Implementing Associations among Classes in an Environment of Active Databases

P og amming and C mpu e So wa e, Vol. 26, No. 4, 2000, pp. 207-215. O iginal English Tex Copy igh 9 2000 by To es, Ma in, l oyano, Time. Implemen ing Associa ions among Classes in an En i onmen o Ac i e Da abases J. To es, O. Ma in, J. A. T oyano, and M. To o Depa men o Languages and Compu e Sys ems, Uni e si y o Se ille (Spain) e-mail: j o es( oc a io )( oyano )( m o o ) @ lsi. us.es Recei ed Sep embe 23, 1999 Abs ac --The associa ion is a na i e concep om ela ional da abases, one ha has been adap ed o objec o ien ed (OO) modelling. I is an in e es ing ope a o used o desc ibe links among objec s o a sys em, com- monly included in he mos popula diag am-based OO me hodologies. Howe e , hose me hodologies some- imes p esen a lack o o mali y ha may unde mine i s use. In his pape we o malize he seman ics o associa- ions. Fi s ly, we will desc ibe an OO model based on di e en kinds o cons ain s. Some o hem will be espe- cially use ul o desc ibing he seman ics o associa ions. Finally, we will p esen some ema ks abou implemen a ion by means o igge s, a new ea u e inco po a ed in da abases o speci y an inne ac i e beha io . I. INTRODUCTION The associa ion is a na i e concep om ela ional da abases ( ela ionships a e one o he pilla s o he En i y-Rela ionship model). This ope a o has been adap ed o OO modelling om he e y s a , by some e y impo an me hods [14, 15]. Associa ion is, oge he wi h inhe i ance, one o he mos popula mechanisms in OO me hods based on diag ams. Asso- cia ions among classes a e used o desc ibe links be ween objec s o a sys em. Links may be c ea ed and des oyed eely (al hough i is common o de ine se - e al kinds o cons ain s o es ic his eedom) [16]. Howe e , he associa ion usually has many in e p e- a ions (an e en mo e se ious p oblem a ises wi h he agg ega ion) [2, 7, 12]. In his wo k, we p esen a o - maliza ion o he p ope ies o associa ions by means o a po en OO model. We do no in end he e o gi e a new de ini ion o associa ion. Nei he do we in end o sub- s i u e me hods based on diag ams. These a e e y use- ul, because hey acili a e communica ion wi h use s and he alida ion o models. Howe e , we belie e ha i is necessa y o o malize hese me hods [4]. This way, ou sole objec i e is o o malize one o he possible in e p e a ions ha can be gi en [3, 14, 15]. This pape is o ganized as ollows. This in oduc- ion cons i u es he i s sec ion. In he second sec ion we will desc ibe an OO model based mainly on he de - ini ion o cons ain s. In he hi d sec ion, bo h he p ope ies and ea u es o associa ions will be desc ibed. These p ope ies a e ep esen ed in ou model acco ding o he s eps desc ibed in he ou h sec ion. In he i h sec ion, we will desc ibe ou main ideas in o de o hold he de ined seman ics in an en i- onmen o ac i e da abases (like O acle 8). Finally, in 1 This a icle was submi ed by he au ho s in English. he six h sec ion we will ex ac some conclusions o ou wo k. 2. AN OBJECT ORIENTED MODEL Objec s a e he undamen al elemen s in any OO model. In ou model, an objec is cha ac e ized by a g oup o a ibu es ha de ine i s s uc u e, a g oup o e en s ha desc ibe i s beha io and some ansi ion ules ha deno e he s a e changes o objec s. Objec s sha ing cha ac e is ics a e g ouped in o classes. Each a ibu e has a ype, de ined by an abs ac da a ype (ADT) o a class o objec s. Values o he a ibu es o an objec gi e in o ma ion abou i s s a e. A ibu es can be cons an , a iable o de i ed. Each objec has an iden i ica ion ha emains unchanged du ing i s li e. Iden i ica ion should be unique o each objec in he sys em. We conside ha each objec has a p ede ined a ibu e, called oid (objec iden i ie ) [ I I ]. Beha io aspec s o a class a e desc ibed by means o e en s. An e en desc ibes some hing ha happens in a momen o ime. Objec s in e ac wi h hei en i on- men by means o e en s, which ake place h ough communica ion channels. These channels ini ially coincide wi h he names o e en s. All objec s o he same class sha e each communica ion channel de ined in ha class. A name and se e al pa ame e s ha will be communica ed h ough he e en s o his name de ine a channel. E en s a e e y impo an because hey a e synch oniza ion and communica ion elemen s. We de ine in e ac ions be ween di e en objec s wi h hem. Objec s can be c ea ed and des oyed dynamically. All