This book is about describing the meaning of programming languages. The author teaches the skill of writing semantic descriptions as an efficient way to understand the features of a language. While a compiler or an interpreter offers a form of formal description of a language, it is not something that can be used as a basis for reasoning about that language nor can it serve as a definition of a programming language itself since this must allow a range of implementations. By writing a formal semantics of a language a designer can yield a far shorter description and tease out, analyse and record design choices. Early in the book the author introduces a simple notation, a meta-language, used to record descriptions of the semantics of languages. In a practical approach, he considers dozens of issues that arise in current programming languages and the key techniques that must be mastered in order to write the required formal semantic descriptions. The book concludes with a discussion of the eight key challenges: delimiting a language (concrete representation), delimiting the abstract content of a language, recording semantics (deterministic languages), operational semantics (non-determinism), context dependency, modelling sharing, modelling concurrency, and modelling exits. The content is class-tested and suitable for final-year undergraduate and postgraduate courses. It is also suitable for any designer who wants to understand languages at a deep level. Most chapters offer projects, some of these quite advanced exercises that ask for complete descriptions of languages, and the book is supported throughout with pointers to further reading and resources. As a prerequisite the reader should know at least one imperative high-level language and have some knowledge of discrete mathematics notation for logic and set theory.

ThisvolumehasitsoriginsinameetingheldatMicrosoftResearch,Cambridge,in April2009tocelebrateTonyHoare's75thBirthday(actually11Jan2009). Allthe technicalpapersexceptforthosewrittenbyAbramsky,Jackson,JonesandMeyer arebased-sometimesclosely,sometimesnot-onpresentationsgivenatthatme- ing. TheideaforthemeetingaroseinconversationsbetweenourselvesandAndrew HerbertofMicrosoft,whohostedatrulymemorableandhappyevent. ThemeetingwasorganisedbyourselvesandKenWood,withthe?nancials- portofMicrosoftResearchandFormalSystems(Europe)Ltd,andheldovertwo days. We wouldlike to recordparticularthanksto Angela Still of Microsoftfor makingallthelocalarrangementsatCambridgeandmuchmore:themeetingwould nothavehappenedwithouther. Whilethemajorityofthepapersinthisvolumearetechnical,weaskedauthorsto re?ectonthein?uenceofHoare'sworkontheirown?eldsandtomakeappropriate remarksonit. Allthetechnicalpaperswererefereed. DiscussionswithWayneWheelerofSpringerinspiredthetwoofustowritethe scienti?cbiographyofHoarethatisthe?rstpaperinthisvolume. Thoughwehave bothknownTonywellformanyyears,wewereamazedathowmanydiscoveries abouthimwemadeduringtheprocessofwritingthisarticle. WewouldlikethankWayneandhisassistantSimonReesfortheirhelpinprep- ingthisvolumeaswellastheirpatience. Muchoftheworkingatheringthepapers, ensuringconsistencyofLaTeXstyles,etc. ,wasdonebyLucyLiofOxfordUniv- sityComputingLaboratoryandwethankherwarmly. Tragically,KenWood'swifeLisadiedafteralongillnessinSeptember2009. Wededicatethisvolumetohermemory. January2010 CliffJones BillRoscoe ix Contents 1 Insight,InspirationandCollaboration...1 C. B. JonesandA. W. Roscoe 2 FromCSPtoGameSemantics...33 SamsonAbramsky 3 OnMereologiesinComputingScience...47 DinesBjorner 4 Roles,Stacks,Histories:ATripleforHoare...71 Johannes Borgstrom, .. Andrew D. Gordon, andRiccardoPucella 5 ForwardwithHoare...101 MikeGordonandHel 'ene ' Collavizza 6 ProbabilisticProgrammingwithCoordination...123 HeJifeng 7 TheOperationalPrincipleandProblemFrames...143 MichaelJackson 8 TheRoleofAuxiliaryVariablesintheFormal DevelopmentofConcurrentPrograms...167 C. B. Jones 9 AvoidaVoid:TheEradicationofNullDereferencing...189 BertrandMeyer,AlexanderKogtenkov,andEmmanuelStapf 10 UnfoldingCSP...213 MikkelBundgaardandRobinMilner xi xii Contents 11 Quicksort:CombiningConcurrency,Recursion, andMutableDataStructures...2 29 DavidKitchin,AdrianQuark,andJayadevMisra 12 TheThousand-and-OneCryptographers...255 A. K. McIverandC. C. Morgan 13 On Process-AlgebraicExtensions of Metric TemporalLogic...283 ChristophHaase,Joel .. Ouaknine,andJamesWorrell 14 FunwithTypeFunctions...301 OlegKiselyov,SimonPeytonJones,andChung-chiehShan 15 OnCSPandtheAlgebraicTheoryofEffects...333 RobvanGlabbeekandGordonPlotkin 16 CSPisExpressiveEnoughfor ...371 A. W. Roscoe 17 TheTokeneerExperiments...405 JimWoodcock,EmineGokc .. ,eAydal,andRodChapman Chapter1 Insight,InspirationandCollaboration C. B. JonesandA. W. Roscoe Abstract TonyHoare'smanycontributionstocomputingsciencearemarkedby insightthatwasgroundedinpracticalprogramming. Manyofhispapershavehada profoundimpactontheevolutionofour?eld;theyhavemoreoverprovidedasource ofinspirationtoseveralgenerationsofresearchers. Weexaminethedevelopmentof hisworkthroughareviewofthedevelopmentofsomeofhismostin?uentialpieces ofworksuchasHoarelogic,CSPandUnifyingTheories. 1. 1 Introduction To many who know Tony Hoare only through his publications, they must often looklikepolishedgemsthatcomefromamindthatrarelymakesfalsesteps,nor evenperhapshastoworkattheircreation. Assooften,thisimpressionisafurther complimenttosomeonewhoactuallyaddstoveryhardworkandmanydiscarded attempts the ?nal polish thatmakes complexideas relatively easy for the reader tocomprehend. Asindicatedonpagexiof[HJ89],hisideastypicallygothrough manyrevisions. ThetwoauthorsofthecurrentpapereachhadthehonourofTonyHoaresuperv- ingtheirdoctoralstudiesinOxford. Theyknowat?rsthandhiskindandgenerous styleandwillcountitasanachievementifthispapercanconveysomethingofthe workingmethodsofsomeonebigenoughtoeschewcompetitionandpointscoring. Indeedit willbe apparentfromthe followingsectionshowoften,havingstarted somenewwayofthinkingorexcitingideas,hehappilyleavestheirexplorationand developmenttoothers. Wehavebothbene?tedpersonallyfromthis. C. B. Jones( ) SchoolofComputingScience,NewcastleUniversity,UK e-mail:cliff. jones@ncl. ac. uk A. W. Roscoe OxfordUniversityComputingLaboratory,UK e-mail:Bill. Roscoe@comlab. ox. ac. uk C. B. Jonesetal. (eds. ),Re?ectionsontheWorkofC. A. R.

