Scientists and engineers often have to deal with systems that exhibit random or unpredictable elements and must effectively evaluate probabilities in each situation. Computer simulations, while the traditional tool used to solve such problems, are limited in the scale and complexity of the problems they can solve. Formalized Probability Theory and Applications Using Theorem Proving discusses some of the limitations inherent in computer systems when applied to problems of probabilistic analysis, and presents a novel solution to these limitations, combining higher-order logic with computer-based theorem proving. Combining practical application with theoretical discussion, this book is an important reference tool for mathematicians, scientists, engineers, and researchers in all STEM fields.

This volume constitutes the proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics (TPHOLs 2008), which was held during August 18-21, 2008 in Montreal, Canada. TPHOLs covers all aspects of theorem proving in higher order logics as well as related topics in theorem proving and veri?cation. There were 40 papers submitted to TPHOLs 2008 in the full research c- egory, each of which was refereed by at least four reviewers selected by the ProgramCommittee. Of these submissions, 17 researchpapers and 1 proofpearl were accepted for presentation at the conference and publication in this v- ume. In keeping with longstanding tradition, TPHOLs 2008 also o?ered a venue for the presentation of emerging trends, where researchers invited discussion by means of a brief introductory talk and then discussed their work at a poster session. A supplementary proceedings volume was published as a 2008 technical report of Concordia University. The organizersaregratefulto MichaelGordonand StevenMiller for agreeing togiveinvitedtalksatTPHOLs2008.Aspartofthecelebrationofthe20yearsof TPHOLs, TPHOLs 2008 invited tool developers and expert users to give special tool presentations of the most representative theorem provers in higher order logics. The following speakers kindly accepted our invitation and we aregrateful tothem: YvesBertot(Coq), MattKaufmann(ACL2), SamOwre(PVS), Konrad Slind (HOL), and Makarius Wenzel (Isabel