objec s composing a sys em a a gi en ins an in e - ac concu en ly. Howe e , he indi idual beha io o 0361-7688/00/2604-0207525.00 9 2000 MAIK "Nauka/ln e pe iodica" 208 TORRES e al. each objec is sequen ial. Remembe ha objec s in e - ac synch onously by means o e en s. O he impo an cha ac e is ics in ou model a e he ollowing: We use an ADT lib a y o desc ibe he s uc u e and unc ionali y o objec s. Speci ica ion is ca ied ou wi h di e en kinds o cons ain s. These cons ain s allow us o de ine h ee undamen al aspec s o objec s: (I) wha alues he a ibu es o objec s can ake, (2) how objec s can beha e in unc ion o hei s a e and (3) how objec s can in e ac and wi h whom. The model o in e ac ion be ween objec s is qui e lexible. The classes o objec s ha should in e ac a e de ined s a ically, while objec s o hese classes ha eally in e ac a e chosen dynamically. All objec s ul- illing hei cons ain s can pa icipa e. Facili ies a e p o ided o manipula e he ex ension o classes (g oup o objec s o a class ha exis a a ce - ain ins an ). This allows us o impose cons ain s on objec s on mul iple le els, as we will see in he nex sec ion. 2. I. Kinds o Cons ain s A la ge di e si y o cons ain s exis s in ou model [17]. Acco ding o he scope whe e cons ain s a e de ined, hey can be o wo kinds: 9 lndi Mual cons ain s. These cons ain s a e de ined in he class empla e. They mus be ul illed indi idually by all objec s belonging o ha class. 9 Collec i e cons ain s. Objec s o a class, consid- e ed as a collec ion, mus sa is y hese cons ain s, a he han indi idual objec s. Acco ding o he way cons ain s a ec he objec s, hey can be o h ee kinds: 1. Cons ain s on s a es o objec s. They allow us o de ine cons ain s on alues o a ibu es. Acco ding o he numbe o s a es a ec ed, hese cons ain s can be o wo kinds: (a) S a ic cons ain s. They es ic he alues o a ibu es and hey should no be iola ed in any s a e. I hey a e ul illed in he cu en s a e, hey should con- inue being ul illed in he nex s a e. I an objec does no ul ill hese cons ain s in he ini ial s a e, i will no be c ea ed. These cons ain s can be de ined in an indi- idual o collec i e way. (b) Dynamic cons ain s. They a e bonds be ween wo s a es: he cu en and he nex . The e a e wo kinds o dynamic cons ain s: (1) s a e changes associa ed wi h he occu ence o an e en , which ha e he es ic ed o m o an assignmen , and (2) mo e gene ic ansi ion cons ain s, which a e no associa ed wi h e en s and ac acco ding o de ined s a e changes. They can be de ined ei he in an indi idual o a collec i e way. 2. Pa icipa ion cons ain s. They de ine when an objec is in e es ed in pa icipa ing in an e en o when i mus pa icipa e. They can be speci ied in wo ways: (a) Pa icipa ion pe missions. They a e p edica es es ablished bo h on he s a e o an objec and on he pa ame e s o an e en . I hey a e no ul illed, hey will p e en he objec om pa icipa ing in ha e en . They can be de ined ei he in an indi idual o collec i e way. (b) Pa icipa ion obliga ions. Pe missions uniquely allow o objec s pa icipa e in an e en , wi hou assu - ing i s pa icipa ion ( o example, when cons ain s on s a es a e no ul illed). I pa icipa ion obliga ions a e ul illed, we a e assu ed ha objec s will pa icipa e in ha e en . They can only be de ined in an indi idual way. 3. In e ac ion cons ain s among objec s. They de ine how objec s in e ac be ween hem ( h ough e en s). Objec s ha should in e ac h ough an e en ha e o: (a) Synch onize. Ou model is o ally synch onous. I is necessa y ha all obliged objec s pa icipa e. I some objec ha is obliged o pa icipa e canno make i , hen he e en will no be able o happen. (b) Communica e. A communica ion o alues migh ake place be ween in e ac ing objec s. Values should ul ill all cons ain s imposed by hose objec s, bo h locally and globally. This way, a nego ia ion should be es ablished. I mo e han one alue is alid, he selec ion o he alue will be non-de e minis ic. Each class will ha e a local iew o e en s in which i pa icipa es. By means o in e ac ions, we uni y in a single global e en he di e en local iews o ha e en in he pa icipan classes. 2.2. Well-Fo med Exp essions Exp essions should be o med by e ms ha a e syn- ac ically co ec . This is done by any ope a ion de ined in he lib a y whose pa ame e s a e also syn ac ically co ec e ms o a iables o he co esponding so s (also de ined in he lib a y). Va iables o hese exp es- sions can be: 9 A ibu es e alua ed in he objec i sel . 