1. Week 2: Directed Reading Relational Database Design Nick Rossiter
Database Modelling
Week 2: Directed Reading
Relational Database Design
Nick Rossiter
April 6, 2017

2. Learning Objectives To consider atomic data in relations
To consider data types in a relation
To consider missing data & NULLs in relations
To consider Integrity Constraints
To consider the principles of Candidate Keys
To consider Candidate Keys in SQL
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3. The Information Principle
A relation contains only data values, i.e. facts.
Each attribute-in-a-tuple contains just a single data value.
In particular there are no pointers or OIDs.
Pointers point to variables
because they reference the storage location of the variable) and thus are different in nature to data values.
The reason for this principle is to keep relations simple.
Following work by EF Codd (1970)
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4. Efficiency and Human Productivity
Handling of relations is a simple abstraction:
of what is going on at the physical level of a computer
queries that used to take many hours to write for earlier types of DB can be written in a few minutes in a relational language.
It would be foolish to throw away this productivity
Use computer power to increase human productivity.
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5. Use of Pointers
Pointers are often advocated as a means to make DBs more efficient.
But their place is in the implementation of the relational model that the user uses, not in the model itself where it complicates things.
It is important to distinguish between the relational model and its implementation.
Object-based DBMS provide pointers at the logical level.
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6. Atomic Data
Since it is now known that an atom consists of component parts –
a nucleus of protons and neutrons with electrons orbiting round it - perhaps atom is no longer the best word to describe this concept.
However until the 20th century, an atom was regarded as the smallest, indivisible particle of matter possible
The tradition of using atom/atomic to describe this concept has remained.
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7. Definition of Atomic Value
Definition: An atomic value is a single, indivisible value, not a composite value or a collection of values.
The data in one attribute of one tuple must be atomic.
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8. Example of Atomic Data Example: In this EMPLOYEE relation there
is only one value in each attribute-in-a-tuple.
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9. Atomicity Requirement
Maintains the inherent simplicity of relations, and is of great practical benefit.
Occasionally it is not obvious whether a value is atomic or not.
For example, is a date atomic?
On the one hand, it represents a particular day in the calendar, and thus should be atomic.
On the other hand, it has 3 components, day-of-the-month, month and year.
Another example is a person’s full name
should this be atomic ?
or split into its component parts, (set of) forename(s) and surname?
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10. Designer’s choice The DB designer must decide
based on what precisely the data means in the context of the database and how it will be used.
Typically a date will be regarded as atomic, through a date type predefined in the database standard SQL.  
Names are more diverse and are usually handled through definitions to suit the application.
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11. Non-Atomic Data Example: A “relation” containing non-atomic data.
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12. Multiple Atomic Values
The attributes ‘Component’ and ‘’Quantity’ clearly contain multiple atomic values.
Although not shown in the above example, it is possible that some tuples could contain single values of ‘Component’ and ‘Quantity’.
Traditional prohibition against repeating values has weakened in the last few years.
allowing relations and other “container types” such as arrays, records, etc to be stored as the single atomic value in an attribute.
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13. Data Types Definition: A data type has a set of permissible values.
Each attribute value must be drawn from the set of permissible values of the data type specified for that attribute.
More than one attribute in a relation may draw its values from the same data type.
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14. Example of Type Assignment
Every attribute must have a data type, just as every variable in a program must have a type.
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15. Example of Using Data Types
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16. Comments on Example
All the attribute values in the top tuple are drawn from their respective data types
Would not be acceptable otherwise.
Only 1 out of 4 values in the bottom tuple are drawn from their respective data types; so that tuple cannot be stored in the relation.
If even one attribute has a value that is not drawn from its type’s set of permissible values
that tuple cannot be in the relation.
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17. Data Types -- Operators
Definition: A Data Type has a set of permissible operators.
Examples : 
Number : +, -, /, x, <, > apply to all possible numbers
Text : length( ), sub( ), concat( ) apply to all possible texts
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18. Data Type Implementation
A data type needs logical representations for its values and operators.