This Festschrift volume, published in honor of Brian Randell on the occasion of his 75th birthday, contains a total of 37 refereed contributions. Two biographical papers are followed by the six invited papers that were presented at the conference 'Dependable and Historic Computing: The Randell Tales', held during April 7-8, 2011 at Newcastle University, UK. The remaining contributions are authored by former scientific colleagues of Brian Randell. The papers focus on the core of Brian Randell's work: the development of computing science and the study of its history. Moreover, his wider interests are reflected and so the collection comprises papers on software engineering, storage fragmentation, computer architecture, programming languages and dependability. There is even a paper that echoes Randell's love of maps. After an early career with English Electric and then with IBM in New York and California, Brian Randell joined Newcastle University. His main research has been on dependable computing in all its forms, especially reliability, safety and security aspects, and he has led several major European collaborative projects.

Both object orientation and parallelism are modern programming paradigms which have gained much popularity in the last 10-15 years. Object orientation raises hopes for increased productivity of software generation and maintenance methods. Parallelism can serve to structure a problem but also promises faster program execution. The two areas of computing science in which these paradigms play the most prominent role are programming languages and databases. In programming languages, one can take an academic approach with a primary focus on the generality of the semantics of the language constructs which support the respective paradigm. In databases, one is willing to restrict the power of the constructs in the interest of increased efficiency. Inter- and intra-object parallelism have received an increasing amount of attention in the last few years by researchers in the area of object- oriented programming. At first glance, an object is very similar to a process which offers services to other processes and demands services from them. It has, however, transpired that object-oriented concepts cause problems when combined with parallelism. In programming languages, the introduction of parallelism and the synchronization constraints it brings with it can get in the way of code reusability. In databases, the combination of object orientation and parallelism requires, for example, a generalization of the transaction model, new approaches to the specification of information systems, an implementation model of object communication, and the design of an overall system architecture. There has been insufficient communication between researchers in programming languages and in databases on these issues. Object Orientation with Parallelism and Persistence grew out of a Dagstuhl Seminar of the same title in April 1995 whose goal it was to put the new research area object orientation with parallelism' on an interdisciplinary basis. Object Orientation with Parallelism and Persistence will be of interest to researchers and professionals working in software engineering, programming languages, and database systems.

