Abstract
KeYmaera X is a theorem prover for differential dynamic logic (
), a logic for specifying and verifying properties of hybrid systems. Reasoning about complicated hybrid systems models requires support for sophisticated proof techniques, efficient computation, and a user interface that crystallizes salient properties of the system. KeYmaera X allows users to specify custom proof search techniques as tactics, execute these tactics in parallel, and interface with partial proofs via an extensible user interface.
Advanced proof search features—and user-defined tactics in particular—are difficult to check for soundness. To admit extension and experimentation in proof search without reducing trust in the prover, KeYmaera X is built up from a small trusted kernel. The prover kernel contains a list of sound
axioms that are instantiated using a uniform substitution proof rule. Isolating all soundness-critical reasoning to this prover kernel obviates the intractable task of ensuring that each new proof search algorithm is implemented correctly. Preliminary experiments suggest that a single layer of tactics on top of the prover kernel provides a rich language for implementing novel and sophisticated proof search techniques.
This material is based upon work supported by the National Science Foundation under NSF CAREER Award CNS-1054246, NSF CNS-1035800, and CNS-0931985, and by ERC under PIOF-GA-2012-328378 (Mitsch on leave from Johannes Kepler University Linz).
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References
Ahrendt, W., Baar, T., Beckert, B., Bubel, R., Giese, M., Hähnle, R., Menzel, W., Mostowski, W., Roth, A., Schlager, S., Schmitt, P.H.: The KeY tool. Softw. Syst. Model. 4(1), 32–54 (2005)
Alur, R., Courcoubetis, C., Henzinger, T.A., Ho, P.-H.: Hybrid automata: an algorithmic approach to the specification and verification of hybrid systems. In: Grossman, R.L., Ravn, A.P., Rischel, H., Nerode, A. (eds.) HS 1991 and HS 1992. LNCS, vol. 736, pp. 209–229. Springer, Heidelberg (1993)
Beckert, B., Hähnle, R., Schmitt, P.H. (eds.): Verification of Object-Oriented Software. LNCS (LNAI), vol. 4334, pp. 453–479. Springer, Heidelberg (2007)
Bowen, J., Stavridou, V.: Safety-critical systems, formal methods and standards. Softw. Eng. J. 8(4), 189–209 (1993)
Felty, A., Howe, D.: Tactic theorem proving with refinement-tree proofs and metavariables. In: Bundy, A. (ed.) CADE 1994. LNCS, vol. 814, pp. 605–619. Springer, Heidelberg (1994)
Heisel, M., Reif, W., Stephan, W.: Tactical theorem proving in program verification. In: Stickel, M.E. (ed.) CADE 1990. LNCS, vol. 449, pp. 117–131. Springer, Heidelberg (1990)
The Coq development team: The Coq proof assistant reference manual. LogiCal project, version 8.0 (2004). http://coq.inria.fr
Mitsch, S., Platzer, A.: ModelPlex: verified runtime validation of verified cyber-physical system models. In: Bonakdarpour, B., Smolka, S.A. (eds.) RV 2014. LNCS, vol. 8734, pp. 199–214. Springer, Heidelberg (2014)
Nipkow, T., Paulson, L.C., Wenzel, M. (eds.): Isabelle/HOL: A Proof Assistant for Higher-Order Logic. LNCS, vol. 2283. Springer, Heidelberg (2002)
Platzer, A.: Differential dynamic logic for hybrid systems. J. Autom. Reas. 41(2), 143–189 (2008)
Platzer, A.: Logical Analysis of Hybrid Systems: Proving Theorems for Complex Dynamics. Springer, Heidelberg (2010)
Platzer, A.: Logics of Dynamical Systems. In: LICS, pp. 13–24. IEEE (2012)
Platzer, A.: Differential Game Logic. CoRR abs/1408.1980 (2014)
Platzer, A.: A uniform substitution calculus for differential dynamic logic. In: Felty, A.P., Middeldorp, A. (eds.) CADE-25. LNCS, vol. 9195, pp. xx–yy. Springer, Heidelberg (2015)
Platzer, A., Quesel, J.-D.: KeYmaera: a hybrid theorem prover for hybrid systems (system description). In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 171–178. Springer, Heidelberg (2008)
Quesel, J.D., Mitsch, S., Loos, S., Aréchiga, N., Platzer, A.: How to model and prove hybrid systems with KeYmaera: a tutorial on safety. STTT (2015)
Acknowledgments
The authors thank the anonymous reviewers for their helpful feedback, and Ran Ji for help with testing and extending KeYmaera X.
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Fulton, N., Mitsch, S., Quesel, JD., Völp, M., Platzer, A. (2015). KeYmaera X: An Axiomatic Tactical Theorem Prover for Hybrid Systems. In: Felty, A., Middeldorp, A. (eds) Automated Deduction - CADE-25. CADE 2015. Lecture Notes in Computer Science(), vol 9195. Springer, Cham. https://doi.org/10.1007/978-3-319-21401-6_36
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