Abstract
In this work, we present an interoperability framework that enables the translation of specifications (signature of functions and lemma statements) among different theorem provers. This translation is based on a new intermediate XML language, called XLL, and is performed almost automatically. As a case study, we focus on porting developments from Isabelle/HOL to ACL2. In particular, we study the transformation to ACL2 of an Isabelle/HOL theory devoted to verify an algorithm computing a diagonal form of an integer matrix (looking for the ACL2 executability that is missed in Isabelle/HOL). Moreover, we provide a formal proof of a fragment of the obtained ACL2 specification — this shows the suitability of our approach to reuse in ACL2 a proof strategy imported from Isabelle/HOL.
Partially supported by Ministerio de Ciencia e Innovación, project MTM2009-13842, by European Union’s 7th Framework Programme under grant agreement nr. 243847 (ForMath), and by Universidad de La Rioja, research grant FPI-UR-12.
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References
ForMath: Formalisation of Mathematics, European project, http://wiki.portal.chalmers.se/cse/pmwiki.php/ForMath/ForMath
MDT/OCL in Ecore, http://wiki.eclipse.org/MDT/OCLinEcore
Aransay, J., et al.: A report on an experiment in porting formal theories from Isabelle/HOL to Ecore and ACL2. Technical report, ForMath European project (2013), http://wiki.portal.chalmers.se/cse/uploads/ForMath/isabelle_acl2_report
Benzmüller, C.E., Rabe, F., Sutcliffe, G.: THF0 – The Core of the TPTP Language for Higher-Order Logic. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 491–506. Springer, Heidelberg (2008)
Bradley, G.H.: Algorithms for Hermite and Smith Normal Matrices and Linear Diophantine Equations. Mathematics of Computation 25(116), 897–907 (1971)
Codescu, M., Horozal, F., Kohlhase, M., Mossakowski, T., Rabe, F., Sojakova, K.: Towards Logical Frameworks in the Heterogeneous Tool Set Hets. In: Mossakowski, T., Kreowski, H.-J. (eds.) WADT 2010. LNCS, vol. 7137, pp. 139–159. Springer, Heidelberg (2012)
Cohen, H.: A Course in Computational Algebraic Number Theory. Springer (1995)
Cormen, T.H., et al.: Introduction to Algorithms. McGraw-Hill (2003)
Cruanes, S., Hamon, G., Owre, S., Shankar, N.: Tool integration with the evidential tool bus. In: Giacobazzi, R., Berdine, J., Mastroeni, I. (eds.) VMCAI 2013. LNCS, vol. 7737, pp. 275–294. Springer, Heidelberg (2013)
Denney, E.: A Prototype Proof Translator from HOL to Coq. In: Aagaard, M.D., Harrison, J. (eds.) TPHOLs 2000. LNCS, vol. 1869, pp. 108–125. Springer, Heidelberg (2000)
Gonthier, G., Mahboubi, A.: An introduction to Small Scale Reflection in Coq. Journal of Formalized Reasoning 3(2), 95–152 (2010)
Gordon, M.J.C., et al.: The Right Tools for the Job: Correctness of Cone of Influence Reduction Proved Using ACL2 and HOL4. Journal of Automated Reasoning 47(1), 1–16 (2011)
Hendrix, J.: Matrices in ACL2. In: ACL2 2003 (2003)
Heras, J., Mata, G., Romero, A., Rubio, J., Sáenz, R.: Verifying a plaftorm for digital imaging: A multi-tool strategy. In: Carette, J., Aspinall, D., Lange, C., Sojka, P., Windsteiger, W. (eds.) CICM 2013. LNCS, vol. 7961, pp. 66–81. Springer, Heidelberg (2013)
Jacquel, M., Berkani, K., Delahaye, D., Dubois, C.: Verifying B Proof Rules Using Deep Embedding and Automated Theorem Proving. In: Barthe, G., Pardo, A., Schneider, G. (eds.) SEFM 2011. LNCS, vol. 7041, pp. 253–268. Springer, Heidelberg (2011)
Kaufmann, M., et al.: Computer-Aided Reasoning: An Approach. Kluwer Academic Publishers (2000)
Keller, C., Werner, B.: Importing HOL Light into Coq. In: Kaufmann, M., Paulson, L.C. (eds.) ITP 2010. LNCS, vol. 6172, pp. 307–322. Springer, Heidelberg (2010)
Naumov, P., Stehr, M.-O., Meseguer, J.: The HOL/NuPRL Proof Translator (A Practical Approach to Formal Interoperability). In: Boulton, R.J., Jackson, P.B. (eds.) TPHOLs 2001. LNCS, vol. 2152, pp. 329–345. Springer, Heidelberg (2001)
Nipkow, T., Paulson, L.C., Wenzel, M. (eds.): Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)
Obua, S., Nipkow, T.: Flyspeck II: the basic linear programs. Annals of Mathematics and Artificial Intelligence 56(3-4), 245–272 (2009)
Obua, S., Skalberg, S.: Importing HOL into isabelle/HOL. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 298–302. Springer, Heidelberg (2006)
Sexton, A.P., et al.: Computing with Abstract Matrix Structures. In: ISSAC 2009, pp. 325–332. ACM (2009)
Siekmann, J.H., Brezhnev, V., Cheikhrouhou, L., Fiedler, A., Horacek, H., Kohlhase, M., Meier, A., Melis, E., Moschner, M., Normann, I., Pollet, M., Sorge, V., Ullrich, C., Wirth, C.-P.: Proof Development with ΩMEGA. In: Voronkov, A. (ed.) CADE-18. LNCS (LNAI), vol. 2392, pp. 144–149. Springer, Heidelberg (2002)
Steele, G.L.: Common Lisp the Language. Digital Press (1990)
W3C. XSLT 2.0, http://www.w3.org/TR/xslt-xquery-serialization/
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Aransay-Azofra, J. et al. (2014). Obtaining an ACL2 Specification from an Isabelle/HOL Theory. In: Aranda-Corral, G.A., Calmet, J., Martín-Mateos, F.J. (eds) Artificial Intelligence and Symbolic Computation. AISC 2014. Lecture Notes in Computer Science(), vol 8884. Springer, Cham. https://doi.org/10.1007/978-3-319-13770-4_6
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DOI: https://doi.org/10.1007/978-3-319-13770-4_6
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