Informationslogistik Unit 5: Data Integrity & Functional Dependency

Transcription

1 Informationslogistik Unit 5: Data Integrity & Functional Dependency 27. III. 2012

2 Outline 1 Reminder: The Relational Algebra 2 The Relational Calculus 3 Data Integrity Keeping data consistent 4 Functional Dependency

3 Formal Languages for Information Extraction What this is about (Reminder): The Relational Model: abstract model for (relational) databases Given a relational database, what information can be abstracted? describe all possible queries (resp. their result sets) on a relational database Two (abstract) languages for description: The relational algebra The relational calculus

4 Summary: The Relational Algebra What is this relational algebra stuff about? Define basic operations: selection ( WHERE) projection ( SELECT) union, set difference ( UNION, MINUS) Cartesian product ( JOIN) renaming ( AS) we may extract from database everything that can be expressed with these operations (corresponds to SQL query)

5 The Relational Algebra vs. The Relational Calculus the relational algebra: gives description how to extract information the relation calculus: describes information which can be extracted (based on so-called predicate logic)

6 The Main Idea of the Relational Calculus The Main Idea of the Relational Calculus Describe extractable information by a generalized selection. Reminder: The selection in the relational algebra was defined as: A Selection chooses all tuples t of a relation R that satisfy the so-called selection-predicate F: σ F (R) := {t R F(t)} The predicate F may consist of constants attribute names of the relation R operators for comparison: <, >,,, =, logical connectives: (and), (or), (not)

7 The Main Idea of the Relational Calculus A Selection chooses all tuples t of a relation R that satisfy the so-called selection-predicate F: σ F (R) := {t R F(t)} The predicate F may consist of constants attribute names of the relation R operators for comparison: <, >,,, =, logical connectives: (and), (or), (not) The Main Idea of the Relational Calculus Describe extractable information by a generalized selection. allow more general predicates in selection

8 The Relational Calculus Two distinct languages for relational calculus: relational tuple calculus: based on relations relational domain calculus: based on domains

9 The Relational Tuple Calculus Examples: all countries in Europe: { c c country and c.region= Europe } also allowed in selection of relational algebra

10 The Relational Tuple Calculus Examples: all countries in Europe: { c c country and c.region= Europe } also allowed in selection of relational algebra all countries that are larger than some other country in the same region: { c c country and there is c with c.region=c.region such that: c.area>c.area } more complex predicate than allowed in selection of rel. algebra

11 The Relational Tuple Calculus Examples: all countries in Europe: { c c country and c.region= Europe } also allowed in selection of relational algebra all countries that are larger than some other country in the same region: { c c country and there is c with c.region=c.region such that: c.area>c.area } more complex predicate than allowed in selection of rel. algebra all pairs of countries that lie in the same region: { (c, c ) c country and c country and c.region=c.region} tuples (c, c ) do not exist in table of database

12 The Relational Tuple Calculus: Formal Definition Similar to selection: { t F(t) } where F(t) is a formula as for selection, but now also quantifiers are allowed: all quantifier (symbol: ): for all existence quantifier (symbol: ): there is

13 The Relational Tuple Calculus: Safe Expressions It is possible to build expressions with infinite result set: { c c is not a country } Solution: define domain (=all possible values in database) consider only safe expressions where the result set is part of domain.

14 The Relational Domain Calculus very similar to relational tuple calculus only difference: not tuples but values { v P(v) } instead of { t P(t) } in tuple calculus, t has to be a tuple in domain calculus, v is just a value taken from a domain definition of safe expressions has to be modified

15 Expressiveness Theorem The following three languages have the same expressiveness: the relational algebra, the relational tuple calculus when restricted to safe expressions, the relational domain calculus when restricted to safe expressions. What does it mean? For each expression in one of the languages there is a corresponding expression in the two other languages. Note SQL is a stronger language, as it offers e.g. aggregation.

