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A Compositional Logic for Control Flow

  • Conference paper
Verification, Model Checking, and Abstract Interpretation (VMCAI 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3855))

Abstract

We present a program logic, \(\mathcal{L}_{c}\), which modularly reasons about unstructured control flow in machine-language programs. Unlike previous program logics, the basic reasoning units in \(\mathcal{L}_{c}\) are multiple-entry and multiple-exit program fragments. \(\mathcal{L}_{c}\) provides fine-grained composition rules to compose program fragments. It is not only useful for reasoning about unstructured control flow in machine languages, but also useful for deriving rules for common control-flow structures such as while-loops, repeat-until-loops, and many others. We also present a semantics for \(\mathcal{L}_{c}\) and prove that the logic is both sound and complete with respect to the semantics. As an application, \(\mathcal{L}_{c}\) and its semantics have been implemented on top of the \(\mathcal{L}_{c}\) machine language, and are embedded in the Foundational Proof-Carrying Code project to produce memory-safety proofs for machine-language programs.

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References

  1. Hoare, C.A.R.: An axiomatic basis for computer programming. Communications of the Association for Computing Machinery 12, 578–580 (1969)

    Google Scholar 

  2. Necula, G.: Proof-carrying code. In: 24th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 106–119. ACM Press, New York (1997)

    Chapter  Google Scholar 

  3. Morrisett, G., Walker, D., Crary, K., Glew, N.: From System F to typed assembly language. ACM Trans. on Programming Languages and Systems 21, 527–568 (1999)

    Article  Google Scholar 

  4. Appel, A.W.: Foundational proof-carrying code. In: Symposium on Logic in Computer Science (LICS 2001), pp. 247–258. IEEE, Los Alamitos (2001)

    Chapter  Google Scholar 

  5. Clint, M., Hoare, C.A.R.: Program proving: Jumps and functions. Acta Informatica, 214–224 (1972)

    Google Scholar 

  6. Kowaltowski, T.: Axiomatic approach to side effects and general jumps. Acta Informatica 7, 357–360 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  7. Arbib, M., Alagic, S.: Proof rules for gotos. Acta Informatica 11, 139–148 (1979)

    Article  Google Scholar 

  8. de Bruin, A.: Goto statements: Semantics and deduction systems. Acta Informatica 15, 385–424 (1981)

    Article  MATH  Google Scholar 

  9. O’Donnell, M.J.: A critique of the foundations of hoare style programming logics. Communications of the Association for Computing Machinery 25, 927–935 (1982)

    MATH  Google Scholar 

  10. Floyd, R.W.: Assigning meanings to programs. In: Proceedings of Symposia in Applied Mathematics, pp. 19–32. Providence, Rhode Island (1967)

    Google Scholar 

  11. Cardelli, L.: Program fragments, linking, and modularization. In: 24th ACM Symposium on Principles of Programming Languages, pp. 266–277 (1997)

    Google Scholar 

  12. Glew, N., Morrisett, G.: Type-safe linking and modular assembly language. In: 26th ACM Symposium on Principles of Programming Languages, pp. 250–261 (1999)

    Google Scholar 

  13. Benton, N.: A typed, compositional logic for a stack-based abstract machine. In: 3rd Asian Symposium on Programming Languages and Systems (2005)

    Google Scholar 

  14. Ni, Z., Shao, Z.: Certified assembly programming with embedded code pointers. In: 33rd ACM Symposium on Principles of Programming Languages (2006) (to appear)

    Google Scholar 

  15. Saabas, A., Uustalu, T.: A compositional natural semantics and Hoare logic for low-level languages. In: Proceedings of the Second Workshop on Structured Operational Semantics, SOS 2005 (2005)

    Google Scholar 

  16. Tan, G.: A Compositional Logic for Control Flow and its Application in Foundational Proof-Carrying Code. PhD thesis, Princeton University (2005)

    Google Scholar 

  17. Appel, A.W., McAllester, D.: An indexed model of recursive types for foundational proof-carrying code. ACM Trans. on Programming Languages and Systems 23, 657–683 (2001)

    Article  Google Scholar 

  18. Tan, G., Appel, A.W., Swadi, K.N., Wu, D.: Construction of a semantic model for a typed assembly language. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol. 2937, pp. 30–43. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  19. Sørensen, M.H., Urzyczyn, P.: Lectures on the Curry-Howard isomorphism. Available as DIKU Rapport 98/14 (1998)

    Google Scholar 

  20. Cook, S.A.: Soundness and completeness of an axiom system for program verification. SIAM Journal on Computing 7, 70–90 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  21. Chen, J., Wu, D., Appel, A.W., Fang, H.: A provably sound TAL for back-end optimization. In: ACM Conference on Programming Language Design and Implementation, pp. 208–219 (2003)

    Google Scholar 

  22. Swadi, K.N.: Typed Machine Language. PhD thesis, Princeton University (2003)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Computer Science Department, Boston College,  

    Gang Tan

  2. Computer Science Department, Princeton University,  

    Andrew W. Appel

Authors
  1. Gang Tan
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  2. Andrew W. Appel
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Editor information

Editors and Affiliations

  1. Aiken Computation Laboratory, Harvard University,, 02138, Cambridge, Mass, USA

    E. Allen Emerson

  2. Bell Laboratories, Alcatel-Lucent,  

    Kedar S. Namjoshi

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© 2005 Springer-Verlag Berlin Heidelberg

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Tan, G., Appel, A.W. (2005). A Compositional Logic for Control Flow. In: Emerson, E.A., Namjoshi, K.S. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2006. Lecture Notes in Computer Science, vol 3855. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11609773_6

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  • DOI: https://doi.org/10.1007/11609773_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31139-3

  • Online ISBN: 978-3-540-31622-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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