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Proof Pearl: Wellfounded Induction on the Ordinals Up to ε 0

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Theorem Proving in Higher Order Logics (TPHOLs 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4732))

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Abstract

We discuss a proof of the wellfounded induction theorem for the ordinals up to ε 0. The proof is performed on the embedding of ACL2 in HOL-4, thus providing logical justification for that embedding and supporting the claim that the ACL2 logic has a model.

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References

  1. Franzen, T.: Inexhaustibility, a non-exhaustive treatment. Lecture Notes in Logic, vol. 16. A.K. Peters (2004)

    Google Scholar 

  2. Gentzen, G.: The consistency of elementary number theory. In: Szabo, M.E. (ed.) The Collected Papers of Gerhard Gentzen. Studies in Logic and the Foundations of Mathematics, North Holland, Amsterdam (1969)

    Google Scholar 

  3. Gentzen, G.: Provabillity and nonprovability of restricted transfinite induction in elementary number theory. In: Szabo, M.E. (ed.) The Collected Papers of Gerhard Gentzen. Studies in Logic and the Foundations of Mathematics, North Holland, Amsterdam (1969)

    Google Scholar 

  4. Goodstein, R.: On the restricted ordinal theorem. Journal of Symbolic Logic 9, 33–41 (1944)

    Article  MATH  MathSciNet  Google Scholar 

  5. Gordon, M.J.C., Hunt, W.A., Kaufmann, M., Reynolds, J.: An embedding of the ACL2 logic in HOL. In: Proceedings of ACL2 2006. ACM International Conference Proceeding Series, vol. 205, pp. 40–46. ACM Press, New York (2006)

    Chapter  Google Scholar 

  6. Gordon, M.J.C., Hunt, W.A., Kaufmann, M., Reynolds, J.: An integration of HOL and ACL2. In: Proceedings of FMCAD 2006, pp. 153–160. IEEE Computer Society Press, Los Alamitos (2006)

    Google Scholar 

  7. Huffman, B.: Countable ordinals. Isabelle Archive of Formal Proofs (November 2005)

    Google Scholar 

  8. Kaufmann, M., Moore, J.S.: Structured theory development for a mechanized logic. Journal of Automated Reasoning 26(2), 161–203 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  9. Manolios, P., Vroon, D.: Ordinal arithmetic: Algorithms and mechanization. Journal of Automated Reasoning, 1–37 (2006)

    Google Scholar 

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Klaus Schneider Jens Brandt

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© 2007 Springer-Verlag Berlin Heidelberg

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Kaufmann, M., Slind, K. (2007). Proof Pearl: Wellfounded Induction on the Ordinals Up to ε 0 . In: Schneider, K., Brandt, J. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2007. Lecture Notes in Computer Science, vol 4732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74591-4_22

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  • DOI: https://doi.org/10.1007/978-3-540-74591-4_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74590-7

  • Online ISBN: 978-3-540-74591-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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