Skip to main content
SpringerLink
Log in

\(\mathbb {K}\)—A Semantic Framework for Programming Languages and Formal Analysis

  • Chapter
  • First Online:
Engineering Trustworthy Software Systems (SETSS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12154))

Abstract

We give an overview on the applications and foundations of the \(\mathbb {K}\) language framework, a semantic framework for programming languages and formal analysis tools. \(\mathbb {K}\) represents a 20-year effort in pursuing the ideal language framework vision, where programming languages must have formal definitions, and tools for a given language, such as parsers, interpreters, compilers, semantic-based debuggers, state-space explorers, model checkers, deductive program verifiers, etc., can be derived from just one reference formal definition of the language, which is executable, and no other semantics for the same language should be needed. The correctness of the language tools is guaranteed on a case-by-case basis by proof objects, which encode rigorous mathematical proofs as certificates for every individual task that the tools do and can be mechanically checked by third-party proof checkers.

This paper follows the lecture notes presented by the second author at the School on Engineering Trustworthy Software Systems (SETSS) in 2019.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Substitution can be defined fully generically in \(\mathbb {K}\) (not shown here) and then used to give semantics to various constructs in various languages.

References

  1. Clang: A C language family frontend for LLVM. https://clang.llvm.org/

  2. GCC, the GNU compiler collection. https://gcc.gnu.org/

  3. TrustInSoft–cybersecurity and safety provider. https://trust-in-soft.com/

  4. Ahrendt, W., Beckert, B., Bubel, R., Hahnle, R., Schmitt, P.H., Ulbrich, M.: Deductive Software Verification-The KeY Book. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-319-49812-6

  5. Barendregt, H.: The lambda calculus: its syntax and semantics. Studies in Logic and the Foundations of Mathematics, Elsevier Science Publishers (1984)

    Google Scholar 

  6. Barnett, M., Chang, B.-Y.E., DeLine, R., Jacobs, B., Leino, K.R.M.: Boogie: a modular reusable verifier for object-oriented programs. In: de Boer, F.S., Bonsangue, M.M., Graf, S., de Roever, W.-P. (eds.) FMCO 2005. LNCS, vol. 4111, pp. 364–387. Springer, Heidelberg (2006). https://doi.org/10.1007/11804192_17

    Chapter  Google Scholar 

  7. Bertot, Y., Castran, P.: Interactive Theorem Proving and Program Development. Coq’Art the Calculus of Inductive Constructions. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-662-07964-5

    Book  Google Scholar 

  8. Bogdănaş, D., Roşu, G.: K-Java: a complete semantics of Java. In: Proceedings of the 42\(^{\rm nd}\) Symposium on Principles of Programming Languages (POPL 2015), pp. 445–456. ACM, January 2015. https://doi.org/10.1145/2676726.2676982

  9. Brady, E.: IDRIS – systems programming meets full dependent types. In: Proceedings of the 5\(^{\rm th}\) ACM Workshop on Programming Languages Meets Program Verification (PLPV 2011), pp. 43–54. ACM (2011). https://doi.org/10.1145/1929529.1929536

  10. Chen, X., Roşu, G.: Applicative matching logic. Technical Report, University of Illinois at Urbana-Champaign, July 2019. http://hdl.handle.net/2142/104616

  11. Chen, X., Roşu, G.: Matching \(\mu \)-logic. In: Proceedings of the 34\(^{\rm th}\) Annual ACM/IEEE Symposium on Logic in Computer Science (LICS 2019) (2019)

    Google Scholar 

  12. Chen, X., Roşu, G.: A language-independent program verification framework. In: Proceedings of the 8th International Symposium on Leveraging Applications of Formal Methods (ISoLA 2018), vol.11245, pp. 92–102. Springer (2018). https://doi.org/10.1007/978-3-030-03421-4

  13. Church, A.: The Calculi of Lambda-Conversion. Princeton University Press, New Jersey (1941)

    MATH  Google Scholar 

  14. Cohen, E., et al.: VCC: a practical system for verifying concurrent C. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) TPHOLs 2009. LNCS, vol. 5674, pp. 23–42. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03359-9_2

    Chapter  Google Scholar 

  15. Dasgupta, S., Park, D., Kasampalis, T., Adve, V.S., Roşu, G.: A complete formal semantics of x 86–64 user-level instruction set architecture. In: Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI 2019), pp. 1133–1148. ACM, June 2019. https://doi.org/10.1145/3314221.3314601

  16. De Moura, L., Bjørner, N.: Z3: an efficient SMT solver. In: Proceedings of the 14\(^{\rm th}\) International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS 2008). pp. 337–340. Springer, Cham (2008). https://doi.org/10.1007/978-3-540-78800-3_24

  17. Ethereum: Solidity documentation (2019). http://solidity.readthedocs.io

  18. Ethereum: Vyper documentation (2019). https://vyper.readthedocs.io

  19. Filliâtre, J.-C., Marché, C.: The Why/Krakatoa/caduceus platform for deductive program verification. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 173–177. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-73368-3_21