9 A ibu es e alua ed in o he objec s, whose iden- i ica ion is known. Thus, i he class cll has he de ini- ion a j : c 2, he a ibu e ah is used o iden i y an objec o he class cl2. Then, he exp ession a e.a 2, being an a 2 a ibu e o objec s o he class cl2, is well o med. The ype o his exp ession is he same as he ype o he a ibu e a 2, and i deno es he alue o his a ibu e e alua ed in he objec a I. 9 Pa ame e s o e en s. These can only be used in speci ying pe missions, obliga ions and s a e changes. Exp essions o he ex ension can be o med in a simila way. We will conside ha : PROGRAMMING AND COMPUTER SOFTWARE Vol. 26 No. 4 2000 IMPLEMENTING ASSOCIATIONS AMONG CLASSES 209 1. The e exis s an implici ly de ined a ibu e ha holds he se o iden i ica ions o all objec s o each class. We will deno e by c~ he se o class cl. 2. The ollowing collec ion cons uc o s can be used: (a) {xi : cl ..... x, : c, I p ed(xl ..... x,) 9 exp(xl ..... x,,) }. Fo each combina ion x I ..... x,, o elemen s, i builds a se wi h alues e u ning he exp ession exp i he p edica e p ed is ue. This no a ion is only used i he se s c, ..... c, a e ini e. (b) [xi : bl ..... b,, :l p ed(xl ..... x,) 9 exp(x I ..... x,)]. Fo each combina ion xj ..... x, o elemen s, i builds a bag wi h alues e u ning he exp ession exp, when he p edica e p ed is ue. This no a ion is only used i bags bj ..... b,, a e ini e. 3. Since se s and bags a e manipula ed in he ex en- sion, we can also ha e ope a ions like add, p oduc , max, min, and, o , and so on. These ope a ions a e con- side ed as gene aliza ions o he co esponding bina y ope a ions. ~ Objec s.willing ~----'~ ~ pa clpa e "~ L I Objec s.obliged ~ ~ ] o pa icipa e - ~,,.._ Fig. 1. When can happen an e en ? An e en will be able o happen i (~ ~ ~c,( ) (Fig. 1) and ~,.,,( ,) ~: O, 'Vi 9 {l..n}. Finally, i he e en cn( ) happens, all objec s o 9 ~c,,,,~ will ca y ou he s a e changes associa ed o his e en . In sho , in ou model, se e al classes can pa ici- pa e in an e en and o each class all hose objec s ul- illing hei cons ain s. So, we ha e a mo e lexible communica ion model han he adi ional clien -se e app oach. 2.3. Dynamics o he Sys em An e en will be able o happen i , o each class synch onizing h ough his e en , he e is a leas one in e es ed objec . I some class does no ha e any objec s in e es ed in pa icipa ing, hen ha e en will no be able o happen. Cons ain s on s a es a e condi ions ha mus be ul- illed du ing he li e ime o objec s. Since he occu - ence o an e en can change he alue o some a ibu es, o he es ablished cons ain s should no be iola ed. In o de o exp ess hese ideas o mally, we will de ine wo se s. Le o,( ) be an e en o he sys em, wi h he channel cn and pa ame e s , in which he classes cl i pa icipa e h ough hei local iews cni( i), ' 'i e { I ..n }. We de ine: 9 ~c,,(,,,) o deno e he se o objec s o he class cli ha can pa icipa e h ough he local iew cni( i) o he e en . This se is composed o hose objec s o cl i ha ul ill hei pe missions on he local iew cni( i) and i s cons ain s on s a es a e no iola ed (a any le el). Then, he se o objec s ha can pa icipa e h ough all local iews o cn( ) will be ~c,,( ) = k..) ~c,,( i)" ie {I...n} 9 ~,.,,( ,) o deno e he se o objec s o cli ha mus pa icipa e h ough he local iew cni( 3 o he e en . This se is composed o hose objec s o cli ha ul ill i s obliga ions o pa icipa ing in cni( i). The se o objec s ha mus pa icipa e h ough all local iews o cn( ) will be: ie { I...n} 3. ASSOCIATIONS AMONG CLASSES In OO sys ems, he s a e is s uc u ed on di e en le els. This way, he s a e o an objec is de ined by he alues o i s a ibu es a a gi en momen . The s a e o he sys em, in p inciple, is de ined by he s a e o all objec s a es composing i a a gi en momen . Howe e , he s a e o a sys em canno always be desc ibed in his way. Such a s a e should also con ain links be ween objec s. These links a e speci ied by means o associa ions; i.e., links a e ins ances o asso- cia ions. 3.1. Cha ac e is ics o Associa ions Acco ding o he numbe o classes in ol ed, asso- cia ions can be o h ee ypes: bina y, i hey a e de ined be ween objec s o wo di e en classes, una y, i hey a e de ined be ween objec s o he same class and com- plex, i hey a e de ined be ween objec s o h ee o mo e classes. Hence o h, we will no