ER Modelling: Summary

Transcription

1 ER Modelling: Summary ER describes the world (the set of possible worlds) what it is and the laws of this world ER is static: it does not describe (legal) transitions Useful for two purposes build software to answer questions about the world judge whether something is legal or illegal Use Case 1: build software to answer questions we will learn that methodology next (ER->relational) Use Case 2: judge what is legal you need a mapping from ER to the real world What does drink mean? What does has mean? you need to be consistent with that mapping. Not easy in a model with 30,000 entities and 70,000 relationships Main tools of modelling: scissors (abstraction & classification) 1

2 Relational Data Model Relation: R D 1 x... x D n D 1, D 2,..., D n are domains Example: AddressBook string x string x integer Tuple: t R Example: t = ( Mickey Mouse, Main Street, 4711) Schema: associates labels to domains Example: AddrBook: {[Name: string, Address: string, Tel#:integer]} 2

3 AddrBook Name Street Tel# Mickey Mouse Main Street 4711 Minnie Mouse Broadway Donald Duck Broadway Instance: the state of the database Key: minimal set of attributes that identify each tuple uniquely E.g., {Tel#} or {Name, BirthDate} Primary Key: (marked in schema by underlining) select one key use primary key for references 3

4 Uni-Schema Legi Name Student Semester N N requires followup prerequisite attends M N Lecture M M N Nr CP Title Grade tests gives PersNr 1 1 Level Name Assistant N Works-for 1 Professor Room Area PersNr Name 4

5 Rule #1: Implementation of Entities Student: {[Legi:integer, Name: string, Semester: integer]} Lecture: {[Nr:integer, Title: string, CP: integer]} Professor: {[PersNr:integer, Name: string, Level: string, Room: integer]} Assistant: {[PersNr:integer, Name: string, Area: string]} 5

6 Rule #2: Relationships A 21 A 2k 2 A 11 E 1... E 2 R... E n A 1k1 A R 1 R A k R A n1 A nk n R R A11,..., A1 k, A21,..., A2,..., 1,...,, 1,..., 1 k A 2 n Ank A A n kr R:{[ ]} Key of E 1 Key of E 2 Key of E n Attributesof R 6

7 Implementation of Relationships attends : {[Legi: integer, Nr: integer]} gives : {[PersNr: integer, Nr: integer]} works-for : {[AssistentPersNr: integer, ProfPersNr: integer]} requires: {[prerequisite: integer, follow-up: integer]} tests : {[Legi: integer, Nr: integer, PersNr: integer, Grade: decimal]} 7

8 Instance of attends Student Legi Legi Student N attends LegiNr Nr attends M Lecture Nr Nr Lecture 8

9 Rule 2: How to call the attributes If the ER specifies roles use the names of the roles Otherwise use the names of the key attributes in the entities in case of ambiguity, invent new names Example: friend : {[ProfNr: integer, AssiNr: integer]} Professor PersNr N friend M Assistant PersNr 9

10 Exercise Implement the following ER diagram using the rel. data model Number 1 1 plus 1 10

11 Rule #3: Merge relations with the same key Professor gives 1 N Lecture Implementation according to Rule #2 Lecture : {[Nr, Title, CP]} Professor : {[PersNr, Name, Level, Room]} gives: {[Nr, PersNr]} Merge according to Rule #3 Lecture : {[Nr, Title, CP, PersNr]} Professor : {[PersNr, Name, Level, Room]} Why is this better? When can this be done? Zusammenwachsen, was zusammen gehört! 1 11

12 Instance of Professor and Lecture Professor PersNr Name Level Room 2125 Sokrates FP Russel FP Kopernikus AP Popper AP Augustinus AP Curie FP Kant FP 7 Lecture Nr Title CP PersNr 5001 Grundzüge Ethik Erkenntnistheorie Mäeutik Logik Wissenschaftstheorie Bioethik Der Wiener Kreis Glaube und Wissen Die 3 Kritiken Professor gives 1 N Lecture 12

13 This will NOT work Professor PersNr Name Level Room gives 2125 Sokrates FP Sokrates FP Sokrates FP Augustinus AP Curie FP 36?? Lecture Nr Title CP 5001 Grundzüge Ethik Erkenntnistheorie Mäeutik Logik Wissenschaftstheorie Bioethik Der Wiener Kreis Glaube und Wissen Die 3 Kritiken 4 Professor gives 1 N Lecture 13

14 This will NOT work Professor PersNr Name Level Room gives 2125 Sokrates FP Sokrates FP Sokrates FP Augustinus AP Curie FP 36?? Lecture Nr Title CP 5001 Grundzüge Ethik Erkenntnistheorie Mäeutik Logik Wissenschaftstheorie Bioethik Der Wiener Kreis Glaube und Wissen Die 3 Kritiken 4 Problem: Redundancy and Anomalies PersNr is no longer key of Professor (issue will be revisited when we talk about normal forms) 14