ThisvolumehasitsoriginsinameetingheldatMicrosoftResearch,Cambridge,in April2009tocelebrateTonyHoare's75thBirthday(actually11Jan2009). Allthe technicalpapersexceptforthosewrittenbyAbramsky,Jackson,JonesandMeyer arebased-sometimesclosely,sometimesnot-onpresentationsgivenatthatme- ing. TheideaforthemeetingaroseinconversationsbetweenourselvesandAndrew HerbertofMicrosoft,whohostedatrulymemorableandhappyevent. ThemeetingwasorganisedbyourselvesandKenWood,withthe?nancials- portofMicrosoftResearchandFormalSystems(Europe)Ltd,andheldovertwo days. We wouldlike to recordparticularthanksto Angela Still of Microsoftfor makingallthelocalarrangementsatCambridgeandmuchmore:themeetingwould nothavehappenedwithouther. Whilethemajorityofthepapersinthisvolumearetechnical,weaskedauthorsto re?ectonthein?uenceofHoare'sworkontheirown?eldsandtomakeappropriate remarksonit. Allthetechnicalpaperswererefereed. DiscussionswithWayneWheelerofSpringerinspiredthetwoofustowritethe scienti?cbiographyofHoarethatisthe?rstpaperinthisvolume. Thoughwehave bothknownTonywellformanyyears,wewereamazedathowmanydiscoveries abouthimwemadeduringtheprocessofwritingthisarticle. WewouldlikethankWayneandhisassistantSimonReesfortheirhelpinprep- ingthisvolumeaswellastheirpatience. Muchoftheworkingatheringthepapers, ensuringconsistencyofLaTeXstyles,etc. ,wasdonebyLucyLiofOxfordUniv- sityComputingLaboratoryandwethankherwarmly. Tragically,KenWood'swifeLisadiedafteralongillnessinSeptember2009. Wededicatethisvolumetohermemory. January2010 CliffJones BillRoscoe ix Contents 1 Insight,InspirationandCollaboration...1 C. B. JonesandA. W. Roscoe 2 FromCSPtoGameSemantics...33 SamsonAbramsky 3 OnMereologiesinComputingScience...47 DinesBjorner 4 Roles,Stacks,Histories:ATripleforHoare...71 Johannes Borgstrom, .. Andrew D. Gordon, andRiccardoPucella 5 ForwardwithHoare...101 MikeGordonandHel 'ene ' Collavizza 6 ProbabilisticProgrammingwithCoordination...123 HeJifeng 7 TheOperationalPrincipleandProblemFrames...143 MichaelJackson 8 TheRoleofAuxiliaryVariablesintheFormal DevelopmentofConcurrentPrograms...167 C. B. Jones 9 AvoidaVoid:TheEradicationofNullDereferencing...189 BertrandMeyer,AlexanderKogtenkov,andEmmanuelStapf 10 UnfoldingCSP...213 MikkelBundgaardandRobinMilner xi xii Contents 11 Quicksort:CombiningConcurrency,Recursion, andMutableDataStructures...2 29 DavidKitchin,AdrianQuark,andJayadevMisra 12 TheThousand-and-OneCryptographers...255 A. K. McIverandC. C. Morgan 13 On Process-AlgebraicExtensions of Metric TemporalLogic...283 ChristophHaase,Joel .. Ouaknine,andJamesWorrell 14 FunwithTypeFunctions...301 OlegKiselyov,SimonPeytonJones,andChung-chiehShan 15 OnCSPandtheAlgebraicTheoryofEffects...333 RobvanGlabbeekandGordonPlotkin 16 CSPisExpressiveEnoughfor ...371 A. W. Roscoe 17 TheTokeneerExperiments...405 JimWoodcock,EmineGokc .. ,eAydal,andRodChapman Chapter1 Insight,InspirationandCollaboration C. B. JonesandA. W. Roscoe Abstract TonyHoare'smanycontributionstocomputingsciencearemarkedby insightthatwasgroundedinpracticalprogramming. Manyofhispapershavehada profoundimpactontheevolutionofour?eld;theyhavemoreoverprovidedasource ofinspirationtoseveralgenerationsofresearchers. Weexaminethedevelopmentof hisworkthroughareviewofthedevelopmentofsomeofhismostin?uentialpieces ofworksuchasHoarelogic,CSPandUnifyingTheories. 1. 1 Introduction To many who know Tony Hoare only through his publications, they must often looklikepolishedgemsthatcomefromamindthatrarelymakesfalsesteps,nor evenperhapshastoworkattheircreation. Assooften,thisimpressionisafurther complimenttosomeonewhoactuallyaddstoveryhardworkandmanydiscarded attempts the ?nal polish thatmakes complexideas relatively easy for the reader tocomprehend. Asindicatedonpagexiof[HJ89],hisideastypicallygothrough manyrevisions. ThetwoauthorsofthecurrentpapereachhadthehonourofTonyHoaresuperv- ingtheirdoctoralstudiesinOxford. Theyknowat?rsthandhiskindandgenerous styleandwillcountitasanachievementifthispapercanconveysomethingofthe workingmethodsofsomeonebigenoughtoeschewcompetitionandpointscoring. Indeedit willbe apparentfromthe followingsectionshowoften,havingstarted somenewwayofthinkingorexcitingideas,hehappilyleavestheirexplorationand developmenttoothers. Wehavebothbene?tedpersonallyfromthis. C. B. Jones( ) SchoolofComputingScience,NewcastleUniversity,UK e-mail:cliff. jones@ncl. ac. uk A. W. Roscoe OxfordUniversityComputingLaboratory,UK e-mail:Bill. Roscoe@comlab. ox. ac. uk C. B. Jonesetal. (eds. ),Re?ectionsontheWorkofC. A. R.