conside he las one because i can become a se o bina y associa ions. An associa ion is de ined by (1) a name (2) he ole played by objec s o a class wi h ega d o he o he class, and (3) he mul iplici y o each ole. The mul i- plici y indica es how many objec s o a class can be ela ed wi h an objec o he o he class o he associa- ion. Associa ions a e commonly ep esen ed as con inu- ous lines be ween he pa icipan classes in he ela ion- ship, as shown in Fig. 2 (in UML no a ion [3]), whe e he name o he associa ion is omi ed o easons o cla i y. A each endpoin o he line he ole and he mul iplici y o he nea es class is indica ed. This deno es ha each objec o Class can be ela ed wi h mul iplici y2 objec s o Class2. On he o he hand, each PROGRAMMING AND COMPUTER SOFTWARE Wol. 26 No. 4 2000 210 TORRES e al. Classl I ole I mul iplici yl ole 2 mul iplici y2 Class2 Fig. 2. UML ep esen a ion o a bina y associa ion. Pe son Teaches in I I ca : Ca ego y I p o esso . i 1..*(se ) cen e O..l(se ) Uni e si y Fig. 3. Associa ion wi h a ibu es. objec o Class 2 can be ela ed wi h he mul iplici y 1 objec s o Classl. Mul iplici y is de ined by means o a ange no a ion (in ..sup). The lowe limi speci ies he minimum num- be o objec s linked wi h he gi en one. Acco ding o his numbe , an associa ion can be manda o y (posi i e numbe ) o op ional (0). The uppe limi speci ies he maximum numbe o objec s linked wi h he gi en one. I he lowe and uppe limi s coincide, a unique numbe will be indica ed. An as e isk (*) deno es a non-exis ing uppe limi [2, 3, 7]. In Fig. 2, ole I deno es he ole ha objec s o Class play wi h ega d o he Class2, I is like a unc ion ha , gi en an objec o Classy, e u ns he associa ed objec o collec ion o objec s o Classl. On he o he hand, ole2 has a simila meaning. Roles can be o ganized in a se (uno de ed collec ion o objec s o he same class, wi hou duplica es) o bag (uno de ed collec ion o he same class o objec s, wi h duplica es). We can also de ine a ibu es o associa ions. These a ibu es will ake alue when objec s a e associa ed, bu hey do no belong o hose objec s. Simila ly, e en s and ansi ions can be added like in classes. The e o e, we ha e a homogeneous ea men o classes and associa ions. Figu e 3 shows he associa ion be ween a uni e si y and people ha a e p o esso s o his uni e si y. Each p o esso belongs o a ca ego y and has a sala y. These a ibu es a e no common o he es o he people. This way, in he associa ion eaches in he e will be a link wi h hese a ibu es o each p o- esso wo king a he uni e si y. Ano he in e es ing p ope y ha can be conside ed in associa ions is he exclusi i y. By de aul , we con- side ha pa icipa ion o a class in an associa ion is no exclusi e. I a class has mo e han one associa ion, and in some o hem i s pa icipa ion is exclusi e, objec s wi h links in he exclusi e associa ion canno ha e links in o he s. This way, in he p e ious example we can also de ine he associa ion s udies in be ween Uni e - si y and Pe son. Now, o ins ance, we can de ine a con- s ain indica ing ha a p o esso canno be a s uden , o ha a pe son canno be in bo h associa ions. 3.2. Dynamics o Associa ions In he p e ious sec ion we ha e de ined s a ic aspec s o associa ions. In his sec ion we will exp ess dynamic aspec s o associa ions; i.e., how links be ween wo objec s a e es ablished and elimina ed. We ha e o emembe ha objec s o associa ed classes a e obliged o ce ain hings. They a e no able o wo k independen ly. As we ha e said, links can be c ea ed and des oyed. Thus, in associa ion shown in Fig. 3a pe son can lea e his job as p o esso in a uni e si y (whe he he inishes his con ac o o ano he eason). So i is necessa y o emo e he co esponding link. Howe e , we will no be able o des oy a link i i implies iola ing some o he de ined cons ain s ( o example, abou he mul iplici y). When an associa ed objec disappea s, i s links should also be dele ed. A link will no be able o exis i he objec i connec s does no exis . So, in he example in Fig. 3, i a uni e si y is elimina ed, all links o p o es- so s ha each in ha uni e si y will also be elimina ed. 4. FORMALIZING ASSOCIATIONS AMONG CLASSES The e a e wo common app oaches ha a e adop ed when associa ions a e ep esen ed in languages ha do no ha e a co esponding high-le el mechanism [7- 9, 12]: 1s app oach. Rep esen ing associa ions by means o a ibu es in associa ed classes. I