Limitations of Applicative Bisimulation (Preliminary Report)

Authors Vasileios Koutavas, Paul Blain Levy, Eijiro Sumii

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Vasileios Koutavas
Paul Blain Levy
Eijiro Sumii

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Vasileios Koutavas, Paul Blain Levy, and Eijiro Sumii. Limitations of Applicative Bisimulation (Preliminary Report). In Modelling, Controlling and Reasoning About State. Dagstuhl Seminar Proceedings, Volume 10351, pp. 1-9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


We present a series of examples that illuminate an important aspect of the semantics of higher-order functions with local state. Namely that certain behaviour of such functions can only be observed by pro- viding them with arguments that contain the functions themselves. This provides evidence for the necessity of complex conditions for functions in modern semantics for state, such as logical relations and Kripke-like bisimulations, where related functions are applied to related arguments (that may contain the functions). It also suggests that simpler semantics, such as those based on applicative bisimulations where functions are ap- plied to identical arguments, would not scale to higher-order languages with local state.
  • Imperative languages
  • higher-order functions
  • local state


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