Calculi of Generalised β-Reduction and Explicit Substitutions: The Type-Free and Simply Typed Versions (1998)
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BibTeX
@MISC{Kamareddine98calculiof,
author = {Fairouz Kamareddine and Alejandro Ríos and J. B. Wells},
title = {Calculi of Generalised β-Reduction and Explicit Substitutions: The Type-Free and Simply Typed Versions},
year = {1998}
}
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Abstract
Extending the λ-calculus with either explicit substitution or generalized reduction has been the subject of extensive research recently, and still has many open problems. This paper is the first investigation into the properties of a calculus combining both generalized reduction and explicit substitutions. We present a calculus, gs, that combines a calculus of explicit substitution, s, and a calculus with generalized reduction, g. We believe that gs is a useful extension of the - calculus, because it allows postponement of work in two different but complementary ways. Moreover, gs (and also s) satisfies properties desirable for calculi of explicit substitutions and generalized reductions. In particular, we show that gs preserves strong normalization, is a conservative extension of g, and simulates fi-reduction of g and the classical -calculus. Furthermore, we study the simply typed versions of s and gs, and show that well-typed terms are strongly normalizing and that other properties,...
