1. for Computer Professionals
Relational Theory
for Computer Professionals
a technical tutorial by
C. J. Date
Copyright © C.J. Date All rights reserved. No part of this material may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photographic, or otherwise, without the explicit written permission of the copyright owner.

2. INTENDED AUDIENCE : I assume you know something about computers and
programming in general
I do NOT assume you know anything about databases (relational or otherwise) … though you very likely do know that essentially all modern DB systems are supposed to be
“relational”
/* whatever that means! */
Objectives:
To explain relational database (RDB) basics
More specifically, to describe the relational model
/* theoretical underpinnings for RDB technology */
Copyright C. J. Date 2013

3. INTENDED AUDIENCE bis :
To repeat: I do NOT assume you know anything about
databases (relational or otherwise)
In fact, if you do already know something about databases,
please pay extra careful attention! …
Because you might have to do some unlearning …
Copyright C. J. Date 2013

4. ANOTHER PRELIMINARY :
There’s inevitably a certain amount of overlap between this seminar and its companion seminar SQL and Relational Theory
But unlike this seminar, SQL and Relational Theory is explicitly aimed at audiences who do know something about databases—in fact, audiences that have several years of direct SQL experience
To repeat, the present seminar is for (database) beginners
Copyright C. J. Date 2013

5. OVERALL AGENDA : Part I : Foundations Entr’acte Part II : SQL
Copyright C. J. Date 2013

6. PART I :
Foundations
Copyright C. J. Date 2013

7. WHAT’S A DATABASE ???
“Electronic filing cabinet”: Digitized information (“data”), kept
in persistent storage, typically magnetic disk
User /* online user or application programmer */ can insert new information & delete, change, or retrieve existing information
How? By issuing requests or commands to the DB system
Requests can be formulated in numerous different ways (e.g., by pointing and clicking) … but for our purposes I’ll assume text format … E.g.,
EMP WHERE JOB = 'Programmer'
Copyright C. J. Date 2013

8. THE SUPPLIERS-AND-PARTS DATABASE :
SNO
SNAME
STATUS
CITY S1
Smith 20
London S2
Jones 10
Paris S3
Blake 30 S4
Clark S5
Adams
Athens
SNO
PNO
QTY S1 P1
300 P2
200 P3
400 P4 P5
100 P6 S2 S3 S4 S SP
PNO
PNAME
COLOR
WEIGHT
CITY P1
Nut
Red
12.0
London P2
Bolt
Green
17.0
Paris P3
Screw
Blue
Oslo P4
14.0 P5
Cam P6
Cog
19.0 P
Copyright C. J. Date 2013

9. DB SYSTEM ARCHITECTURE :
suppliers, parts, and shipments (“logical DB”)
DB management system (DBMS)
data as physically stored (“physical DB”)
Copyright C. J. Date 2013

10. IN OTHER WORDS :
“Logical DB” is the DB as perceived by the user (an abstraction)
... hence data independence
“Physical DB” is the DB as perceived by the DBMS (still an abstraction!)
Copyright C. J. Date 2013

11. SO WHAT’S A DBMS ??? Intermediary between logical and physical DBs …
Supports user interface
Interprets and responds to (“executes”) user
requests ... both queries and updates
Protects users from data (low level details)
Protects data from users! … Provides security,* concurrency,* integrity, and recovery controls
* Such controls are necessary because DB is typically shared
Copyright C. J. Date 2013

12. Security: Users can perform only those operations
they’re allowed to perform
Concurrency: Operations performed by one user aren’t allowed to interfere with those performed “at the same time” by some other user
Integrity: Operations that are known to be
“incorrect” aren’t allowed
Recovery: The database never forgets anything
it’s been told
Copyright C. J. Date 2013

13. I do not use the term database
BY THE WAY :
Please note:
I do not use the term database
to mean a DBMS !!!
Copyright C. J. Date 2013

14. SO WHAT’S AN RDBMS ??? Well, it’s a DBMS …
So it provides all of the usual DBMS functionality (data storage, query / update, security, concurrency, integrity, recovery, etc.)
But it’s also relational …
So the user interface is based on the relational model
/* better: is a faithful implementation of the relational model */
I.e., the relational model is a recipe for what the user interface
is supposed to look like
Copyright C. J. Date 2013

15. SIMPLIFY , SIMPLIFY :
To repeat: The relational model is a recipe for what the user interface is supposed to look like ...
And that recipe is very simple !!!
The rules of the relational model are not a straitjacket, but rather a discipline that makes life much easier for the user
“Our life is frittered away by detail ... Simplify, simplify.”
—Henry David Thoreau
Copyright C. J. Date 2013

