Formalising in Nominal Isabelle Crary's Completeness Proof for Equivalence Checking.
Abstract
In the book on Advanced Topics in Types and Programming Languages, Crary illustrates the reasoning method of logical relations in a case study about equivalence checking. He presents a type-driven equivalence checking algorithm and verifies its completeness with respect to a definitional characterisation of equivalence. We present in this paper a formalisation of Crary's proof using Isabelle/HOL and the nominal datatype package.
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