Samin S. Ishtiaq
ABSTRACT
Reynolds has developed a logic for reasoning about mutable data structures in which the pre- and postconditions are written in an intuitionistic logic enriched with a spatial form of conjunction. We investigate the approach from the point of view of the logic BI of bunched implications of O'Hearnand Pym. We begin by giving a model in which the law of the excluded middleholds, thus showing that the approach is compatible with classical logic. The relationship between the intuitionistic and classical versions of the system is established by a translation, analogous to a translation from intuitionistic logic into the modal logic S4. We also consider the question of completeness of the axioms. BI's spatial implication is used to express weakest preconditions for object-component assignments, and an axiom for allocating a cons cell is shown to be complete under an interpretation of triplesthat allows a command to be applied to states with dangling pointers. We make this latter a feature, by incorporating an operation, and axiom, for disposing of memory. Finally, we describe a local character enjoyed by specifications in the logic, and show how this enables a class of frame axioms, which say what parts of the heap don't change, to be inferred automatically.
- 1.Alur, R., and Grosu, R. Modular refinement of hierarchic reactive machines. In POPL {31}.]] Google Scholar
Digital Library
- 2.Borgida, A., Mylopoulos, J., and Reiter, R. On the frame problem in procedure specifications. IEEE Transactions of Software Engineering 21 (1995), 809-838.]] Google ScholarDigital Library
- 3.Bornat, R. Proving pointer programs in Hoare logic. In Fifth Internationsl Conference on Mathematics of Program Construction, LNCS 1837, Ponte de Lima, Portugal, 2000.]] Google ScholarDigital Library
- 4.Brookes, S., Main, M., Melton, A., and Mislove, M., Eds. Mathematical Foundations of Programming Semantics, Eleventh Annual Conference (Tulane University, New Orleans, Louisiana, March 29-April 1 1995), vol. 1 of Electronic Notes in Theoretical Computer Science, Elsevier Science.]]Google Scholar
- 5.Burstall, R. Some techniques for proving correctness of programs which alter data structures. Machine Intelligence 7 (1972), 23-50.]]Google Scholar
- 6.Calcagno, C., Ishtiaq, S., and O'Hearn, P. Semantic analysis of pointer aliasing, allocation and disposal in Hoare logic. Proceedings of the 2nd international ACM SIGPLAN conference on on Principles and practice of declarative programming, 2000.]] Google ScholarDigital Library
- 7.Cardelli, L., and Ghelli, G. A query language for semistructured data based on the ambient logic. Manuscript, 4 April 2000.]]Google Scholar
- 8.Cardelli, L., and Gordon, A. D. Anytime, anywhere. modal logics for mobile ambients. In POPL {31}.]] Google ScholarDigital Library
- 9.Cervesato, I., and Pfenning, F. A linear logical framework. In Proceedings of the Eleventh Annual Symposium on Logic in Computer Science | LICS'96 (27-30 July 1996), IEEE Computer Society Press, pp. 264-275.]] Google ScholarDigital Library
- 10.Cook, S. A. Soundness and completeness of an axiomatic system for program verification. SIAM J. on Computing 7 (1978), 70-90.]]Google ScholarCross Ref
- 11.de Boer, F. A WP calculus for OO. In Proceedings of FOSSACS'99 (1999).]] Google ScholarDigital Library
- 12.Girard, J.-Y. Linear logic. Theoretical Computer Science (1987), 1-102.]] Google ScholarDigital Library
- 13.Girard, J.-Y. Towards a geometry of interaction. In Categories in Computer Science and Logic (1989), American Mathematical Society, pp. 69-108. Contemporary Mathematics Volume 92.]]Google Scholar
- 14.Guttag, J., Horning, J., and Wing, J. Larch in five easy pieces. TR 5, DEC Systems Research Center, 1985.]]Google Scholar
- 15.Hoare, C., and He, J. A trace model for pointers and objects. In ECCOP'99 - Object-Oriented Programming, 13th European Conference (1999), R. Guerraoui, Ed., pp. 1-17. Lecture Notes in Computer Science, Vol. 1628, Springer.]] Google ScholarDigital Library
- 16.Hoare, C. A. R., and Wirth, N. An axiomatic definition of the programming language Pascal. Acta Informatica 2 (1973), 335-355.]]Google ScholarDigital Library
- 17.Honsell, F., Mason, I. A., Smith, S., and Talcott, C. A variable typed logic of effects. Information and Computation 119, 1 (may 1995), 55-90.]] Google ScholarDigital Library
