Functional reactive programming (FRP) is an elegant and successful approach to programming reactive systems declaratively. The high levels of abstraction and expressivity that make FRP attractive as a programming model do, however, often lead to programs whose resource usage is excessive and hard to predict. In this paper, we address the problem of space leaks in discretetime functional reactive programs. We present a functional reactive programming language that statically bounds the size of the dataflow graph a reactive program creates, while still permitting use of higher-order functions and higher-type streams such as streams of streams. We achieve this with a novel linear type theory that both controls allocation and ensures that all recursive definitions are well-founded. We also give a denotational semantics for our language by combining recent work on metric spaces for the interpretation of higher-order causal functions with length-space models of spacebounded computation. The resulting category is doubly closed and hence forms a model of the logic of bunched implications.

The TRELLYS project has produced several designs for practical dependently typed languages. These languages are broken into two fragments—a logical fragment where every term normalizes and which is consistent when interpreted as a logic, and a programmatic fragment with general recursion and other convenient but unsound features. In this paper, we present a small example language in this style. Our design allows the programmer to explicitly mention and pass information between the two fragments. We show that this feature substantially complicates the metatheory and present a new technique, combining the traditional Girard–Tait method with step-indexed logical relations, which we use to show normalization for the logical fragment. 1