Temporal logic with "Until", functional reactive programming with processes, and concrete process categories

Authors:
Wolfgang Jeltsch
Affiliations:
TTÜ Küberneetika Instituut, Tallinn, Estonia
Venue:
PLPV '13 Proceedings of the 7th workshop on Programming languages meets program verification
Year:
2013

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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.