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Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 6 The Relational Algebra and Relational Calculus.

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... konulu sunumlar: "Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 6 The Relational Algebra and Relational Calculus."— Sunum transkripti:

1 Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 6 The Relational Algebra and Relational Calculus

2 Copyright © 2011 Ramez Elmasri and Shamkant Navathe

3

4 Chapter 6 Outline  Tekli İlişkisel Operasyon: SELECT ve PROJECT  Kümeler Kuramı ile İlişkisel Cebir  İkili ilişkisel işlemler: JOIN ve BÖLÜMÜ  Diğer işlemler

5 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Chapter 6 Outline (cont’d.)  Ilişkisel işlemler örnekleri  Tuple İlişkisel Hesaplama  Domain İlişkisel Hesaplama

6 Copyright © 2011 Ramez Elmasri and Shamkant Navathe The Relational Algebra and Relational Calculus  İlişkisel Cebir  Ilişkisel model için operasyonların temel seti  İlişkisel cebir ifadesi  Ilişkisel cebir işlemleri sırası  Bağıntı analizi  Ilişkisel sorgular belirtmek için üst düzey açıklayıcı bir dil

7 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Unary Relational Operations: SELECT and PROJECT  SELECT işlevi  Bir seçim koşulu karşılayan bir ilişki dizilerini Altkümesi : Boole ifadesi formun hükümler içeren or

8 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Unary Relational Operations: SELECT and PROJECT (cont’d.)  Örnek:  R içindeki her tuple t ye ayrı olarak uygulanır  Koşul DOĞRU olarak değerlendirilirse, tuple seçilir  Koşullar AND, OR, and NOT  Tekli  (tek ilişki üzerinde çalışır)

9 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Unary Relational Operations: SELECT and PROJECT (cont’d.)  Seçicilik  Bir seçim koşulu tarafından seçilen dizilerini bir kesimi  SELECT işlev değişmeli  Farlı SELECT işlemlerini AND Operatörü kullanarak basamakla

10 Copyright © 2011 Ramez Elmasri and Shamkant Navathe The PROJECT Operation  Tablodan sütun seçer ve diğer sütunları atar:  Degree  Niteliklerin sayısı  Çiftlerin eliminanasyonu  PROJECT işlem sonucu farklı tuple dizileridir

11 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Sequences of Operations and the RENAME Operation  In-line expression:  Işemlerin sırası, oluşan ara ilişkilerin gösterilmesi:  Rename Ara sonuçların öznitelikleri

12 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Relational Algebra Operations from Set Theory  UNION, INTERSECTION, and MINUS  Çeşitli şekillerde iki set elemanları Birleştirme  İkili işlemler  İlişki dizilerini aynı tür olmalıdır  UNION  R ∪ S  R veya/ ve S içindeki tüm tupleları içerir  Çift tuples elenir

13 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Relational Algebra Operations from Set Theory (cont’d.)  INTERSECTION  R ∩ S  Hem R ve hem de S olan tüm dizilerini içermektedir  SET DIFFERENCE (or MINUS)  R – S  S de olmayıp R de olan tüm tuple ları içerir

14 Copyright © 2011 Ramez Elmasri and Shamkant Navathe The CARTESIAN PRODUCT (CROSS PRODUCT) Operation  KRTEZYEN ÇARPIM  Çapraz Çarpım or Çapraz Birleşim  × ile gösterilir  Ikili küme işlemidir.  Ilişkilerin UNION uyumlu olmasıan gerek yoktur  Niteliklerin arasında bir seçim ile kullanılırsa anlamlı olacaktır.

15 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Binary Relational Operations: JOIN and DIVISION  The JOIN işlemi  gösterimi  Iki ilişki içindeki Alakalı kayıtları tek ve “uzun” bir kayıtta birleştirir  Genel Join şartları AND AND...AND  Example:

16 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Binary Relational Operations: JOIN and DIVISION (cont’d.)  THETA JOIN  Her formunda ki A i θ B j  A i, R nin bir niteliği  B j, S nin bir niteliği  A i ve B j aynı domain e sahipler  θ (theta) bir kıyaslama operatörüdür: {=,, ≥, ≠}

17 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Variations of JOIN: The EQUIJOIN and NATURAL JOIN  EQUIJOIN  Sadece = karşılaştırma operatörü  Aynı değere sahip kayıtları içerir ayrıca tüm alanları içerir  NATURAL JOIN  *, Gözterilir  ikinci nitelik içindeki (fazladan ) nitelikleri kaldırır EQUIJOIN farklı olarak

