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λ-Calculi with conditional rules

  • Masako Takahashi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 664)

Abstract

A variety of typed/untyped λ-calculi and related reduction systems have been proposed in order to study various aspects of programs, some of which contain rules subject to side conditions. As a framework to study fundamental properties of such reduction systems, we first introduce the notion of conditional λ-calculus. Then we give a sufficient condition for them to be confluent (Church-Rosser) as well as to have a normalizing strategy à la Gross. The proof, being a generalization of Tait-Martin-Löf proof for the confluence of λβ, is inductive and simple.

Keywords

Induction Hypothesis Reduction Step Reduction System Closure Property Side Condition 
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References

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    P. Aczel: A General Church-Rosser Theorem, (Technical Report, University of Manchester, 1978).Google Scholar
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    H. P. Barendregt: The Lambda Calculus, second edition (North-Holland, 1984).Google Scholar
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    J. R. Hindley: Reduction of residuals are finite, Trans. A.M.S. 240 (1978) pp 345–361.Google Scholar
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    J. W. Klop: Combinatory Reduction Systems (Mathematisch Centrum, 1980).Google Scholar
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    F. van Raamsdonk: A Simple Proof of Confluence for Weakly Orthogonal Combinatory Reduction Systems, (Technical Report, CWI, 1992).Google Scholar
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    M. Takahashi: Parallel Reductions in λ-Calculus, J. Symbolic Computation 7 (1989) pp 113–123. Also Parallel Reductions in λ-Calculus, revised version (Research Report, Tokyo Institute of Technology, 1992).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Masako Takahashi
    • 1
  1. 1.Department of Information ScienceTokyo Institute of TechnologyTokyoJapan

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