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

Authors:
Manfred Schmidt-Schauss;Elena Machkasova
Affiliations:
Dept. Informatik und Mathematik, Inst. Informatik, J.W. Goethe-University, Frankfurt, Germany D-60054;Division of Science and Mathematics, University of Minnesota, Morris, U.S.A. MN 56267-2134
Venue:
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Year:
2008

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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.