16 Keeping data consistent Outline 1 Reminder: The Relational Algebra 2 The Relational Calculus 3 Data Integrity Keeping data consistent 4 Functional Dependency

17 Keeping data consistent Data Integrity Data integrity deals with the maintenance of the consistency of the stored data. Implicit demands on data integrity so far:

18 Keeping data consistent Data Integrity Data integrity deals with the maintenance of the consistency of the stored data. Implicit demands on data integrity so far: Primary Keys: No multiple rows with same primary key. e.g. no two students with the same matriculation number

19 Keeping data consistent Data Integrity Data integrity deals with the maintenance of the consistency of the stored data. Implicit demands on data integrity so far: Primary Keys: No multiple rows with same primary key. e.g. no two students with the same matriculation number Foreign Keys: For each given values in primary key there is unique foreign key. e.g. unique director for each film in movie database

20 Keeping data consistent Data Integrity Data integrity deals with the maintenance of the consistency of the stored data. Implicit demands on data integrity so far: Primary Keys: No multiple rows with same primary key. e.g. no two students with the same matriculation number Foreign Keys: For each given values in primary key there is unique foreign key. e.g. unique director for each film in movie database Domains for attributes: determines data type for attributes e.g. population in cia is integer etc.

21 Keeping data consistent Data Integrity Two kinds of data integrity: static integrity: shall hold for snapshot at each time step dynamic integrity: shall hold for changes on the database ( guarantees maintenance of static integrity)

22 Keeping data consistent Referential Integrity Basic idea: A value for a foreign key needs corresponding value in the respective primary key. Reminder: When a primary key of a table is used as attribute in a different table, this is called a foreign key. Example: director in the movie database is a foreign key: it refers to the primary key id in the table actor. For each value of director there shall be corresponding value of id in actor.

23 Keeping data consistent Referential Integrity: Formal Definition Definition (foreign key, referential integrity) Given two relations (tables) R and R with κ being a primary key of R, we say that α is a foreign key in R if for all tuples (rows) r in R : 1 Either r.α contains only NULL values or only values NULL. 2 If r.α contains no NULL values, then there is an r in R such that r.α = r.κ. If this holds, this is called referential integrity. Example: Each director is either NULL or otherwise refers to value for id in actor.

24 Keeping data consistent Referential Integrity: Dangling References Example: Each director is either NULL or otherwise refers to value for id in actor. Now we could insert new film into movie: id title votes score director Adventures in InfoLog where 0 does not occur as id in actor! Such references are called dangling. They obviously violate referential integrity. When making changes in database, dangling references must be avoided!

25 Keeping data consistent Maintaining Referential Integrity According to definition we must have Allowed changes in database: Π α (R ) Π κ (R)

26 Keeping data consistent Maintaining Referential Integrity According to definition we must have Allowed changes in database: Π α (R ) Π κ (R) 1 inserting r in R when r (α) in Π κ (R): e.g. inserting new film with director which exists in actor

27 Keeping data consistent Maintaining Referential Integrity According to definition we must have Allowed changes in database: Π α (R ) Π κ (R) 1 inserting r in R when r (α) in Π κ (R): e.g. inserting new film with director which exists in actor 2 changing attribute value r.α from w to w with w in Π κ (R): e.g. changing the director of film to some value that exists in actor

28 Keeping data consistent Maintaining Referential Integrity According to definition we must have Allowed changes in database: Π α (R ) Π κ (R) 1 inserting r in R when r (α) in Π κ (R): e.g. inserting new film with director which exists in actor 2 changing attribute value r.α from w to w with w in Π κ (R): e.g. changing the director of film to some value that exists in actor 3 changing or deleting r.κ in R when σ α=r.κ (R ) = : e.g. changing or deleting an entry with id n in actor when there are no films in movie with director n

29 Keeping data consistent In Case of Violation What can / shall be done in case of violation of referential integrity? (caused by a change in the database)

30 Keeping data consistent In Case of Violation What can / shall be done in case of violation of referential integrity? (caused by a change in the database) 1 do not allow / reverse operation

31 Keeping data consistent In Case of Violation What can / shall be done in case of violation of referential integrity? (caused by a change in the database) 1 do not allow / reverse operation 2 setting to NULL (cf. Fig. 5.2): Example: If a director in actor is deleted or his id changed, then set the value of director in movie to NULL.

