Simulation in the call-by-need lambda-calculus with letrec, case, constructors, and seq

  • This paper shows equivalence of applicative similarity and contextual approximation, and hence also of bisimilarity and contextual equivalence, in LR, the deterministic call-by-need lambda calculus with letrec extended by data constructors, case-expressions and Haskell's seqoperator. LR models an untyped version of the core language of Haskell. Bisimilarity simplifies equivalence proofs in the calculus and opens a way for more convenient correctness proofs for program transformations. The proof is by a fully abstract and surjective transfer of the contextual approximation into a call-by-name calculus, which is an extension of Abramsky's lazy lambda calculus. In the latter calculus equivalence of similarity and contextual approximation can be shown by Howe's method. Using an equivalent but inductive definition of behavioral preorder we then transfer similarity back to the calculus LR. The translation from the call-by-need letrec calculus into the extended call-by-name lambda calculus is the composition of two translations. The first translation replaces the call-by-need strategy by a call-by-name strategy and its correctness is shown by exploiting infinite tress, which emerge by unfolding the letrec expressions. The second translation encodes letrec-expressions by using multi-fixpoint combinators and its correctness is shown syntactically by comparing reductions of both calculi. A further result of this paper is an isomorphism between the mentioned calculi, and also with a call-by-need letrec calculus with a less complex definition of reduction than LR.

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Author:Manfred Schmidt-SchaußORCiDGND, David SabelORCiDGND, Elena Machkasova
Parent Title (German):Technical report Frank / Johann-Wolfgang-Goethe-Universität, Fachbereich Informatik und Mathematik, Institut für Informatik ; 49
Series (Serial Number):Technical report Frank / Johann-Wolfgang-Goethe-Universität, Fachbereich Informatik und Mathematik, Institut für Informatik (49 [v.2])
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
Date of Publication (online):2013/08/22
Date of first Publication:2013/08/22
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2014/07/03
Issue:Vers. 22. August 2013
Page Number:42
First Page:1
Last Page:42
Institutes:Informatik und Mathematik / Informatik
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik
Licence (German):License LogoDeutsches Urheberrecht