OlafKummer
UniversitätHamburg,FachbereichInformatik
Vogt-Kölln-Straÿe30, D-22527Hamburg
Abstract
In this paper we investigate how the Java programming language can be integrated in an
object-orientedPetrinetformalism. Itbecomesapparenthowacarefullydesigned unication
algorithmsupportsthisgoal,despitethefactthatJavaitselfisnotbasedonunication. Some
dedicatedalgorithmsfor aPetrinetsimulatorareproposed.
1 Introduction
The basic net formalismdiscussed in this paper are reference nets. In reference nets, a net can
beinstantiatedarbitrarilyoftenandreferencestonetinstancescanbeused astokensinothernet
instances. Fordetailssee[6]. ReferencenetsuseavariantofJavaastheirinscriptionlanguage. See
[2]fortheoriginalJavaspecication.
Thispapercanbeseenasacompaniontotheearlierwork[4],wherethereferencenetformalism
andthelargescalearchitectureofthePetrinetsimulatorRenewaredescribed. Herewewilldiscuss
somefurtheraspectsthatwereonlyverybrieysketchedin[4].
2 Tuples
The Java languagehas no support for tuples. Theonly case where tuples would come inhandy
inJavawouldbemulti-valuereturns. However,theseoccurnotveryoftenandcanbesubstituted
bythereturnofacomplexobjectthataggregatesthereturnvalues. Inothercases,whenwehave
multiplevaluesthat shouldbeprocessed together, wecansimply usemultiplevariablesthathold
onevalueeach.
ButforPetrinets,tuplesaremoreimportant.Itisdangeroustostorerelatedvaluesinmultiple
places,because,ifmultipletokenshavetobeputthere,tokensfordierentdatasetscanbemixed.
Tuplessolvethisproblem.
Java's syntax oers two opportunities for adding tuples. Either a tuple is written (1,2,3)
or [1,2,3]. The rst form hasthe disadvantagethat it is impossibleto write 1-tuples, because
theycouldbemistakenforgroupingoperations,e.g."string"+(true|false)wouldbeambiguous.
Hence it wasdecidedto usethesquarebracketnotation. However,whenwe wantto support lists
aswellastuples, wehaveto llboth syntactic niches. Inthat case, 1-tuplesmightbeconsidered
dispensable,but lists of length 1would bemandatory, so that the decisionwould havebeen the
otherwayround.
[father,son]
father+
" is the father of "+
["Isaac","Jacob"] son ["Jacob","Joseph"]
["Abraham","Isaac"]
Figure1: Thenettuples
Aswehavetuplesinthelanguages,itseemssensibleto provide apattern matching capability
and thusunication. In Fig.1youcan see asimpleexamplenet. Eachtoken intheplacecanbe
uniedwiththeinputarcinscriptiontoassignvaluestothevariablesfatherandson.
Itwasdecidedtoimplementanoccurrencecheckintheunicationalgorithm,i.e.,atuplemust
notcontainitself. Duetoeciencyconsiderations,thischeckisoftenomitted. Butthismightlead
canholdavalue,althoughtheyarenotsupposedtobeusedasvaluesthemselves.Unknownobjects
are theinitialvalueofvariables. Theyrepresenttheidentityofvalueswhenthevaluesthemselves
arenotyetknown. Considerforexampletwounassignedvariablesxandy. Afterunication,both
willreferencethesameunknownobjectastheirvalue. Afterunifyingxwith1,alsoywillbevalued
with1.
TheunicationalgorithmmustalsounifyordinaryJavavalues,whichcanappearascomponents
intuplesorasvaluesofvariables. Hereuniablilitycouldbebasedonidentityoronequality. Java
providesamethodequals(...) initsobjectmodelthatissupposedtotestobjectsforequalityand
an operator== thatchecksidentity. Identityis safeinthesense that itis aconstant equivalence.
Ontheotherhand,equalityissupposed tobeanequivalence,butthiscannotbeenforced,andthe
equalitycanchangeovertime.
Nevertheless, we chose equalityas the basis of unication. Firstly, it is not even guaranteed
that eventwoequaltextstringsareidentical,sothatunexpectedresultscouldoccur. Secondly,all
existingcontainerlibrariesarebasedonequality. As wehadto uselotsof containerclassesinthe
design, we had to rely on the functionality of equals(...) in any case. It turned outthat the
resultingproblemsarecomparablyminor,but stillcarehastobetaken.
The unication algorithm works in-place, i.e., the original tuples are modied, if necessary.