18 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Variations of JOIN: The EQUIJOIN and NATURAL JOIN (cont’d.)  Join seçiciliği  Beklenen büyüklükteki birleşmenin max büyüklüğe bölünmesi n R * n S  Inner joins  Eşle ve birleştir operasyonudur.  Daha önceden Kartezyen çarpım kombinasyonu olarak ve Seçim olarak iffade edildi

19 Copyright © 2011 Ramez Elmasri and Shamkant Navathe A Complete Set of Relational Algebra Operations  Set of relational algebra operations {σ, π, ∪, ρ, –, ×} is a complete set  Any relational algebra operation can be expressed as a sequence of operations from this set

20 Copyright © 2011 Ramez Elmasri and Shamkant Navathe The DIVISION Operation  Denoted by ÷  Example: retrieve the names of employees who work on all the projects that ‘John Smith’ works on  Apply to relations R(Z) ÷ S(X)  Attributes of R are a subset of the attributes of S

21 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Operations of Relational Algebra

22 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Operations of Relational Algebra (cont’d.)

23 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Notation for Query Trees  Query tree  Represents the input relations of query as leaf nodes of the tree  Represents the relational algebra operations as internal nodes

24 Copyright © 2011 Ramez Elmasri and Shamkant Navathe

25 Additional Relational Operations  Generalized projection  Allows functions of attributes to be included in the projection list  Aggregate functions and grouping  Common functions applied to collections of numeric values  Include SUM, AVERAGE, MAXIMUM, and MINIMUM

26 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Additional Relational Operations (cont’d.)  Group tuples by the value of some of their attributes  Apply aggregate function independently to each group

27 Copyright © 2011 Ramez Elmasri and Shamkant Navathe

28 Recursive Closure Operations  Operation applied to a recursive relationship between tuples of same type

29 Copyright © 2011 Ramez Elmasri and Shamkant Navathe OUTER JOIN Operations  Outer joins  Keep all tuples in R, or all those in S, or all those in both relations regardless of whether or not they have matching tuples in the other relation  Types LEFT OUTER JOIN, RIGHT OUTER JOIN, FULL OUTER JOIN  Example:

30 Copyright © 2011 Ramez Elmasri and Shamkant Navathe The OUTER UNION Operation  Take union of tuples from two relations that have some common attributes  Not union (type) compatible  Partially compatible  All tuples from both relations included in the result  Tut tuples with the same value combination will appear only once

31 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Examples of Queries in Relational Algebra (cont’d.)

32 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Examples

33 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Examples of Queries in Relational Algebra (cont’d.)

34 Copyright © 2011 Ramez Elmasri and Shamkant Navathe

35 The Tuple Relational Calculus  Declarative expression  Specify a retrieval request nonprocedural language  Any retrieval that can be specified in basic relational algebra  Can also be specified in relational calculus

36 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Tuple Variables and Range Relations  Tuple variables  Ranges over a particular database relation  Satisfy COND(t):  Specify:  Range relation R of t  Select particular combinations of tuples  Set of attributes to be retrieved (requested attributes)

37 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Expressions and Formulas in Tuple Relational Calculus  General expression of tuple relational calculus is of the form:  Truth value of an atom  Evaluates to either TRUE or FALSE for a specific combination of tuples  Formula (Boolean condition)  Made up of one or more atoms connected via logical operators AND, OR, and NOT

38 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Existential and Universal Quantifiers  Universal quantifier ( ∀ )  Existential quantifier ( ∃ )  Define a tuple variable in a formula as free or bound

39 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Sample Queries in Tuple Relational Calculus

40 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Notation for Query Graphs

41 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Transforming the Universal and Existential Quantifiers  Transform one type of quantifier into other with negation (preceded by NOT)  AND and OR replace one another  Negated formula becomes unnegated  Unnegated formula becomes negated

42 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Using the Universal Quantifier in Queries

43 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Safe Expressions  Guaranteed to yield a finite number of tuples as its result  Otherwise expression is called unsafe  Expression is safe  If all values in its result are from the domain of the expression

44 Copyright © 2011 Ramez Elmasri and Shamkant Navathe The Domain Relational Calculus  Differs from tuple calculus in type of variables used in formulas  Variables range over single values from domains of attributes  Formula is made up of atoms  Evaluate to either TRUE or FALSE for a specific set of values Called the truth values of the atoms

45 Copyright © 2011 Ramez Elmasri and Shamkant Navathe The Domain Relational Calculus (cont’d.)  QBE language  Based on domain relational calculus

46 Copyright © 2011 Ramez Elmasri and Shamkant Navathe Summary  Formal languages for relational model of data:  Relational algebra: operations, unary and binary operators  Some queries cannot be stated with basic relational algebra operations But are important for practical use  Relational calculus  Based predicate calculus


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