These are what the user uses.
They become part of the logical model.
A data type needs physical representations for its values and executable code for each of its operators.
These form the implementation of the logical model.
 We need Strong Typing.
Object classes as described in traditional object-oriented programming meet precisely these criteria.
Thus object classes are data types.
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19. Built-in Data Types
Commonly needed data types are Built-In, i.e. provided with the DBMS.
Examples: Number, Text, (and usually Date ).
Text appears as char, varchar in SQL
Also have data types for multimedia (blob, clob in SQL)
Can also add new data types (later in module)
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20. Underlying/Specific Data Types
When specifying an attribute‘s type, there are typically 2 stages :
Specify the general kind of data required, e.g. numbers, text, dates.
This is the Underlying Type.
Specify that subset of it that the attribute values must be limited to,
e.g. only the integer numbers ,000.
This is the Specific Type.
It uses the same operators as the underlying type.
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21. Example of Specific Type
Note that data types have sets of values that are permitted to be used.
Specific Type allows a subset of those in Underlying Type
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22. Ways to Define a Mathematical Set
Set enumeration
the values in the set are individually specified;
useful for comparatively small sets of values.
Set comprehension
a constraint or rule applied to any potential member of the set to see if it is in fact a member of the set
Both these methods can be used to constrain the underlying type to get the specific type.
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23. CHECK constraint Some underlying types have parameters
which can be used to constrain them to the specific type.
SQL has a Check constraint option, allows
the enumeration of the specific type within the underlying type
and more ad hoc constraints on the underlying type
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24. SQL Data Types
SQL data types are often based on their physical storage.
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25. Explanation of Types
The “2” in Varchar2(x) indicates that it is Oracle’s second version of the variable length text type.
It has nothing to do with the number of characters in the text.
It is the standard Oracle variable length text type now.
The text type is often known as the character string type.
SQL attributes/columns are assigned their types when the relation/table is created with the Create Table statement.
The SQL Create Table statement is the statement used to specify all aspects of a table.
the Alter Table statement can be used to add, delete and modify any aspect of a table already created with a Create Table.
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26. SQL : Example
The SQL Create Table statement creates a table type with the required columns of specified names and specific types (which will use the operators of the underlying types), and creates the table variable EMPLOYEE of that type.
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27. Missing Data
In the real world, data is not always available to put in the DB.
Reasons for this include the value being :
unknown
 not available
 not applicable
 not yet known
 undefined
 to be announced
 does not exist
 not supplied, etc 
One paper recorded 42 different reasons!
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28. Solutions to Missing Data
Use a special value to represent missing data.
Example: ‘N/A’, ‘T.B.A.’
It gives the reason why the data is missing.
The special value must have the same type as the data that is missing, so it can be stored with the data that is known.
So cannot use ‘N/A’ in numeric field
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29. Use of NULL
Null requires special support from the DBMS. SQL DBMSs provide this support. But which reason does it represent ?
In reality, no-one yet has come up with a good way of handling missing data that is generally accepted . These options are the main ones used in practice, but there is considerable controversy about them.
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30. NULL terminology We might say :
“The attribute ‘Sal’ in a tuple has a null value.”
This is wrong !
Null is the absence of a value, so it can’t be a value.
“The attribute ‘Sal’ in a tuple contains a null.”
This is better, but not very precise.
“The attribute ‘Sal’ in a tuple is null.”
This is accurately stated.
‘Sal’ is null does not mean that there is no such value or that the salary is £0.
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31. 2-Valued Logic
Normal Boolean logic only has the truth values true and false.
The result (or value) of any comparison will be true or false.
Thus, the Boolean logic operators AND, OR and NOT can be used to combine comparisons, forming an expression.
Example:- ( X = 3 AND Y < X ) OR NOT ( Y > 0 )
 The value of this expression will be true or false, and can be derived if the values of X and Y are known.
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32. Truth Table
The rules which the logic operators apply to their operands to yield a Boolean result are represented by truth tables
In the tables, T and F stand for true and false respectively.