is he mos basic o m. The main p oblem is ha a ibu ed associa ions canno be ep esen ed, bu can only ep esen oles. 2 id app oach. Rep esen ing associa ions by means o classes and a se o cons ain s o hold hei p ope - ies. We will ollow he second, mo e gene al app oach. We will mainly make use o simple classes, collec i e cons ain s and in e ac ion cons ain s o ou model. Le as be an associa ion be ween he classes cl~ and cl 2 aking he oles ole I and ole 2, espec i ely. Things o do o hold cons ain s imposed by ha associa ion a e he ollowing: 1. The associa ion will be ep esen ed by a class ha will ini ially ha e all i s cha ac e is ics. Each objec o his class will ep esen a link be ween wo objec s o associa ed classes. 2. I is necessa y o add o his class he ollowing concep s: (a) Two cons an a ibu es o he associa ed class ypes o ep esen he iden i ica ions o linked objec s. We will deno e hese a ibu es by he name o he co - esponding oles o he associa ed classes. PROGRAMMING AND COMPUTER SOFTWARE Vol. 26 No. 4 2000 IMPLEMENTING ASSOCIATIONS AMONG CLASSES 211 (b) Two channels o he collec i e des uc ion o links, so ha when we des oy an objec o an associa ed class, i s links also be des oyed. I is also necessa y o add bo h pe missions and obliga ions so ha all implied links pa icipa e (and only hose links)9 We deno ed by cnds ' he channel o collec i e des uc ion o he class cli, Vi ~ { 1..2}; i s pe missions and obliga ions will be he ollowing: Cnds,(sid, idi) pe missions oid ~ sid obliga ions oid ~ sid The channel Cnd,~, will ha e wo pa ame e s sid and id~ whe e sid is he se o links o ha objec o cl i whose iden i ica ion is ida. (c) I is also necessa y o add pe missions o his e en in he ex ension in o de o calcula e which a e he implied links. The se sid ha idi has wi h objec s o he o he class o he associa ion, is calcula ed as ollows: cnds,(sid, idi) pe missions sid = {y : 631y. olei = id i9 y} (d) S a e changes o e en s o he collec i e des uc ion o links, in o de o elimina e hese links om he ex ension: cnds,(sid, idi) s a e changes 63' = 63- sid whe e 63' deno es he alue o he a ibu e 63' in he s a e ollowing he occu ence o an e en 9 (e) Cons ain s on he ex ension o hold cons ain s imposed by oles de ined in he associa ion. Fi s ly, i is calcula ed wha objec s o a class a e linked wi h a gi en objec o he o he class. Fo example, o he class cl I we ha e: link1(63, id i) = [y : 631y. olel = id I * y. ole2], whe e id I is he iden i ica ion o an objec o Cll. A e wa ds i is necessa y o e i y ha cons ain s on he co esponding oles a e ul illed, i.e., cons ain s on bo h he numbe o objec s and he kind o o ganiza- ion. The e o e, o he class cl~, he ollowing p edi- ca es mus be calcula ed: p edl(63, id ) = le m = linkj(63, idl) in in_ ange2(#m ) and p 2(m ) end le in_ ange2(n) = (n >= in 2) and (n <= sip2 ) is_se (m) i o g2 is se p E(m) = ~ [ ue i o g 2 is no se , whe e he p edica e in_ ange con ols ha he numbe o objec s linked wi h he gi en one is in he co ec ange. I he uppe limi is an *, i is no necessa y o speci y he condi ion and (#m <= sup2). On he o he hand, he p edica e p e i ies ha he o ganiza ion is he co ec one. The necessa y p edica es o cl2 a e ob ained in a symme ical way. Finally, i is necessa y o e i y ha all objec s o he associa ed classes ul ill he p e ious p edica es. So we will de ine he ollowing s a ic cons ain on he ex en- sion: and([idi : cl i 9 p edi(63, idi)]); ' 'i ~ { 1..2}. Such and ope a ion is he and ope a ion on Booleans ex ended o ope a e wi h a Boolean bag. 3. We should ex end he in e ac ion cons ain s so ha whene e an objec is des oyed, i s links a e also des oyed. So, o each in e ac ion whe e he channel o des uc ion o cl~ appea s, i will be necessa y o include he channel cnd.,. 