15 Rule #4: Generalization Area Assistant is_a Employee Professor PersNr Name Room Level 15

16 Rule #4: Generalization Area Assistant is_a Employee Professor PersNr Name Room Level Employee: {[PersNr, Name]} Professor: {[PersNr, Level, Room]} Assistant: {[PersNr, Area]} 16

17 Rule #4: Generalization-alternative Area Assistant is_a Employee Professor PersNr Name Room Level What is better? Employee: {[PersNr, Name]} Professor: {[PersNr, Name, Level, Room]} Assistant: {[PersNr, Name, Area]} 17

18 Rule #5: Weak Entities Student 1 takes N Exam Grade Part Legi covers N N gives Nr M M PersNr Lecture Professor Exam: {[Legi: integer, Part: string, Grade: integer]} covers: {[Legi: integer, Part: string, Nr: integer]} gives: {[Legi: integer, Part: string, PersNr: integer]} 18

19 Weak Entities in detail: takes takes: {[StudiLegi: int, ExamLegi: int, Part: string, Nr: int]} What is/are the key(s) of the takes relation? Why can it be merged with the Exam relation (Rule #3)? What happened to the StudiLegi column as part of this merge? 19

20 Food for Thought: OO vs. Relations How do Java and C++ implement ER? Are they a better match than the relational model? Specifically, how do Java and C++ implement Generalization? Is it good or bad to have several possible ways? Concept of Reference: Compare Java and Relational Model Which one is better? Life-time of objects: Compare Java and Relational Model Why different? 20

21 Relational Model of Uni-DB Professor PersNr Name Level Room 2125 Sokrates FP Russel FP Kopernikus AP Popper AP Augustinus AP Curie FP Kant FP 7 requires Prerequisite Follow-up tests Legi Nr PersNr Grade Student Legi Name Semester Xenokrates Jonas Fichte Aristoxenos Schopenhauer Carnap Theophrastos Feuerbach 2 attends Legi Nr Lecture Nr Title CP PersNr 5001 Grundzüge Ethik Erkenntnistheorie Mäeutik Logik Wissenschaftstheorie Bioethik Der Wiener Kreis Glaube und Wissen Die 3 Kritiken Assistant PerslNr Name Area Boss 3002 Platon Ideenlehre Aristoteles Syllogistik Wittgenstein Sprachtheorie Rhetikus Planetenbewegung Newton Keplersche Gesetze Spinoza Gott und Natur

22 Selection Projection X Cartesian Product A Join Rename Set Minus Relational Division Union Intersection F Semi-Join (left) E Semi-Join (right) C left outer Join D right outer Join Relational Algebra 22

23 Formal Definition of Rel. Algebra Atoms (basic expressions) A relation in the database A constant relation Operators (composite expressions) Selection: p (E 1 ) Projection: S (E 1 ) Cartesian Product: E 1 x E 2 Rename: V (E 1 ), A B (E 1 ) Union: E 1 E 2 Minus: E 1 - E 2 23

24 Selection and Projection Selection Semester > 10 (Student) Semester > 10 (Student) Legi Name Semester Xenokrates Jonas 12 Projection Level (Professor) Rang (Professor) Level FP AP 24

25 Cartesian Product L A B C a 1 b 1 c 1 a 2 b 2 c 2 D R E x = d 1 e 1 d 2 e 2 Result A B C D E a 1 b 1 c 1 d 1 e 1 a 1 b 1 c 1 d 2 e 2 a 2 b 2 c 2 d 1 e 1 a 2 b 2 c 2 d 2 e 2 25

26 Cartesian Product (ctd.) Professor x attends Professoren attends PersNr Name Level Raum Legi Nr 2125 Sokrates FP Sokrates FP Kant FP Huge result set (n * m) Usually only useful in combination with a selection (-> Join) 26

27 Natural Join Two relations: R(A 1,..., A m, B 1,..., B k ) S(B 1,..., B k, C 1,..., C n ) R A S = A1,..., Am, R.B1,..., R.Bk, C1,..., Cn ( R.B1=S. B1... R.Bk = S.Bk (RxS)) R A S R S R S S R A 1 A 2... A m B 1 B 2... B k C 1 C 2... C n 27

28 Three-way natural Join (Student A attends) A Lecture (Student A attends) A Lecture Legi Name Semester Nr Title CP PersNr Fichte Grundzüge Jonas Glaube und Wissen Carnap Wissenschftstheorie

29 Two Relations: R(A1,..., An) S(B1,..., Bm) Theta-Join R R A S = (R x S) R A S R A S S A 1 A 2... A n B 1 B 2... B m 29

30 Theta Join Example Train(name, start, destination,, length) Track(station, number,, length) Find all possible tracks for the CIS Alpino in Zurich station= Zurich (Track) A Train.length < Track.length name= CIS (Train) Source: anonymous student from the 2011 class 30

31 natural join Join Variants L A B C a 1 b 1 c 1 a 2 b 2 c 2 A R C D E c 1 d 1 e 1 = c 3 d 2 e 2 Result A B C D E a 1 b 1 c 1 d 1 e 1 left outer join L R A B C C D E a 1 b 1 c C 1 c 1 d 1 e 1 = a 2 b 2 c 2 c 3 d 2 e 2 Result A B C D E a 1 b 1 c 1 d 1 e 1 a 2 b 2 c