The 3 operators yield commonsense results. AND yields false unless both its operands are true, OR yields true unless both operands are false, and NOT reverses the truth value of its operand.
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33. 3-valued Logic With NULL, results of queries can be maybe.
For example, for X = Y, if both NULL, result is unclear.
We still want to use logical expressions. Therefore AND, OR and NOT must be extended to cope with maybe.
This logic offends Gödel’s theorem on decidability.
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34. 3-valued Logic Truth Tables
In the tables, M stands for maybe.
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35. SQL : Not NULL Constraint
Sometimes we want to prevent a column from ever holding NULLs.
To achieve this in SQL, add a “Not NULL” constraint to the definition of the column.
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36. Advantages of NOT NULL
Because 3-valued logic is more complex than 2-valued
it sometimes gives unexpected results
It is desirable to avoid having missing data if at all possible.
It would be better to stick to 2-valued logic.
 Thus we often specify a “not NULL” constraint for a column to ensure that it always contains a data value in every row.
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37. Integrity Constraints
Definition: An Integrity Constraint is a constraint on the values that a given DB relation is permitted to hold.
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38. Purpose
To try to ensure that the relations in the DB only hold data that is true, accurate and up-to-date.
A constraint is a validation check that the DBMS automatically applies when a relation’s value is altered.
The requirement that a data type be assigned to every attribute is itself an integrity constraint.
However, more integrity constraints are possible.
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39. Applying Constraints in SQL
In SQL, integrity constraints are usually applied when the relation is created using the Create Table statement.
But can also be enforced in the Alter Table statement
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40. Categories of Integrity Constraints
Attribute type constraints:
already considered.
Candidate Key constraints:
these apply to an individual relation.
 Referential Integrity constraints:
these correlate two relations.
Ad hoc constraints:
these apply to one or more relations.
 This is not the only possible categorisation of integrity constraints
but it is a convenient and practical one.
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41. Candidate Keys
There are no duplicate tuples in a relation, because it is a set of tuples.
So every tuple must be unique.
Often, indeed typically, the values of only one attribute, or a small number of attributes, in a relation are sufficient to make each tuple in it unique.
Whether it requires one attribute, several attributes, or all the attributes in a relation to make each tuple unique, that set of 1 or more attribute(s) is called a Candidate Key.
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42. Candidate Keys for ID
The candidate key attribute(s) can also be considered as uniquely identifying each tuple in the relation.
A relation may contain two or more candidate keys.
Often a candidate key consists of just one attribute.
For example passport number.
Nevertheless it is quite normal for a candidate key to consist of 2 or more attributes
For example student number + module number in marks
Occasionally in an extreme case
all of a relation’s attributes form the candidate key.
If there is only one key, it is still called the Candidate Key.
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43. Properties of a Candidate Key
Uniqueness: No two distinct tuples may contain the same key value.
Irreducibility: No attribute can be removed from the set forming the key, and the remaining attributes still possess the uniqueness property.
Underlining attribute(s) is a common way of specifying a candidate key.
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44. Benefits of these two Properties
Candidate keys provide (the only) guaranteed way to find a particular tuple.
Checks on the uniqueness of tuples can be limited to the candidate key attribute(s), giving greater efficiency.
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45. Candidate Keys: Example (1)
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46. Rationale for Candidate Keys
Relation EMPLOYEE :
Employee names are not guaranteed to be unique,
Many employees may be on the same salary.
So none of the attributes apart from ‘ENo’, either on their own or taken in combination, is sufficient to form a candidate key for EMPLOYEE.
Relation CAR :
A car’s registration number is guaranteed to be unique, and so can be a candidate key.
As ‘Owner’ is an employee number which the company will ensure is unique, that can also be a candidate key
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47. Candidate Keys : Example (2)
Re-consider CAR. Let us change the assumptions. The company now has a “share and park” scheme whereby a group of employees can share a car to work; a group may use several of the members’ cars.
Now neither ‘RegNo’ or ‘ENo’ on its own is sufficient to identify a tuple in CAR.