    Chapter  Google Scholar 

  20. Guth, D.: A formal semantics of Python 3.3. Master’s thesis, University of Illinois at Urbana-Champaign (2013). http://hdl.handle.net/2142/45275

  21. Hathhorn, C., Ellison, C., Roşu, G.: Defining the undefinedness of C. In: Proceedings of the 36\(^{\rm th}\) ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI 2015). pp. 336–345. ACM, June 2015. https://doi.org/10.1145/2813885.2737979

  22. Hildenbrandt, E., et al.: KEVM: a complete semantics of the Ethereum virtual machine. In: Proceedings of the 2018 IEEE Computer Security Foundations Symposium (CSF 2018). IEEE (2018). http://jellopaper.org

  23. Kasampalis, T., et al.: IELE: a rigorously designed language and tool ecosystem for the blockchain. In: Proceeding of the 23\(^{\rm rd}\) International Symposium on Formal Methods (FM 2019) (2019)

    Google Scholar 

  24. Kroening, D., Tautschnig, M.: CBMC – C bounded model checker. In: Ábrahám, E., Havelund, K. (eds.) TACAS 2014. LNCS, vol. 8413, pp. 389–391. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54862-8_26

    Chapter  Google Scholar 

  25. The Coq development team: The Coq proof assistant reference manual. LogiCal Project (2004). http://coq.inria.fr

  26. Norell, U.: Dependently typed programming in agda. In: Koopman, P., Plasmeijer, R., Swierstra, D. (eds.) AFP 2008. LNCS, vol. 5832, pp. 230–266. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-04652-0_5

    Chapter  MATH  Google Scholar 

  27. Park, D., Ştefănescu, A., Roşu, G.: KJS: a complete formal semantics of JavaScript. In: Proceedings of the 36\(^{\rm th}\) ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI 2015), pp. 346–356. ACM, June 2015. https://doi.org/10.1145/2737924.2737991

  28. Reynolds, J.C.: Separation logic: a logic for shared mutable data structures. In: Proceedings of the 17\(^{\rm th}\) Annual IEEE Symposium on Logic in Computer Science (LICS 2002), pp. 55–74. IEEE (2002). https://doi.org/10.1109/lics.2002.1029817

  29. Roşu, G.: K–a semantic framework for programming languages and formal analysis tools. In: Dependable Software Systems Engineering. IOS Press (2017)

    Google Scholar 

  30. Roşu, G.: Matching logic. Logic. Methods Comput. Sci. 13(4), 1–61 (2017). https://doi.org/10.23638/lmcs-13(4:28)2017

    Article  MathSciNet  MATH  Google Scholar 

  31. Roşu, G., Ştefănescu, A.: Checking reachability using matching logic. In: Proceedings of the 27\(^{\rm th}\) Conference on Object-Oriented Programming, Systems, Languages, and Applications (OOPSLA 2012), pp. 555–574. ACM, October 2012. http://dl.acm.org/citation.cfm?doid=2384616.2384656

  32. Roşu, G., Ştefănescu, A., Ciobâcă, Ş., Moore, B.M.: One-path reachability logic. In: Proceedings of the 28\(^{\rm th}\) Symposium on Logic in Computer Science (LICS 2013), pp. 358–367. IEEE (2013). https://doi.org/10.1109/lics.2013.42

  33. Roşu, G., Serbanuta, T.F.: K overview and simple case study. In: Proceedings of International K Workshop (K 2011). ENTCS, vol. 304, pp. 3–56. Elsevier, June 2014. https://doi.org/10.1016/j.entcs.2014.05.002

  34. Roşu, G., Şerbănuţă, T.F.: An overview of the K semantic framework. J. Logic Algebraic Program. 79(6), 397–434 (2010). https://doi.org/10.1016/j.jlap.2010.03.012

    Article  MathSciNet  MATH  Google Scholar 

  35. Tarski, A.: A lattice-theoretical fixpoint theorem and its applications. Pacific J. Math. 5(2), 285–309 (1955). https://doi.org/10.2140/pjm.1955.5.285

    Article  MathSciNet  MATH  Google Scholar 

  36. The Isabelle development team: Isabelle (2018). https://isabelle.in.tum.de/

Download references

Author information

Authors and Affiliations

  1. University of Illinois at Urbana-Champaign, Champaign, USA

    Xiaohong Chen & Grigore Roşu

Authors
  1. Xiaohong Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Grigore Roşu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaohong Chen .

Editor information

Editors and Affiliations

  1. Southwest University, Chongqing, China

    Jonathan P. Bowen

  2. Southwest University, Chongqing, China

    Zhiming Liu

  3. Southwest University, Chongqing, China

    Zili Zhang

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Chen, X., Roşu, G. (2020). \(\mathbb {K}\)—A Semantic Framework for Programming Languages and Formal Analysis. In: Bowen, J., Liu, Z., Zhang, Z. (eds) Engineering Trustworthy Software Systems. SETSS 2019. Lecture Notes in Computer Science(), vol 12154. Springer, Cham. https://doi.org/10.1007/978-3-030-55089-9_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-55089-9_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-55088-2

  • Online ISBN: 978-3-030-55089-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation