CHAPTER 2 RELATIONAL MODEL

Transcription

1 CHAPTER RELATIONAL MODEL

2 Chpter : Reltionl Model Structure of Reltionl Dtbses Fundmentl Reltionl Algebr Opertions Additionl Reltionl Algebr Opertions Extended Reltionl-Algebr-Opertions Null Vlues Modifiction of the Dtbse Copyright by S.-g. Lee Chp -

3 Exmple of Reltion Copyright by S.-g. Lee Chp - 3

4 Bsic Structure Formlly, given sets D, D,. D n reltion r is subset of D x D x x D n or R D, X.. X D n (n: degree of R) R = { <d,..., d n > d D,..., d n D n } (set of tuples) Exmple: customer-nme = {Jones, Smith, Curry, Lindsy} customer-street = {Min, North, Prk} customer-city = {Hrrison, Rye, Pittsfield} Then r = { (Jones, Min, Hrrison), (Smith, North, Rye), (Curry, North, Rye), (Lindsy, Prk, Pittsfield)} is reltion over customer-nme x customer-street x customer-city Copyright by S.-g. Lee Chp - 4

5 Attribute Types Ech ttribute of reltion hs nme The set of llowed vlues for ech ttribute is clled the domin of the ttribute Attribute vlues re (normlly) required to be tomic, tht is, indivisible E.g. multivlued ttribute vlues re not tomic E.g. composite ttribute vlues re not tomic The specil vlue null is member of every domin The null vlue cuses complictions in the definition of mny opertions we shll ignore the effect of null vlues in our min presenttion nd consider their effect lter Copyright by S.-g. Lee Chp - 5

6 Reltion Schem A, A,, A n re ttributes R = (A, A,, A n ) is reltion schem E.g. Customer-schem = (customer-nme, customer-street, customer-city) r(r) is reltion (vrible) on the reltion schem R E.g. customer(customer-schem) Copyright by S.-g. Lee Chp - 6

7 Reltion Instnce The current vlues (reltion instnce) of reltion re specified by tble An element t of r is tuple, represented by row in tble ttributes customer-nme customer-street customer-city Jones Smith Curry Lindsy Min North North Prk Hrrison Rye Rye Pittsfield tuples customer Copyright by S.-g. Lee Chp - 7

8 Reltions re Unordered Order of tuples is irrelevnt (tuples my be stored in n rbitrry order) E.g. ccount reltion with unordered tuples Copyright by S.-g. Lee Chp - 8

9 Reltionl Dtbse A dtbse consists of multiple reltions Informtion bout n enterprise is broken up into prts, with ech reltion storing one prt of the informtion E.g.: ccount : informtion bout ccounts customer : informtion bout customers depositor : informtion bout which customer owns which ccount Storing ll informtion s single reltion such s results in repetition of informtion (e.g. two customers own n ccount) the need for null vlues (e.g. represent customer without n ccount) bnk(ccount-number, blnce, customer-nme,... ) Reltionl dtbse design (Chpter 6 & 7) dels with how to design reltionl schems Copyright by S.-g. Lee Chp - 9

10 The customer reltion & depositor reltion Copyright by S.-g. Lee Chp - 0

11 Keys Let K R K is superkey of R if vlues for K re sufficient to identify unique tuple of ech possible reltion r(r). By possible r we men reltion r tht could exist in the enterprise we re modeling. Exmple: {customer-nme, customer-street} nd {customer-nme} re both superkeys of Customer, if no two customers cn possibly hve the sme nme. K is cndidte key if K is miniml Exmple: {customer-nme} is cndidte key for Customer, since it is superkey, nd no subset of it is superkey. Copyright by S.-g. Lee Chp -

12 Schem Digrm for the Bnking Enterprise Copyright by S.-g. Lee Chp -

13 Query Lnguges Lnguge in which user requests informtion from the dtbse. Ctegories of lnguges procedurl specify wht dt re needed nd how to get those dt nonprocedurl declrtive specify only wht dt re needed Pure lnguges: Reltionl Algebr Tuple Reltionl Clculus Domin Reltionl Clculus Pure lnguges form underlying bsis of query lnguges tht people use. Copyright by S.-g. Lee Chp - 3

14 Reltionl Algebr Algebr : opertors nd opernds Reltionl lgebr opernds : reltions opertors : bsic opertors (+ dditionl opertions) tke two or more reltions s inputs nd give new reltion s result. Procedurl lnguge 6 Fundmentl Opertors select project union set difference Crtesin product renme Copyright by S.-g. Lee Chp - 4

