Query Language #1/3: Relational Algebra Pure, Procedural, and Set-oriented

Transcription

1 Quey Language #1/3: Relational Algeba Pue, Pocedual, and Set-oiented To expess a quey, we use a set of opeations. Each opeation takes one o moe elations as input paamete (set-oiented). Since each opeation poduces a new elation, the opeations can be input paametes. pocedual Relational-Algeba opeations: Relational algeba consists of a set of opeations. Composing elational algeba opeations into an expession is just like composing aithmetic opeations (e.g., +, -, /, *) into an aithmetic expession. Fundamental Set of Relational-Algeba Opeations: Selection (sigma σ), Pojection (pi Π), Union ( ), Set-diffeence (- ), Catesian-poduct ( ), Rename (ho ρ) Some Additional Opeations: Set-intesection ( ), Natual-join (><), Oute-join (=><, ><=, o =><=), Division ( ), Assignment ( ) The additional opeations can be expessed though some fundamental opeations. Howeve, they ae included in the elational algeba to facilitate easie constuction of moe complex queies. In addition, some people include moe opeations, e.g. complement opeation. These additional D. Byunggu Yu 1

2 opeations do not impove the expessive powe of elational algeba. Selection (sigma σ) Unay opeation on a elation (R), which poduces a elation '(R) (R). Let F be a pedicate A i = a, whee A i is an attibute name in R and a is a value in the domain of A i. Then, σ F () = {t t t[a i ] = a}. Pedicate can involve: Constant and attibutes; Compaative opeatos: =, >, <,,, and ; Logical opeatos:,, and ; Paenthesis: ( and ). Example1 A 2 b2 c1 3 b2 c2 σ A>1 A < 3 () A 2 b2 c1 Example2 σ banch-name="laamie" balance>2000 (account) D. Byunggu Yu 2

3 Pojection (pi Π) Π X () is an unay opeation on a elation (R), which poduces a elation '(X) in which X R. Any duplicate tuple is eliminated. Π X () = {t (X R) t } Genealized Pojection: X can be F1, F2,, Fn; Each F can be: an attibute o an aithmetic expession (e.g., balance, balance*0.3, balance-limit) Example1 A 2 b2 c2 3 b2 c2 Π B,C () b2 c2 Example2 Π account#, balance (account) Π account#, balance*0.25 (account) D. Byunggu Yu 3

4 Union ( ) Set (R) s(s) is a elation q(r), which contains tuples fom o fom s. Any duplicate tuple is eliminated. R and S must be the same. (R) s(s) = {t t t s} Example A 2 b2 c2 3 b2 c2 s b4 c5 Π B, C () s b2 c2 b4 c5 D. Byunggu Yu 4

5 Set-diffeence (-) Set (R) - s(s) is a elation q(r), which contains tuples in that ae not in s. R and S must be the same. (R)-s(S) = {t t t s} Example A 2 b2 c2 3 b2 c2 s b4 c5 Π B, C () - s b2 c2 D. Byunggu Yu 5

6 Catesian-poduct ( ) Set (R) s(s) is a elation q(q) whose schema Q is the concatenation of R and S. (R) s(s) = {t (Q=R+ 1 S) t1 (t[r] = t1) t2 s (t[s] = t2)} Example A 2 b2 c2 3 b2 c2 s b4 c5 s A.B.C s.b s.c b4 c5 2 b2 c2 2 b2 c2 b4 c5 3 b2 c2 3 b2 c2 b4 c5 D. Byunggu Yu 6

7 Rename (ho ρ) ρ x (), whose is on elation schema R, is an unay opeation that etuns a elation x(r). If one use ρ x(a1, A2,, An) () then the attibutes of R ae enamed to A1, A2,, An. Example b4 c5 ρ s(d) (Π C ()) D c1 c5 b4 c5 c1 b4 c5 c5 1 Concatenation D. Byunggu Yu 7

8 Set-intesection ( ) Set (R) s(s) is a elation q(r) that contains common tuples in and s afte emoving the duplicates. R and S must be the same. (R) s(s) = {t t t s} Example A 2 b2 c2 3 b2 c2 s b4 c5 Π B, C () s D. Byunggu Yu 8

9 Natual-join (><) Set (R) >< s(s) is a elation q(q) whose schema Q is the union of R and S. Evey tuple in elation q satisfies (t q t[q R] t[q S] s) (R) >< s(s) = {t (Q=R S) t[q R] t[q S] s} = Π R S (σ.a1=s.a1.a2=s.a2.an=s.an s) whee R S = {A1, A2,, An}. We can give a simple o composite pedicate θ on attibutes in R+ 2 S, i.e. >< θ s (theta join). Example A 2 b2 c2 3 b2 c2 s b4 c5 >< s A 2 concatenation D. Byunggu Yu 9

10 Oute-join (Left oute-join: =><, Right oute-join: ><=, and full oute-join: =><=) (R) =>< s(s): takes all tuples in that did not match with any tuple in s, pads the tuples with null values fo the attibutes S-R, and adds them to the esult of the natual join. (R) ><= s(s): takes all tuples in s that did not match with any tuple in the, pads the tuples with null values fo the attibutes R-S, and adds them to the esult of the natual join. (R) =><= s(s) = (R) =>< s(s) (R) ><= s(s) Example A B 1 b1 2 b2 3 b2 s B D b1 d1 b4 d2 =>< s A B D 2 b2 null 3 b2 null D. Byunggu Yu 10

