HOAS and strong normalization
نویسنده
چکیده
We develop some Higher-Order Abstract Syntax (HOAS) concepts and proof principles as a collection of definitions and propositions on top of the original syntax with bindings. Our approach brings together hassle-free (i.e., bindingand substitution-free) manipulation of the objects on the one hand, and inductive reasoning about the same objects on the other. We present our approach by providing adequate representations of the untyped λ-calculus, its βreduction and its Curry-style System F typing. The HOAS induction and recursion principles extracted from the encoding are illustrated by employing them in tandem to naturally (re)discover a proof of strong normalization for typable terms in System F.
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