Abstract
sec:abstractAs of version 2.7, the ACL2 theorem prover has been extended to automatically verify sets of polynomial inequalities that include nonlinear relationships. In this paper we describe our mechanization of linear and nonlinear arithmetic in ACL2. The nonlinear arithmetic procedure operates in cooperation with the pre-existing ACL2 linear arithmetic decision procedure. It extends what can be automatically verified with ACL2, thereby eliminating the need for certain types of rules in ACL2’s database while simultaneously increasing the performance of the ACL2 system when verifying arithmetic conjectures. The resulting system lessens the human effort required to construct a large arithmetic proof by reducing the number of intermediate lemmas that must be proven to verify a desired theorem.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Armando, A., Ranise, S.: A Practical Extension Mechanism for Decision Procedures. Journal of Universal Computer Science 7(2), 124–140 (2001)
Boyer, R., Moore, J.: Integrating Decision Procedures into Heuristic Theorem Provers: A Case Study of Linear Arithmetic. Machine Intelligence 11, 83–124 (1988)
Cyrluk, D., Kapur, D.: Reasoning about Nonlinear Inequality Constraints: A Multi-level Approach. In: Proceedings DARPA workshop on Image Understanding, pp. 904–915 (1989)
Harrison, J.: Theorem Proving with the Real Numbers. Technical Report TR-408, University of Cambridge Computer Laboratory (December 1996)
Harrison, J.: Verifying the Accuracy of Polynomial Approximations in HOL. In: Gunter, E.L., Felty, A.P. (eds.) TPHOLs 1997. LNCS, vol. 1275, pp. 137–152. Springer, Heidelberg (1997)
Kapur, D.: A Rewrite Rule Based Framework for Combining Decision Procedures. In: Armando, A. (ed.) FroCos 2002. LNCS (LNAI), vol. 2309, pp. 87–102. Springer, Heidelberg (2002)
Kaufmann, M., Manolios, P., Moore, J. (eds.): Computer-Aided Reasoning: An Approach. Kluwer Academic Publishers, Dordrecht (2000)
Kaufmann, M., Manolios, P., Moore, J.: Computer-Aided Reasoning: ACL2 Case Studies. Kluwer Academic Publishers, Dordrecht (2000)
Kaufmann, M., Moore, J.: ACL2: An Industrial Strength Version of Nqthm. In: Proceedings of the Eleventh Annual Conference on Computer Assurance (COMPASS 1996), pp. 23–34. IEEE Computer Society Press, Los Alamitos (1996)
Miner, P., Leathrum, J.: Verification of IEEE Compliant Subtractive Division Algorithms. In: Srivas, M., Camilleri, A. (eds.) FMCAD 1996. LNCS, vol. 1166, pp. 64–78. Springer, Heidelberg (1996)
Nelson, G., Oppen, D.C.: Simplification by Cooperating Decision Procedures. In: ACM Transactions on Programming Languages and Systems (TOPLAS), October 1979, vol. 1(2), pp. 245–257. Springer, Heidelberg (1996)
Rueß, H., Shankar, N.: Combining Shostak Theories. In: Tison, S. (ed.) RTA 2002. LNCS, vol. 2378, pp. 1–18. Springer, Heidelberg (2002)
Russinoff, D.: A Mechanically Checked Proof of IEEE Compliance of a Register- Transfer-Level Specification of the AMD K7 Floating Point Multiplication, Division and Square Root Instructions. LMS Journal of Computation and Mathematics 1, 148–200 (1998)
Shostak, R.: Deciding Combinations of Theories. Journal of the ACM (JACM) 31(1), 1–12 (1984)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hunt, W.A., Krug, R.B., Moore, J. (2003). Linear and Nonlinear Arithmetic in ACL2. In: Geist, D., Tronci, E. (eds) Correct Hardware Design and Verification Methods. CHARME 2003. Lecture Notes in Computer Science, vol 2860. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39724-3_29
Download citation
DOI: https://doi.org/10.1007/978-3-540-39724-3_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20363-6
Online ISBN: 978-3-540-39724-3
eBook Packages: Springer Book Archive