webeginbyde ninganotionofmodularreasoningthatcorrespondstoParnasscomprehensibilitybene tModularreasoningistheprocessofunderstandingasystemorprovingpropertiesaboutitonemoduleatatimeAlanguagesuppo ID: 387352
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Obliviousness,ModularReasoning,andtheBehavioralSubtypingAnalogyCurtisCliftonandGaryT.Leavens1IowaStateUniversity,226Atanaso Hall,AmesIA50011,USA,fcclifton,leavensg@cs.iastate.edu,WWWhomepage:http://www.cs.iastate.edu/~fcclifton,leavensgAbstract.TheobliviousnesspropertyofAspectJ-likelanguagescon- ictswiththeabilitytoreasonaboutprogramsinamodularfashion.Thiscanmakedebuggingandmaintenancedicult.Inobject-orientedprogramming,thedisciplineofbehavioralsubtypingallowsonetoreasonaboutprogramsmodularly,despitetheobliviousna-tureofdynamicbinding;however,itisnotclearwhatdisciplinewouldhelpprogrammersinAspectJ-likelanguagesobtainmodularreasoning.Behavioralsubtypingwasbornoutofthestoriesprogrammersweretellingintheirobject-orientedprogramsandhowtheyreasonedaboutthem.ProgrammersuseAspectJ-likelanguagestotellwhatwecall\su-perimposition"and\adaptation"stories.Thus,adisciplineofmodularreasoningforanAspectJ-likelanguagemustaccountforbothsortsofstories.WedescribethemodularreasoningproblemforAspectJ-likelanguages.Wedonotyethaveasolution,butconciselyarticulatetheissuesinvolved.1IntroductionMuchoftheworkonaspect-orientedprogramminglanguagesreferstotheworkofParnas[31].Parnasarguesthatthemodulesintowhichasystemisdecom-posedshouldprovidebenetsinthreeareas(p.1054):Thebenetsexpectedofmodularprogrammingare:1.managerial|developmenttimeshouldbeshortenedbecausesepa-rategroupswouldworkoneachmodulewithlittleneedforcommu-nication;2.product exibility|itshouldbepossibletomakedrasticchangestoonemodulewithoutaneedtochangeothers;3.comprehensibility|itshouldbepossibletostudythesystemonemoduleatatime.Thewholesystemcanthereforebebetterdesignedbecauseitisbetterunderstood.Itseemsclearthataspect-orientedlanguagesprovidemanybenetsrelatedtoParnas'ssecondpoint[13,18].Amongthesebenetsareareductionintangling webeginbydeninganotionofmodularreasoningthatcorrespondstoParnas'scomprehensibilitybenet.Modularreasoningistheprocessofunderstandingasystem(orprovingprop-ertiesaboutit)onemoduleatatime.AlanguagesupportsmodularreasoningiftheactionsofamoduleMwritteninthatlanguagecanbeunderstoodbasedsolelyonthecodecontainedinMandthecodesurroundingM,alongwiththesignatureandbehaviorofanymodulesreferredtobythatcode.Thenotionofamoduleandthesurroundingcodeforamodulearedeterminedbytheprogram-minglanguage.InJava,wemightconsideracompilationunittobeamodule,andinstandardJavanocodesurroundsamodule3.Code,C,referstoamoduleNifCexplicitlynamesN,ifCislexicallynestedwithinN,orifNisastandardmoduleinaxedplace(suchasObjectinJava).Weusecontractstospecifythecode'sbehavior.Inthemostconcretecase,thecontractisthemethod'scode,butweprefertothinkofmoreabstractcontracts.Thesecanbewritteninaformalspecicationlanguage[21,25],orinformallybywritingcommentssuchas\Thismethodreturnstrueifthegivenleexists".Ourinterestinmodularreasoninginaspect-orientedprogramminglanguagesismotivatedinpartbyourinitialworkoncombiningMultiJava[6,8]andJML[21].3TheProblem:UndisciplinedObliviousnessIntypicalobject-orientedlanguages,thedynamictypeofthereceiverobjectisusedtoselecttheappropriatemethodtoinvokeforagivenmessagesend.Suchdynamicselectionofthetargetmethodcanpreventmodularreasoning.Forexample,considerthedeclarationofPointinFigure1anditsmethod,move.The//@-commentsbeforemove'sdeclarationgiveitsbehavioralspecicationinJML.{Theclause\requirestrue"saysthatclientsarenotobligedtoestablishanyprecondition.{Theclause\assignablepos"saysthattheposeldofthereceiverobjectmaybechangedbythemethod,butnotanyotherlocations.