Similarly,thecontentsofvariablesmaybechangedbyaunication. Thiswaywecanavoidexcessive
copying during each unication. Of course, we have to add a backtracking mechanism to undo
unications,becausethestatebeforetheunicationisdestroyed. Backtrackingisinvokedwhenever
aproposed bindingofvariablesis discardedbythesimulationalgorithm.
Allmodicationsto uniableobjectliketuples and variablesare collectedinaso-called state
recorder. It is possible to have multiple state recorders that can concurrently record and undo
changesindierentuniableobjects. However,theunicationsinasingleuniableobjectshaveto
beundoneinthecorrectorder.
Pattern matching is useful for input arcs inscribed with tuples. Here one component of the
tuplemightalreadybeknowntothePetrinetsimulator,andtheremightbeveryfewtuplesinthe
place thatmatchthisvaluecomparedtothenumberofalltokens. Thereforeindexesallowaquick
lookupofpartiallyspeciedtuples. However,dueto performanceconsiderationsonlysingletuple
componentsareusedasindexes.
Ifallcombinationsoftuple componentsweremaintainedasindexes,acombinatorialexplosion
would result. Of course this means that arc inscriptionslike ["Joe","Average",phone]do not
allowan extremely ecient lookup of JoeAverage's phone numberin theplace that contains all
phone numbers,becausetwocomponentswouldhavetoberespected. However,thesimulatorwill
stilllimitits search toall Joesor allAverages, whicheverconstitutesthe smallerset. Tohelpthe
simulator,you could use nested tuples for storing the data. Now, [["Joe","Average"],phone]
doesgiveyouaconstanttimelookup,becausetherst componentofthe tuple,apairactually,is
completelyknownandformsavalidindex.
A similarindexingalgorithmmightbecontainedinseveralother simulators, but literatureon
this topicisverysparse. Only[3]givesinformationonarelatedapproach,whichissomewhatless
exible andnotasecientastheproposedscheme, however.
3 Actions
Many high-level Petri net formalisms support the execution of some additional code during the
ringofatransitionthatdoesnotinuencetheenablednessofatransition. Referencenetssupport
this concept by so-calledaction inscriptions,which cantriggerside eects, but mayalso beused
to determinethevalueofoutput arcvariables. Acommonusewouldbethetransitioninscription
action x=y.aLongMethodCall(u,v)to initiate along method call that has no inuence on the
activationofthetransition.
Becausetheresultofanactionisunknowable,wemustmakesurethateveryresultwillleadto
alegalringofthetransition. Thesimulatorshoulddetectthefollowingillegalsituations:
Avariableiscalculatedbyanactionbutisalreadycomputedduringthesearchforabinding.
becomputedbyadierentaction.
Luckily, we can integrate the detection algorithminto the already implemented unication algo-
rithm. We representan action callby a calculatorobject that is uniableonly with itself. This
objectreferencesitsarguments,whichmightbeJavaobjects,tuples,unknown,orevenothercalcu-
latorobjects. Theoccurrencecheckcanthus detecteventhose cyclesthatarise outofrecursively
embeddedtuplesandcalculatorobjects.
x
y
u
v
Figure2: Adatastructureofuniableobjects
Fig.2 visualizesthe actualdata structure generated by action x=y.aLongMethodCall(u,v).
Thevariablesaredenotedbyrectangles,thecalculatorobjectbyacircle,theunknownsbyrhombi.
Therearetwotupleobjectsdepictedastrianglesthatresultfromtheinternalrepresentationofthe
expressions. One tuple groups the argumentsand onetuple combines the target objectand the
othertuple. This simpliessomeinternalprocedures.
Atthispoint,itwouldbeimpossibleto unifyxandy,becauseacyclewouldarise. Itwouldbe
impossibletounify xwith1,becausethecalculatorobjectcanonlybeuniedwithitself.
Another part of the unication algorithmdetects when a calculatedvalue is required for the
evaluation of an input arc. In that case the transition cannot be enabled, because the value is
requiredearlytoseeifanappropriatetokenisavailable,butontheotherhand,thevaluemustnot
becomputedearly,becauseitresultsfromanaction.
