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.
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