Static and Dynamic Scoping

The scope of a variable x is the region of the program in which uses of x refers to its declaration. One of the basic reasons of scoping is to keep variables in different parts of program distinct from one another.

Scoping is generally divided into two classes:
1.Static Scoping
2.Dynamic Scoping

Static Scoping:

Static scoping is also called lexical scoping. In this scoping a variable always refers to its top level environment. This is a property of the program text and unrelated to the run time call stack. Static scoping also makes it much easier to make a modular code as programmer can figure out the scope just by looking at the code. In contrast, dynamic scope requires the programmer to anticipate all possible dynamic contexts.

Dynamic Scoping:

With dynamic scope, a global identifier refers to the identifier associated with the most recent environment, and is uncommon in modern languages. In technical terms, this means that each identifier has a global stack of bindings and the occurrence of a identifier is searched in the most recent binding.

A perl code to demonstrate dynamic scoping

$x = 10;

sub f 

{ 

   return $x; 

}

sub g 

{ 

   # Since local is used, x uses

   # dynamic scoping. 

   local $x = 20; 

  

   return f(); 

}

print g()."\n";

Static Vs Dynamic Scoping

In most of the programming languages static scoping is dominant. This is simply because in static scoping it’s easy to reason about and understand just by looking at code. We can see what variables are in the scope just by looking at the text in the editor.

Dynamic scoping does not care how the code is written, but instead how it executes. Each time a new function is executed, a new scope is pushed onto the stack.

Perl supports both dynamic and static scoping. 

DBMS Normalization : 1NF, 2NF, 3NF, BCNF

Normalization of Database

Database Normalization is a technique of organizing the data in the database.

Normalization is a systematic approach of decomposing tables to eliminate

data redundancy (repetition) and undesirable characteristics like Insertion, Update

and Deletion Anomalies.

It is a multi-step process that puts data into tabular form, removing duplicated data

from the relation tables.

Normalization is used for mainly two purposes,

• Eliminating redundant (useless) data.
• Ensuring data dependencies make sense i.e data is logically stored.

Problems Without Normalization

If a table is not properly normalized and have data redundancy then it will take a lots

of memory space and also it will be difficult to handle and update the database,

without facing data loss. Insertion, Updation and Deletion Anomalies are very frequent if

database is not normalized.

Let's consider an example of a Student table.

rollno	name	branch	hod	office_tel
401	Akon	CSE	Mr. X	53337
402	Bkon	CSE	Mr. X	53337
403	Ckon	CSE	Mr. X	53337
404	Dkon	CSE	Mr. X	53337

In the table above, we have data of 4 Computer Sci. students. As we can see, data

for the fields branch, hod(Head of Department) and office_tel is repeated for the students

who are in the same branch in the college, this is Data Redundancy.

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Insertion Anomaly

Suppose for a new admission, until and unless a student opts for a branch, data of the

student cannot be inserted, or else we will have to set the branch information as NULL.

Also, if we have to insert data of 100 students of same branch, then the branch information

will be repeated for all those 100 students.

These scenarios are nothing but Insertion anomalies.

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Updation Anomaly

What if Mr. X leaves the college? or is no longer the HOD of computer science department?

In that case all the student records will have to be updated, and if by mistake we miss

any record, it will lead to data inconsistency. This is Updation anomaly.

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Deletion Anomaly

In our Student table, two different informations are kept together, Student information and

Branch information. Hence, at the end of the academic year, if student records are deleted,

we will also lose the branch information. This is Deletion anomaly.

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Normalization Rule

Normalization rules are divided into the following normal forms:

• First Normal Form
• Second Normal Form
• Third Normal Form
• BCNF
• Fourth Normal Form

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First Normal Form (1NF)

For a table to be in the First Normal Form, it should follow the following 4 rules:

1. It should only have single(atomic) valued attributes/columns.
2. Values stored in a column should be of the same domain
3. All the columns in a table should have unique names.
4. And the order in which data is stored, does not matter.

Second Normal Form (2NF)

For a table to be in the Second Normal Form,

1. It should be in the First Normal form.
2. And, it should not have Partial Dependency.

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Third Normal Form (3NF)

A table is said to be in the Third Normal Form when,

1. It is in the Second Normal form.
2. And, it doesn't have Transitive Dependency.

Boyce and Codd Normal Form (BCNF)

Boyce and Codd Normal Form is a higher version of the Third Normal form.

This form deals with certain type of anomaly that is not handled by 3NF. A 3NF table which

does not have multiple overlapping candidate keys is said to be in BCNF.

For a table to be in BCNF, following conditions must be satisfied:

• R must be in 3rd Normal Form
• and, for each functional dependency ( X → Y ), X should be a super Key.

Rules for First Normal Form

The first normal form expects you to follow a few simple rules while designing your database,

and they are:

Rule 1: Single Valued Attributes

Each column of your table should be single valued which means they should not contain

multiple values. We will explain this with help of an example later, let's see the other rules

for now.

