Transcript Slide 1
Chapter 6
The Relational
Algebra and
Relational
Calculus
Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Copyright © 2011 Ramez Elmasri and Shamkant Navathe
Copyright © 2011 Ramez Elmasri and Shamkant Navathe
Chapter 6 Outline
Tekli İlişkisel Operasyon: SELECT ve
PROJECT
Kümeler Kuramı ile İlişkisel Cebir
İkili ilişkisel işlemler: JOIN ve BÖLÜMÜ
Diğer işlemler
Copyright © 2011 Ramez Elmasri and Shamkant Navathe
Chapter 6 Outline (cont’d.)
Ilişkisel işlemler örnekleri
Tuple İlişkisel Hesaplama
Domain İlişkisel Hesaplama
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
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
• <attribute name> <comparison op> <constant value>
or
• <attribute name> <comparison op> <attribute
name>
Copyright © 2011 Ramez Elmasri and Shamkant Navathe
Unary Relational Operations:
SELECT and PROJECT (cont’d.)
Örnek:
<selection condition> 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)
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
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The PROJECT Operation
Tablodan sütun seçer ve diğer sütunları
atar:
Degree
Niteliklerin sayısı <attribute list>
Çiftlerin eliminanasyonu
PROJECT işlem sonucu farklı tuple dizileridir
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Sequences of Operations and
the RENAME Operation
In-line expression:
Işemlerin sırası, oluşan ara ilişkilerin
gösterilmesi:
Rename Ara sonuçların öznitelikleri
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
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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
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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.
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Binary Relational Operations:
JOIN and DIVISION
The JOIN işlemi
gösterimi
Iki ilişki içindeki Alakalı kayıtları tek ve “uzun”
bir kayıtta birleştirir
Genel Join şartları <condition> AND
<condition> AND...AND <condition>
Example:
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Binary Relational Operations:
JOIN and DIVISION (cont’d.)
THETA JOIN
Her <condition> formunda ki Ai θ Bj
Ai , R nin bir niteliği
Bj , S nin bir niteliği
Ai ve Bj aynı domain e sahipler
θ (theta) bir kıyaslama operatörüdür:
• {=, <, ≤, >, ≥, ≠}
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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
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 nR * nS
Inner joins
Eşle ve birleştir operasyonudur.
Daha önceden Kartezyen çarpım
kombinasyonu olarak ve Seçim olarak iffade
edildi
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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
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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
Copyright © 2011 Ramez Elmasri and Shamkant Navathe
Operations of Relational Algebra
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Operations of Relational Algebra
(cont’d.)
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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
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Copyright © 2011 Ramez Elmasri and Shamkant Navathe
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
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
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Copyright © 2011 Ramez Elmasri and Shamkant Navathe
Recursive Closure Operations
Operation applied to a recursive
relationship between tuples of same type
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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:
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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
Copyright © 2011 Ramez Elmasri and Shamkant Navathe
Examples of Queries
in Relational Algebra (cont’d.)
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Examples
Copyright © 2011 Ramez Elmasri and Shamkant Navathe
Examples of Queries
in Relational Algebra (cont’d.)
Copyright © 2011 Ramez Elmasri and Shamkant Navathe
Copyright © 2011 Ramez Elmasri and Shamkant Navathe
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
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)
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
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
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Sample Queries in Tuple
Relational Calculus
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Notation for Query Graphs
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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
Copyright © 2011 Ramez Elmasri and Shamkant Navathe
Using the Universal Quantifier in
Queries
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
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
Copyright © 2011 Ramez Elmasri and Shamkant Navathe
The Domain Relational Calculus
(cont’d.)
QBE language
Based on domain relational calculus
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
Copyright © 2011 Ramez Elmasri and Shamkant Navathe