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Kripke Open Bisimulation

A Marriage of Game Semantics and Operational Techniques

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Programming Languages and Systems (APLAS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9458))

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Abstract

Proving that two programs are contextually equivalent is notoriously hard, particularly for functional languages with references (i.e., local states). Many operational techniques have been designed to prove such equivalences, and fully abstract denotational model, using game semantics, have been built for such languages. In this work, we marry ideas coming from trace semantics, an operational variant of game semantics, and from Kripke logical relations, notably the notion of worlds as transition systems of invariants, to define a new operational technique: Kripke open bisimulations. It is the first framework whose completeness does not rely on any closure by contexts.

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Notes

  1. 1.

    We also consider the non-deterministic reduction \(\mapsto _{nd}\), defined in the same way but for the rule of allocation, which is defined as \((K[\mathrm {ref} \, v],h) \mapsto _{nd}(K[l],h \cdot [l \hookrightarrow v])\) for any \(l \notin \mathrm {dom}(h)\).

  2. 2.

    By seeing functional names as variables, the operational semantics of RefML can be extended straightforwardly to abstract values.

  3. 3.

    Even if we use a relation \(\mathcal {K}_{\mathcal {A}}\left[\![\sigma ,\tau \right]\!]_{} {}\) on evaluation contexts, our definition does not make any use of biorthogonality.

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Author information

Authors and Affiliations

  1. Queen Mary University, London, UK

    Guilhem Jaber

  2. Inria, Nantes, France

    Nicolas Tabareau

Authors
  1. Guilhem Jaber
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  2. Nicolas Tabareau
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Correspondence to Guilhem Jaber .

Editor information

Editors and Affiliations

  1. Univ. of Science and Technology of China, Hefei, Anhui, China

    Xinyu Feng

  2. Pohang Univ. of Science and Technology, Nam-Gu, Pohang, Korea (Republic of)

    Sungwoo Park

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Jaber, G., Tabareau, N. (2015). Kripke Open Bisimulation. In: Feng, X., Park, S. (eds) Programming Languages and Systems. APLAS 2015. Lecture Notes in Computer Science(), vol 9458. Springer, Cham. https://doi.org/10.1007/978-3-319-26529-2_15

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  • DOI: https://doi.org/10.1007/978-3-319-26529-2_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26528-5

  • Online ISBN: 978-3-319-26529-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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