ibmcom Abstract A duality can be thought of as a pair of concepts and a mapping between their terminology such that substituting the conceptspeci64257c terminology turns a statement about one concept into a statement about the other For example in 19 ID: 80375
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3.IncrementalComputation=Demand-DrivenComputationWearenotawareofpriorworkthatpointsoutthedualityofincrementalcomputation=demand-drivencomputation.Thoughbothconceptsareusefulinmanydomains,wecameacrosstheminthedomainofpointeranalysis.Incrementalpointeranalysiscomputesinitialpoints-tosetsfrominitially-knownfacts.Whennewfactsbecomeavailable(forinstance,duetodynamicclassloading),itincrementallyupdatesthepoints-tosets[5].Demand-drivenpointeranalysiscomputesinitialpoints-tosetsfromaninitialquery.Whennewqueriesareissued(forinstance,duetojust-in-timecompilation),itupdatesthepoints-tosetsinademand-drivenway[4]. Incrementalcomputationevaluatesanexpressiononlywhenanewinputbecomesavailabletoit.Demand-drivencomputationevaluatesanexpres-siononlywhenanewoutputisrequestedfromit.Recursively,whenincrementalcomputationpushesoutputfromasub-expressiontoanenclosingexpression,thattriggersevaluationoftheenclosingexpression.Recursively,whendemand-drivencomputationpullsinputtoanenclosingexpressionfromasub-expression,thattriggersevaluationofthesub-expression.Intheabsenceofside-effects,incrementalcomputationdiffersfromcompletefrom-scratchre-computationonlybydoinglessworkatatime.Intheabsenceofside-effects,demand-drivencom-putationdiffersfromcompletefrom-scratchpre-computationonlybydoinglessworkaheadoftime.Incrementalcomputationcanbeimplementedbymemo-tablesthatrememberoldinputswherethosedidnotchange.Demand-drivencomputationcanbeimplementedbymemo-tablesthatrememberoldoutputswherethosedidnotchange.Makinganyalgorithmincrementalordemand-drivencanbeachallengingresearchproblem.Ofcourse,researchitselfoftentstheseconcepts:researchisoftenincremental(asreviewersfrequentlycontest)ordemand-driven(asdeadlinesmakepainfullyclear).4.OtherDualitiesinProgrammingLanguagesWhenwritingapaper,twoexamplesqualifyas“general”andthreeexamplesqualifyas“universal”.Here,wegobeyonduniversalbygivingmorethanthreeexamplesofdualitiesinprogramminglanguages.Dualitiesabound,justwaitingtobedescribed.Staticanalysisndsanover-approximationofwhatitislookingfor.Itsuffersfromfalsepositives,becauseitcannottellwhetherthecodeitislookingatwilleveractuallyexecute.Dynamicanalysisndsanunder-approximationofwhatitislookingfor.Itsuffersfromfalsenegatives,becauseitcannotlookatcodethatdoesnotactuallyexecuteinaparticularrun.Reachability-basedgarbagecollectionstartsatroots(denitely-liveobjects),andtraversesthetransitiveclosure(moreliveobjects),incrementingamark-bit[2].Reference-countinggarbagecollectionstartsatanti-roots(denitely-deadobjects),andtraversesthetransitiveclosure(morepossibly-deadobjects),decrementingareference-count[2].Changepropagationisatechniqueforincrementalcomputationthatre-runspartialcomputationsaffectedbyaninputchange[1].Memoizationisatechniqueforincrementalcomputationthatre-usespartialresultsunaffectedbyaninputchange[1].Alanguageruntimesystemvirtualizesoverphysicalhardware,maintainingspaceresourceswithamemorymanager,whileprovidingprotectionwithtypes.Anoperatingsystemvirtualizesoverphysicalhardware,maintainingspaceresourceswithapagingsubsystem,whileprovidingprotectionwithvirtualmemory.Amethod-basedJITcompilesonemethodatatime.Toprovidemorecontextforoptimizationandreducecalloverheads,itofteninlinesothermethods.Atrace-basedJITcompilesonetraceatatime.Toprovidemorecontextforoptimizationandreducestitchingoverheads,itoftencollatestraces.Thedetaileddevelopmentofthesedualities,andthediscoveryofmoredualities,areleftasanexercisetothereader.5.Problem=SolutionResearchoftenstartsfromarelevantproblem,andthechallengeisdevelopingadeepsolution.Researchoftenstartsfromadeepsolution,andthechallengeisndingarelevantproblem.Inotherwords,ittreatsthesolutionasameta-problem.Inotherwords,itseekstheproblemasameta-solution.Onewaytodothisistolookatadualproblemthatalreadyhasadeepsolution,thenadaptthatsolutiontotheproblemathand.Onewaytodothisistolookatadualsolutionthatalreadyhasarelevantproblem,thenadaptthatproblemtothesolutionathand.Ifthedualdomainsaretoosimilar,thenitmaybetooobvioushowasolutionfromoneappliesintheother.Ifthedualdomainsaretoosimilar,thenitmaybetooobvioushowaproblemfromoneappearsintheother.Therefore,adualitythatisnotquiteperfectisactuallydesirablefromaresearchperspective,becauseworkingaroundtheimperfectionslendsnoveltytotheadaptedsolution.Therefore,adualitythatisnotquiteperfectisactuallydesirablefromaresearchperspective,becauseworkingaroundtheimper-fectionslendsnoveltytotheadaptedproblem.References[1]UmutA.Acar,GuyE.Blelloch,MatthiasBlume,RobertHarper,andKanatTangwongsan.Anexperimentalanalysisofself-adjustingcomputation.TransactionsonProgrammingLanguagesandSystems(TOPLAS),2009.[2]DavidBacon,PerryCheng,andV.T.Rajan.Auniedtheoryofgarbagecollection.InObject-OrientedProgramming,Systems,Lan-guages,andApplications(OOPSLA),2004.[3]DanGrossman.Thetransactionalmemory/garbagecollectionanal-ogy.InEssayTrackofObject-OrientedProgramming,Systems,Lan-guages,andApplications(OOPSLA),2007.[4]NevinHeintzeandOlivierTardieu.Demand-drivenpointeranaly-sis.InProgrammingLanguageDesignandImplementation(PLDI),2001.[5]MartinHirzel,DanielvonDincklage,AmerDiwan,andMichaelHind.Fastonlinepointeranalysis.TransactionsonProgrammingLanguagesandSystems(TOPLAS),2007.[6]HughC.LauerandRogerM.Needham.Onthedualityofoperatingsystemstructures.OperatingSystemsReview,1979.[7]JenniferB.Sartor,MartinHirzel,andKathrynS.McKinley.Nobitleftbehind:Thelimitsofheapdatacompression.InInternationalSymposiumonMemoryManagement(ISMM),2008.[8]BenL.TitzerandJensPalsberg.Verticalobjectlayoutandcompres-sionforxedheaps.InCompilers,Architectures,andSynthesisforEmbeddedSystems(CASES),2007.2