The growing complexity of modern software systems increases the di?culty of ensuring the overall dependability of software-intensive systems. Complexity of environments, in which systems operate, high dependability requirements that systems have to meet, as well as the complexity of infrastructures on which they rely make system design a true engineering challenge. Mastering system complexity requires design techniques that support clear thinking and rigorous validation and veri?cation. Formal design methods help to achieve this. Coping with complexity also requires architectures that are t- erant of faults and of unpredictable changes in environment. This issue can be addressed by fault-tolerant design techniques. Therefore, there is a clear need of methods enabling rigorous modelling and development of complex fault-tolerant systems. This bookaddressessuchacuteissues indevelopingfault-tolerantsystemsas: - Veri?cation and re?nement of fault-tolerant systems - Integrated approaches to developing fault-tolerant systems - Formal foundations for error detection, error recovery, exception and fault handling - Abstractions, styles and patterns for rigorousdevelopment of fault tolerance - Fault-tolerant software architectures - Development and application of tools supporting rigorous design of depe- able systems - Integrated platforms for developing dependable systems - Rigorous approaches to speci?cation and design of fault tolerance in novel computing systems TheeditorsofthisbookwereinvolvedintheEU(FP-6)projectRODIN(R- orous Open Development Environment for Complex Systems), which brought together researchers from the fault tolerance and formal methods communi- 1 ties. In 2007 RODIN organized the MeMoT workshop held in conjunction with the Integrated Formal Methods 2007 Conference at Oxford University.

This book constitutes the refereed proceedings of the 4th International Colloquium on Theoretical Aspects of Computing, ICTAC 2007 held in Macau, China in September 2007.

The 29 revised full papers presented together with 3 invited talks and summaries of 2 tutorials were carefully reviewed and selected from 69 submissions. The aim of the colloquium is to bring together practitioners and researchers from academia, industry and government to present research results, and exchange experience, ideas, and solutions for their problems in theoretical aspects of computing such as automata theory and formal languages, principles and semantics of programming languages, software architectures and their description languages, software specification, refinement, and verification, model checking and theorem proving, real-time, embedded and hybrid systems, theory of parallel, distributed, and internet-based (grid) computing, simulation and modeling, and service-oriented development.

