Functional reactive programming (FRP) is a paradigm for programming with signals and events, allowing the user to describe reactive programs on a high level of abstraction. For this to make sense, an FRP language must ensure that all programs are causal, and can be implemented without introducing space leaks and time leaks. To this end, some FRP languages do not give direct access to signals, but just to signal functions.

Recently, modal types have been suggested as an alternative approach to ensuring causality in FRP languages in the synchronous case, giving direct access to the signal and event abstractions. This paper presents Simply RaTT, a new modal calculus for reactive programming. Unlike prior calculi, Simply RaTT uses a Fitch-style approach to modal types, which simplifies the type system and makes programs more concise.

In the context of modal FRP, the delay modality is used to represent computations that can be executed in the next time step. This is a computational effect and controlling this is crucial for FRP as many space and time leaks arise from moving computations across time steps. Echoing a previous result by Krishnaswami for a different language, we devise an operational semantics that safely executes Simply RaTT programs without space leaks.