11 Division ( ) Set (R) s(s) is a elation q(q) satisfying the following conditions: (1) S R Q=R-S (2) t q t s S ( t R (t [S]=t s t [R-S] = t)) (R) s(s) = {t(q=r-s) t s s ( t (t [S]=t s t [R-S] = t))} Example A 1 b4 c5 3 b2 c2 s b4 c5 s A 1 D. Byunggu Yu 11

12 Assignment ( ) Assignment to tempoay elation vaiable: A quey can be witten as a sequential pogam. e.g., temp1 Π R-S () temp2 Π R-S ((temp1 s) - ) temp1 - temp2 vs. Π R-S () - Π R-S ((Π R-S () s) - ) Assignment to pemanent elation: used to expess database modification (insetion, deletion, update). e.g., Insetion: account account {("Laamie", 28345, 5000)} Deletion: account account - σ account#=28345 (account) Update: account Π banch-name, account#, balance*1.05 (account) account σ account# (account) Π banch-name, account#, balance*1.05 (σ account#=28345 (account)) D. Byunggu Yu 12

13 Quey Language #2/3: Tuple Relational Calculus Pue, Non-pocedual, Relational We descibe what we want without how to obtain it. Specifically, {t P(t)}, whee "t" means "esult tuple", is ead as: (I want) The set of all tuples t such that the quey pedicate P is tue fo t. e.g.1 {t t account t[balance] > 1200} Note, t[a] denote the values of tuple t on attibute (o attibutes) A e.g. 2 {t a account (t[account#] = a[account#] a[balance] > 1200)} Note, the diffeence between e.g.1 and e.g.2 is that the esult of e.g.2 consist of only one attibute "account#" e.g. 3 {t c checking (t[custome#] = c[custome#]) } s saving (t[custome#] = s[custome#]) e.g. 4 {t c checking (t[custome#] = c[custome#]) s saving (t[custome#] = s[custome#]) } l loan (t[custome#] = l[custome#]) D. Byunggu Yu 13

14 e.g. 5 {t b banch (b[banch-city] = "Laamie" => a acc-cust (t[custome#] = a[custome#]) a[banch#] = b[banch#] ) ) } Note, P1 => P2 means "P1 implies P2 o if P1 is tue then P2 must be tue" (P2 is the supeset of P1). (P1 => P2) (P1 P2) ( P1 P2) D. Byunggu Yu 14

15 Quey Language #3/3: Domain Relational Calculus Pue, Non-pocedual, Relational Domain calculus is the same as tuple calculus except that the expession is always "domain-oiented" (attibute-oiented). Specifically, {<x1, x2,, xn> P(x1, x2,, xn)} whee x1, x2,, and xn ae the 1 st, 2 nd,, and 3 d attibute values of a esult tuple, espectively. e.g.1 find evey tuple, whose balance is geate than 1200, fom "account" elation: {<a, b, c> <a, b, c> account b > 1200} e.g.2 {<a> b, c(<a, b, c> account b > 1200)} Same as e.g.1 except that we want only "account#". e.g.3 {<c> a, b, o (<a, b, c, o> checking) a, b, i (<a, b, c, i> saving) } Note, 'a' stands fo account#, 'b' fo balance, 'c' fo custome#, 'o' fo ovedaft-amount, and 'i' fo inteest-ate D. Byunggu Yu 15

16 e.g. 4 {<c> a, b, o (<a, b, c, o> checking) a, b, i (<a, b, c, i> saving) a, l (<l, a, c> loan) } Note, 'l' stands fo loan# and a fo loan-amount e.g. 5 {<c> b, c1 (<b, c1> banch c1 = "Laamie" => a (<a, c, b> acc-cust) ) } Note, 'b' stands fo banch#, 'c1' stands fo banch-city, and 'a' stands fo account#. A dot (.) in a pedicate is used to indicate that the scope of the peceding quantifie extends to the end of the entie pedicate. This is a convenient way to eliminate deep nesting of paenthesis. Note, people geneally agee with that the expessive powes of all thee elational languages ae the same. D. Byunggu Yu 16

17 1. View A view is a vitual elation that is made visible to a use (o a goup of uses) but does not exist in logical level database (ecall the thee level schema). We define a view with a quey expession. e.g., ceate view Checking_Customes as Π c-name, custome#, account#, telephone#, addess (custome >< checking-account) Since a view is vitually a elation, it changes dynamically. Theefoe, in the peceding example, if we modify custome o checking-account elations, view must be also modified. If views exist physically, data edundancy and inconsistency poblems occu. Usually, DBMSs don t stoe views as actual elations but stoe thei definitions. Howeve, if the undelying database has only the definitions, wheneve a view is used as a elation in a quey, each view name must be eplaced by the quey expession in the view definition. That is, the view must be ecomputed evey time. With this, the pefomance will D. Byunggu Yu 17

18 deteioate. Theefoe, some people have poposed mateialized views. In this appoach, views ae actually stoed as physical elations. Howeve, thee ae added complexity and ovehead fo updates. Since each view is a elation to the uses, the uses may update thei views. Howeve, because of its complexity, view modifications ae geneally not allowed. Note, to uses, views ae elations. D. Byunggu Yu 18

19 Stuctued Quey Language (SQL) Commecial, Pocedual + Non-pocedual, Not always elational Easy to use Based on both elational algeba and elational calculus. (e.g., You don't explicitly expess pojection opeation athe the opeation is expessed in select statement as what you want. In contast, you expess the pocedue in some complex queies, such as union of two sub select statements, embedded select, ). Details will be explained and discussed in LectueNote#4. D. Byunggu Yu 19