This book constitutes the refereed proceedings of the International Symposium of Formal Methods Europe, FME 2001, held in Berlin, Germany, in March 2001.The 32 revised full papers presented together with abstracts of three invited talks were carefully reviewed and selected from a total of 72 submissions. Focusing on increasing software productivity, all current aspects in formal methods are covered. Among the application areas addressed are avionics, smart cards, financial engineering, E-commerce, middleware, security, telecommunications, etc.

Inthisvolumeyouwill?ndthelecturenotescorrespondingtothepres- rd tationsgivenatthe3 summerschoolonAdvancedFunctionalProgramming, heldinBraga,PortugalfromSeptember12-19,1998. ThisschoolwasprecededbyearlieronesinB?astad(1995,Sweden,LNCS925) andOlympia,WA(1996,USA,LNCS1129). Thegoalofthisseriesofschoolsis tobringrecentdevelopmentsintheareaoffunctionalprogrammingtoalarge groupofstudents. Thenotesarepublishedinordertoenableindividuals,small studygroups,andlecturerstobecomeacquaintedwithrecentworkinthefast developingareaoffunctionalprogramming. Whatmadethisschoolparticularlyinterestingwasthefactthatalllectures introducedusefulsoftware,thatwasusedbythestudentsintheclassestoget hands-onexperiencewiththesubjectstaught. Weurgereadersofthisvolumeto downloadthelatestversionofthissoftwarefromtheInternetandtrytodothe exercisesfromthetextthemselves;theproofoftheprogramisinthetyping. The?rstlecture,onSortingMorphisms,servesasagentleintroductiontothe thingstocome. Ifyouhavealwaysbeenafraidoftheword"morphism",andyou havebeenwonderingwhatcatamorphisms,anamorphisms,hylomorphims,and paramorphimswereabout,thisisthepapertoread?rst;youwilldiscoverthat theyaremerelynamesforrecursionpatternsthatoccuroverandoveragainwhen writingfunctionalprograms. Thealgorithmsinthepaperareallaboutsorting, andsinceyouarelikelytoknowthosealgorithmsbyheartalready,seeingthem structuredandanalyzedinanovelwayshouldserveasamotivationtoreadon tothesecondlecture. Thesecondlecture,onGenericProgramming,isalmostabookinabook. ThenotescanbeseenastheculminatingpointoftheSTOP-project,sponsored bytheDutchgovernmentattheendofthe80'sandthebeginningofthe90's. Its overallgoalwasthedevelopmentofacalculationalwayofderivingprograms. The projecthasprovideddeeperinsightintorealfunctionalprogrammingandinto thetheorybehindmanythingscommonlywrittenbyfunctionalprogrammers. Oneofthemainachievementsoftheprojecthasbeentomakepeopleaware ofthefactthatmanyalgorithmscanbedescribedinadata-independentway. ThePolyPsystemintroducedinthesenotesisoneofthetranslationstothe Haskell-worldofthistheoreticalunderpinning. Thethirdlecture,onGenericProgramTransformation,canalsobeseenas anapplicationofthetheoryintroducedinlecturetwo. Manye?ciency-improving programtransformationscanbeperformedinamechanicalway,andthesewould nothavebeenpossiblewithoutinsightintothecorrectnessofsuchtransfor- tionsgainedinthelectureonGenericProgramming. Thefourthlecture,onDesigningandImplementingCombinatorLanguages, introducesaneasytowriteformalismforwritingdownthecatamorphismsint- ducedinearlierchapters. Itisshownhowquitecomplicatedcatamorphisms,that at?rstsightseemratherforbiddingbymakingextensiveuseofhigher-orderdo- VI Preface mains,canactuallybedevelopedinastep-wisefashion,usinganattributegr- marview;itisfurthermoreshownhowtorelatethiswayofprogrammingwith conceptsfromtheobject-orientedworldthusmakingclearwhatthestrengths andweaknessesofeachworldare. The?fthlecture,titledUsingMetaML:AStagedProgrammingLanguage, introducestheconceptofpartialevaluation. Itservesasanotherinstanceof thequestfor"themostgenericofwritingprogramsatthelowestcost". The stagingtechniquesshowhowcoststhatwereintroducedbyaddingextralevels ofabstraction,maybemovedfromrun-timetocompile-time. Ithasbeencommonknowledgetousersofmodernfunctionallanguagesthat thetypesystemcanbeagreathelpinshorteningprogramsandreducingerrors. Intheextremeonemightseeatypeasapredicatecapturingtheproperties ofanyexpressionwiththattype. InthesixthlectureonCayenne-Spiceup yourProgrammingwithDependentTypesitisshowninwhatdirectionfunctional languagesaremostlikelytodevelop,andwhatmaybeexpectedofthenewtype systemstobeintroduced. Thelastlecture,titledHaskellasanAutomationController,showsthat writingfunctionalprogramsdoesnothavetoimplythatoneisboundtoremain isolatedfromtherestoftheworld. Beingabletocommunicatewithsoftware writtenbyothersinauniformway,isprobablyoneofthemostinteresting newdevelopmentsincurrentcomputerscience. Itappearsthattheconceptofa monadtogetherwiththeHaskelltypingrules,isquiteadequatetodescribethe interfacebetweenHaskellprogramsandtheouterworld. Finallywewanttothankeveryonewhocontributedtothisschoolandmade itsuchasuccessfulevent:sponsors,localsystemmanagers,localorganizers, students,andlastbutnotleastthelecturers. Weareconvincedthateveryone presentattheschoolenjoyedthiseventasmuchaswedid,andweallhopethat youwillfeelsomeofthespiritofthiseventwhenstudyingtheselecturenotes. March1999 DoaitseSwierstra PedroHenriques Jos'eOliveira VII Sponsorship Theschoolhasreceivedgeneroussponsorshipfrom: FCT-Fundac",aoparaaCienciaeTecnologia,Minist'eriodaCienciae Tecnologia AdegaCooperativadePontedeLima AgenciaAbreu CGD-CaixaGeraldeDep'ositos CIUM-CentrodeInform'aticadaUniversidadedoMinho DI-DepartamentodeInform'aticadaUniversidadedoMinho GEPL-GrupodeEspeci?cac",aoeProcessamentodeLinguagens LESI-Direc,c"aodeCursodeEngenhariadeSistemaseInform'atica Enabler Lactolima Latic'?niosdasMarinhas,Lda NovabasePorto-SistemasdeInforma,c"aoSA PrimaveraSoftware ProjectoCamila-GrupodeM'etodosFormais Sidereus-SistemasdeInforma,c"aoeConsultoriaInformat'icaLda SIBS-SociedadeInterbanc'ariadeServico,s VieiradeCastro LocalCommittee: Jos'eAlmeida,Minho Lu'?sBarbosa,Minho Jos'eBarros,Minho M. Joao " Frade,Minho PedroHenriques,Minho F. M'arioMartins,Minho F. LuisNeves,Minho CarlaOliveira,Minho JorgePinto,Lix JorgeRocha,Minho CesarRodrigues,Minho Joa"oSaraiva,Minho M. Joa"s. Its overallgoalwasthedevelopmentofacalculationalwayofderivingprograms. The projecthasprovideddeeperinsightintorealfunctionalprogrammingandinto thetheorybehindmanythingscommonlywrittenbyfunctionalprogrammers. Oneofthemainachievementsoftheprojecthasbeentomakepeopleaware ofthefactthatmanyalgorithmscanbedescribedinadata-independentway. ThePolyPsystemintroducedinthesenotesisoneofthetranslationstothe Haskell-worldofthistheoreticalunderpinning. Thethirdlecture,onGenericProgramTransformation,canalsobeseenas anapplicationofthetheoryintroducedinlecturetwo. Manye?ciency-improving programtransformationscanbeperformedinamechanicalway,andthesewould nothavebeenpossiblewithoutinsightintothecorrectnessofsuchtransfor- tionsgainedinthelectureonGenericProgramming. Thefourthlecture,onDesigningandImplementingCombinatorLanguages, introducesaneasytowriteformalismforwritingdownthecatamorphismsint- ducedinearlierchapters. Itisshownhowquitecomplicatedcatamorphisms,that at?rstsightseemratherforbiddingbymakingextensiveuseofhigher-orderdo- VI Preface mains,canactuallybedevelopedinastep-wisefashion,usinganattributegr- marview;itisfurthermoreshownhowtorelatethiswayofprogrammingwith conceptsfromtheobject-orientedworldthusmakingclearwhatthestrengths andweaknessesofeachworldare. The?fthlecture,titledUsingMetaML:AStagedProgrammingLanguage, introducestheconceptofpartialevaluation. Itservesasanotherinstanceof thequestfor"themostgenericofwritingprogramsatthelowestcost". The stagingtechniquesshowhowcoststhatwereintroducedbyaddingextralevels ofabstraction,maybemovedfromrun-timetocompile-time. Ithasbeencommonknowledgetousersofmodernfunctionallanguagesthat thetypesystemcanbeagreathelpinshorteningprogramsandreducingerrors. Intheextremeonemightseeatypeasapredicatecapturingtheproperties ofanyexpressionwiththattype. InthesixthlectureonCayenne-Spiceup yourProgrammingwithDependentTypesitisshowninwhatdirectionfunctional languagesaremostlikelytodevelop,andwhatmaybeexpectedofthenewtype systemstobeintroduced. Thelastlecture,titledHaskellasanAutomationController,showsthat writingfunctionalprogramsdoesnothavetoimplythatoneisboundtoremain isolatedfromtherestoftheworld. Beingabletocommunicatewithsoftware writtenbyothersinauniformway,isprobablyoneofthemostinteresting newdevelopmentsincurrentcomputerscience. Itappearsthattheconceptofa monadtogetherwiththeHaskelltypingrules,isquiteadequatetodescribethe interfacebetweenHaskellprogramsandtheouterworld. Finallywewanttothankeveryonewhocontributedtothisschoolandmade itsuchasuccessfulevent:sponsors,localsystemmanagers,localorganizers, students,andlastbutnotleastthelecturers. Weareconvincedthateveryone presentattheschoolenjoyedthiseventasmuchaswedid,andweallhopethat youwillfeelsomeofthespiritofthiseventwhenstudyingtheselecturenotes. March1999 DoaitseSwierstra PedroHenriques Jos'eOliveira VII Sponsorship Theschoolhasreceivedgeneroussponsorshipfrom: FCT-Fundac"caoparaaCienciaeTecnologia,Minist'eriodaCienciae Tecnologia AdegaCooperativadePontedeLima AgenciaAbreu CGD-CaixaGeraldeDep'ositos CIUM-CentrodeInform'aticadaUniversidadedoMinho DI-DepartamentodeInform'aticadaUniversidadedoMinho GEPL-GrupodeEspeci?cac"caoeProcessamentodeLinguagens LESI-Direccc"aodeCursodeEngenhariadeSistemaseInform'atica Enabler Lactolima Latic'?niosdasMarinhas,Lda NovabasePorto-SistemasdeInformacc"aoSA PrimaveraSoftware ProjectoCamila-GrupodeM'etodosFormais Sidereus-SistemasdeInformacc"aoeConsultoriaInformat'icaLda SIBS-SociedadeInterbanc'ariadeServicocs VieiradeCastro LocalCommittee: Jos'eAlmeida,Minho Lu'?sBarbosa,Minho Jos'eBarros,Minho M. Joao " Frade,Minho PedroHenriques,Minho F. M'arioMartins,Minho F. LuisNeves,Minho CarlaOliveira,Minho JorgePinto,Lix JorgeRocha,Minho CesarRodrigues,Minho Joa"oSaraiva,Minho M. Joa"oVaranda,Minho IX TableofContents SortingMorphisms...1 LexAugusteijn 1 Introduction...1 2 MorphismsonLists...2 2. 1 TheListCatamorphism...2 2. 2 TheListAnamorphism...4 2. 3 TheListHylomorphism...5 2. 4 InsertionSort...6 2. 5 SelectionSorts...7 3 LeafTrees...9 3. 1 TheLeaf-TreeCatamorphism...9 3. 2 TheLeaf-TreeAnamorphism...10 3. 3 TheLeaf-TreeHylomorphism...11 3. 4 MergeSort...12 4 BinaryTrees...13 4. 1 TheTreeCatamorphism...13 4. 2 TheTreeAnamorphism...14 4. 3 TheTreeHylomorphism...14 4. 4 Quicksort...15 4. 5 HeapSort...16 5 Paramorphisms...18 5. 1 TheListParamorphism...18 5. 2 InsertAsParamorphism...18 5. 3 RemoveAsParamorphism...19 6 GeneralizingDataStructures...20 6. 1 GeneralizingQuicksort...20 6. 2 GeneralizingHeapSort...21 7 Conclusions...23 GenericProgramming-AnIntroduction-...28 RolandBackhouse,PatrikJansson,JohanJeuring,LambertMeertens 1 Introduction...

