Abstract
A maximal reduction strategy in untyped λ-calculus computes for a term a longest (finite or infinite) reduction path. Some types of reduction strategies in untyped λ-calculus have been studied, but maximal strategies have received less attention. We give a systematic study of maximal strategies, recasting the few known results in our framework and giving a number of new results, the most important of which is an effective maximal strategy in λΒη. We also present a number of applications illustrating the relevance and usefulness of maximal strategies.Keywordsλ-calculusreduction strategieseffectiveness
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