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Higher-Order Abstract Syntax in Isabelle/HOL

  • Douglas J. Howe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6172)

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 + TT for a HOAS representation of the untyped lambda-calculus. This paper describes an effort to apply these semantic ideas in a proof assistant.

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References

  1. 1.
    Harper, R., Honsell, F., Plotkin, G.: A framework for defining logics. Journal of the Association for Computing Machinery 40(1), 143–184 (1993)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Howe, D.J.: Higher-order abstract syntax in classical higher-order logic. In: Proceedings of the 4th International Workshop on Logical Frameworks and Meta-languages: Theory and Practice (LFMTP 2009) (2009)Google Scholar
  3. 3.
    Nipkow, T., Paulson, L.C., Wenzel, M.T.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Douglas J. Howe
    • 1
  1. 1.Carleton UniversityOttawaCanada

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