Abstract
In this paper we present a formalization and proof of Higman’s Lemma in ACL2. We formalize the constructive proof described in [10] where the result is proved using a termination argument justified by the multiset extension of a well-founded relation. To our knowledge, this is the first mechanization of this proof.
This work has been supported by project TIN2004-03884 (Ministerio de Educación y Ciencia, Spain) and FEDER founds.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)
Berghofer, S.: A constructive proof of Higman’s lemma in Isabelle. In: Berardi, S., Coppo, M., Damiani, F. (eds.) TYPES 2003. LNCS, vol. 3085, pp. 66–82. Springer, Heidelberg (2004)
Coquand, T., Fridlender, D.: A proof of Higman’s lemma by structural induction. Unpublished draft (1993), available at http://www.brics.dk/~daniel/texts/open.ps
Dershowitz, N., Manna, Z.: Proving Termination with Multiset Orderings. Communications of the ACM 22(8), 465–476 (1979)
Kaufmann, M., Manolios, P., Moore, J.S.: Computer-Aided Reasoning: An Approach. Kluwer Academic Publishers, Dordrecht (2000)
Kaufmann, M., Moore, J.S.: ACL2 Version 2.9 (2005), Homepage: http://www.cs.utexas.edu/users/moore/acl2/
Kaufmann, M., Moore, J.S.: Structured Theory Development for a Mechanized Logic. Journal of Automated Reasoning 26(2), 161–203 (2001)
Martín–Mateos, F.J., Alonso, J.A., Hidalgo, M.J., Ruiz–Reina, J.L.: A Formal Proof of Dickson’s Lemma in ACL2. In: Y. Vardi, M., Voronkov, A. (eds.) LPAR 2003. LNCS, vol. 2850, pp. 49–58. Springer, Heidelberg (2003)
Medina–Bulo, I., Palomo, F., Alonso, J.A., Ruiz–Reina, J.L.: Verified Computer Algebra in Acl2. In: Buchberger, B., Campbell, J. (eds.) AISC 2004. LNCS, vol. 3249, pp. 171–184. Springer, Heidelberg (2004)
Murthy, C., Russell, J.R.: A Constructive Proof of Higman’s Lemma. In: Fifth annual IEEE Symposium on Logic in Computer Science, pp. 257–267 (1990)
Nash–Williams, C.: On well-quasi-ordering finite trees. Proceedings of the Cambridge Philosophical Society 59, 833–835 (1963)
Perdry, H.: Strong noetherianity: a new constructive proof of Hilbert’s basis theorem. Available at http://perdry.free.fr/StrongNoetherianity.ps
Ruiz–Reina, J.L., Alonso, J.A., Hidalgo, M.J., Martín–Mateos, F.J.: Termination in ACL2 Using Multiset Relations. In: Thirty Five Years of Automating Mathematics. Kluwer Academic Publishers, Dordrecht (2003)
Seisenberger, M.: An Inductive Version of Nash-Williams’ Minimal-Bad-Sequence Argument for Higman’s Lemma. In: Callaghan, P., Luo, Z., McKinna, J., Pollack, R. (eds.) TYPES 2000. LNCS, vol. 2277, pp. 233–242. Springer, Heidelberg (2002)
Simpson, S.G.: Ordinal numbers and the Hilbert basis theorem. Journal of Symbolic Logic 53(3), 961–974 (1988)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Martín-Mateos, F.J., Ruiz-Reina, J.L., Alonso, J.A., Hidalgo, M.J. (2005). Proof Pearl: A Formal Proof of Higman’s Lemma in ACL2. In: Hurd, J., Melham, T. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2005. Lecture Notes in Computer Science, vol 3603. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11541868_23
Download citation
DOI: https://doi.org/10.1007/11541868_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28372-0
Online ISBN: 978-3-540-31820-0
eBook Packages: Computer ScienceComputer Science (R0)