Simulation in the call-by-need lambda-calculus with letrec
- 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. 1998 ACM Subject Classification: F.4.2, F.3.2, F.3.3, F.4.1. Key words and phrases: semantics, contextual equivalence, bisimulation, lambda calculus, call-by-need, letrec.
Author: | Manfred Schmidt-SchaußORCiDGND, David SabelORCiDGND, Elena Machkasova |
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URN: | urn:nbn:de:hebis:30-68385 |
DOI: | https://doi.org/10.4230/LIPIcs.RTA.2010.295 |
ISBN: | 978-3-939897-18-7 |
ISSN: | 1868-8969 |
Parent Title (English): | Proceedings of the 21st International Conference on Rewriting Techniques and Applications (RTA'10) |
Publisher: | Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH |
Place of publication: | Wadern |
Document Type: | Conference Proceeding |
Language: | English |
Date of Publication (online): | 2010/12/01 |
Year of first Publication: | 2010 |
Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
Release Date: | 2010/12/01 |
Tag: | bisimulation; call-by-need; contextual equivalence; lambda calculus; letrec; semantics |
Page Number: | 16 |
First Page: | 295 |
Last Page: | 310 |
Note: | (c) M. Schmidt-Schauß, D. Sabel, and E. Machkasova ; CC Creative Commons Non-Commercial No Derivatives License |
Source: | International Conference on Rewriting Techniques and Applications 2010 (Edinburgh), pp. 295-310 ; Digital Object Identifier: 10.4230/LIPIcs.RTA.2010.295 |
HeBIS-PPN: | 229215289 |
Institutes: | Informatik und Mathematik / Informatik |
Dewey Decimal Classification: | 0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik |
Sammlungen: | Universitätspublikationen |
Licence (German): | Creative Commons - Namensnennung-Nicht kommerziell-Keine Bearbeitung 3.0 |