{Theclause\ensures..."saysthat,aftermovereturns,thevaluereturnedbygetPos()isequaltothesumofthedistargumentandthevaluereturnedbygetPos()beforemovewascalled.SupposeanobjectofstatictypePointispassedtoamethodclient,asinFigure2.Ifmodularreasoningissound,thentheprogrammercanreasonabouttheinvocationofmovebasedonitsspecicationinPoint.Thatis,iftherstassertioninFigure2holds,thenthesecondassertionisvalidbasedonthespecicationofPoint'smovemethod.Thedenitionofmodularreasoning 3Anotherinterpretationof\module"and\surroundingcode"inJavamightbethatatypedeclarationisamodule,and,fornestedtypedeclarations,thecodefortheenclosingtypedeclarationisthesurroundingcode. requiresthattheprogrammershouldnothavetoconsiderpossiblesubtypesofPointwhendoingthisreasoning,sincetheyarenotmentionedintheclientcode.However,bysubsumption,aninstanceofanunseensubtypeofPoint,sayRightMovingPoint,maybepassedtoclient.Whatif(asinFigure3)RightMovingPointoverridesmethodmove,buttheoverridedoesnotsatisfythespecicationofmoveinPoint?Thenmodularreasoningsuchasthatdescribedforclientisnotvalid.UsingFigure3,aftertheclient'sinvocationofp.move(-10),p.getPos()returns10,not-10asasserted.Theconceptofbehavioralsubtypingrestoressoundmodularreasoningbyim-posingthespecicationofPointonallitssubtypes[11,22,24].Thus,RightMov-ingPointdoesnotcorrectlyimplementabehavioralsubtypeofPoint,becauseitsimplementationdoesnotsatisfythespecicationofmoveinPoint.Behavioralsubtypingisoftendescribedbysayingthatthebehaviorofasubtypeshouldnotbesurprising,withrespecttothespeciedbehaviorofasupertype.publicclassRightMovingPointextendsPointfpublicvoidmove(intdist)fif(dist0)super.move(-dist);elsesuper.move(dist);ggFig.3.ARightMovingPointclassAspointedoutbyFilmanandFriedman[14],subtypingwithsubsumption,asabove,isanexampleofobliviousness.Aspect-orientedprogramminglanguagesallowprogrammersmuchgreaterlatitudeindeningobliviousbehaviors.3.1Non-modularReasoninginAspectJNextweshowthat,justasmodularreasoningisnotageneralpropertyofobject-orientedprogramminglanguagesintheabsenceofbehavioralsubtyping,modularreasoningisnotageneralpropertyofAspectJ.Wedothisbyconsideringanaspect-orientedextensiontoourPointexample.Figure4givesanaspect,MoveLimiting,thatmodiesthebehaviorofPointinstancesinthesamewayasRightMovingPoint.MoveLimitingdeclaresapieceofaround-advice.ThisadviceinterceptscallstoPoint'smovemethod.Ifthear-gumentpassedtotheclientisnegative,then,justasinRightMovingPoint,controlproceedstoPoint'smovemethodwiththeparametersettotheabsolutevalueoftheoriginalparameter.AswithRightMovingPoint,theclientpro-grammer'sreasoning,asindicatedbytheassertstatementsinFigure2,isnotcorrectinthepresenceoftheMoveLimitingaspect. storiesareanalogoustothestoriestoldwithsubtypesinobject-orientedlan-guages;bothseektoenhanceexistingbehaviorwithoutintroducingsurprisingbehavior.Inthebehavioralsubtypingliterature,notintroducing\surprisingbehavior"meansthatanoverridingmethodcannotcontradictthespeciedbehaviorofthemethoditoverrides.Suchmethodscan,however,introducenewbehaviorinar-easthatareunspeciedinthesupertype.Theclassicexampleisthespecicationofadrawmethodforshapes.ThemethodisunderspeciedintheShapesuper-type,whichallowsoverridingmethodsinRectangleandCircletospecializeitsbehaviorinappropriateways.Onewaytothinkaboutbehavioralsubtypingisthatanoverridingmethodinheritsthespecicationofthesupertypemethodthatitoverrides[12].Thisforcestheoverridingmethodtoobeythesupertype'sspecication.Inanas-pectdesignedforsuperimposition,theanalogousrequirementwouldbethattheadvicemustobeythespecicationsofthecodethatitadvises.AdaptationStoriesAdaptationstoriesareaboutmodifyingthebehaviorofexistingprogramswithoutchangingtheircode.Thesestoriescomeintwostyles:{Localadaptationstoriesareaboutchangingthebehaviorofasubsetofaprogramasviewedbyotherclientcodewithintheprogram.Anexampleoflocaladaptationisanaspectforpersistence,wheresomecodemustexplicitlyestablishlinkstoadatabasewhiletheremainderoftheprogrambenetsfrompersistencewithoutanyexplicitchangestoitscode[32].