16. THE RELATIONAL MODEL* : As far as the user is concerned:
Data looks relational
Relational operators are available (for operating on data in relational form and hence for formulating user requests): e.g.,
S WHERE CITY = 'London'
/* restrict suppliers to just the ones in London */
* E.F. Codd : 1969, 1970, …
Copyright C. J. Date 2013

17. SO HERE’S THE PLAN : Data looks relational
So we’ll take a closer look at exactly what RELATIONS are
Relational operators are available
So we’ll take a closer look at various RELATIONAL OPERATORS and see how they can be used
Please note: The treatment is not meant to be exhaustive !!!
Copyright C. J. Date 2013

18. UNFORTUNATELY ... There’s a problem!
The relational model as such doesn’t prescribe a concrete syntax for how its concepts are supposed to be realized in
practice
/* i.e., it’s somewhat abstract */
There is a standard concrete language, viz. SQL, which is supported (more or less) by most current DB products
But that standard is very bad … It’s complex, incomplete, hard to learn, and actively misleading in numerous ways
Copyright C. J. Date 2013

19. SO HERE’S THE PLAN bis : First, teach the relational model without SQL
… using a language called Tutorial D that has been expressly designed for the purpose
Second, show how ideas from the relational model map into SQL syntax
… NOT attempting to teach the whole of the SQL language, only as much as we need
Be aware, therefore, that what’s coming up does NOT look
much like most “RDB intro” books or presentations !!!
Copyright C. J. Date 2013

20. PROGRAMMING 101 : VAR i , n , sum INTEGER ;
VAR A ARRAY[1..n] OF INTEGER ;
sum := 0 ; i := 0 ;
DO WHILE i < n ; i := i + 1 ;
sum := sum + A[i] ; END DO ;
PRINT ( ‘The sum is ’, sum ) ;
/* nine STATEMENTS */
Copyright C. J. Date 2013

21. POINTS TO NOTE :
Types (sets of legal values): INTEGER, array of INTEGERs, CHAR
Variables: i, n, sum, A
Assignment: “:=” ... for updating variables
Literals: 0, 1, 'The sum is '
Values: Denoted by expressions /* possibly literals or variable refs */
“Read-only” operators: “+” ... for deriving “new” values from “old”
Comparison operators: “<” ... /* special case of previous */
All of these concepts are directly relevant to databases!
Copyright C. J. Date 2013

22. MORE ON TYPES : Types: INTEGER, array of INTEGERs, CHAR, BOOLEAN
Example didn’t illustrate the point, but types can be either
system defined or user defined /* of arbitrary complexity */ …
E.g., in a geometric application, we might have user defined
types POINT, RECTANGLE, ELLIPSE, etc.
But to the user who merely uses them (as opposed to the user who defines them), user defined types look just like system defined types anyway
All of these concepts are directly relevant to databases!
Copyright C. J. Date 2013

23. FURTHERMORE : Every value is of some type … Hence:
Every variable, every parameter to every operator, every read-only operator, and every expression (in particular, every literal and every variable reference) is declared to be of some type
… because these constructs all denote values
All of these concepts are directly relevant to databases!
Copyright C. J. Date 2013

24. FINALLY :
Associated with type T is a set of operators for operating on values and variables of type T … E.g., system defined type INTEGER:
System defines “:=”, “=”, “<”, etc., for assigning and
comparing integers
And “+”, “*”, etc., for arithmetic on integers
Perhaps CAST to convert integers to character strings
But not “||”, SUBSTR, etc.
Copyright C. J. Date 2013

25. NOTE THAT : Operators defined for type T must include “:=” and “=” !!!
Regarding “=” in particular:
v1 = v2 is TRUE if and only if v1 and v2 are the very same value ... Hence if Op(v1) ≠ Op(v2) for some operator Op, v1 = v2 must be FALSE
Copyright C. J. Date 2013

26. EXERCISES : /* and/or review questions ... */
What’s a database? What’s a DBMS?
What do you understand by (a) security controls, (b) integrity controls, (c) concurrency controls, (d) recovery controls?
What’s SQL? What’s Tutorial D?
Copyright C. J. Date 2013

27. EXERCISES (cont.) :
What do you think the following Tutorial D expressions represent?
P WHERE WEIGHT < 12.5
P { PNO , COLOR , CITY }
What do you think the following Tutorial D statements do?
DELETE S WHERE STATUS = 10 ; UPDATE S WHERE STATUS > 10 :
{ STATUS := STATUS + 5 } ;
Copyright C. J. Date 2013

28. EXERCISES (cont.) : Explain the following: Type Value Variable Literal
Assignment
Comparison
Read-only operator
Update operator
Copyright C. J. Date 2013