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DOI: 10.4230/LIPIcs.RTA.2010.295
URN: urn:nbn:de:0030-drops-26593
URL: http://drops.dagstuhl.de/opus/volltexte/2010/2659/
Schmidt-Schauss, Manfred ; Sabel, David ; Machkasova, Elena

Simulation in the Call-by-Need Lambda-Calculus with letrec

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Abstract

This paper shows the equivalence of applicative similarity and contextual approximation, and hence also of bisimilarity and contextual equivalence, in the deterministic call-by-need lambda calculus with letrec. Bisimilarity simplifies equivalence proofs in the calculus and opens a way for more convenient correctness proofs for program transformations. Although this property may be a natural one to expect, to the best of our knowledge, this paper is the first one providing a proof. The proof technique is to transfer the contextual approximation into Abramsky's lazy lambda calculus by a fully abstract and surjective translation. This also shows that the natural embedding of Abramsky's lazy lambda calculus into the call-by-need lambda calculus with letrec is an isomorphism between the respective term-models. We show that the equivalence property proven in this paper transfers to a call-by-need letrec calculus developed by Ariola and Felleisen.

BibTeX - Entry

@InProceedings{schmidtschauss_et_al:LIPIcs:2010:2659,
  author =	{Manfred Schmidt-Schauss and David Sabel and Elena Machkasova},
  title =	{Simulation in the Call-by-Need Lambda-Calculus with letrec},
  booktitle =	{Proceedings of the 21st International Conference on Rewriting Techniques and Applications},
  pages =	{295--310},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-18-7},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{6},
  editor =	{Christopher Lynch},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2010/2659},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.RTA.2010.295},
  annote =	{Keywords: Lambda calculus, semantics, contextual equivalence, bisimulation,call-by-need}
}

Keywords: Lambda calculus, semantics, contextual equivalence, bisimulation,call-by-need
Seminar: Proceedings of the 21st International Conference on Rewriting Techniques and Applications
Issue date: 2010
Date of publication: 06.07.2010

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