This book constitutes the refereed proceedings of the workshops which complemented the 23rd Symposium on Formal Methods, FM 2019, held in Porto, Portugal, in October 2019. This volume presents the papers that have been accepted for the following workshops: Third Workshop on Practical Formal Verification for Software Dependability, AFFORD 2019; 8th International Symposium From Data to Models and Back, DataMod 2019; First Formal Methods for Autonomous Systems Workshop, FMAS 2019; First Workshop on Formal Methods for Blockchains, FMBC 2019; 8th International Workshop on Formal Methods for Interactive Systems, FMIS 2019; First History of Formal Methods Workshop, HFM 2019; 8th International Workshop on Numerical and Symbolic Abstract Domains, NSAD 2019; 9th International Workshop on Open Community Approaches to Education, Research and Technology, OpenCERT 2019; 17th Overture Workshop, Overture 2019; 19th Refinement Workshop, Refine 2019; First International Workshop on Reversibility in Programming, Languages, and Automata, RPLA 2019; 10th International Workshop on Static Analysis and Systems Biology, SASB 2019; and the 10th Workshop on Tools for Automatic Program Analysis, TAPAS 2019.

This book constitutes the refereed proceedings of the workshops which complemented the 23rd Symposium on Formal Methods, FM 2019, held in Porto, Portugal, in October 2019. This volume presents the papers that have been accepted for the following workshops: Third Workshop on Practical Formal Verification for Software Dependability, AFFORD 2019; 8th International Symposium From Data to Models and Back, DataMod 2019; First Formal Methods for Autonomous Systems Workshop, FMAS 2019; First Workshop on Formal Methods for Blockchains, FMBC 2019; 8th International Workshop on Formal Methods for Interactive Systems, FMIS 2019; First History of Formal Methods Workshop, HFM 2019; 8th International Workshop on Numerical and Symbolic Abstract Domains, NSAD 2019; 9th International Workshop on Open Community Approaches to Education, Research and Technology, OpenCERT 2019; 17th Overture Workshop, Overture 2019; 19th Refinement Workshop, Refine 2019; First International Workshop on Reversibility in Programming, Languages, and Automata, RPLA 2019; 10th International Workshop on Static Analysis and Systems Biology, SASB 2019; and the 10th Workshop on Tools for Automatic Program Analysis, TAPAS 2019.

This book constitutes the refereed proceedings of the 23rd Symposium on Formal Methods, FM 2019, held in Porto, Portugal, in the form of the Third World Congress on Formal Methods, in October 2019. The 44 full papers presented together with 3 invited presentations were carefully reviewed and selected from 129 submissions. The papers are organized in topical sections named: Invited Presentations; Verification; Synthesis Techniques; Concurrency; Model Checking Circus; Model Checking; Analysis Techniques; Specification Languages; Reasoning Techniques; Modelling Languages; Learning-Based Techniques and Applications; Refactoring and Reprogramming; I-Day Presentations.