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    Comparing Calculi of Explicit Substitutions with Eta-reduction1 1Partially supported by the Brazilian CNPq research council grant number 47488101-6.

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    AbstractThe 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. Three styles of explicit substitutions are treated in this paper: the 位蟽 and the 位se which have proved useful for solving practical problems like higher order unification, and the suspension calculus related to the implementation of the language 位-Prolog. We enlarge the suspension calculus with an adequate eta-reduction which we show to preserve termination and confluence of the associated substitution calculus and to correspond to the eta-reductions of the other two calculi. Additionally, we prove that 位蟽 and 位se as well as 位蟽 and the suspension calculus are non comparable while 位se is more adequate than the suspension calculus
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