This Festschrift volume is published to honour both Dines Bjorner and Zhou Chaochen on the occasion of their 70th birthdays. The volume includes 25 refereed papers by leading researchers, current and former colleagues, who congregated at a celebratory symposium held in Macao, China, in the course of the International Colloquium on Theoretical Aspects of Computing, ICTAC 2007. The papers cover a broad spectrum of subjects."

This volume, like the symposium CSP25 which gave rise to it, commemorates the semi-jubilee of Communicating Sequential Processes. 1 Tony Hoare s paper Communicating Sequential Processes is today widely regarded as one of the most in?uential papers in computer science. To comm- orate it, an event was organized under the auspices of BCS-FACS (the British Computer Society s Formal Aspects of Computing Science specialist group). CSP25 was one of a series of such events organized to highlight the use of formal methods, emphasize their relevance to modern computing and promote their wider application. BCS-FACS is proud that Tony Hoare presented his original ideas on CSP at one of its ?rst meetings, in 1978. The two-day event, 7 8 July 2004, was hosted by London South Bank U- versity s Institute for Computing Research, Faculty of Business, Computing and Information Management. The intention was to celebrate, re?ect upon and look beyondthe?rstquarter-centuryofCSP scontributionstocomputerscience. The meeting examined the impact of CSP on many areas stretching from semantics (mathematical models for understanding concurrency and communications) and logic(forreasoningaboutbehavior), throughthedesignofparallelprogramming languages (i/o, parallelism, synchronization and threads) to applications va- ing from distributed software and parallel computing to information security, Web services and concurrent hardware circuits. It included a panel discussion with panelists Brookes, Hoare, de Roever and Roscoe (chaired by Je? Sanders), poster presentations by PhD students and others, featured a ?re alarm (requ- ing evacuation in the rain ) and concluded with the presentation of a fountain pen to Prof. Sir C. A. R. Hoare."

This book constitutes the refereed proceedings of FME '97, the 4th International Symposium of Formal Methods Europe devoted to Industrial Applications and Strengthened Foundations of Formal Methods , held in Graz, Austria, in September 1997. The 35 revised full papers presented in the volume were selected from a total of 94 submissions. Formal methods and mathematically based techniques are increasingly recognized as a viable technology for the development and engineering of computing systems. The majority of the papers in this volume describe industrial applications, extensions to existing techniques, or case studies; papers on theoretical aspects show clear potential applicability.

Both object orientation and parallelism are modern programming paradigms which have gained much popularity in the last 10-15 years. Object orientation raises hopes for increased productivity of software generation and maintenance methods. Parallelism can serve to structure a problem but also promises faster program execution. The two areas of computing science in which these paradigms play the most prominent role are programming languages and databases. In programming languages, one can take an academic approach with a primary focus on the generality of the semantics of the language constructs which support the respective paradigm. In databases, one is willing to restrict the power of the constructs in the interest of increased efficiency. Inter- and intra-object parallelism have received an increasing amount of attention in the last few years by researchers in the area of object- oriented programming. At first glance, an object is very similar to a process which offers services to other processes and demands services from them. It has, however, transpired that object-oriented concepts cause problems when combined with parallelism. In programming languages, the introduction of parallelism and the synchronization constraints it brings with it can get in the way of code reusability. In databases, the combination of object orientation and parallelism requires, for example, a generalization of the transaction model, new approaches to the specification of information systems, an implementation model of object communication, and the design of an overall system architecture. There has been insufficient communication between researchers in programming languages and in databases on these issues. Object Orientation with Parallelism and Persistence grew out of a Dagstuhl Seminar of the same title in April 1995 whose goal it was to put the new research area object orientation with parallelism' on an interdisciplinary basis. Object Orientation with Parallelism and Persistence will be of interest to researchers and professionals working in software engineering, programming languages, and database systems.