- 18.Jenson, J., Jorgensen, M., Klarkund, N., and Schwartzback, M. Automatic verification of pointer programs using monadic second-order logic. In Proceedings of the ACM SIGPLAN'97 Conference on Programming Language Design and Implementation (1997), pp. 225-236. SIGPLAN Notices 32(5).]] Google ScholarDigital Library
- 19.Kripke, S. A. Semantical analysis of intuitionistic logic I. In Formal Systems and Recursive Functions, J. N. Crossley and M. A. E. Dummett, Eds. North-Holland, Amsterdam, 1965, pp. 92-130.]]Google Scholar
- 20.Leino, K. Toward Reliable Modular Programs. Ph.D. thesis, California Institute of Technology, Pasadena, California, 1995.]] Google ScholarDigital Library
- 21.Miller, D. Observations about using logic as a specification language. In GULP-PRODE'95 - Joint Conference on Declarative Programming (Marina de Vietri, Salerno, Italy, September 1995).]]Google Scholar
- 22.Moller, B. Calculating with pointer structures. In Proceedings of Mathematics for Software Construction, (1997), Chapman and Hall, pp. 24-48.]] Google ScholarDigital Library
- 23.Morris, J. A general axiom of assignment. Assignment and linked data structure. A proof of the Schorr-Waite algorithm. In Theoretical Foundations of Programming Methodology (1982), M. Broy and G. Schmidt, Eds., Reidel, pp. 25-51.]]Google ScholarCross Ref
- 24.Necula, G. Proof-carrying code. In In Proceedings of the 24th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Langauges (POPL '97) (1997).]] Google ScholarDigital Library
- 25.O'Hearn, P., and Pym, D. The logic of bunched implications. Bulletin of Symbolic Logic 5, 2 (June 99), 215-244.]]Google ScholarCross Ref
- 26.O'Hearn, P., Pym, D., and Yang, H. Possible worlds and resources: The semantics of BI. Submitted, October 2000.]]Google Scholar
- 27.O'Hearn, P., and Yang, H. Local reasoning about pointer programs using bunched implications. In Preparation, 2000.]]Google Scholar
- 28.O'Hearn, P. W., Power, A. J., Takeyama, M., and Tennent, R. D. Syntactic control of interference revisited. Theoretical Computer Science 228, 1-2 (October 1999), 211-252. Preliminary version in {4} and in {29}, vol 2.]] Google ScholarDigital Library
- 29.O'Hearn, P. W., and Tennent, R. D., Eds. Algol-like Languages. Two volumes, Birkhauser, Boston, 1997.]] Google ScholarDigital Library
- 30.Oppen, D. C., and Cook, S. A. Proving assertions about programs that manipulate data structures. In Conference Record of Seventh Annual ACM Symposium on Theory of Computation (Albuquerque, New Mexico, 5-7 May 1975), pp. 107-116.]] Google ScholarDigital Library
- 31.Conference Record of the 27th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (2000), ACM, New York.]]Google Scholar
- 32.Pym, D. The semantics and proof theory of the logic of bunched implications. Monograph in Preparation, 2000. See http://www.dcs.qmw.ac.uk/~pym.]]Google Scholar
- 33.Reiter, R. The frame problem in the situation calculus: a simple solution (sometimes) and a completeness result for goal regression. In V. Lifschitz, editor, Artificial Intelligence and Mathematical Theory of Computation: Papers in Honor of John McCarthy, pages 359-380. Academic Press, 1991.]] Google ScholarDigital Library
- 34.Reynolds, J. C. Syntactic control of interference. In Conference Record of the Fifth Annual ACM Symposium on Principles of Programming Languages (Tucson, Arizona, January 1978), ACM, New York, pp. 39-46. Also in {29}, vol 1.]] Google ScholarDigital Library
- 35.Reynolds, J. C. Intuitionistic reasoning about shared mutable data structure. In Millenial Perspectives in Computer Science, Palgrove, 2000.]]Google Scholar
- 36.Reynolds, J. C. Lectures on reasoning about shared mutable data structure. IFIP Working Group 2.3 School/Seminar on State-of-the-Art Program Design Using Logic. Tandil, Argentina, September 2000.]]Google Scholar
- 37.Sagiv, M., Reps, T., and Wilhelm, R. Parametric shape analysis via 3valued logic. In POPL'99.]] Google ScholarDigital Library
- 38.Smith, F., Walker, D., and Morrisett, G. Alias types. Proceedings of ESOP'99.]] Google ScholarDigital Library
- 39.Walker, D., and Morrisett, G. Alias types for recursive data structures. Manuscript, April 2000.]]Google Scholar
- 40.Xu, Z., Miller, B., and Reps, T. Safety checking of machine code. In PLDI'00.]] Google ScholarDigital Library
Index Terms
- BI as an assertion language for mutable data structures
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