Towards safe and efficient functional reactive programming

Functional Reactive Programming (FRP) is an approach to reactive programming where systems are structured as networks of functions operating on time-varying values (signals). FRP is based on the synchronous data-flow paradigm and supports both continuous-time and discretetime signals (hybrid systems). What sets FRP apart from most other reactive languages is its support for systems with highly dynamic structure (dynamism) and higher-order reactive constructs (higher-order data-flow). However, the price paid for these features has been the loss of the safety and performance guarantees provided by other, less expressive, reactive languages. Statically guaranteeing safety properties of programs is an attractive proposition. This is true in particular for typical application domains for reactive programming such as embedded systems. To that end, many existing reactive languages have type systems or other static checks that guarantee domain-specific constraints, such as feedback being well-formed (causality analysis). However, compared with FRP, they are limited in their capacity to support dynamism and higher-order data-flow. On the other hand, as established static techniques do not suffice for highly structurally dynamic systems, FRP generally enforces few domain-specific constraints, leaving the FRP programmer to manually check that the constraints are respected. Thus, there is currently a trade-off between static guarantees and dynamism among reactive languages. This thesis contributes towards advancing the safety and efficiency of FRP by studying highly structurally dynamic networks of functions operating on mixed (yet distinct) continuoustime and discrete-time signals. First, an ideal denotational semantics is defined for this kind of FRP, along with a type system that captures domain-specific constraints. The correctness and practicality of the language and type system are then demonstrated by proof of concept implementations in Agda and Haskell. Finally, temporal properties of signals and of functions on signals are expressed using techniques from temporal logic, as motivation and justification for a range of optimisations.