15 Select Opertion? Exmple Reltion r: A B C D A=B ^ D>5 (r) : A B C D Copyright by S.-g. Lee Chp - 5

16 Select Opertion Nottion: p (r) p is clled the selection predicte Defined s: p (r) = {t t r nd p(t)} Where p is formul in propositionl clculus consisting of terms connected by : (nd), (or), (not) Ech term is one of: <ttribute> op <ttribute> or <constnt> where op is one of: =,, >,, <, Exmple: brnch-nme= Perryridge (ccount) Copyright by S.-g. Lee Chp - 6

17 Project Opertion? Exmple Reltion r: A B C A,C (r) A C A C = Copyright by S.-g. Lee Chp - 7

18 Project Opertion Nottion: A, A,, Ak (r) where A, A re ttribute nmes nd r is reltion nme. The result is defined s the reltion of k columns obtined by ersing the columns tht re not listed Duplicte rows removed from result? since reltions re sets Exmple: To eliminte the brnch-nme ttribute of ccount ccount-number, blnce (ccount) Copyright by S.-g. Lee Chp - 8

19 Union Opertion? Exmple Reltions r, s: A B A B 3 r s r s: A B 3 Copyright by S.-g. Lee Chp - 9

20 Union Opertion Nottion: r s Defined s: r s = {t tr or ts} For r s to be vlid (Union comptible). r, s must hve the sme rity (sme number of ttributes). The ttribute domins must be comptible (e.g., nd column of r dels with the sme type of vlues s does the nd column of s) E.g.: to find ll customers with either n ccount or lon customer-nme (depositor) customer-nme (borrower) Copyright by S.-g. Lee Chp - 0

21 Set Difference Opertion? Exmple Reltions r, s: A B A B 3 r s r? s: A B Copyright by S.-g. Lee Chp -

22 Set Difference Opertion Nottion r? s Defined s: r? s = {t t r nd t s} Set differences must be tken between comptible reltions. r nd s must hve the sme rity ttribute domins of r nd s must be comptible Copyright by S.-g. Lee Chp -

23 Crtesin-Product Opertion? Exmple Reltions r, s: A B C D E r b b s r x s: A B C D E b b b b Copyright by S.-g. Lee Chp - 3

24 Crtesin-Product Opertion Nottion: r x s Defined s: r x s = { t q t r nd q s} Assume tht ttributes of r(r) nd s(s) re disjoint; i.e., R S =. If not, renming of ttributes is needed. Copyright by S.-g. Lee Chp - 4

25 Composition of Opertions Cn build expressions using multiple opertions Exmple: A=C (r x s) r x s A B C D E b b b b A=C (r x s) A B C D E b Copyright by S.-g. Lee Chp - 5

26 Renme Opertion Allows us to nme, nd therefore to refer to, the results of reltionl-lgebr expressions. Allows us to refer to reltion by more thn one nme. N (E) returns the expression E under the nme N If reltionl-lgebr expression E hs rity n, then N (A, A,, An ) (E) returns the result of expression E under the nme N, nd with the ttributes renmed to A, A,., An. Copyright by S.-g. Lee Chp - 6

27 Bnking Exmple brnch (brnch-nme, brnch-city, ssets) customer (customer-nme, customer-street, customer-only) ccount (ccount-number, brnch-nme, blnce) lon (lon-number, brnch-nme, mount) depositor (customer-nme, ccount-number) borrower (customer-nme, lon-number) Copyright by S.-g. Lee Chp - 7

28 Exmple Queries Find ll lons of over $00 mount >00 (lon) Find the lon number for ech lon of n mount greter thn $00 lon-number ( mount>00 (lon)) Copyright by S.-g. Lee Chp - 8

29 Exmple Queries Find the nmes of ll customers who hve lon, n ccount, or both, from the bnk customer-nme (borrower) customer-nme (depositor) Find the nmes of ll customers who hve lon nd n ccount t bnk. customer-nme (borrower) customer-nme (depositor) Copyright by S.-g. Lee Chp - 9