Thisvolumecontainstheproceedingsofthe 15th International Conference on TheoremProvinginHigherOrderLogics(TPHOLs2002)heldon20-23August 2002inHampton,Virginia,USA. Theconferenceservesasavenueforthep- sentationofworkintheoremprovinginhigher-orderlogics,andrelatedareas indeduction,formalspeci?cation,softwareandhardwareveri?cation,andother applications. Eachofthe34paperssubmittedinthefullresearchcategorywasrefereedby atleastthreereviewersfromtheprogramcommitteeorbyareviewerappointed bytheprogramcommittee. Ofthesesubmissions,20paperswereacceptedfor presentationattheconferenceandpublicationinthisvolume. Followingawell-establishedtraditioninthisconferenceseries,TPHOLs2002 alsoo?eredavenueforthepresentationofworkinprogress. Fortheworkin progresstrack,shortintroductorytalksweregivenbyresearchers,followedby anopenpostersessionforfurtherdiscussion. Papersacceptedforpresentation inthistrackhavebeenpublishedasConferenceProceedingsCPNASA-2002- 211736. TheorganizerswouldliketothankRickyButlerandG'erardHuetforgra- fullyacceptingourinvitationtogivetalksatTPHOLs2002. RickyButlerwas instrumentalintheformationoftheFormalMethodsprogramattheNASA LangleyResearchCenterandhasledthegroupsinceitsbeginnings. TheNASA LangleyFormalMethodsgroup,underRickyButler'sguidance,hasfunded, beeninvolvedin,orin?uencedmanyformalveri?cationprojectsintheUSover morethantwodecades. In1998G'erardHuetreceivedtheprestigiousHerbrand Awardforhisfundamentalcontributionstotermrewritingandtheoremproving inhigher-orderlogic,aswellasmanyotherkeycontributionstothe?eldof- tomatedreasoning. HeistheoriginatoroftheCoqSystem,underdevelopment atINRIA-Rocquencourt. Dr. Huet'scurrentmaininterestiscomputationall- guistics,howeverhisworkcontinuestoin?uenceresearchersaroundtheworldin awidespectrumofareasintheoreticalcomputerscience,formalmethods,and softwareengineering. ThevenueoftheTPHOLsconferencetraditionallychangescontinenteach yearinordertomaximizethelikelihoodthatresearchersfromallovertheworld willattend. Startingin1993,theproceedingsofTPHOLsanditspredecessor workshopshavebeenpublishedinthefollowingvolumesoftheSpringer-Verlag LectureNotesinComputerScienceseries: 1993(Canada) 780 1998(Australia)1479 1994(Malta) 859 1999(France) 1690 1995(USA) 971 2000(USA) 1869 1996(Finland)1125 2001(UK) 2152 1997(USA) 1275 VI Preface The2002conferencewasorganizedbyateamfromNASALangleyResearch Center,theICASEInstituteatLangleyResearchCenter,andConcordiaU- versity. FinancialsupportcamefromIntelCorporation. Thesupportofallthese organizationsisgratefullyacknowledged. August2002 V'?ctorA. Carreno " C'esarA. Muno "z VII Organization TPHOLs2002isorganizedbyNASALangleyandICASEincooperationwith ConcordiaUniversity. Organizing Committee ConferenceChair: V'?ctorA. Carren"o(NASALangley) ProgramChair: C'esarA. Muno "z(ICASE,NASALaRC) So?'eneTahar(ConcordiaUniversity) ProgramCommittee MarkAagaard(Waterloo) MichaelKohlhase(CMU&Saarland) DavidBasin(Freiburg) ThomasKropf(Bosch) V'?ctorCarren"o(NASALangley) TomMelham(Glasgow) Shiu-KaiChin(Syracuse) JStrotherMoore(Texas,Austin) PaulCurzon(Middlesex) C'esarMuno "z(ICASE,NASALaRC) GillesDowek(INRIA) SamOwre(SRI) HaraldGanzinger(MPISaarbruc ken) ChristinePaulin-Mohring(INRIA) GaneshGopalakrishnan(Utah) LawrencePaulson(Cambridge) JimGrundy(Intel) FrankPfenning(CMU) ElsaGunter(NJIT) KlausSchneider(Karlsruhe) JohnHarrison(Intel) HennySipma(Stanford) DougHowe(Carleton) KonradSlind(Utah) BartJacobs(Nijmegen) DonSyme(Microsoft) PaulJackson(Edinburgh) So? 'eneTahar(Concordia) SaraKalvala(Warwick) WaiWong(HongKongBaptist) Additional Reviewers OtmaneAit-Mohamed AlfonsGeser HaraldRuess BehzadAkbarpour HanneGottliebsen LeonvanderTorre NancyDay MikeKishinevsky TomasUribe BenDiVito HansdeNivelle Jean-ChristopheFilliatre AndrewPitts Invited Speakers RickyButler(NASALangley) G'erardHuet(INRIA) VIII Preface Sponsoring Institutions NASALangley ICASE ConcordiaUniversity INTEL Table of Contents Invited Talks FormalMethodsatNASALangley...1 RickyButler HigherOrderUni?cation30YearsLater...3 G' erardHuet Regular Papers CombiningHigherOrderAbstractSyntaxwithTacticalTheoremProving and(Co)Induction ...13 Simon J. Ambler,RoyL. Crole,AlbertoMomigliano E?cientReasoningaboutExecutableSpeci?cationsinCoq...31 GillesBarthe,PierreCourtieu Veri?edBytecodeModelCheckers...47 DavidBasin,StefanFriedrich,MarekGawkowski The5ColourTheoreminIsabelle/Isar...67 GertrudBauer,TobiasNipkow Type-TheoreticFunctionalSemantics...83 YvesBertot,VenanzioCapretta,KuntalDasBarman AProposalforaFormalOCLSemanticsinIsabelle/HOL...99 AchimD. Brucker,BurkhartWol? ExplicitUniversesfortheCalculusofConstructions...115 Judica. elCourant FormalisedCutAdmissibilityforDisplayLogic...1 31 JeremyE. Dawson,RajeevGor'e FormalizingtheTradingTheoremfortheClassi?cationofSurfaces...148 ChristopheDehlinger,Jean-Fran,coisDufourd Free-StyleTheoremProving...164 DavidDelahaye AComparisonofTwoProofCritics:Powervs. Robustness...182 LouiseA. Dennis,AlanBundy X TableofContents Two-LevelMeta-reasoninginCoq...198 AmyP. Felty PuzzleTool:AnExampleofProgrammingComputationandDeduction . . 214 MichaelJ. C. Gordon AFormalApproachtoProbabilisticTermination...230 JoeHurd UsingTheoremProvingforNumericalAnalysis...246 MicaelaMayero QuotientTypes:AModularApproach...263 AlekseyNogin SequentSchemaforDerivedRules ...281 AlekseyNogin,JasonHickey AlgebraicStructuresandDependentRecords ...298 VirgilePrevosto,DamienDoligez,Th' er' eseHardin ProvingtheEquivalenceofMicrostepandMacrostepSemantics...314 KlausSchneider WeakestPreconditionforGeneralRecursiveProgramsFormalizedinCoq .

This book constitutes the proceedings of the 11th International Conference International Conference on Verification and Evaluation of Computer and Communication Systems ( VECoS 2017 ), held at Concordia University, Montreal, Canada, in August 2017. The 13 full papers, together with 3 abstracts in this volume were carefully reviewed and selected from 35 submissions. The aim of the VECoS conference is to bring together researchers and practitioners in the areas of verification, control, performance and dependability evalu-ation in order to discuss state-of-the-art and challenges in modern computer and communication systems in which functional and extra-functional properties are strongly interrelated. Thus, the main motivation for VECoS is to encourage the cross-fertilization between various formal verification and evaluation approaches, methods and techniques, and especially those developed for concurrent and dis-tributed hardware/software systems.

Traditionally, computer simulation techniques are used to perform probabilistic analysis. However, they provide less accurate results and cannot handle large-scale problems due to their enormous CPU time requirements. Recently, a significant amount of formalization has been done in higher-order logic that allows us to conduct precise probabilistic analysis using theorem proving and thus overcome the limitations of the simulation based probabilistic analysis approach. Some major contributions include the formalization of both discrete and continuous random variables and the verification of corresponding probabilistic and statistical properties. This book presents a concise description of the infrastructures behind these capabilities and their utilization to conduct the probabilistic analysis of real-world systems. The case studies of the round-off error of a digital processor, the Coupon Collector's problem and the Stop-and-Wait protocol are used to illustrate the proposed analysis approach. Designed as an independent research tool, the book presents a well-thought-out treatment of a rapidly emerging multidisciplinary field across Mathematics, Computer Science and Engineering.