Functional reactive programming (FRP) is a paradigm extending functional languages with primitives which operate on state. Typical FRP systems contain many dozens of such primitives. This thesis aims to identify a minimal subset of primitives which captures the same set of behavior as these systems, and to provide an axiomatic semantics for them using first-order linear temporal logic, with the aim of utilizing these semantics in formal verification of FRP programs. Furthermore, we identify several important properties of these primitives and prove that they are satisfied using the Coq proof assistant.

Functional Reactive Programming (FRP) offers a declarative way to express reactive systems such as animations, user interfaces and games. Various topics related to FRP like optimization, generalization and debugging were studied. However, the use of FRP in distributed systems has not been investigated extensively. Focused on the use of the Dunai FRP library implemented in the Haskell programming language, the aim of this thesis is to develop and evaluate a way to apply FRP to distributed systems. A library is implemented to extend Dunai with means to create distributed systems. There is support for the Client/Server network architectural model and algorithms to synchronize applications across a network. As the synchronization of distributed systems has been a topic of research for decades, this thesis explores whether developed ideas, such as Time Warp (Jefferson, 1985), can be expressed in FRP. Additionally, Client Side Prediction (Bernier, 2001) and Dead Reckoning (DIS Steering Committee, 1994) are used to predict server reactions on client-side. An exemplary application demonstrates the implementation. The application is then evaluated in a performance test and a user test. TimeWarp synchronization has a significant impact on performance. Despite this, the application is playable up to a latency of 100 ms. The result of Dead Reckoning is acceptable, whereas Client Side Prediction is not usable. The thesis shows that the developed way can be used to run FRP on distributed systems. Further work should focus the performance to enable more complex applications. Moreover, Dead Reckoning can be improved to a smoother result. Non-trivial changes are necessary to make Client Side Prediction usable.:1 Introduction ... 1 2 Functional Reactive Programming ... 4 2.1 The Arrow Type Class ... 5 2.2 The Dunai FRP Library ... 7 2.2.1 Monadic Stream Functions ... 7 2.2.2 Combining Monads ... 8 2.2.3 Monads in Monadic Stream Functions ... 9 2.3 The BearRiver FRP Library ... 10 2.4 Executing FRP ... 11 3 Synchronization of Distributed Systems ... 13 3.1 Distributed Systems ... 13 3.2 Consistency of Distributed Systems ... 14 3.3 Client/Server Architecture ... 15 3.4 Time Warp Synchronization ... 16 3.5 Dead Reckoning ... 17 3.6 Client Side Prediction ... 19 4 Cloud Haskell ... 21 4.1 Exchanging Messages ... 22 4.2 Fault Tolerance ... 23 4.3 The Cloud Haskell Platform ... 23 5 Concept ... 25 5.1 Concept of the Implemented Library ... 25 5.2 Concept of the Sample Application ... 27 5.3 Functional Requirements ... 28 5.4 Non-Functional Requirements ... 30 6 Implementation ... 32 6.1 Client/Server Architecture ... 33 6.1.1 Establishing Connections between Clients and Servers ... 33 6.1.2 Distributed Execution of FRP ... 35 6.1.3 Implementation of Servers ... 36 6.1.4 Implementation of Clients ... 38 6.2 Time Warp Synchronization ... 39 6.2.1 Rollbacks of Monadic Stream Functions ... 39 6.2.2 Executing FRP using Time Warp Synchronization ... 41 6.3 Dead Reckoning ... 45 6.4 Client Side Prediction ... 46 7 Evaluation ... 48 7.1 Evaluation of Functional Requirements ... 48 7.2 Concept of the Performance Test ... 52 7.3 Concept of the User Test ... 53 7.4 Results of the Performance Test ... 54 7.5 Results of the User Test ... 56 8 Summary ... 60 Bibliography ... A Listings ... M List of Figures ... O List of Tables ... P Glossary .. Q Abbreviations ... U

This thesis studies the use of the functional reactive programming (FRP) framework reactive-banana in a prototype which simulates a part of a Long-Term Evolution (LTE) base station: the Radio Resource Control connection setup procedure. The investigated problem is to determine whether using this FRP framework leads to an implementation with suitable performance and improved maintainability compared to the current implementation. Enhancing the maintainability of the base station software enables quicker and more efficient maintenance activities, which lead to an improved customer satisfaction. Moreover, it means that less programmers need to work on maintenance, so they can work on developing new products instead. In order to compare the use of the FRP paradigm to the one currently used in the base station implementation, the object-oriented programming (OOP) paradigm, a second prototype using this paradigm was also implemented. Having two prototypes implementing the same designed reference model (which is a simplified version of the Radio Resource Control connection setup procedure) enables a relevant comparison of the two paradigms. The two prototypes were then compared in terms of performance and maintainability. The maintainability evaluation consisted in using both software metrics and experts’ assessment, as this has been proven to be the most efficient way to evaluate software maintainability. Four experts were asked to fill in a questionnaire after reviewing the code of the two implementations. The comparison of the two prototypes indicates that the FRP prototype is more maintainable than the OOP one, but the OOP prototype has better performances than the FRP one. Moreover, the performance of the FRP prototype during the conducted tests indicates that such an implementation of the FRP paradigm is not suitable for a real base station.

Computers have been assisting in recording, sound synthesis and other fields of music production for quite some time. The actual performance of music continues to be an area in which human players are chosen over computer performers. Musical performance is an area in which personalization is more important than consistency. Human players play with each other, reacting to phrases and ideas created by the players that they are playing with. Computer performers lack the ability to react to the changes in the performance that humans perceive naturally, giving the human players an advantage over the computer performers. This thesis creates a framework for describing unique musical performers that can play along in realtime with human players. FrTime, a reactive programming language, is used to constantly create new musical phrases. Musical phrases are constructed by unique user programmed performers and by chord changes that the framework provides. The reactive language creates multiple musical phrases for each point in time. A simple module which chooses musical phrases to be performed at the time of performance is created.