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This
paper is a pioneer work by E.F. Codd in relational database systems, concepts of
which are used to develop a sound database model even today. When we study a
good database model, the key characteristic that defines the model is the non-alteration
of activities of users and application programs when changes are made to
internal or external representation of data. The Paper talks about the existing
database models (until 1970), its drawbacks by considering the problem of data
dependency and subsequent solutions to fix them. Ordering dependency
resulted in the failure of an application program, as the program failed
to differentiate between the stored ordering and the presentation ordering of
the data due to the changes made to the data stored indexing. Indexing dependency slowed down during addition and deletion operations. Since,
indexing is redundant, indices needed to be created and destroyed accordingly. The
problem of Access Path dependency could be handled by not making the path as obsolete only
when all the application programs using the paths have become obsolete.

 

The
relational view of the data is presented well in the next section of the paper
with its characteristics: an array representation of relations where each row being
distinct represents an n-tuple in relation R and its ordering is not necessary,
but the ordering of columns is important as they represent the domains on which
R is defined. It also solves the problem which one can encounter with identical
domain names and time varying relations. With higher order, unique domain names
and relations are domain-unordered (relationship). This itself provided the new
idea of using relationships instead of relations to interact with the relational
model.

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Next
the paper discusses about the ways to establish a good relational model by the
process of Normalization. A domain that is unique over all the tuples in a
relation is called the primary key of the relation. It can be a simple
domain or a combination and if there are more than one such, one among them is
to be selected as the primary key. It is used to cross reference other elements
of the same relation or elements of a different relation. To cross reference
elements in other relations, the foreign key of a relation should be a primary
key for other relation. Identifying these keys and removing the redundant domains
in all the relations to a simple domain normalizes the data.

 

Simple
domains are those whose elements are atomic. The non-normalized data should satisfy
the conditions to be normalized. The graphs of interrelationships of the
nonsimple domains is a collection of trees and the primary key have a simple
component domain. The relational model of data also permits for the development
of a universal high-level language based on applied predicate calculus. The required arithmetic functions
can be defined in the programming language and invoked in relation.

 

For
an n-ary relation to support symmetric exploitation it needs n factorial paths
to be named and controlled. To represent an n-ary relation using only (nested)
binary representation it needs 2n-1 names instead of n+1 names using n-ary
notation. The two collections of relations
are named set and expressible set where ‘named set’ is a subset of ‘expressible
set’. A named set is a collection of relations, which has a simple name. A
relation can be a member of a named set if declared by an authorized user. An
expressible set is collection of relations designated by expressions in data
language. These are constructed from simple names of relations in named set.

 

Since
relations are sets all usual set operations are applicable. The paper lists the
unusual set of operations which include Permutation, Projection, Join,
Composition and Restriction and how these are used on the relations.

Permutation (interchanging the columns) is done with n! possible results.

Projection is when a certain column and removing from the resulting array any
duplicates in the rows. A Join is performed when two relations, which can be
joined without loss of information to form new relation is performed by using
the concept of Cartesian product. Composition
is a projection of a join thus only joinable relations are composable and two
relations need not have n composition even though there exist n joins among
them. Restriction is defined only if
equality is applicable among the elements of the relations and is also a subset
of a relation.

 

In the
final section, it addresses the two types of redundancies: Strong and Weak redundancy.

According to the paper generally, if a collection of operations (?) in a
certain order on relation R results in a particular relation S for all time
then Relation R is ? derivable from set S.The paper defines a set of relations
strongly redundant if it contains at least one relation that possesses a
projection which is derivable from the other projections of relations in the
set where as a collection of relations is weakly redundant if it contains a
relation that has a projection which is not derivable from other members but is
at all times a projection of some join of other projections of relations in the
collection.

 

Closely
associated concept of consistency is also explained well in the paper. When the
instantaneous value of a time varying relation always gives rise to the same results
it is said to be consistent. Consistency checks could be performed on updates, deletions
and insertions and the inconsistencies could be recorded.

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