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

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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.

Keywords

temporal logic
modal logic
functional reactive programming
categorical semantics

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This work was partly supported by the ERDF through the Estonian Center of Excellence in Computer Science (EXCS).