Butwhathappensduringtheringofthetransition? Avaluemustbeassignedto x,therefore
thevariablemustnolongerbeboundtoacalculatorobject. Theremovalofthecalculatorobjects
is doneimmediatelyafter asuccessfulsearch. Imaginethat thesearchalgorithmhasfoundavalid
binding. An output arcexpressionhas been computed, resultinginatuple. Wecannot put that
tupledirectlyintotheplace,becausethetuple'scontentmightbesubjecttobacktracking. Therefore
wemakeacopyofall variablesandtuples andensurethat thecopiesareimmutable. Duringthis
process,whichhastobedoneinanycase,wecansafelyremoveallcalculatorobjectswithoutfurther
ineciencies. Theyserved theirpurpose of ensuringuniquelycalculated valuesand areno longer
needed.
4 Calling Nets from Java
In [5] an architecture was discussed that allows the integration of Java and Petri nets that are
implementedwiththe Design/CPNtool. UsingJava-inscribedPetrinetswecanprovidean even
smothertransitionbetweenthetwoworlds. Infact wehavealreadyseenthatcallstoJavaposeno
problemseveninthepresenceof sideeects whenweuseactioninscriptions.
Whenwewanttocallnets,wemustdenemethodsfornets. Thewishtoimplementnetmethods
isnotnewandplentyofschemeshavealreadybeendevised,[7]couldbenamedasanexample.
Inreferencenets,theonlymeansofcommunicationwithnetsaresynchronouschannels. Chan-
nelsareparameterizedandallowabidirectionalinformationtransfer. Inorderto synchronize,two
transitioninstanceshavetoagreeonachannelandonasequenceofmatchingarguments.Thetran-
sitioninstancethatinitiatesthesynchronizationmustexplicitlyreferencethenetinstancewherethe
targettransitionislocated. E.g.,net:channel(2,3,5)wouldbeaninvocationthroughthechannel
channelofatransitioninthenetnetwiththreeparameters. Thetargettransitionwouldhaveto
provideaninscriptionlike:channel(x,y,z)tosignalthat itwantstoengage insynchronizations
0 old :deposit(amount)
old+amount :amount(amount)
amount
:withdraw(amount) this:deposit(-amount)
money
amount deposit
withdraw
Figure3: Thenetaccount
Thenet fromFig. 3models avery simplebank account. The customer canonly deposit and
withdrawmoneyandviewthecurrentamount. Whatweneednowisawrapperclassthatconverts
method callsto channel invocations, so that wecan usethe net asan ordinaryJava object. We
havedescribehowtheconversionisdone.
package samples.call;
class Account for net account {
void deposit(int amount) {
this:deposit(amount);
}
void withdraw(int amount) {
this:deposit(amount);
}
int currentAmount() {
this:amount(return);
}
}
Thedeclaringpackagesamples.callisgiveninaspecialstatement. Acompilercannowbeinvoked
that convertsthedescriptionintoJavacode. Theresultingclass Accountwillbeknownasastub
class.
Eachtime yougenerateastubobject,theassociatednetisautomaticallycreated,too. Thisis
thereasonforlistingthenetnameafterthekeywordsfor netintheheader.
Thebody ofa classdescription consistsof asequence of method descriptionsand constructor
inscriptions. Inour examplewe donothaveconstructors, such that adefault constructorwillbe
automaticallyinserted. Thebodyofeachmethodconsistsofasequenceofchannelinvocationsand
variabledeclarations,separatedbysemicolons.
As in reference nets, variablesneed not be declared. If variablesare declared, they must be
declaredbeforetheyareused. Inourexampletherearenovariablesexceptfortheinputparameters
andthespecialvariablereturn,whichisusedinthelastmethodcurrentAmount(). Thisvariable
is automatically declared in each method that has a non-void return type. A non-void method
returnsthevalueof returnattheendofitsbody.
[]
acc acc
acc action acc=new
samples.call.Account() action
acc.deposit(500)
action amount=
acc.currentAmount()
account
init created deposited amount amount
create deposit query
Figure4: Thenetcustomer
vides a synchronizationrequest to the search algorithm. The search algorithm can then try to
nd anappropriatesynchronizationorreadditionalspontaneous transitionsinthecasethat the
synchronizationisnotpossibleatthemoment. Afterthesynchronizationsucceeds,thestubobject
isinformed,sothatthemethodcan return.
