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. Bisimilar
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.
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Metadaten
Author:Manfred Schmidt-Schauß, David Sabel, Elena Machkasova
URN:urn:nbn:de:hebis:30-77888
Series (Serial Number):Technical report Frank / Johann-Wolfgang-Goethe-Universität, Fachbereich Informatik und Mathematik, Institut für Informatik (40)
Publisher:Johann Wolfgang Goethe-Univ., Fachbereich Informatik und Mathematik, Inst. für Informatik, Research group for Artificial Intelligence and Software Technology
Place of publication:Frankfurt [am Main]
Document Type:Working Paper
Language:English
Date of Publication (online):2010/06/22
Year of first Publication:2010
Publishing Institution:Univ.-Bibliothek Frankfurt am Main
Release Date:2010/06/22
Tag:Kontextuelle Gleichheit
contextual equivalence ; lambda calculus ; letrec; semantics
SWD-Keyword:Formale Semantik ; Lambda-Kalkül
HeBIS PPN:224533819
Institutes:Informatik
Dewey Decimal Classification:004 Datenverarbeitung; Informatik
Sammlungen:Universitätspublikationen
Licence (German):License Logo Veröffentlichungsvertrag für Publikationen

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