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International Conference on Rewriting Techniques and Applications

RTA 2008: Rewriting Techniques and Applications pp 321–335Cite as

A Finite Simulation Method in a Non-deterministic Call-by-Need Lambda-Calculus with Letrec, Constructors, and Case

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5117))

Abstract

The paper proposes a variation of simulation for checking and proving contextual equivalence in a non-deterministic call-by-need lambda-calculus with constructors, case, seq, and a letrec with cyclic dependencies. It also proposes a novel method to prove its correctness. The calculus’ semantics is based on a small-step rewrite semantics and on may-convergence. The cyclic nature of letrec bindings, as well as non-determinism, makes known approaches to prove that simulation implies contextual preorder, such as Howe’s proof technique, inapplicable in this setting. The basic technique for the simulation as well as the correctness proof is called pre-evaluation, which computes a set of answers for every closed expression. If simulation succeeds in finite computation depth, then it is guaranteed to show contextual preorder of expressions.

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Author information

Authors and Affiliations

  1. Dept. Informatik und Mathematik, Inst. Informatik, J.W. Goethe-University, PoBox 11 19 32, D-60054, Frankfurt, Germany

    Manfred Schmidt-Schauss

  2. Division of Science and Mathematics, University of Minnesota, Morris, MN 56267-2134, U.S.A.

    Elena Machkasova

Authors
  1. Manfred Schmidt-Schauss
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  2. Elena Machkasova
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Andrei Voronkov

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Schmidt-Schauss, M., Machkasova, E. (2008). A Finite Simulation Method in a Non-deterministic Call-by-Need Lambda-Calculus with Letrec, Constructors, and Case. In: Voronkov, A. (eds) Rewriting Techniques and Applications. RTA 2008. Lecture Notes in Computer Science, vol 5117. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70590-1_22

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  • DOI: https://doi.org/10.1007/978-3-540-70590-1_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70588-8

  • Online ISBN: 978-3-540-70590-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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