The Relational Model

The Relational Model Chapter 3

History of the Relational Model The objectives of the relational model : • allow a high degree of data independence, application programs should not be affected by modifications to the internal data representation, file organisation record orderings or access paths • deal with data semantics, consistency and redundancy problems, the database files should be based on normalised relations • enable the expansion of set-oriented data manipulation languages, using a many-records-at-a-time logic.

Terminology Relation • A relation is a table with rows and columns • Mathematical definition Attribute • An attribute is a named column of a relation Domain • A domain is the set of allowable values for one ore more attributes Tuple • A tuple is a row of a relation

The DOMAIN concept The domain concept is used to describe a set of possible values for an attribute. This offers more flexibility. Domain description Domain part-number character 6 Domain part-name character 20 Domain color character 6 Domain weight numeric 4 Domain location character 15 Relation PART (P# : Domain part-number pname : Domain part-name color : Domain color weight : Domain weight city : Domain location

Sample Database S S# SNAME STATUS CITY S1 Smith 20 London S2 Jones 10 Paris S3 Blake 30 Paris S4 Clark 20 London S5 Adams 30 Athens • SP S# P# QTY • S1 P1 300 • S1 P2 200 • S1 P3 400 • S1 P5 200 • S1 P6 100 • S2 P1 300 • S2 P2 400 • S3 P2 200 • S4 P2 200 • S4 P4 300 • S4 P5 400 • P P# PNAME COLOR WEIGHT CITY • P1 Nut Red 12 London • P2 Bolt Green 17 Paris • P3 Screw Blue 17 Rome • P4 Screw Red 14 London • P5 Cam Blue 19 London • P6 Cog Red 19 London

Terminology 2 Degree • The degree of a relation is the number of attributes it contains Cardinality • The cardinality of a relation is the number of tuples it contains Relational database • A collection of normalised relations Relation Schema • A relation name followed by a set of attribute and domain name pairs

Alternative Terminology

Properties of a Relation • A relation in a database has a unique name. • Each cell of the relation contains exactly one atomic value. • Each attribute has a distinct name within a relation. • The values of an attribute are all from the same domain. • column homogenious • The order of the attributes has no significance. • Each tuple is distinct; there are no duplicate tuples. • The order of tuples has no significance, theoretically. Most properties can be derived from the mathematical definition

Mathematical Relations Mathematical definition of relation • Consider two sets, D1 and D2, where D1 = {2, 4} and D2 = {1, 3, 5}. • Cartesian product is D1 D2, the set of all ordered pairs, first element is member of D1 and second element is member of D2. • Alternative way is to find all combinations of elements with first from D1 and second from D2. • D1D2 = {(2, 1), (2, 3), (2, 5), (4, 1), (4, 3), (4, 5)}

Mathematical Relation • Any subset of Cartesian product is a relation. For example R = {(2, 1), (4, 1)} • May specify which pairs are in relation using some condition for selection. For example, second element is 1 R = {(x, y) | xD1, yD2, and y = 1}

Relational Keys • Superkey • An attribute or a set of attributes that uniquely identifies a tuple within a relation.

Relational Keys • Candidate Key • A superkey (K) such that no proper subset is a superkey within the relation. • In each tuple of R, the values of K uniquely identify that tuple (uniqueness). • No proper subset of K has the uniqueness property (irreducibility).

Relational Keys • Primary Key • Candidate key selected to identify tuples uniquely within relation. • Alternate Keys • Candidate keys that are not selected to be the primary key.

Relational Keys • Foreign Key • An attribute or set of attributes within one relation that matches candidate key of some (possibly same) relation.

Relational Integrity • Null (value) • Represents a value for an attribute that is currently unknown or is not applicable for this tuple. • Deals with incomplete or exceptional data. • Null represents the absence of a value and is not the same as zero or spaces, which are values.

Relational Integrity • Entity Integrity • In a base relation, no attribute of a primary key can be null. • Referential Integrity • If foreign key exists in a relation, either the foreign key value must match a candidate key value of some tuple in its home relation or foreign key value must be wholly null.

Relational Integrity • Enterprise Constraints • Additional rules specified by users or database administrators.

Views Base relation • a named relation, corresponding to an entity in the conceptual schema, whose tuples are physically stored in the database. View • a view is the dynamic result of one or more relational operations operating on the base relations to produce another relation. A view is a virtual relation that does not actually exist in the database but is produced upon request by a particular user, at the time of request.

Views • A view is a virtual relation that does not actually exist in the database but is produced upon request, at time of request. • Contents of a view are defined as a query on one or more base relations. • Views are dynamic, meaning that changes made to base relations that affect view attributes are immediately reflected in the view.

Purpose of Views • Provides a powerful and flexible security mechanism by hiding parts of database from certain users. • Permits users to access data in a customized way, so that same data can be seen by different users in different ways, at same time. • It can simplify complex operations on base relations.

Updating Views • All updates to a base relation should be immediately reflected in all views that reference that base relation. • If view is updated, underlying base relation should reflect change.

Updating Views • However, there are restrictions on types of modifications that can be made through views: • Updates are allowed if query involves a single base relation and contains a candidate key of base relation. • Updates are not allowed involving multiple base relations. • Updates are not allowed involving aggregation or grouping operations.

Updating Views • Classes of views are defined as theoretically not updateable, theoretically updateable and partially updateable.

Relational Database Architecture Data Language application External level view 1 view 2 Conceptual level Base table B2 Base table B3 Base table B1 Base table B4 Stored file S2 Stored file S3 Stored file S1 Stored file S4 Internal level

The Relational Model