However, both together will identify any tuple. Therefore, they jointly become the only candidate key.
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48. 2-attribute candidate key
The ‘ENo’ attribute need not represent the owner of the car in question;
s/he need not even own a car.
We simply need to know which cars each employee may come to work in, or
alternatively which employees may be allowed to come to work in each car.
It is essential to be able to distinguish:
two 1-attribute candidate keys and
one 2-attribute candidate key.
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49. Candidate Keys in SQL SQL has Primary and Alternate Keys.
If there is only one candidate key, it becomes the primary key; there are no alternate keys.
If there is more than one candidate key, choose one as the primary key;
the rest become the alternate keys.
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50. Making the choice Any candidate key can become the primary key.
So choose one that makes the most practical sense.
Usually the shortest - easiest for the user, most efficient for the computer.
While SQL defines a Primary Key using the phrase Primary Key, it defines an Alternate Key using the word Unique! 
SQL does not make specifying at least one candidate key mandatory !
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51. Define a Primary Key So bags can occur. To insist on a set
Therefore ensure every SQL table has at least a primary key.
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52. SQL Key Requirements SQL requires that a primary key never be null.
However, it will let an alternate key be null, thereby permitting duplicate null keys, a contradiction in terms.
To prevent this, a “not NULL” constraint can be added to an alternate key.
It is desirable to specify any other candidate keys that happen to exist as alternate keys.  
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53. Entity Integrity
This is an additional constraint for relational DBs that allow nulls.
Definition: Entity Integrity requires that no attribute in a primary key can ever be null.
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54. Rationale Each tuple represents an entity in the real world
Each entity must be identifiable by definition
Primary keys serve as identifiers of tuples
Therefore a primary key can never be partly or wholly null, to ensure that it does identify each tuple.
Note entity integrity does not apply to alternate keys
which can be null, either wholly or in part.
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55. Constraint Names
Most relational DBMSs give integrity constraints a name when they store the constraint in the DB.
Thus a candidate key constraint would receive a name.
If the user does not supply a name when assigning the constraint, a unique default name is created for it by the DBMS.
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56. Use of naming Constraints
The naming of integrity constraints can be of great practical use :
It helps users find out about what integrity constraints have been assigned to relations.
It allows more meaningful error messages to be provided to the user if there is an attempt to break an integrity constraint.
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57. Constraints in Oracle
Oracle allows user to provide integrity constraint names, and generate default names if the user does not provide them.
Oracle default names are not very user-friendly.
Therefore assign your own names to integrity constraints.
Constraint names must be unique within the entire user’s DB, not just within a single relation.
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58. Specifying Candidate Keys in SQL
Keys (primary and alternate) can be assigned in two places :
in the same sub-statement in which an attribute is assigned its type,
in a separate sub-statement at the end of a Create Table statement.
The first method is only possible if the SQL key consists of one attribute.
The second method must be used if the key consists of two or more attributes.
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59. Constraint Definition
In either case, starting the assignment of an SQL key with the phrase Constraint constraint-name assigns a name to the key constraint as well
In Oracle, if a primary or alternate key constraint is assigned in its own sub-statement at the end of the Create Table statement, then it is mandatory to give the constraint a name.
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60. Examples of SQL Keys (1) In Oracle, note that :
Create Table
EMPLOYEE (
ENo
Char( 2 )
Primary
Key ,
EName
Varchar2( 30 M - S 1
Check
( M In
(‘S’, ‘M’, ‘W’, ‘D’ ) ),
Sal
Number
( Sal >999
And
Sal < )
) ;
Sal < ),
Primary Key( ENo
) );
These 2 versions of
have a
default
constraint name.
In Oracle, note that :
 the first example is permissible
 the second example would not be permissible, because no name has been assigned to the key constraint and so a default name must be given.
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61. Examples of SQL Keys (2) In Oracle, both examples are permissible.
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62. Examples of SQL Keys (3)
Note that, in any version of SQL, only the second method is permissible if a primary or alternate key consists of 2 or more attributes.
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