How to prove similarity a precongruence in non-deterministic call-by-need lambda calculi

  • Extending the method of Howe, we establish a large class of untyped higher-order calculi, in particular such with call-by-need evaluation, where similarity, also called applicative simulation, can be used as a proof tool for showing contextual preorder. The paper also demonstrates that Mann’s approach using an intermediate “approximation” calculus scales up well from a basic call-by-need non-deterministic lambdacalculus to more expressive lambda calculi. I.e., it is demonstrated, that after transferring the contextual preorder of a non-deterministic call-byneed lambda calculus to its corresponding approximation calculus, it is possible to apply Howe’s method to show that similarity is a precongruence. The transfer is not treated in this paper. The paper also proposes an optimization of the similarity-test by cutting off redundant computations. Our results also applies to deterministic or non-deterministic call-by-value lambda-calculi, and improves upon previous work insofar as it is proved that only closed values are required as arguments for similaritytesting instead of all closed expressions.

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Author:Matthias Mann, Manfred Schmidt-SchaußORCiDGND
Parent Title (English):Technical report Frank / Johann-Wolfgang-Goethe-Universität, Fachbereich Informatik und Mathematik, Institut für Informatik ; 22
Series (Serial Number):Technical report Frank / Johann-Wolfgang-Goethe-Universität, Fachbereich Informatik und Mathematik, Institut für Informatik (22)
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
Year of Completion:2006
Year of first Publication:2006
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2006/04/19
Tag:call-by-need lambda calculus; contextual equivalence; non-determinism; precongruence; similarity
Page Number:31
Last Page:31
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