The Relational Model Our Mathematical Foundation
Origins • First proposed by E.F. Codd, 1969-70 • subsequently modified and extended
• An abstract theory of data • based on aspects of maths • set theory
• Basis of most modern DBMS • none implement it entirely • we can compare them with the idea
3 Aspects of the Model • It concerns • 1) data objects • storing it
• 2) data integrity • making sure it corresponds to reality
• 3) data manipulation • working with it
Relational Data Objects Storing information
Tables – or is it? • We say that databases have tables • data are stored in them
• This is a simplification • helps user understanding • may be misleading
Two sets of nomenclature Model
RDBMS (Inituitive)
Relation
Table
Tuple
Row (record)
Attribute
Column
Primary key
Column(s) uniquely identifying a row A pool of possible values for an attribute
Domain
Domain • Pool of possible values for an attribute • Each tuple has one of these values for the attribute • Allows meaningful comparisons • They are data types • traditionally supported poorly in most systems • area of recent development
Relation • Based on a collection of domains • Heading • a set of attribute:domain pairs, such that each attribute Ai has its own domain Di. • {, , …, , … }
• Body • a set of tuples • each tuple is a set of name:value pairs • {, , …, , … }
Illustration of notation As a table
UID
Tel
nwh
2434
hoh
2436
xxh
7659
As a relation Heading {, } Body { {, }, {, }, {, } }
Venn diagram notation {, } {, } {, }
Are Relations Tables? • A table is a practical way to write down a relation • Relations are defined on sets • • • •
a set of attributes in the heading a set of tuples in the body sets have no ordering attributes come in no particular sequence • but columns do have sequence
• tuples come in no particular sequence • but rows do have sequence
Properties of relations • Tuples and attributes are unordered • There are no duplicate tuples • All attributes are atomic
Relations/attributes are unordered • Tables seems to be • Don’t believe it!
• We do not work in terms of: • “next row” • “previous record” • “first tuple”
• We do not rely on:
Output can be made to be ordered
• “next attribute” • “first column”
• Do not try to write for loops
No duplicate tuples (= rows) • i.e.. • No two tuples in a relation have all the same values for corresponding attributes
• Crucial point • Can seem like a weakness • It is a strength • Learn to exploit it
Example of duplication Name
Age
Employee ID
Jones
42
3895
Smith
27
6830
Jones
42
3895
Williams
62
4692
• We do not want two records for Jones • The DBMS will prevent this silly duplication • A simple example of exploiting “no duplication”
All attribute values are atomic Jackie Chan
Acting, Filming, Computing
Jackie Chan
Acting
Bob Dylan
Singing, Dancing
Jackie Chan
Filming
Jackie Chan
Computing
Bob Dylan
Singing
Bob Dylan
Dancing
Atomic Values • Strings have characters, incl. spaces • not the problem
• Problem: Jim
Monday
Squash
Wednesday Cinema Saturday
Chess
Mary Wednesday Cinema Friday
Tennis
• Bad solution Person Day1
Act1
Day2
Act2
Day3
Jim
Mon
Squash Wed
Cinema Sat
Mary
Wed
Cinema Fri
Tennis
• Which is “day 1” How do we search this? Could get the day and activity separated Think about what we are modelling
Act3 Chess
• Solution: Name Day
Activity
Jim
Monday
Squash
Jim
Wednesday Cinema
Jim
Saturday
Chess
Mary Wednesday Cinema Mary Friday
• • • •
Tennis
Looks like adding more lines Not complicated therefore Can seem “cosmetic” Will return to this
Relational Data Objects End
Relational Data Integrity making sure the data corresponds to reality
A database as a model • A DB “models” a real-world enterprise • i.e. the DB must abstract from reality • the attribute values and their combination must reflect the true state of the world
• We try to enforce plausibility • We do this by implementing integrity rules (constraints)
Data-specific integrity rules • Domain specific • Employee age is between 20 and 70 • We only sell CDs in multiples of 10 • Car registrations must be of the form: A DDD AAA • where A = alphabetic, D = digit • A temperature cannot be lower than −273.15 deg C
• Inter-attribute (inter-relational) • Only senior managers and sales reps can have cars over 2000cc
• “Cardinality” constraints • A team has 11 players
General Integrity Rules •
There are two general integrity features Part of the relational model 1. Entity integrity - tuple identification through candidate/primary keys 2. Referential integrity – foreign keys
•
There may be application-specific rules • • •
must be identified and implemented may be able to use DBMS we will return to this
Candidate Keys (CKs) • A candidate key for relation R is a subset K of the attributes of R such that • no two tuples of R have the same value of K
the “uniqueness property” • no proper subset of K has the uniqueness property
the “irreducibility property” • All relations have at least 1 (everything) • may have several
• Uniqueness applies to all possible tuples • not just the current ones
What are candidate keys for? • Tuple-level addressing • allows unambiguous identification of 1 tuple • content addressing
• The tuple where X has value Y • not unique unless X is a candidate key
• Access mechanisms are more general • e.g. indexes • although CKs may be implemented using them
The primary key (PK) • A specified candidate key • The choice of PK is arbitrary • There may only be one candidate
• Practical factors may help decide • It is common to think only of “the” key (i.e. the primary key) • but remember there may be other candidates
Why bother with CKs ? Suppose that we have attributes: uid, ucas, national heath, surname, first name, d.o.b., city. Here are some data: UID xxh8 jjo1 jja1 llo2
UCAS 987632 003872 013873 003874
NH 234179 139873 243179 264902
Surname Kerr Jones Jones Lamb
FirstNameDOB Kevin 26.07.82 Jane 13.12,81 Jane 10.06.81 Louis 14.07.82
City Borth Lampeter Llanon Borth
Let us declare UCAS to be the primary key. This constrains UCAS numbers to be distinct for different people, but permits UID xxh8 jja1 jja1 llo2
UCAS 987632 003872 013873 003874
!
