Higher-Order abstract syntax in Isabelle/HOL

Abstract

Higher Order Abstract Syntax, or HOAS, is a technique for using a higher-order logic as a metalanguage for an object language with binding operators. It avoids formalizing syntactic details related to variable binding by identifying variables of the object logic with variables of the metalogic. In another paper we extended the usual set-theoretic semantics of HOL with a notion of parametric function, and showed how to use this extension to give solutions to the recursive type equations characteristic of HOAS, for example T = T × T + T → T for a HOAS representation of the untyped lambda-calculus. This paper describes an effort to apply these semantic ideas in a proof assistant. © 2010 Springer-Verlag.