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Rule 2: Attribute Domain should not change

This is more of a "Common Sense" rule. In each column the values stored must be of the

same kind or type.

For example: If you have a column dob to save date of births of a set of people, then you

cannot or you must not save 'names' of some of them in that column along with 'date of birth'

of others in that column. It should hold only 'date of birth' for all the records/rows.

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Rule 3: Unique name for Attributes/Columns

This rule expects that each column in a table should have a unique name. This is to avoid

confusion at the time of retrieving data or performing any other operation on the stored data.

Example

roll_no	name	subject
101	Akon	OS, CN
103	Ckon	Java
102	Bkon	C, C++

Our table already satisfies 3 rules out of the 4 rules, as all our column names are unique,

we have stored data in the order we wanted to and we have not inter-mixed different type

of data in columns.

But out of the 3 different students in our table, 2 have opted for more than 1 subject.

And we have stored the subject names in a single column. But as per the 1st Normal form

each column must contain atomic value.

How to solve this Problem?

It's very simple, because all we have to do is break the values into atomic values.

Here is our updated table and it now satisfies the First Normal Form.

roll_no	name	subject
101	Akon	OS
101	Akon	CN
103	Ckon	Java
102	Bkon	C
102	Bkon	C++

By doing so, although a few values are getting repeated but values for the subject column are

now atomic for each record/row.

Using the First Normal Form, data redundancy increases, as there will be many columns with

same data in multiple rows but each row as a whole will be unique.

What is Second Normal Form?

For a table to be in the Second Normal Form, it must satisfy two conditions:

1. The table should be in the First Normal Form.
2. There should be no Partial Dependency.

What is Partial Dependency? Do not worry about it. First let's understand what is

Dependency in a table?

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What is Dependency?

Let's take an example of a Student table with columns student_id, name, reg_no(registration number), branch and address(student's home address).

student_id	name	reg_no	branch	address

In this table, student_id is the primary key and will be unique for every row, hence we can

use student_id to fetch any row of data from this table

Even for a case, where student names are same, if we know the student_id we can easily

fetch the correct record.

student_id	name	reg_no	branch	address
10	Akon	07-WY	CSE	Kerala
11	Akon	08-WY	IT	Gujarat

Hence we can say a Primary Key for a table is the column or a group of columns(composite

key) which can uniquely identify each record in the table.

I can ask from branch name of student with student_id 10, and I can get it. Similarly, if I ask for name of student with student_id 10 or 11, I will get it. So all I need is student_id and every other column depends on it, or can be fetched using it.

This is Dependency and we also call it Functional Dependency.

---

What is Partial Dependency?

Now that we know what dependency is, we are in a better state to understand what partial

dependency is.

For a simple table like Student, a single column like student_id can uniquely identfy all the records in a table.

But this is not true all the time. So now let's extend our example to see if more than 1 column together can act as a primary key.

Let's create another table for Subject, which will have subject_id and subject_name fields and subject_id will be the primary key.

subject_id	subject_name
1	Java
2	C++
3	Php

Now we have a Student table with student information and another table Subject for storing

subject information.

Let's create another table Score, to store the marks obtained by students in the respective

subjects. We will also be saving name of the teacher who teaches that subject along with

marks.

score_id	student_id	subject_id	marks	teacher
1	10	1	70	Java Teacher
2	10	2	75	C++ Teacher
3	11	1	80	Java Teacher

In the score table we are saving the student_id to know which student's marks are these and

subject_id to know for which subject the marks are for.

Together, student_id + subject_id forms a Candidate Key for this table, which can be the Primary key.

How this combination can be a primary key?

See, if I ask you to get me marks of student with student_id 10, can you get it from this table? No, because you don't know for which subject. And if I give you subject_id, you would not know for which student. Hence we need student_id + subject_id to uniquely identify any row.

But where is Partial Dependency?

Now in the Score table, we have a column names teacher which is only dependent on the subject, for Java it's Java Teacher and for C++ it's C++ Teacher & so on.

Now as we just discussed that the primary key for this table is a composition of two columns which is student_id & subject_id but the teacher's name only depends on subject, hence the subject_id, and has nothing to do with student_id.

This is Partial Dependency, where an attribute in a table depends on only a part of the primary key and not on the whole key.

---

How to remove Partial Dependency?

There can be many different solutions for this, but out objective is to remove teacher's name

from Score table.

The simplest solution is to remove columns teacher from Score table and add it to the Subject table. Hence, the Subject table will become:

subject_id	subject_name	teacher
1	Java	Java Teacher
2	C++	C++ Teacher
3	Php	Php Teacher

And our Score table is now in the second normal form, with no partial dependency.

score_id	student_id	subject_id	marks
1	10	1	70
2	10	2	75
3	11	1	80

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Quick Recap

For a table to be in the Second Normal form, it should be in the First Normal form and it should

not have Partial Dependency.

