Abstract
Nitpick is a counterexample generator for Isabelle/HOL that builds on Kodkod, a SAT-based first-order relational model finder. Nitpick supports unbounded quantification, (co)inductive predicates and datatypes, and (co)recursive functions. Fundamentally a finite model finder, it approximates infinite types by finite subsets. As case studies, we consider a security type system and a hotel key card system. Our experimental results on Isabelle theories and the TPTP library indicate that Nitpick generates more counterexamples than other model finders for higher-order logic, without restrictions on the form of the formulas to falsify.
This work is supported by the DFG grant Ni 491/11-1.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Andrews, P.B., Bishop, M., Issar, S., Nesmith, D., Pfenning, F., Xi, H.: TPS: A theorem-proving system for classical type theory. J. Auto. Reas. 16(3), 321–353 (1996)
Bell, J.M., Bellegarde, F., Hook, J.: Type-driven defunctionalization. ACM SIGPLAN Notices 32(8), 25–37 (1997)
Benzmüller, C., Paulson, L., Theiss, F., Fietzke, A.: Progress report on LEO-II, an automatic theorem prover for higher-order logic. In: Schneider, K., Brandt, J. (eds.) TPHOLs: Emerging Trends. C.S. Dept., University of Kaiserslautern, Internal Report 364/07 (2007)
Berghofer, S., Nipkow, T.: Random testing in Isabelle/HOL. In: Cuellar, J., Liu, Z. (eds.) SEFM 2004, pp. 230–239. IEEE C.S., Los Alamitos (2004)
Biere, A., Cimatti, A., Clarke, E.M., Zhu, Y.: Symbolic model checking without BDDs. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, pp. 193–207. Springer, Heidelberg (1999)
Blanchette, J.C., Krauss, A.: Monotonicity inference for higher-order formulas. In: Giesl, J., Hähnle, R. (eds.) IJCAR 2010. LNCS, Springer, Heidelberg (to appear, 2010)
Bulwahn, L., Krauss, A., Nipkow, T.: Finding lexicographic orders for termination proofs in Isabelle/HOL. In: Schneider, K., Brandt, J. (eds.) TPHOLs 2007. LNCS, vol. 4732, pp. 38–53. Springer, Heidelberg (2007)
Claessen, K., Sörensson, N.: New techniques that improve MACE-style model finding. In: MODEL (2003)
de Medeiros Santos, A.L.: Compilation by Transformation in Non-Strict Functional Languages. Ph.D. thesis, C.S. Dept., University of Glasgow (1995)
Dunets, A., Schellhorn, G., Reif, W.: Bounded relational analysis of free datatypes. In: Beckert, B., Hähnle, R. (eds.) TAP 2008. LNCS, vol. 4966, pp. 99–115. Springer, Heidelberg (2008)
Frias, M.F., Pombo, C.G.L., Moscato, M.M.: Alloy Analyzer + PVS in the analysis and verification of Alloy specifications. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 587–601. Springer, Heidelberg (2007)
Gordon, M.J.C., Melham, T.F. (eds.): Introduction to HOL: A Theorem Proving Environment for Higher Order Logic. Cambridge University Press, Cambridge (1993)
Jackson, D.: Software Abstractions: Logic, Language, and Analysis. MIT Press, Cambridge (2006)
Kuncak, V., Jackson, D.: Relational analysis of algebraic datatypes. In: Gall, H.C. (ed.) ESEC/FSE 2005 (2005)
McCune, W.: A Davis–Putnam program and its application to finite first-order model search: Quasigroup existence problems. Technical report, ANL (1994)
Nipkow, T.: Verifying a hotel key card system. In: Barkaoui, K., Cavalcanti, A., Cerone, A. (eds.) ICTAC 2006. LNCS, vol. 4281, pp. 1–14. Springer, Heidelberg (2006)
Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)
Schumann, J.M.: Automated Theorem Proving in Software Engineering. Springer, Heidelberg (2001)
Snelting, G., Wasserrab, D.: A correctness proof for the Volpano/Smith security typing system. In: Klein, G., Nipkow, T., Paulson, L.C. (eds.) AFP (September 2008)
Sutcliffe, G., Suttner, C.: The TPTP problem library for automated theorem proving, http://www.cs.miami.edu/~tptp/
Torlak, E., Jackson, D.: Kodkod: A relational model finder. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 632–647. Springer, Heidelberg (2007)
Volpano, D., Smith, G., Irvine, C.: A sound type system for secure flow analysis. J. Comp. Sec. 4(3), 167–187 (1996)
Weber, T.: SAT-Based Finite Model Generation for Higher-Order Logic. Ph.D. thesis, Dept. of Informatics, T.U. München (2008)
Zhang, J., Zhang, H.: SEM: A system for enumerating models. In: Kaufmann, M. (ed.) IJCAI 95, vol. 1, pp. 298–303 (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Blanchette, J.C., Nipkow, T. (2010). Nitpick: A Counterexample Generator for Higher-Order Logic Based on a Relational Model Finder. In: Kaufmann, M., Paulson, L.C. (eds) Interactive Theorem Proving. ITP 2010. Lecture Notes in Computer Science, vol 6172. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14052-5_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-14052-5_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14051-8
Online ISBN: 978-3-642-14052-5
eBook Packages: Computer ScienceComputer Science (R0)