Abstract
We consider the normalization proof for a simply-typed lambda calculus with Mendler-style recursion using logical relations. This language is powerful enough to encode total recursive functions using recursive types. A key feature of our proof is the semantic interpretation of recursive types, which requires higher-kinded polymorphism in the reasoning language. We have implemented the proof in Coq due to this requirement. However, we believe this proof can serve as a challenge problem for other proof environments, especially those supporting binders, since our mechanization in Coq requires proofs of several substitution properties.
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