Two Formal Systems of the λδ Family Revised

11/28/2019

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by   Ferruccio Guidi, et al.

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We present the framework λδ-2B that significantly improves and generalizes two previous formal systems of the λδ family, i.e., λδ-1A and λδ-2A. Our main contributions are, on the one hand, a short definition for the framework and, on the other hand, some important results that we are presenting here for the first time. The definition stands just on two notions, i.e., bound rt-reduction and parametric validity. Our new results are the confluence of bound rt-reduction on valid terms, the decidability of validity, of type inference and type checking and an axiomatization of the type judgment for the system λδ-2A. As a key feature, the framework and its theory have been developed and checked with the unavoidable help of the interactive prover Matita.