32 Keeping data consistent In Case of Violation What can / shall be done in case of violation of referential integrity? (caused by a change in the databaseexamples:) 1 do not allow / reverse operation 2 setting to NULL (cf. Fig. 5.2)

33 Keeping data consistent In Case of Violation What can / shall be done in case of violation of referential integrity? (caused by a change in the databaseexamples:) 1 do not allow / reverse operation 2 setting to NULL (cf. Fig. 5.2) 3 use cascading (cf. Fig. 5.1): Examples:

34 Keeping data consistent In Case of Violation What can / shall be done in case of violation of referential integrity? (caused by a change in the databaseexamples:) 1 do not allow / reverse operation 2 setting to NULL (cf. Fig. 5.2) 3 use cascading (cf. Fig. 5.1): Examples: If id is changed in actor change also director of corresponding films in movie.

35 Keeping data consistent In Case of Violation What can / shall be done in case of violation of referential integrity? (caused by a change in the databaseexamples:) 1 do not allow / reverse operation 2 setting to NULL (cf. Fig. 5.2) 3 use cascading (cf. Fig. 5.1): Examples: If id is changed in actor change also director of corresponding films in movie. If director is deleted in actor delete all corresponding films in movie.

36 Keeping data consistent In Case of Violation What can / shall be done in case of violation of referential integrity? (caused by a change in the databaseexamples:) 1 do not allow / reverse operation 2 setting to NULL (cf. Fig. 5.2) 3 use cascading (cf. Fig. 5.1): Examples: If id is changed in actor change also director of corresponding films in movie. If director is deleted in actor delete all corresponding films in movie. Attention: Cascading may be risky as it may trigger more than one deletion operation!

37 Keeping data consistent In Case of Violation What can / shall be done in case of violation of referential integrity? (caused by a change in the database) 1 do not allow / reverse operation 2 setting to NULL (cf. Fig. 5.2) 3 use cascading (cf. Fig. 5.1)

38 Keeping data consistent In Case of Violation What can / shall be done in case of violation of referential integrity? (caused by a change in the database) 1 do not allow / reverse operation 2 setting to NULL (cf. Fig. 5.2) 3 use cascading (cf. Fig. 5.1) 4 use triggers: i.e., run certain procedures when changes occur

39 Keeping data consistent In Case of Violation What can / shall be done in case of violation of referential integrity? (caused by a change in the database) 1 do not allow / reverse operation 2 setting to NULL (cf. Fig. 5.2) 3 use cascading (cf. Fig. 5.1) Attention: Using triggers implies similar risks as cascading!

40 Keeping data consistent More Complex Data Integrity Topics Foreign key constraints are simple form of data integrity constraints. More complex data integrity constraints possible. Example: Allow only exams of students who have attended lecture.

41 Keeping data consistent SQL and Data Integrity Depending on which SQL implementation you use, you may define primary and foreign keys when creating tables (MySQL ) check static data integrity (MySQL ) use cascading (MySQL ) define triggers (MySQL )

42 Reminder and Overview In Unit 3 (The Relational Model) we already had some guidelines on how to design a relational database: start with entities, relations, and attributes put them in relational database (cf. slides of Unit 3) Now we deal with some refinements. The base for these refinements is the notion of functional dependency.

43 Abstract Schemes and Their Realizations So far we have been a bit sloppy. In the following we distinguish between: abstract relational database schemes ( table structure without data) Notation: R realizations of such schemes R ( the data in these tables) Notation: R

44 Functional Dependency Definition (functional dependency) Given: an abstract relational database scheme R, and (sets of) attributes α, β in R. We say that β is functional dependent (FD) from α, if for all realizations R of R: Whenever two tuples have the same values for α, they also have the same values for β. Notation: α β Examples: { name} { region, area, population, gdp} in cia { jahr, monat} { tmin, tmax, gmin, sun, rain} in sowe

45 Functional Dependency: An Example We have: {A} {B} {A} {C} {C,D} {B} {B} {C} A B C D a 4 b 2 c 4 d 3 a 1 b 1 c 1 d 1 a 1 b 1 c 1 d 2 a 2 b 2 c 3 d 2 a 3 b 2 c 4 d 3

46 Checking Functional Dependency Checking a FD α β for a given realization R is easy: Sort R according to α. Check whether tuples with the same α-values have the same β-values. [ complexity for sorting: O(n log n) for n rows]

47 Trivial Functional Dependencies A FD is called trivial, if it holds for all possible realizations. Characterization of trivial FDs Each trivial FD is of the form α β with β α.