Partial Dependency exists, when for a composite primary key, any attribute in the

table depends only on a part of the primary key and not on the complete primary key.

To remove Partial dependency, we can divide the table, remove the attribute which

is causing partial dependency, and move it to some other table where it fits in well.

Third Normal Form (3NF)

Student Table

student_id	name	reg_no	branch	address
10	Akon	07-WY	CSE	Kerala
11	Akon	08-WY	IT	Gujarat
12	Bkon	09-WY	IT	Rajasthan

Subject Table

subject_id	subject_name	teacher
1	Java	Java Teacher
2	C++	C++ Teacher
3	Php	Php Teacher

Score Table

score_id	student_id	subject_id	marks
1	10	1	70
2	10	2	75
3	11	1	80

In the Score table, we need to store some more information, which is the exam name and total

marks, so let's add 2 more columns to the Score table.

score_id	student_id	subject_id	marks	exam_name	total_marks

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Requirements for Third Normal Form

For a table to be in the third normal form,

1. It should be in the Second Normal form.
2. And it should not have Transitive Dependency.

---

What is Transitive Dependency?

With exam_name and total_marks added to our Score table, it saves more data now. Primary key for our Score table is a composite key, which means it's made up of two attributes or columns → student_id + subject_id.

Our new column exam_name depends on both student and subject. For example, a mechanical engineering student will have Workshop exam but a computer science student won't. And for some subjects you have Prctical exams and for some you don't. So we can say that exam_name is dependent on both student_id and subject_id.

And what about our second new column total_marks? Does it depend on our Score table's primary key?

Well, the column total_marks depends on exam_name as with exam type the total score changes. For example, practicals are of less marks while theory exams are of more marks.

But, exam_name is just another column in the score table. It is not a primary key or even a part of the primary key, and total_marks depends on it.

This is Transitive Dependency. When a non-prime attribute depends on other non-prime attributes rather than depending upon the prime attributes or primary key.

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How to remove Transitive Dependency?

Again the solution is very simple. Take out the columns exam_name and total_marks from Score

table and put them in an Exam table and use the exam_id wherever required.

Score Table: In 3rd Normal Form

score_id	student_id	subject_id	marks	exam_id

The new Exam table

exam_id	exam_name	total_marks
1	Workshop	200
2	Mains	70
3	Practicals	30

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Advantage of removing Transitive Dependency

The advantage of removing transitive dependency is,

• Amount of data duplication is reduced.
• Data integrity achieved.

Boyce-Codd Normal Form (BCNF)

Rules for BCNF

For a table to satisfy the Boyce-Codd Normal Form, it should satisfy the following two

conditions:

1. It should be in the Third Normal Form.
2. And, for any dependency A → B, A should be a super key.

The second point sounds a bit tricky, right? In simple words, it means, that for a

dependency A → B, A cannot be a non-prime attribute, if B is a prime attribute.

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Time for an Example

Below we have a college enrolment table with columns student_id, subject and professor.

student_id	subject	professor
101	Java	P.Java
101	C++	P.Cpp
102	Java	P.Java2
103	C#	P.Chash
104	Java	P.Java

As you can see, we have also added some sample data to the table.

In the table above:

• One student can enrol for multiple subjects. For example, student with student_id 101, has opted for subjects - Java & C++
• For each subject, a professor is assigned to the student.
• And, there can be multiple professors teaching one subject like we have for Java.

What do you think should be the Primary Key?

Well, in the table above student_id, subject together form the primary key, because using

student_id and subject, we can find all the columns of the table.

One more important point to note here is, one professor teaches only one subject, but one

subject may have two different professors.

Hence, there is a dependency between subject and professor here, where subject depends

on the professor name.

This table satisfies the 1st Normal form because all the values are atomic, column names

are unique and all the values stored in a particular column are of same domain.

This table also satisfies the 2nd Normal Form as their is no Partial Dependency.

And, there is no Transitive Dependency, hence the table also satisfies the 3rd Normal Form.

But this table is not in Boyce-Codd Normal Form.

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Why this table is not in BCNF?

In the table above, student_id, subject form primary key, which means subject column

is a prime attribute.

But, there is one more dependency, professor → subject.

And while subject is a prime attribute, professor is a non-prime attribute, which is not

allowed by BCNF.

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How to satisfy BCNF?

To make this relation(table) satisfy BCNF, we will decompose this table into two tables,

student table and professor table.

Below we have the structure for both the tables.

Student Table

student_id	p_id
101	1
101	2
and so on...

And, Professor Table

p_id	professor	subject
1	P.Java	Java
2	P.Cpp	C++
and so on...

And now, this relation satisfy Boyce-Codd Normal Form. Next we will learn

about the Fourth Normal Form.

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A more Generic Explanation

In the picture below, we have tried to explain BCNF in terms of relations.