32 Join Variants right outer join L R A B C C D E a 1 b 1 c D 1 c 1 d 1 e 1 = a 2 b 2 c 2 c 3 d 2 e 2 Resultat A B C D E a 1 b 1 c 1 d 1 e c 3 d 2 e 2 32

33 Join Variants (full) outer join L R A B C C D E a 1 b 1 c B 1 c 1 d 1 e 1 = a 2 b 2 c 2 c 3 d 2 e 2 Resultat A B C D E a 1 b 1 c 1 d 1 e 1 a 2 b 2 c c 3 d 2 e 2 left semi join L A B C a 1 b 1 c 1 a 2 b 2 c 2 E R C D E c 1 d 1 e 1 = c 3 d 2 e 2 Resultat A B C a 1 b 1 c 1 33

34 Join Variants right semi join L A B C a 1 b 1 c 1 a 2 b 2 c 2 F R C D E c 1 d 1 e 1 = c 3 d 2 e 2 Resultat C D E c 1 d 1 e 1 34

35 Rename operator: Rename Operator Renaming of relation names Needed to process self-joins and recursive relationships E.g., two-level dependencies of lectures ( grandparents ) L1.Prerequisite( L2. Follow-up=5216 L1.Follow-up = L2.Prerequisite ( L1 (requires) x L2 (requires))) Renaming of attribute names Requirement Prerequisite (requires) 35

36 Intersection PersNr (Lecture) PersNr ( Level=FP (Professor)) Only works if both relations have the same schema Same attribute names and attribute domains Intersection can be simulated with minus: R S = R (R S) 36

37 Relational Division Find students who attended all lectures with 4CP. attends Nr ( CP=4 (Lecture)) 37

38 Definition of Division t R S, iff for each ts S exists a tr R such that: tr.s = ts.s tr.(r-s) = t M R V m 1 v 1 m 1 v 2 m 1 v 3 m 2 v 2 m 2 v 3 Division can be simulated with other operators: S V = v 1 v 2 R S R S = (R S) (R) (R S) (( (R S) (R) x S) R) M m 1 38

39 Division: Example R S = (R S) (R) (R S) (( (R S) (R) x S) R) R = attends; S = Lecture Legi (attends) All students (who attend at least one lecture) Legi (attends) x Lecture All students attend all lectures ( Legi (attends) x Lecture) attends Lectures a student does not attend Legi (( Legi (attends) x Lecture) attends): Students who miss at least one lecture Legi (hören) - Legi (( Legi (attends) x Lecture) attends) Students who attend all lectures What happens if there are no lectures or no attendance? 39

40 Relational Calculus Queries have the following form: {t P(t)} with t a variable, P(t) a predicate. Examples: All full professors {p p Professor p.level = FP'} Students who attend at least one lecture of Curie {s s Student a attends(s.legi=a.legi l Lecture(a.Nr=l.Nr p Professor(p.PersNr=l.PersNr p.name = 'Curie')))} 40

41 Who attends all lectures with 4 CP? {s s Student l Lecture (l.cp=4 a attends(a.nr=l.nr a.legi= s.legi))} There are two variants of relational calculus: tuple relational calculus (as in examples above, tuple vars) domain relational calculus (variables iterate over domains) 41

42 Tuple Relational Calculus Atoms s R s is a tuple variable, R is a name of a relation s.a t.b or s. A c s and t tuple variables, A and B attribute names a comparison (i.e.,,,,...) c is a constant (i.e., 25) Formulas All atoms are legal formulas If P is a formula, then P and (P) are also formulas If P 1 and P 2 are formulas, then P 1 P 2, P 1 P 2 and P 1 P 2 If P(t) is a formula with a free variable t, then t R(P(t)) and t R(P(t)) 42

43 Safety Restrict formulas to queries with finite answers Semantic not syntactic property! Example: The following expression is not safe {n (n Professor)} Definition of safety result must be subset of the domain of the formula domain of the formula All constants used in the formula All domains of relations used in the formula 43

44 Domain Relational Calculus An expression has the following form {[v 1, v 2,..., v n ] P (v 1,..., v n )} each v 1,..., v n is either a domain variable or a constant. P is a formula. Example: Legi and Name of all students tested by Curie: {[l, n] s ([l, n, s] Student v, p, g ([l, v, p, g] tests a,r, b([p, a, r, b] Professor a = 'Curie')))} 44

45 Safety in the DRC Defined in same way as for tuple relational calculus Example: The following expression is not safe {[p,n,r,o] ([p,n,r,o] Professoren) } (see text book for exact definition of safety in DRC) 45

46 Codd`s Theorem The three languages 1. relational algebra, 2. tuple relational calculus (safe expressions only) 3. domain relational calculus (safe expressions only) are equivalent Impact of Codd`s theorem SQL is based on the relational calculus SQL implementation is based on relational algebra Codd`s theorem shows that SQL implementation is correct and complete. 46