λ-Calculi with conditional rules
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.
KeywordsInduction Hypothesis Reduction Step Reduction System Closure Property Side Condition
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