Itis importantto note that amethod callcanconsist of multiplesynchronizationrequests,so
that you arenotlimited to actionsthat can be performed atomicallyby asingletransition. Itis
allowedto startlarge subprocessesduringthe execution of anet method. Typically, exactlytwo
synchronizationsarerequired,oneto startthemethod,andonetocollectheresults,but thismay
vary. Acommonmethod descriptionmightbe
type method(type0 arg0, type1 arg1, type2 arg2) {
this:method(instance,arg0,arg1,arg2);
this:result(instance,return);
}
Here weprovidean additionalargumentinstancethat is set by theinvoked netduringthe rst
synchronization. It can be used during the second synchronization to collect the correct return
valuejustincasemultiplemethodcallshavebeenmade. Wedonotspecifythetypeof instance,
but itmightbeauniquecallnumberorareferencetoanetinstancethatiscreatedtoprocessthe
request.
5 Types
Although intheapplicationdomainofrapid prototypingitis desirableto haveatypefreesystem
where variablesdonothaveto be declared,it isalso usefulto havethesecurityof typechecking,
if desired. Therefore reference nets provide both a typed and an untyped formalism. Not only
variables,but also placesmaybetyped. Inbothcasesatypeguaranteesthat only valuesofthat
typemaybestoredinthetypedobject.
Number n;
Integer i;
n
n Integer
Integer
Number i
i Number
Figure5: Thenettypes
ThenetfromFig.5illustratesakeyproblemwhileimplementingatypesystem. Whichconver-
sions shouldbeallowedforinput andoutput arcs? If thearc type andthe placetypeare neither
supertypesnorsubtypesofeachother,isseemsplausibletoreportanerror. Ifthedeveloperknows
that alltransportedvaluesbelongtobothtypes,thisshouldhavebeenindicatedwithacast.
Ifthetypeoftheoutputarcinscriptionisasubtypeoftheplacetype,everythingiscorrect. But
if itisnot, wecannot besurethat the token thatis put intheplacesatises thetypeconstraint.
Thereforewehavetoreportanerrorforthelowerlefttransitioninthegure,becauseanumberis
notnecessarilyaninteger.
Perhapssurprisingly,weallowbothsupertypeandsubtyperelationsforinputarcs. Iftheresult
of aninputarcexpressionturns outtobeofthewrongtype, itisguaranteedthat noappropriate
tokenisintheplace,sothatthis bindingisnotenabledanyways. Ontheotherhand,iftheinput
arcisinscribedwithasubtypeoftheplacetype,wesimplyhavetomakesurethatonlythosevalues
thatarepermissibleareuniedwiththevariable. Othertokensintheplacearesimplyignored.
TheJavatypesystemisrelativelystraightforward,butithasafewroughedgesthatstemfrom
Java's origininC++. Especially, Javawillgladlyconvert 32-bitintegersto 32-bitoating point
numbersorviceversa,althoughinformationislostintheprocess.
This is acceptable, albeit dangerous, for ordinaryassignmentsor method calls. Fortoken re-
withanintegervariable. Itisnotclearwhetherweshouldacceptthelossthatresultsfromconvert-
ingoattokenstointegervalueswhenassigningthevariableorthelossthatresultsfromconverting
theintegervaluetoaoat,sothat thetokencanberemoved.
Therefore a new subtype relation losslessly convertible was introduced into the system. It is
only usedfortypecheckingarcsandit diersfromthenormalsubtyping relationbynotallowing
conversionsfromlongstoeitheroatsor doublesandfromintegerstooats. Formethod callsthe
ordinaryJavasemanticswasretained toachievecompatibility.
Synchronouschannelsareuntyped. Becausethedirectionofinformationtransferisunspecied
forchannels,theconceptoflosslessconvertibilitywillbeusedhere,too,ifitisdecidedtoaddtyped
channelsinthefuture.
Atthemoment,tupleshaveonecommontype,aswedonotdierentiatebetweenintegertriples,
stringpairs,tuplesofarbitraryobjects,andsoon. Typedtupleswouldbeavaluableaddition,but
at themomenttherearetoomanyconictingapproaches,noneof which issupportedbytheJava
environment. Theseissuesshouldprobablybepostponeduntil ithasbeennallydecidedwhether
andhowtointegrateparameterizedtypesintheJavalanguage.
6 Conclusion
We haveseenhowaproperintegrationofJavaandPetrinetsleadstovariousdesigndecisionson
boththe net formalismand itsimplementation. Starting with tuples werequired unication and
patternmatching. Wesawthatactioninscriptions,whichgreatlyaddtoexpressiveness,gaveriseto
asurprisingextensionof theunicationalgorithm. Thewish foraseamlessintegrationmotivated
callsfromJavatonets,whicharesupportedbyautomaticallygeneratedstubobjects.Allalgorithms
havebeenimplementedinRenew1.1, whichisfreelyavailable[6].
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