Abstract
Recent research has revealed that the always and eventually operators from temporal logic correspond to the type constructors for behaviors and events from functional reactive programming (FRP). It is furthermore well-known that the until operators from LTL are generalizations of always and eventually. In this paper, we show that behaviors and events can be generalized analogously. The result is a notion of process, which combines continuous and discrete aspects. We develop a common categorical semantics for an intuitionistic temporal logic with until and FRP with processes. This semantics reflects time-dependent trueness in temporal logic, time-dependent type inhabitance in FRP, and causality of FRP operations.
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