Abstract
Verification of machine code can easily deteriorate into an endless clutter of low-level details. This paper presents a case study which shows that machine-code verification does not necessitate ghastly low-level proofs. The case study we describe is the construction of an x86-64 implementation of arbitrary-precision integer arithmetic. Compared with closely related work, our proofs are shorter and, more importantly, the reasoning is at a more convenient high level of abstraction, e.g. pointer reasoning is largely avoided. We achieve this improvement as a result of using an abstraction for arrays and previously developed tools, namely, a proof-producing decompiler and compiler. The work presented in this paper has been developed in the HOL4 theorem prover. The case study resulted in 800 lines of verified 64-bit x86 machine code.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
GMP, the GNU multiple precision arithmetic library, http://gmplib.org/
Affeldt, R.: On construction of a library of formally verified low-level arithmetic functions. Innovations in Systems and Software Engineering 9(2) (2013)
Appel, A.W.: Foundational proof-carrying code. In: Logic in Computer Science (LICS). IEEE Computer Society (2001)
Berghofer, S.: Verification of dependable software using spark and isabelle. In: Brauer, J., Roveri, M., Tews, H. (eds.) Systems Software Verification (SSV). OASICS, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2011)
Chlipala, A.: Mostly-automated verification of low-level programs in computational separation logic. In: Hall, M.W., Padua, D.A. (eds.) Programming Language Design and Implementation (PLDI). ACM (2011)
Fischer, S.: Formal verification of a big integer library. In: DATE 2008: Workshop on Dependable Software Systems (2008), http://busserver.cs.uni-sb.de/publikationen/Fi08DATE.pdf
Harrison, J.: A HOL theory of euclidean space. In: Hurd, J., Melham, T. (eds.) TPHOLs 2005. LNCS, vol. 3603, pp. 114–129. Springer, Heidelberg (2005)
Jensen, J.B., Benton, N., Kennedy, A.: High-level separation logic for low-level code. In: Principles of Programming Languages (POPL). ACM (2013)
Knuth, D.E.: The art of computer programming, 2nd edn. Seminumerical Algorithms, vol. 2. Addison Wesley Longman Publishing (1981)
Leroy, X.: Formal certification of a compiler back-end, or: programming a compiler with a proof assistant. In: Morrisett, J.G., Jones, S.L.P. (eds.) Principles of Programming Languages (POPL). ACM (2006)
Moore, J.S.: A mechanically verified language implementation. Journal of Automated Reasoning 5 (1989)
Morrisett, G., Tan, G., Tassarotti, J., Tristan, J.B., Gan, E.: RockSalt: better, faster, stronger SFI for the x86. In: Vitek, J., Lin, H., Tip, F. (eds.) Programming Language Design and Implementation (PLDI). ACM (2012)
Myreen, M., Gordon, M.J.C.: Verification of machine code implementations of arithmetic functions for cryptography. In: Schneider, K., Brandt, J. (eds.) Theorem Proving in Higher Order Logics, Emerging Trends Proceedings (TPHOLs, Poster Session), University of Kaiserslautern, Internal Report 364/07 (2007)
Myreen, M.O.: Formal verification of machine-code programs. Ph.D. thesis, University of Cambridge (2009)
Myreen, M.O.: Verified just-in-time compiler on x86. In: Hermenegildo, M.V., Palsberg, J. (eds.) Principles of Programming Languages (POPL). ACM (2010)
Myreen, M.O., Davis, J.: A verified runtime for a verified theorem prover. In: van Eekelen, M., Geuvers, H., Schmaltz, J., Wiedijk, F. (eds.) ITP 2011. LNCS, vol. 6898, pp. 265–280. Springer, Heidelberg (2011)
Necula, G.C.: Proof-carrying code. In: Principles of Programming Languages (POPL). ACM (1997)
Reynolds, J.: Separation logic: A logic for shared mutable data structures. In: Logic in Computer Science (LICS). IEEE Computer Society (2002)
Schirmer, N.: Verification of Sequential Imperative Programs in Isabelle/HOL. Ph.D. thesis, Technical University of Munich (2006)
Slind, K., Norrish, M.: A brief overview of HOL4. In: Mohamed, O.A., Muñoz, C., Tahar, S. (eds.) TPHOLs 2008. LNCS, vol. 5170, pp. 28–32. Springer, Heidelberg (2008)
Tan, G., Appel, A.W.: A compositional logic for control flow. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 80–94. Springer, Heidelberg (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this paper
Cite this paper
Myreen, M.O., Curello, G. (2013). Proof Pearl: A Verified Bignum Implementation in x86-64 Machine Code. In: Gonthier, G., Norrish, M. (eds) Certified Programs and Proofs. CPP 2013. Lecture Notes in Computer Science, vol 8307. Springer, Cham. https://doi.org/10.1007/978-3-319-03545-1_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-03545-1_5
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03544-4
Online ISBN: 978-3-319-03545-1
eBook Packages: Computer ScienceComputer Science (R0)