Comparing and implementing calculi of explicit substitutions with eta-reduction. (English summary) Ann. Pure Appl. Logic 134 (2005), no. 1, 5–41. This is a nice paper on rewrite rules for eta-reduction in explicit substitution calculi. The main contributions are: (1) an extension of the suspension calculus with eta rule: this extension is proved to be confluent and strongly normalizing; (2) a comparison of the adequacy of the reduction process in the λσ, λs and suspension calculi extended with eta-reduction; (3) an implementation of the eta rule for the above calculi which does not mix eta-reduction with the other rules. This implementation is shown to effectively simulate eta-reduction of pure lambda terms
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