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Strong Bisimulation for Control Operators (Invited Talk)

Authors Delia Kesner, Eduardo Bonelli, Andrés Viso

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ACM Subject Classification
  • Theory of computation → Lambda calculus
  • Theory of computation → Linear logic
  • Theory of computation → Operational semantics
Keywords
  • Lambda-mu calculus
  • proof-nets
  • strong bisimulation

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Abstract

The purpose of this paper is to identify programs with control operators whose reduction semantics are in exact correspondence. This is achieved by introducing a relation ≃, defined over a revised presentation of Parigot’s λμ-calculus we dub ΛM.
Our result builds on two fundamental ingredients: (1) factorization of λμ-reduction into multiplicative and exponential steps by means of explicit term operators of ΛM, and (2) translation of ΛM-terms into Laurent’s polarized proof-nets (PPN) such that cut-elimination in PPN simulates our calculus. Our proposed relation ≃ is shown to characterize structural equivalence in PPN. Most notably, ≃ is shown to be a strong bisimulation with respect to reduction in ΛM, i.e. two ≃-equivalent terms have the exact same reduction semantics, a result which fails for Regnier’s σ-equivalence in λ-calculus as well as for Laurent’s σ-equivalence in λμ.

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Delia Kesner, Eduardo Bonelli, and Andrés Viso. Strong Bisimulation for Control Operators (Invited Talk). In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 4:1-4:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.CSL.2020.4

Author Details

Delia Kesner
  • IRIF, Université de Paris and CNRS, France
  • Institut Universitaire de France (IUF), France
Eduardo Bonelli
  • Stevens Institute of Technology, Hoboken, NJ, USA
Andrés Viso
  • Universidad de Buenos Aires, Argentina
  • Universidad Nacional de Quilmes, Bernal, Buenos Aires, Argentina

Funding

This work was partially supported by LIA INFINIS, and the ECOS-Sud program PA17C01.

Acknowledgements

To Olivier Laurent for fruitful discussions.

References

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