30 Exmple Queries Find the nmes of ll customers who hve lon t the Perryridge brnch. customer-nme ( brnch-nme= Perryridge ( borrower.lon-number = lon.lon-number (borrower x lon))) Find the nmes of ll customers who hve lon t the Perryridge brnch but do not hve n ccount t ny brnch of the bnk. customer-nme ( brnch-nme = Perryridge ( borrower.lon-number = lon.lon-number (borrower x lon)))? customer-nme (depositor) Copyright by S.-g. Lee Chp - 30

31 Exmple Queries Find the nmes of ll customers who hve lon t the Perryridge brnch. Query customer-nme ( brnch-nme = Perryridge ( borrower.lon-number = lon.lon-number (borrower x lon))) Query customer-nme ( ( lon.lon-number = borrower.lon-number ( ( brnch-nme = Perryridge (lon) ) x borrower ) ) Copyright by S.-g. Lee Chp - 3

32 Exmple Queries Find the lrgest ccount blnce Renme ccount reltion s d The query is: blnce (ccount)? ccount.blnce ( ccount.blnce < d.blnce (ccount x d (ccount) ) ) Copyright by S.-g. Lee Chp - 3

33 Forml Definition A bsic expression in the reltionl lgebr consists of either one of the following: A reltion in the dtbse A constnt reltion Let E nd E be reltionl-lgebr expressions; the following re ll reltionl-lgebr expressions: E E E? E E x E p (E ), P is predicte on ttributes in E s (E ), S is list consisting of some of the ttributes in E N (E ), N is the new nme for the result of E Copyright by S.-g. Lee Chp - 33

34 Additionl Opertions We define dditionl opertions tht do not dd ny power to the reltionl lgebr, but tht simplify common queries. Set intersection Nturl join Division Assignment Copyright by S.-g. Lee Chp - 34

35 Set-Intersection Opertion Nottion: r s Defined s: r s ={ t t r nd t s } Assume union comptibility: r, s hve the sme rity ttributes of r nd s re comptible Note: r s = r? ( r? s ) Copyright by S.-g. Lee Chp - 35

36 Set-Intersection Opertion? Exmple Reltion r, s: A B A B 3 r s r s A B Copyright by S.-g. Lee Chp - 36

37 Nturl-Join Opertion Nottion: r s Let r nd s be reltions on schems R nd S, respectively. The result is reltion on schem R S which is obtined by considering ech pir of tuples t r from r nd t s from s. If t r nd t s hve the sme vlue on ech of the ttributes in R S, tuple t is dded to the result, where Exmple: t hs the sme vlue s t r on r t hs the sme vlue s t s on s R = (A, B, C, D) S = (E, B, D) Result schem = (A, B, C, D, E) r s is defined s: r.a, r.b, r.c, r.d, s.e ( r.b = s.b r.d = s.d (r x s)) Copyright by S.-g. Lee Chp - 37

38 Copyright by S.-g. Lee Chp - 38 Nturl-Join Opertion? Exmple Reltions r, s: A B 4 C D b b B 3 3 D b b E r A B C D b E s r s

39 Properties A,, A k (r) A,, A k (s) = A,, A k (r s) (r s) t = r (s t) If R S= then r s = r s (importnt) If R=S then r s = r s Thet Join combine selection with Crtesin product r s = σ (r s) where is predicte on RS Copyright by S.-g. Lee Chp - 39

40 Assignment Opertion The ssignment opertion () provides convenient wy to express complex queries, write query s sequentil progrm consisting of series of ssignments followed by n expression whose vlue is displyed s result of the query. Assignment must lwys be mde to temporry reltion vrible. Exmple: Write r s s temp R-S (r) temp R-S ((temp s)? R-S,S (r)) result = temp? temp The result to the right of the is ssigned to the reltion vrible on the left of the. My use the vrible in subsequent expressions. Copyright by S.-g. Lee Chp - 40

41 Exmple Queries Find ll customers who hve n ccount from t lest the Downtown nd the Uptown brnches. Query customer-nme ( brnch-nme= Downtown (depositor customer-nme ( brnch-nme= Uptown (depositor ccount)) ccount)) Query customer-nme, brnch-nme (depositor ccount) temp(brnch-nme) ({( Downtown ), ( Uptown )}) Copyright by S.-g. Lee Chp - 4

42 Exmple Queries Find ll customers who hve n ccount t ll brnches locted in Brooklyn city. customer-nme, brnch-nme (depositor ccount) brnch-nme ( brnch-city = Brooklyn (brnch)) Copyright by S.-g. Lee Chp - 4

43 END OF CHAPTER