4. All links a e among exis ing objec s. The e o e, i is necessa y o add collec i e s a ic cons ain s9 We should: (a) De ine, in he ex ension o he class as, a de i ed a ibu e o each class in he associa ion. This a ibu e will be a bag e e ing o hose objec s ha ha e a link wi h an objec o he o he class: a e~ , = lid " 63 9 id. olei]; Vi ~ { 1..2}. (b) In o de o e i y ha hose objec s eally belong o he ex ension o cli, we will add he ollowing global cons ain : b os(63.a ed, ) inc cli; ' 'i e { 1..2 }, whe e he b os ope a ion, gi en a bag o elemen s, e u ns a se wi hou duplica es. (c) I he pa icipa ion o a class in an associa ion is de ined as exclusi e, hen objec s in ha associa ion canno ha e links in o he associa ions. We will ha e o add mo e collec i e cons ain s9 This way, i he class cl has de ined he associa ions as, wi h he classes clj, 9 , .J . . . Vj ~ { 1 ..m }, and excluswe pamclpa lon m asi, hen we will ha e: ( Ti.a ec n 63-j.a ed) = emp y; Vj ~ { i..m }, j ~ i, whe e a ecl is he de i ed a ibu e de ined in he asso- cia ion as, Vj e { l..m}, in o de o hold iden i ica ions 9 J o objec s o he class cl wi h some link in he associa- ion. 5. IMPLEMENTATION WITH ACTIVE DATABASES T adi ionally, bina y associa ions ha e been main- ained in ela ional da abases by means o e e en ial in eg i y. Howe e , when associa ions a e a bi mo e PROGRAMMING AND COMPUTER SOFTWARE Vol. 26 No. 4 2000 212 TORRES e al. complex, we will need o make use o ano he me hod o main ain hem. The design o ac i e ules allows us o de ine p ocedu al ac ions o be ca ded ou o epai - ing an in eg i y iola ion, al hough i loses he decla a- i e ad an age o being able o speci y he cons ain s. In he ollowing sec ions, we will desc ibe he main poin s o in e es necessa y o implemen p e iously de ined seman ics by means o ac i e da abases [6], a new esea ch a ea ha inc eases he unc ionali y o a- di ional da abases wi h ac i e ules, p o iding an e i- cien and uni o m mechanism o de eloping some asks wi hin he ke nel o a da abase. 5. I. An O e iew o Ac i e Da abases Mos o da abase sys ems a e passi e; i.e., da a can be inse ed, modi ied o dele ed as a esul o eques s om ei he use s o applica ions. A ecen esea ch a ea aims o ex end he unc ionali y o da abase sys ems by including ce ain ype o ac i e beha io in he da a- base. In his way, da abase sys ems can execu e some p ocesses au oma ically in esponse o he occu ence o sa is ac ion o e en s o condi ions [5, 18]. O he e ms, synonyms o ac i e ules, a e p oduc- ion ule-s, e en -condi ion-ac ion o ECA ules, ig- ge s, moni o s, and so on. Al hough se e al implemen- a ions o ac i e ules exis in da abase sys ems, he e a e h ee main componen s: E en is he di ec cause o he ac i e ule o be ig- ge ed. Condi ion mus be sa is ied so ha he ac i e ule can be igge ed. Ac ion is he p ocedu e o be execu ed when he co esponding e en occu s and he condi ion is sa is- ied. Se e al a eas exis whe e ac i e ule se s can be used wi h he pu pose o imp o ing he e iciency o he sys- em. The mos impo an ac i i ies a e: 9 In e nal asks, such as main aining all kinds o cons ain s and de i ed da a. One o hem is he main- enance ela ed o associa ions, which is he objec i e o ou wo k. 9 Ex ended asks, such as eplica ion, e sioning and wo k low managemen . 9 Ex e nal asks, such as he business ules o any applica ion. These ules can be sha ed by all applica ions access- ing he da abase, gua an eeing knowledge indepen- dence because he pa o beha io ha is adi ionally accomplished by applica ions is mo ed in o da abase sys ems. Un o una ely, i he design o ac i e ules was no app op ia e, we could be in ouble because o hei col- lec i e beha io , in e ac ions and mu ual in luences, mainly due o he abili y o ules o igge each o he . To ensu e he global co ec ness o ac i e ules a la ge, we should design an ac i e ule se ha accomplishes he e mina ion p ope y. Some imes, o he p ope ies also mus be aken in o accoun , such as con luence and obse able de e minism [1]. Following, we de ine hese e ms: 9 Te mina ion. A se o ac i e ules is said o possess he e mina ion p ope y when he ule p ocessing ig- ge ed by e e y use -de ined ansac ion is e en ually e mina ed, p oducing a inal s a e. 9 Con luence. A se o ac i e ules is said o gua an- ee he con luence p ope y when such p ocessing e en ually e mina es, and always p oduces an unique inal s a e ha is independen o he execu ion o de o he ules. 9 Obse able de e minism. A se o ac i e ules is said o gua an ee an obse able de e minism when, in addi ion o con luence, o each use -de ined ansac- ion, all isible ac ions pe o med by he ules a e he same. Ano he impo an cha ac e is ic o an ac i e ule is he ime when i s ac ion will be execu ed wi h espec o he e en ime and in ela ion o he cu en ansac- ion. An ac i e ule is said o be immedia e i he ac ion is execu ed immedia ely a e he e en occu s (i con- di ion we e sa is ied), and i is said o be de e ed i he ac ion is execu ed a he end o cu en ansac ion. The la es e sions o