Abstract
Using a predicate transformer semantics of programs, we introduce statements for heap operations and separation logic operators for specifying programs that manipulate pointers. We prove consistent Hoare total correctness rules for pointer manipulating statements according to the predicate transformer semantics. We prove the frame rule in the context of a programming language with recursive procedures with value and result parameters and local variables, where program variables and addresses can store values of any type of the theorem prover. The theory, including the proofs, is implemented in the theorem prover PVS.
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References
Back, R.J., Preoteasa, V.: An algebraic treatment of procedure refinement to support mechanical verification. Formal Aspects of Computing 17, 69–90 (2005)
Back, R.J., von Wright, J.: Refinement Calculus. A systematic Introduction. Springer, Heidelberg (1998)
Church, A.: A formulation of the simple theory of types. J. Symbolic logic 5, 56–68 (1940)
Hoare, C.A.R.: An axiomatic basis for computer programming. Communications of the ACM 12(10), 576–580 (1969)
Ishtiaq, S.S., O’Hearn, P.W.: Bi as an assertion language for mutable data structures. In: POPL 2001: Proceedings of the 28th ACM SIGPLAN-SIGACT symposium on Principles of programming languages, pp. 14–26. ACM Press, New York (2001)
Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL — A Proof Assistant for Higher-Order Logic. LNCS, vol. 2283. Springer, Heidelberg (2002)
O’Hearn, P.W., Reynolds, J.C., Yang, H.: Local reasoning about programs that alter data structures. In: Fribourg, L. (ed.) CSL 2001 and EACSL 2001. LNCS, vol. 2142, pp. 1–19. Springer, Heidelberg (2001)
Owre, S., Shankar, N., Rushby, J.M., Stringer-Clavert, D.W.J.: PVS language reference. Technical report, Computer Science Laboratory, SRI International (December 2001)
Preoteasa, V.: Mechanical verification of mutually recursive procedures for parsing expressions using separation logic. Technical Report 771, TUCS - Turku Centre for Computer Science (May 2006)
Reynolds, J.: Intuitionistic reasoning about shared mutable data structure. In: Millenial Perspectives in Computer Science (2000)
Reynolds, J.: Separation logic: A logic for shared mutable data structures. In: 17th Annual IEEE Symposium on Logic in Computer Science. IEEE, Los Alamitos (2002)
Tarski, A.: A lattice-theoretical fixpoint theorem and its applications. Pacific J. Math. 5, 285–309 (1955)
Weber, T.: Towards mechanized program verification with separation logic. In: Marcinkowski, J., Tarlecki, A. (eds.) CSL 2004. LNCS, vol. 3210, pp. 250–264. Springer, Heidelberg (2004)
Yang, H., O’Hearn, P.W.: A semantic basis for local reasoning. In: Nielsen, M., Engberg, U. (eds.) FOSSACS 2002. LNCS, vol. 2303, pp. 402–416. Springer, Heidelberg (2002)
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Preoteasa, V. (2006). Mechanical Verification of Recursive Procedures Manipulating Pointers Using Separation Logic. In: Misra, J., Nipkow, T., Sekerinski, E. (eds) FM 2006: Formal Methods. FM 2006. Lecture Notes in Computer Science, vol 4085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11813040_34
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DOI: https://doi.org/10.1007/11813040_34
Publisher Name: Springer, Berlin, Heidelberg
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