{Globaladaptationstoriesareaboutchangingthebehaviorofanentirepro-gramasviewedbyusersoftheprogram.Forexample,usinganaspecttoaddauthenticationtoanexistingwebserverwouldbeaglobaladaptationstory[19][20,Ch.10].Globaladaptationsaredistinguishedinthatnopartoftheadaptedprogramreliesonthepresenceoftheadaptation.Incontrasttoaspectsdesignedforsuperimposition,programmersexpectaspectsdesignedforadaptationtochangethebehaviorofthemodulestheyadvise.Adaptationstoriescanbetoldinobject-orientedlanguages.Sometimesthisisdoneusingsubclassing,butthisviolatesthebehavioralsubtypingdisciplineandisgenerallydiscouraged[5,pp.71{77][23,26].Instead,therecommendedapproachistouseawrapperclasswhoseinstancescontainareferencetotheobjecttobeadapted[15,pp.139{150,175{184].Thespecierofthewrapperclass\startsfromscratch";shecanprovidewhateverbehaviorisneeded,inde-pendentoftheoriginalclass'sspecication.Thiswrapperapproachsacricestheobliviousnessofdynamicbindingtoachievemodularreasoning;aclientofthewrapperclasscanreasonusingthewrapperclass'sspecication.Itmaybethecasethatasimilarsacriceofobliviousnessisneededformodularreasoninginaspect-orientedprogramminglanguages.Likethewrappedclass,theadaptedcodecouldremainoblivioustotheadaptationaspect.Butlikethecodethatusesthewrapperclass,perhapsthecodethatreliesonthe 4.2DataRestrictionsAcomplementaryintermediateapproachistorestrictthedatathatmaybemod-iedbyadvice.Thisisexempliedinobject-orientedprogramminglanguagesbytheworkonvariousownershiptypesystems[2,27{29].Thesetypesystemsareprimarilyconcernedwithrestrictingaliasingtopromotedataencapsulation,andhencemodularreasoning.AnanalogousapproachforAspectJ-likelanguagesmightbetolimitthestatethatmaybemutatedbyadvicetojustthatstatethatitowns.Suchalimitationisstaticallycheckable,butrequiresadditionalannotationsinthesourcecode.However,theseannotationo ertheadditionalbenetofcontrollingsomee ectsofaliasing.5SummaryandFutureWorkThereisaparallelbetweentheobliviousnessofdynamicbindinginobject-orientedlanguagesandthatofadvicebindinginaspect-orientedlanguages[14].Wehaveshownthatthisparallelprovokesausefulanalogybetweenreasoninginthetwostyles.Wehavedemonstratedthatbothsortsofobliviousnesscanpreventmodularreasoning,asdemonstratedbytheMoveLimitingaspectandthe(non-behavioral)subtypeRightMovingPoint.Behavioralsubtypingaddsmodularreasoningtoobject-orientedprogram-minglanguages.TheproblemistondasimilarprogrammingdisciplineforAspectJ-likelanguages.Wehavedescribedtwosortsofstoriesthatprogram-merstellabouthowtheyuseAspectJ:superimpositionandadaptationstories.Thesestoriesprovideconstraintsonsolutionstothemodularreasoningproblem,inthatacompletelyviablesolutionshouldsupportbothkinds.Thebehavioralsubtypinganalogyseemstobearichoneforthinkingabouttherelationshipbetweenobject-orientedlanguagesandAspectJ-likelanguages.Despitetheabsenceofasolutiontothemodularreasoningproblem,wehopethatotherresearcherswillbenetfromthebehavioralsubtypinganalogy.Su-perimpositionandadaptationstoriesseemtocharacterizehowaspect-orientedprogramminglanguagesareactuallyused.Wehopethatthischaracterizationwillprovideusefulconstraintsinthedesignofnewaspect-orientedlangaugesandreasoningmechanisms.Inadditiontoconsideringwhatbehavioralsubtypingmaysayaboutaspect-orientedprogramming,itmightbeinterestingtoconsiderwhethertheanalogyworksinreverse.Canaspect-orientedprogrammingprovidenewinsightontheearlierworkonobject-orientedlanguages?Ourfutureworkistoformalizethemodularreasoningproblemandinvesti-gatethesolutionspacebybuildingacorecalculusforanAspectJ-likelanguagewithsupportformodularreasoning.Ourinitialstepstowardsthiscalculusareavailableinatechnicalreport[9],thoughthatworkdoesnotincludemodular-ityfeatures.Ournextstepistoextendthecalculuswithsuchfeatures.Afterprovingtheappropriatemodularityproperties,wewillthenextendthecalculustoafull-scaleprogramminglanguage. 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