NH 243179 139873 243179 264902
Surname Kerr Jones Jones Lamb
FirstNameDOB Kevin 26.07.82 Jane 13.12,81 Jane 10.06.81 Louis 14.07.82
City Borth Lampeter Llanon Borth
:
Penalty of not declaring CKs • A real-world model would not want repetitions of UID and NH for distinct persons. • We want UID to be unique for each person. Similarly for NH. • Remedy: declare UID to be a candidate key. Similarly for NH. • Then, either of UID, NH gives unique identification. This captures two constraints. • Continue to use UCAS as the PK. • UCAS, UID, NH are 3 candidate keys.
Foreign Keys • A reference mechanism between relations • The target of a reference must exist in the referenced relation
no “dangling references” Referential Integrity
Example, Consider a table of employees and a table of car allocations:
Foreign Keys Name(PK)
Jones Smith Davies
Post
…
M.D. Accountant Porter Car(PK)
Violates referential integrity
No car - OK
Allocated
R 345 XYZ Jones P 987 CBA Davies M 567 GHJ Brown
…
Foreign Keys (FKs)- definition • Linking relation R2 to relation R1: • A foreign key in a relation R2 is a subset of its attributes such that: • there is a relation R1 with a candidate key CK • For each value of FK in R2 there must exist an identical value in the CK in some tuple of R1. Interactive Fiction
Foreign keys - notes • All keys are sets of attributes • A candidate key can contain a value not currently found in the foreign key • Chains of references can build up • Relations can reference themselves • personnel relation can have a “manager” attribute - managers are personnel
Foreign key - examples • Earlier example: PERSON{Name(PK), Post} CAR_ALLOC{Car(PK), Allocated*} FK {Allocated} references PERSON
Notation
• Self referential example: a surgeon is supervised by a senior surgeon, called a “consultant”) SURGEON {Surgeon(PK), Consultant*} FK {Consultant} references SURGEON
Referential Integrity • The database must not hold any unmatched foreign keys • The DBMS should prevent the situation arising - most do today • The DBMS can: • reject operation which would compromise integrity or • make other changes to retain integrity
Maintaining R. Integrity • Attempt to delete the • Attempt to update target of a foreign the candidate key key • only allow if there is no matching FK value
or
• only allow if there is no matching FK value
or
• cascade-update the • cascade-delete FK in the matching tuples with FK tuples matches Interactive Fiction
Beware Autogenerated Keys! Some systems readily offer to generate key values for you – e.g. every time another tuple is entered, a numeric key value is automatically allocated. This permits:
!
UID xxh8 jjo1 jja1 xxh8
UCAS 987632 003872 013873 987632
NH 234179 139873 243179 234179
Surname Kerr Jones Jones Kerr
FirstNameDOB Kevin 26.07.82 Jane 13.12,81 Jane 10.06.81 Kevin 26.07.82
City AutoKey Borth 1000 Lampeter 1001 Llanon 1002 Borth 1003
- the same information inserted twice with distinct autokey values!
Beware Autogenerated Keys! • Remedy: make Autokey, UID, UCAS, NH candidate keys and select one as PK. • Remedy: avoid introducing unnecessary new keys. Do we need an AutoKey in this example? • Caution: if you do introduce a new key, you still need to identify other candidate keys (or risk bad modelling).
Multiple Multi-attribute keys • Consider a timetable, with entries for Day, Time, Module, Room, Building, LecturerID • Assume that a Room label such as A6 can appear in different buildings. • Some data:
Day Monday Monday Friday Monday
Time 09.00 09.00 09.00 17.00
Module CI25910 CS23710 CS27310 CS25610
Room C22 A6 A6 C22
Building Lecturer Hugh Owen rrp Hugh Owen dap Llandinam hoh Hugh Owen dap
Candidate Keys? There might be several.
Multiple Multi-attribute Keys •
With business rules: e.g. •
•
a module has only one lecturer, a lecturer lectures in 1 room at a time, only 1 module in a room at a time ...
3 Candidate keys in this case: 1. {Day,Time, Room, Building}, – 4 attributes 2. {Day, Time, Lecturer} – 3 attributes 3. {Day, Time, Module}, – 3 attributes
•
Choose one to be the PK.
Multi-attribute Foreign Keys • A multi-attribute PK may be referenced from another relation • the referencing foreign key then needs to be declared with same structure as that PK (or generally, the CK) • {Room, Building} above could be declared to be a FK that references a relation with PK {Room, Building} describing facilities: Room A6 C22 A6
Building Hugh Owen Hugh Owen Llandinam
BoardType None Fixed Roller
Projection Facilities Lighting Yes Fixed Yes Dimming Yes Dimming
Data Integrity End