DBMSs, bo h ela ional and objec - ela ional, include igge s (which is he e m no mally used in p ac ice). Un o una ely, a p oblem ela ed o hei implemen a ion is he ac ha igge s implemen ed in comme cial da abase sys ems (such as O acle, DB2, Sybase, In e base, among o he s) a e no powe ul enough. This is he case because no comple e s anda iza ion abou igge s in SQL exis s, and none o hem o e s de e ed igge s a all. The cu en SQL3 speci ica ion o igge s is a he long and di i- cul o unde s and, and di e ences be ween p oposals conside ed by s anda diza ion commi ees (bo h ANSI and ISO) [10] a e an addi ional sou ce o con usion. The e a e o he p oblems associa ed wi h ules. One o hem is known as mu a ing ables, and i is ela ed o p oblems ha may a ise because o ansac ion man- agemen : we can nei he modi y no ead ows o ables al eady upda ed du ing he ansac ion. Ano he poin o in e es is he incompa ibili y be ween decla a i e e e en ial in eg i y and igge s. Al hough mos da a- base sys ems o e acili ies, when we ha e o imple- men mo e complex ela ionships, we need o use ig- ge s and such acili ies should no be used. [5] o e s a pa ial solu ion o hose p oblems. Me a- igge ing consis s in a mapping om e e y ac i e ule o a conc e e s o ed p ocedu e ha codes bo h i s con- di ion and i s ac ion. When an e en is igge ed, a lag is upda ed in a empo al able o each ac i e ule ha is igge ed by ha e en , and immedia e ules a e p o- cessed a e wa ds. A he end o he ansac ion, all de e ed ules will be p ocessed. When implemen ing i , we ha e ealized some ex ensions o he me hod, so ha any numbe o he same igge ins ances could be PROGRAMMING AND COMPUTER SOFTWARE Vol. 26 No. 4 2000 IMPLEMENTING ASSOCIATIONS AMONG CLASSES 213 p ocessed, and also allowing pass o objec iden i ie s being a ec ed by ope a ions om igge s o s o ed p ocedu es (all by means o ime s amps). 5.2. Ac i e Rules o Associa ions As men ioned abo e, e e y class can be imple- men ed by means o a able in a ela ional da abase, whe e each objec will be s o ed in a ow. Associa ions, like any class, can also be implemen ed by means o a able, whe e links a e s o ed in such a able by means o e e ences o each pa icipan objec . Channels o e en s can be implemen ed by means o igge s eac ing o he c ea ion and dele ion o objec s. So, e iciency is imp o ed because he explici ea - men o channels o e en s, o he wise e y expensi e, is a oided. Al hough c ea ion is implici ly o malized in seman ics, he execu ion o a igge a e he c ea ion o e e y objec is necessa y o es he cons ain s, such as e e en ial in eg i y, mul iplici y and exclusi i y. A e an objec is dele ed, a igge will be execu ed, and all links whe e ha objec pa icipa es should be dele ed. Like e e y ule, he dele ion ule has h ee componen s: e en , condi ion and ac ion. The o me is easy and has a di ec sc ip . The condi ion o he ule is mo e complex: i is necessa y o e i y ha , o each link whe e an objec pa icipa es, cons ain s o co e- sponding oles a e ul illed a e ha objec has been dele ed. The ac ion will be o p opaga e dele ion o all links o e e y link whe e he objec pa icipa es. C ea ion and dele ion o a link a e simila . A e a new link is c ea ed, pa icipan objec s mus exis , and mul iplici y and exclusi i y mus be sa is ied immedi- a ely a e wa ds. A e an exis ing link is dele ed, he unique cons ain ha should be sa is ied is he mul i- plici y. 5.3. An Example o a T igge Se In his sec ion we show, using O acle syn ax [13], de ini ion o he example in Fig. 3. Now, Pe son, Uni- e si~., and Teachesln classes will be ables s o ing objec s and links o he espec i e classes. No addi- ional p ope ies a e isible. De ini ions o ables a e as ollows: CREATE TABLE Pe son (Oid INTEGER PRIMARY KEY); CREATE TABLE Uni e si y (Oid INTEGER PRIMARY KEY); CREATE TABLE TeachesIn (P o esso INTEGER, Cen e INTEGER, PRIMARY KEY(P o esso , Cen e ) ) ; T igge s de ined o he c ea ion and dele ion o Pe son objec s a e as ollows: CREATE TRIGGER C ea ePe son AFTER INSERT ON Pe son FOR EACH ROW -- WITH DEFERRED EXECUTION BEGIN IF NOT (Re In eg i yACP(New. Oid) AND Mul iplici yACP(New. Oid) AND Exclusi i yACP(New. Oid)) THEN RAISE_APPLICATION_ERROR(-20000, "Cons ain s a e no ul illed'); END IF; END; CREATE TRIGGER Dele ePe son AFTER DELETE ON Pe son FOR EACH ROW -- WITH DEFERRED EXECUTION BEGIN IF NOT Mul iplici yADP(Old. Oid) THEN