Towards a Common Categorical Semantics for Linear-Time Temporal Logic and Functional Reactive Programming

Authors:
Wolfgang Jeltsch
Affiliations:
TTí Küberneetika Instituut, Tallinn, Estonia
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2012

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Abstract

Linear-time temporal logic (LTL) and functional reactive programming (FRP) are related via a Curry-Howard correspondence. Based on this observation, we develop a common categorical semantics for a subset of LTL and its corresponding flavor of FRP. We devise a class of categorical models, called fan categories, that explicitly reflect the notion of time-dependent trueness of temporal propositions and a corresponding notion of time-dependent type inhabitance in FRP. Afterwards, we define the more abstract concept of temporal category by extending categorical models of intuitionistic S4. We show that fan categories are a special form of temporal categories.