48 Keys and Functional Dependencies Actually, FD is a generalization of the key concept. can define keys via FD: Definition (superkey) Given an abstract relational database scheme R, α R is a superkey if α R. Trivially, all attributes in R constitute a superkey for R (since R R).

49 Full Functional Dependency To distinguish keys from superkeys we need the notion of full FD: Definition (full FD) β is fully functional dependent from α if 1 α β, and 2 α is minimal, i.e. when removing any attribute A from α, the FD breaks down, i.e. α A β. Notation: α β

50 Keys and Functional Dependencies ctd. Definition (candidate key) Given an abstract relational database scheme R, α R is a candidate key if α R. A primary key is chosen among the candidate keys. It is not important which one is chosen. It is important that the same primary key is used throughout (e.g. as foreign key in other tables).

51 Properties of FDs Example: Student phone book: {[matrnr, name, street, postal code, town, phone prefix (Vorwahl), phone number]} FDs: {matrnr} {name, street, postal code, town} {postal code} {phone prefix} {matrnr} {phone prefix} Note: The third relation somehow follows from the other two..

52 Properties of FDs: Armstrong Axioms Armstrong Axioms: Reflexivity: If β α then α β. In particular, α α.

53 Properties of FDs: Armstrong Axioms Armstrong Axioms: Reflexivity: If β α then α β. In particular, α α. Strengthening: If α β, then also αγ βγ. (Notation: αγ stands for α γ.)

54 Properties of FDs: Armstrong Axioms Armstrong Axioms: Reflexivity: If β α then α β. In particular, α α. Strengthening: If α β, then also αγ βγ. (Notation: αγ stands for α γ.) Transitivity: If α β and β γ then also α γ.

55 Properties of FDs: The Closure Definition (closure) Given a relation R and a set F of FDs of R, the closure F + of F is the set of all FDs that logically follow from the FDs in F. Soundness and Completeness of Armstrong Axioms Whatever can be derived from F using the Armstrong Axioms is in F + (soundness). All FDs in F + can be derived from F using the Armstrong Axioms (completeness).

56 More Properties of FDs Using the Armstrong Axioms also the following properties can be derived: Union: If α β and α γ then α βγ. Decomposition: If α βγ, then α β and α γ. Pseudotransitivity: If α β and βγ δ then also αγ δ.

57 Properties of FDs: Example revisited Example: Student phone book {[matrnr, name, street, postal code, town, phone prefix (Vorwahl), phone number]} FDs: 1 {matrnr} {name, street, postal code, town} 2 {postal code} {phone prefix} 3 {matrnr} {phone prefix} Deriving the third FD from the other two:

58 Properties of FDs: Example revisited Example: Student phone book {[matrnr, name, street, postal code, town, phone prefix (Vorwahl), phone number]} FDs: 1 {matrnr} {name, street, postal code, town} 2 {postal code} {phone prefix} 3 {matrnr} {phone prefix} Deriving the third FD from the other two: By (repeated) Decomposition we have from (1): {matrnr} {postal code}

59 Properties of FDs: Example revisited Example: Student phone book {[matrnr, name, street, postal code, town, phone prefix (Vorwahl), phone number]} FDs: 1 {matrnr} {name, street, postal code, town} 2 {postal code} {phone prefix} 3 {matrnr} {phone prefix} Deriving the third FD from the other two: By (repeated) Decomposition we have from (1): {matrnr} {postal code} Using this together with (2) we have by Transitivity (3).

60 Determination of Functional Dependent Attributes Given: attributes α, set F of FDs We want: all attributes α + F that are functional dependent from α Algorithm: Initialize α + F := {α}, change:=true; while (change) do{ change=false; for each FD β γ in F do{ if (β α + ) then{ α + F := α+ F γ; change=true; }}} This algorithm can be used to determine superkeys κ: If κ + = R, then κ is a superkey of R.