RAISE_APPLICATION_ERROR(-20000, "Cons ain s a e no END IF; DELETE FROM TeachesIn WHERE P o esso =Old. Oid; END; ul illed') ; PROGRAMMING AND COMPUTER SOFTWARE Vol. 26 No. 4 2000 214 TORRES e al. T igge s o he Uni e si y class a e simila . T ig- ge s C ea ePe son and Dele ePe son will aise an excep ion when any o he p edica es e u ns FALSE. Fo b e i y, s o ed p ocedu es implemen ing he p edi- ca es a e no shown. Following is a sho desc ip ion: Re ln eg i yACP ecei es he iden i ie o a new objec and e u ns TRUE i he e e en ial in eg i y is sa is ied o his objec , o FALSE o he wise. Mul iplici yACP ecei es he iden i ie o a new objec and e u ns TRUE i he mul iplici y cons ain s a e sa is ied o he associa ions in which his objec pa icipa es, o FALSE o he wise. Exclusi i yACP ecei es he iden i ie o a new objec and e u ns TRUE i he exclusi i y cons ain s a e sa is ied o he agg ega ions in which an objec pa icipa es, o FALSE o he wise. Mul iplici yADP ecei es he iden i ie o an old objec and e u ns TRUE i he mul iplici y cons ain s a e sa is ied o he associa ions in which his objec pa icipa es a e his objec has been dele ed, o FALSE o he wise. Finally, igge s o he c ea ion and dele ion o Teachesln links a e simila . A link can be c ea ed i he e e en ial in eg i y, mul iplici y and exclusi i y con- s ain s a e sa is ied by he pa icipan objec s. O he - wise, an excep ion will be aised and no link will be c ea ed. On he o he hand, a link can be dele ed i he mul iplici y cons ain s a e sa is ied a e such an e en Occu s. 5.4. Final Rema ks on he Implemen a ion Each o hese ules should be de e ed execu ion, allowing in e media e s a es ha could empo ally io- la e he cons ain s, bu ha a e necessa y when a ela- ionship is c ea ed o dele ed. As an example, we could c ea e an objec and all links whe e such objec pa ic- ipa es a e wa ds. I he ules a e no de e ed when he objec is c ea ed, an excep ion could be aised because some o he cons ain s we e no sa is ied, despi e links c ea ed ollowing he c ea ion o such objec . Many o he combina ions can be ound, meaning ha all ela ed ope a ions should be g ouped in o ans- ac ions. On commi , when hese ules a e p ocessed, i any p edica e is no ue, hen he ope a ion mus be canceled. This is implemen ed by aising a use -excep- ion ha ollbacks he cu en ansac ion, and he e- o e, undoing all hose changes ha we e pending o being commi ed. As men ioned abo e, some addi ional echniques, such as me a- igge ing, will be necessa y o implemen hem because o he aul s d awbacks inhe en in cu en ac i e da abases. Gene ally, he use o ac i e ules has a be e pe o - mance, because many ac i i ies, o he wise execu ed by an applica ion, a e unning wi hin a da abase, and so communica ions be ween applica ions and da abases ha e a majo e iciency. Un o una ely, his se o ules gua an ees e mina- ion, bu no con luence no obse able de e minism. So, non-de e minism could a ise and hese si ua ions a e no ecommended in many sys ems. Solu ions could lie in applying se e al echniques o a oid i , such as assigning p io i ies and edesigning ule se s, among o he s. 6. CONCLUSIONS We ha e p esen ed in his pape a o maliza ion o seman ics o one o he mo e common ope a o s in he OO concep ual modelling, associa ions among classes o objec s. Fi s , we ha e p esen ed he mos impo an cha ac- e is ics in ou OO model. A speci ica ion is ca ied ou by means o cons ain s o di e en kinds ha can be imposed a h ee di e en le els: objec , class and glo- bal. A e wa ds we ha e de ined some p ope ies o associa ions o classes, inspi ed undamen ally in he mo e popula OO me hodologies. Nex , we ha e de ined he seman ics o associa ions by means o classes and cons ain s allowed in ou model. This way, o change p ope ies o any associa ion, i will simply be necessa y o add new cons ain s o o elimina e some o hem. Finally, we ha e shown some ema ks on ou imple- men a ion by means o ac i e da abases. We a e ac u- ally wo king ha d o au oma ically gene a e a se o ac i e ules om he o malized de ini ions o a sys em. Fu he mo e, we ha e planned o s udy o he de ined ela ionships among objec s, oge he wi h hei imple- men a ion, such as agg ega ions o inhe i ance. ACKNOWLEDGMENTS This wo k was suppo ed by he In e -minis e ial Commission o Science and Technology (CICYT) o Spain, p ojec no. TIC97-0593-C05-03. REFERENCES 1. 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