Abstract
In this paper, we integrate Separation Logic with propositional Projection Temporal Logic (PPTL) to obtain a two-dimensional logic, named \(\text {PPTL}^{\tiny \text{ SL }}\). The spatial dimension is realized by a decidable fragment of separation logic which can be used to describe linked lists, and the temporal dimension is expressed by PPTL. Furthermore, we prove that any \(\text {PPTL}^{\tiny \text{ SL }}\) formula can be transformed into its normal form. Example are given to show how to specify temporal heap properties by this hybrid logic.
This research is supported by the NSFC Grant Nos. 61133001, 61272118, 61272117, 61202038, 91218301, 61322202, 61373043 and National Program on Key Basic Research Project (973 Program) Grant No. 2010CB328102.
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References
Burstall, R.M.: Some techniques for proving correctness of programs which alter data structures. J. Mach. Intell. 7, 23–50 (1972)
Hoare, C.A.R., He, J.: A trace model for pointers and objects. In: Guerraoui, R. (ed.) ECCOP 1999. LNCS, vol. 1628, pp. 1–17. Springer, Heidelberg (1999)
Chase, D.R., Wegman, M., Zadeck, F.K.: Analysis of pointers and structures. In: PLDI, pp. 296–310. ACM Press, New York (1990)
Wilhelm, R., Sagiv, S., Reps, T.W.: Shape analysis. In: Watt, D.A. (ed.) CC/ETAPS 2000. LNCS, vol. 1781, pp. 1–17. Springer, Heidelberg (2000)
Sagiv, M., Reps, T., Wilhelm, R.: Parametric shape analysis via 3-valued logic. J. ACM Trans. Program. Lang. Syst. 24, 217–298 (2002)
Lev-Ami, T., Sagiv, M.: TVLA: A system for implementing static analyses. In: Palsberg, J. (ed.) SAS 2000. LNCS, vol. 1824, pp. 280–302. Springer, Heidelberg (2000)
Reynolds, J.C.: Separation logic: a logic for shared mutable data structures. In: 17th IEEE Symp. on Logic in Comput. Sci., pp. 55–74. IEEE Press, New York (2002)
Berdine, J., Calcagno, C., O’Hearn, P.W.: Symbolic execution with separation logic. In: Yi, K. (ed.) ALAPS 2005. LNCS, vol. 3780, pp. 52–68. Springer, Heidelberg (2005)
Distefano, D., O’Hearn, P.W., Yang, H.: A local shape analysis based on separation logic. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 287–302. Springer, Heidelberg (2006)
Calcagno, C., Gardner, P., Hague, M.: From separation logic to first-order logic. In: Sassone, V. (ed.) FoSSaCS 2005. LNCS, vol. 3441, pp. 395–409. Springer, Heidelberg (2005)
Moszkowski, B.C.: Reasoning about digital circuits. Ph.D. thesis, Stanford University (1983)
Duan, Z.: An extended interval temporal logic and a framing technique for temporal logic programming. Ph.D. thesis, University of Newcastle Upon Tyne (1996)
Duan, Z., Koutny, M.: A framed temporal logic programming language. J. Comput. Sci. Technol. 19, 341–351 (2004)
Duan, Z., Yang, X., Koutny, M.: Framed temporal logic programming. J. Sci. Comput. Program. 70, 31–61 (2008)
Yahav, E., Reps, T., Sagiv, M., Wilhelm, R.: Verifying temporal heap properties specified via evolution logic. In: Degano, P. (ed.) ESOP 2003. LNCS, vol. 2618, pp. 204–222. Springer, Heidelberg (2003)
Distefano, D., Katoen, J.-P., Rensink, A.: Safety and liveness in concurrent pointer programs. In: de Boer, F.S., Bonsangue, M.M., Graf, S., de Roever, W.-P. (eds.) FMCO 2005. LNCS, vol. 4111, pp. 280–312. Springer, Heidelberg (2006)
del Mar Gallardo, M., Merino, P., Sanán, D.: Model checking dynamic memory allocation in operating systems. J. Autom. Reason. 42, 229–264 (2009)
Brochenin, R., Demri, S., Lozes, E.: Reasoning about sequences of memory states. J. Ann. Pure Appl. Logic 161, 305–323 (2009)
Calcagno, C., Yang, H., O’Hearn, P.W.: Computability and complexity results for a spatial assertion language for data structures. In: Hariharan, R., Mukund, M., Vinay, V. (eds.) FSTTCS 2001. LNCS, vol. 2245, pp. 108–119. Springer, Heidelberg (2001)
Berdine, J., Calcagno, C., O’Hearn, P.W.: A decidable fragment of separation logic. In: Lodaya, K., Mahajan, M. (eds.) FSTTCS 2004. LNCS, vol. 3328, pp. 97–109. Springer, Heidelberg (2004)
Duan, Z., Tian, C.: A unified model checking approach with projection temporal logic. In: Liu, S., Maibaum, T., Araki, K. (eds.) ICFEM 2008. LNCS, vol. 5256, pp. 167–186. Springer, Heidelberg (2008)
Duan, Z., Tian, C., Zhang, L.: A decision procedure for propositional projection temporal logic with infinite models. J. Acta Inform. 45, 43–78 (2008)
Tian, C., Duan, Z.: Complexity of propositional projection temporal logic with star. J. Math. Struct. Comput. Sci. 19, 73–100 (2009)
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Lu, X., Duan, Z., Tian, C., Liu, H. (2014). Integrating Separation Logic with PPTL. In: Liu, S., Duan, Z. (eds) Structured Object-Oriented Formal Language and Method. SOFL+MSVL 2013. Lecture Notes in Computer Science(), vol 8332. Springer, Cham. https://doi.org/10.1007/978-3-319-04915-1_3
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