Abstract
By combining program logic and static analysis, we present an automatic approach to construct program proofs to be used in Proof-Carrying Code. We use Hoare logic in representing the proofs of program properties, and the abstract interpretation in computing the program properties. This combination automatizes proof construction; an abstract interpretation automatically estimates program properties (approximate invariants) of our interest, and our proof-construction method constructs a Hoare-proof for those approximate invariants. The proof-checking side (code consumer’s side) is insensitive to a specific static analysis; the assertions in the Hoare proofs are always first-order logic formulas for integers, into which we first compile the abstract interpreters’ results. Both the property-compilation and the proof construction refer to the standard safety conditions that are prescribed in the abstract interpretation framework. We demonstrate this approach for a simple imperative language with an example property being the integer ranges of program variables. We prove the correctness of our approach, and analyze the size complexity of the generated proofs.
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References
Appel, W.A.: Foundational proof-carrying code. In: Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science, June 2001, pp. 247–258 (2001)
Appel, W.A., Felty, A.P.: A semantic model of types and machine instructions for proof-carrying code. In: Proceedings of the ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, January 2000, pp. 243–253 (2000)
Cousot, P.: The calculational design of a generic abstract interpreter. In: Broy, M., Steinbrüggen, R. (eds.) Calculational System Design. NATO ASI Series F, IOS Press, Amsterdam (1999)
Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: Proceedings of the ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, January 1977, pp. 238–252 (1977)
Cousot, P., Cousot, R.: Automatic synthesis of optimal invariant assertions: mathematical foundations. In: ACM Symposium on Artificial Intelligence and Programming Languages, ACM SIGPLAN Notices, Rochester, NY, August 1977, vol. 12, pp. 1–12 (1977)
Cousot, P., Cousot, R.: Systematic design of program analysis frameworks. In: Conference Record of the Sixth Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 269–282. ACM Press, New York (1979)
Hamid, N., Shao, Z., Trifonov, V., Monnier, S., Ni, Z.: A syntactic approach to foundational proof-carrying code. In: Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science, June 2002, pp. 89–100 (2002)
Heintze, N., Jaffar, J., Voicu, R.: A framework for combining analysis and verification. In: Proceedings of the ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, Boston, MA, USA, January 2000, pp. 26–39 (2000)
Hoare, C.A.R.: An axiomatic basis for computer programming. Communications of the ACM 12(10), 576–580 (1969)
Morrisett, G., Walker, D., Crary, K., Glew, N.: From System F to typed assembly language. In: Proceedings of the ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, January 1998, pp. 85–97 (1998)
Necula, G.C.: Proof-carrying code. In: Proceedings of the ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, January 1997, pp. 106–119 (1997)
Necula, G.C., Lee, P.: Safe, untrusted agents using proof-carrying code. In: Vigna, G. (ed.) Mobile Agents and Security. LNCS, vol. 1419, pp. 61–91. Springer, Heidelberg (1998)
Necula, G.C., Rahul, S.P.: Oracle-based checking of untrusted software. In: Proceedings of the ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, January 2001, pp. 142–154 (2001)
Necula, G.C., Schneck, R.: Proof-carrying code with untrusted proof rules. In: Okada, M., Pierce, B.C., Scedrov, A., Tokuda, H., Yonezawa, A. (eds.) ISSS 2002. LNCS, vol. 2609, pp. 283–298. Springer, Heidelberg (2003)
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Seo, S., Yang, H., Yi, K. (2003). Automatic Construction of Hoare Proofs from Abstract Interpretation Results. In: Ohori, A. (eds) Programming Languages and Systems. APLAS 2003. Lecture Notes in Computer Science, vol 2895. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40018-9_16
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DOI: https://doi.org/10.1007/978-3-540-40018-9_16
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