Database System - 3rd theory class : Formal Relational Query Languages (1) 20/03/16

Formal Relational Query Languages (形式化查詢語言)
Query Language : language in which users request information from the database
Categories of languages :

  1. procedural (過程性)
    Relational Algebra (關係代數)
  2. non-procedural (非過程性)
    Turple Kelational (元組關係演算) / Domain Relational Calculus (域關係演算)

" Pure language "

Relational Algebra → Procedural language
operations : Union (並) / Intersection (交) / Defference (差) / Cartesian Product (笛卡爾積) / Project (投影) / Select (選擇) / Join (連接) / Division (除)
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Campatibility (相容性) 👇
relation R&S are campatible when : (1) R , S must have same arity (同元的)
(2) The attribute domains must be compatible

  • Union
    Notation : R ∪ S
    Defined as : R ∪ S = { t | t ∈ R v t ∈ S } R , S should be compatible
    R ∪ S = S ∪ R

  • Difference
    Notation : R - S
    Defined as : R - S = { t | t ∈ R v t 不屬於 S } R , S should be compatible

  • Intersection
    Notation : R ∩ S
    Defined as : R ∩ S = { t | t ∈ R ^ t ∈ S } R , S should be compatible
    R ∩ S = S ∩ R = R - ( R - S ) = S - ( S -R )

  • Cartesian Product
    Notation : R X S
    Defined as : R X S = { t q | t ∈ R ^ q ∈ S } R , S are disjoint ( R ∩ S = 空集 )
    degree : R - n , S - m , R X S - n X m

  • Select
    Notation : 2
    p is called the selection predicate (選擇謂詞)
    Where pis a formula in propositional calculus (命題演算) consisting of terms connected by : aEach term is one of: attribute opattribute or constant

  • Project
    Notation : A1, A2, …,Ak(R)
    where A1 , A2 , … , Akare attribute names and R is a relation name.
    The result is defined as the relation of k columns obtained by erasing the columns that are not listed

  • Join
    Notation : 
    Defined as : -=-=-
    R ( A1 , A2 , … , An ) , A ∈ { A1 , A2 , … , An }
    S ( B1 , B2 , … , Bm ) , B ∈ { B1 , B2 , … , Bm }
    t ∈ R , s ∈ S
    A and B are compatible
    θ ∈ { ≥ , > , ≤ ,<, = , <> }
    Join usually used with Select and Project together

  • Rename
    Notation : ρ
    Rename a relation to another with a different name.
    Duplicate a relation and give a new name.
    R1 → R2 , and only the relation names are different for R1 and R2
    Query : Select all course No.s which both “2015030101” and “2015040101”

  • Equal-Join
    Notation : 1
    Defined as : 2
    R ( A1 , A2 , … , An ) , A ∈ { A1 , A2 , … , An }
    S ( B1 , B2 , … , Bm ) , B ∈ { B1 , B2 , … , Bm }
    t ∈ R , s ∈ S
    A and B are compatible
    Equal-Join is a special case of Join

  • Natural-Join
    Notation: 1
    Defined as: 33
    R and S have one same attribute or a group of same attributes.
    Duplicated columns should be deleted in the result relation.
    Natural-Join is a special case of Equal-Join

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