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DOI: 10.4230/LIPIcs.CSL.2020.4
URN: urn:nbn:de:0030-drops-116473
URL: https://drops.dagstuhl.de/opus/volltexte/2020/11647/
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Kesner, Delia ; Bonelli, Eduardo ; Viso, Andrés

Strong Bisimulation for Control Operators (Invited Talk)

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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.

BibTeX - Entry

@InProceedings{kesner_et_al:LIPIcs:2020:11647,
  author =	{Delia Kesner and Eduardo Bonelli and Andr{\'e}s Viso},
  title =	{{Strong Bisimulation for Control Operators (Invited Talk)}},
  booktitle =	{28th EACSL Annual Conference on Computer Science Logic (CSL 2020)},
  pages =	{4:1--4:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-132-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{152},
  editor =	{Maribel Fern{\'a}ndez and Anca Muscholl},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11647},
  URN =		{urn:nbn:de:0030-drops-116473},
  doi =		{10.4230/LIPIcs.CSL.2020.4},
  annote =	{Keywords: Lambda-mu calculus, proof-nets, strong bisimulation}
}

Keywords: Lambda-mu calculus, proof-nets, strong bisimulation
Seminar: 28th EACSL Annual Conference on Computer Science Logic (CSL 2020)
Issue Date: 2020
Date of publication: 10.01.2020


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