Formalizing Adequacy: A Case Study for Higher-order Abstract Syntax

Authors:
James Cheney;Michael Norrish;René Vestergaard
Affiliations:
Laboratory for Foundations of Computer Science, University of Edinburgh, Edinburgh, UK;Canberra Research Lab, NICTA, Canberra, Australia and Australian National University, Canberra, Australia;Research Center for Integrated Science, JAIST, Ishikawa, Japan
Venue:
Journal of Automated Reasoning
Year:
2012

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Abstract

Adequacy is an important criterion for judging whether a formalization is suitable for reasoning about the actual object of study. The issue is particularly subtle in the expansive case of approaches to languages with name-binding. In prior work, adequacy has been formalized only with respect to specific representation techniques. In this article, we give a general formal definition based on model-theoretic isomorphisms or interpretations. We investigate and formalize an adequate interpretation of untyped lambda-calculus within a higher-order metalanguage in Isabelle/HOL using the Nominal Datatype Package. Formalization elucidates some subtle issues that have been neglected in informal arguments concerning adequacy.