Formalizing adequacy

Adequacy is an important criterion for judging the correctness of formal reasoning. The issue is particularly subtle in the expansive case of approaches to languages with name-binding. We posit that adequacy of a novel representation technique is best addressed by formalizing an isomorphism or, more generally, an interpretation explicating the new approach in terms of a more conventional one. We present an example formalization of an isomorphism relating nominal and higher-order abstract syntax techniques. We also outline steps towards a systematic framework that could be used for proving adequacy results automatically, which we believe would help make representation techniques more transparent to end-users of mechanized metatheory verification systems, and provide insight into the relative merits of different approaches.