit 0

1

2

3

4

5

6

7

8

9

Fig. 3.5.j.1

Now we shall define a signed integer such as

+27
-3415

4.5 - 16

This is simply an unsigned integer preceded by a + or – sign. Thus

<signed integer> ::= + <unsigned integer>| - <unsigned integer>

and we can use the earlier definition of an <unsigned integer>. It is usual to say that
an integer is an unsigned integer or a signed integer. If we do this we get the
following definition, in BNF, of an integer.

<integer> ::= <unsigned integer>|<signed integer>
<signed integer> ::= + <unsigned integer>| - <unsigned integer>
<unsigned integer> ::= <digit>|<digit><unsigned integer>
<digit> ::= 0|1|2|3|4|5|6|7|8|9

There are other valid ways of writing these definitions. However, it is better to use
several definitions than try to put all the possibilities into a single definition. In other
words, try to start at the top with a general definition and then try to break the
definitions down into simpler and simpler ones. That is, we have used top-down
design when creating these definitions. We have broken the definitions down until we
have terms whose values can be easily determined.

Fig. 3.5.j.2 shows the corresponding syntax diagrams.

integer
digit
+

-

digit
0

1

2

3

4

5

6

7

8

9

4.5 - 17

Care must be taken when positioning the recursion in the definitions using BNF.
Suppose we define a variable as a sequence of one or more characters starting with a
letter. The characters can be any letter, digit or the underscore. Valid examples are

A
x
sum
total24
mass_of_product
MyAge

Let us see what happens if we use a similar definition to that for an unsigned integer.

<variable> ::= <letter>|<character><variable>
<character> ::= <letter>|<digit>|<under-score>

Now 2Sum is valid as we use

<character><variable>

with <character> = 2 and <variable> = Sum. Continuing in this way we use 2, S and
u for <character> and then m for <letter>. This means that our definition simply
means that we must end with a letter not start with one. We must rewrite our
definition in such a way as to ensure that the first character is a letter. Moving the
recursive call to the front of <character> can do this. This means that the last time it
is called it will be a letter and this will be at the head of the variable. The correct
definition is

<variable> ::= <letter>|<variable><character>
<character> ::= <letter>|<digit>|<under-score>
<letter> ::= <uppercase>|<lowercase>
<uppercase> ::= A|B|C|D|E|F|G|H|I|J|K|ZL|M|N|O|P|Q|R|S|T|U|V|W|X|Y|Z
<lowercase> ::= a|b|c|d|e|f|g|h|i|j|k|zl|m|n|o|p|q|r|s|t|u|v|w|x|y|z
<digit> ::= 0|1|2|3|4|5|6|7|8|9
<under-score> ::= _

A syntax diagram can also represent this. This is left as an exercise. You should also
note that, in the definition of integer, we used tail recursion, but here we have used
head recursion.

Let us now use our definition of an integer to define a real number such as

0.347
-2.862
+14.34
00235.006

The result is very simple, it is

<real number> ::= <integer> . <unsigned integer>

4.5 - 18

Finally, suppose we do not want to allow leading zeros in our integers. That is

00135 is not allowed
0 is allowed.

This means that an integer can be a

zero digit
non-zero digit
non-zero digit followed by any digit.
This means that an integer is

zero or digits
where digits must start with a non-zero digit. In BNF, this is

<integer> ::= <zero>|<digits>

<digits> must be a single non-zero digit or a non-zero digit followed by any digits.
This gives us
<digits> ::= <non-zero digit>|<digits><digit>

where
<zero> ::= 0
<non-zero integer> ::= 1|2|3|4|5|6|7|8|9
<digit> ::= <zero>|<non-zero digit>

Fig. 3.5.j.4 shows the corresponding syntax diagram.

4.5 - 19

integer 0

digits

digits 1

2 0

3 1

4 2

5 3

6 4

7 5

8 6

9 7

8

9

4.5 - 20

3.5

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