λ-Calculi with conditional rules

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


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.


Induction Hypothesis Reduction Step Reduction System Closure Property Side Condition 
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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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