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

Wolfgang Jeltsch | Zendy

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

Author(s) -

Wolfgang Jeltsch

Publication year - 2012

Publication title -

electronic notes in theoretical computer science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.242

H-Index - 60

ISSN - 1571-0661

DOI - 10.1016/j.entcs.2012.08.015

Subject(s) - categorical variable , semantics (computer science) , temporal logic , linear logic , class (philosophy) , computer science , linear temporal logic , mathematics , programming language , artificial intelligence , theoretical computer science , machine learning

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

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