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Comparing and Implementing Calculi of Explicit Substitutions with Eta Reduction (2005)
| Venue: | Annals of Pure and Applied Logic |
| Citations: | 8 - 8 self |
BibTeX
@ARTICLE{Ayala-Rincon05comparingand,
author = {Mauricio Ayala-Rincon and Flavio L. C. de Moura and Fairouz Kamareddine},
title = {Comparing and Implementing Calculi of Explicit Substitutions with Eta Reduction},
journal = {Annals of Pure and Applied Logic},
year = {2005},
volume = {134},
pages = {5--41}
}
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Abstract
The past decade has seen an explosion of work on calculi of explicit substitutions. Numerous work has illustrated the usefulness of these calculi for practical notions like the implementation of typed functional programming languages and higher order proof assistants. It has also been shown that eta reduction is useful for adapting substitution calculi for practical problems like higher order uni cation. This paper concentrates on rewrite rules for eta reduction in three dierent styles of explicit substitution calculi: , se and the suspension calculus. Both and se when extended with eta reduction, have proved useful for solving higher order uni cation. We enlarge the suspension calculus with an adequate eta-reduction which we show to preserve termination and conuence of the associated substitution calculus and to correspond to the eta-reductions of the other two calculi. We prove that and se as well as and the suspension calculus are non comparable while se is more adequate than the suspension calculus in simulating one step of beta-contraction.
Keyphrases
eta reduction suspension calculus explicit substitution implementing calculus order uni cation practical problem substitution calculus numerous work rewrite rule practical notion dierent style typed functional programming language adequate eta-reduction associated substitution calculus order proof assistant explicit substitution calculus past decade