Refinement is the term used to describe systematic and formal methods of specifying hard- and software and transforming the specifications into designs and implementations. The value of formal methods in producing reliable hard- and software is widely appreciated by academics and workers in industry, despite the fact that certain research areas, such as the application to industrial-scale problems, are still in their infancy. This volume contains the papers presented at the 5th Refinement Workshop held in London, 8-10 January 1992. Its theme was the theory and practice of software specifications, which is the transformation of formal software specifications into more correct specifications, designs and codes. This has been an important area of research for the last 5 years and the workshop addressed specific issues and problems related to it. Among the topics discussed in this volume are: the role of refinement in software development, parallel designs and implementations, methods and tools for verification of critical properties, refinement and confidentiality, concurrent processes as objects, the compliance of Ada programs with Z specifications and a tactic driven refinement tool. This is the latest refinement workshop proceedings to be published in the "Workshops in Computing" series (the 3rd and 4th workshops having appeared in 1990 and 1991 respectively). It will be of interest to academic and industrial researchers, postgraduate students and research-oriented developers in the computer industry.

Sir Tony Hoare has had an enormous influence on computer science, from the Quicksort algorithm to the science of software development, concurrency and program verification. His contributions have been widely recognised: He was awarded the ACM's Turing Award in 1980, the Kyoto Prize from the Inamori Foundation in 2000, and was knighted for "services to education and computer science" by Queen Elizabeth II of England in 2000. This book presents the essence of his various works-the quest for effective abstractions-both in his own words as well as chapters written by leading experts in the field, including many of his research collaborators. In addition, this volume contains biographical material, his Turing award lecture, the transcript of an interview and some of his seminal papers. Hoare's foundational paper "An Axiomatic Basis for Computer Programming", presented his approach, commonly known as Hoare Logic, for proving the correctness of programs by using logical assertions. Hoare Logic and subsequent developments have formed the basis of a wide variety of software verification efforts. Hoare was instrumental in proposing the Verified Software Initiative, a cooperative international project directed at the scientific challenges of large-scale software verification, encompassing theories, tools and experiments. Tony Hoare's contributions to the theory and practice of concurrent software systems are equally impressive. The process algebra called Communicating Sequential Processes (CSP) has been one of the fundamental paradigms, both as a mathematical theory to reason about concurrent computation as well as the basis for the programming language occam. CSP served as a framework for exploring several ideas in denotational semantics such as powerdomains, as well as notions of abstraction and refinement. It is the basis for a series of industrial-strength tools which have been employed in a wide range of applications. This book also presents Hoare's work in the last few decades. These works include a rigorous approach to specifications in software engineering practice, including procedural and data abstractions, data refinement, and a modular theory of designs. More recently, he has worked with collaborators to develop Unifying Theories of Programming (UTP). Their goal is to identify the common algebraic theories that lie at the core of sequential, concurrent, reactive and cyber-physical computations.

Sir Tony Hoare has had an enormous influence on computer science, from the Quicksort algorithm to the science of software development, concurrency and program verification. His contributions have been widely recognised: He was awarded the ACM's Turing Award in 1980, the Kyoto Prize from the Inamori Foundation in 2000, and was knighted for "services to education and computer science" by Queen Elizabeth II of England in 2000. This book presents the essence of his various works-the quest for effective abstractions-both in his own words as well as chapters written by leading experts in the field, including many of his research collaborators. In addition, this volume contains biographical material, his Turing award lecture, the transcript of an interview and some of his seminal papers. Hoare's foundational paper "An Axiomatic Basis for Computer Programming", presented his approach, commonly known as Hoare Logic, for proving the correctness of programs by using logical assertions. Hoare Logic and subsequent developments have formed the basis of a wide variety of software verification efforts. Hoare was instrumental in proposing the Verified Software Initiative, a cooperative international project directed at the scientific challenges of large-scale software verification, encompassing theories, tools and experiments. Tony Hoare's contributions to the theory and practice of concurrent software systems are equally impressive. The process algebra called Communicating Sequential Processes (CSP) has been one of the fundamental paradigms, both as a mathematical theory to reason about concurrent computation as well as the basis for the programming language occam. CSP served as a framework for exploring several ideas in denotational semantics such as powerdomains, as well as notions of abstraction and refinement. It is the basis for a series of industrial-strength tools which have been employed in a wide range of applications. This book also presents Hoare's work in the last few decades. These works include a rigorous approach to specifications in software engineering practice, including procedural and data abstractions, data refinement, and a modular theory of designs. More recently, he has worked with collaborators to develop Unifying Theories of Programming (UTP). Their goal is to identify the common algebraic theories that lie at the core of sequential, concurrent, reactive and cyber-physical computations.