The Correctness of a Code Generator for a Functional Language

  • Nathanaël Courant
  • Antoine Séré
  • Natarajan ShankarEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11990)


Code generation is gaining popularity as a technique to bridge the gap between high-level models and executable code. We describe the theory underlying the PVS2C code generator that translates functional programs written using the PVS specification language to standalone, efficiently executable C code. We outline a correctness argument for the code generator. The techniques used are quite generic and can be applied to transform programs written in functional languages into imperative code. We use a formal model of reference counting to capture memory management and safe destructive updates for a simple first-order functional language with arrays. We exhibit a bisimulation between the functional execution and the imperative execution. This bisimulation shows that the generated imperative program returns the same result as the functional program.



This work was supported by the National Institute of Aerospace Award C18-201097-SRI, NSF Grant SHF-1817204, and DARPA under agreement number HR001119C0075. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of NASA, NSF, DARPA, or the U.S. Government. We thank the anonymous referees for their constructive feedback.


  1. 1.
    Appel, A.W., Blazy, S.: Separation logic for small-step cminor. In: Schneider, K., Brandt, J. (eds.) TPHOLs 2007. LNCS, vol. 4732, pp. 5–21. Springer, Heidelberg (2007). Scholar
  2. 2.
    Aspinall, D., Hofmann, M.: Another type system for in-place update. In: Le Métayer, D. (ed.) ESOP 2002. LNCS, vol. 2305, pp. 36–52. Springer, Heidelberg (2002). Scholar
  3. 3.
    Bevier, W.R., Hunt, W.A., Moore Jr., J.S., Young, W.D.: An approach to systems verification. J. Autom. Reason. 5(4), 411–428 (1989)Google Scholar
  4. 4.
    Chirimar, J., Gunter, C.A., Riecke, J.G.: Reference counting as a computational interpretation of linear logic. J. Funct. Program. 6(2), 195–244 (1996)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Collins, G.E.: A method for overlapping and erasure of lists. Commun. ACM 3(12), 655–657 (1960)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Didrich, K., Fett, A., Gerke, C., Grieskamp, W., Pepper, P.: OPAL: design and implementation of an algebraic programming language. In: Gutknecht, J. (ed.) Programming Languages and System Architectures. LNCS, vol. 782, pp. 228–244. Springer, Heidelberg (1994). Scholar
  7. 7.
    Draghicescu, M., Purushothaman, S.: A uniform treatment of order of evaluation and aggregate update. Theor. Comput. Sci. 118(2), 231–262 (1993)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Emmi, M., Jhala, R., Kohler, E., Majumdar, R.: Verifying reference counting implementations. In: Kowalewski, S., Philippou, A. (eds.) TACAS 2009. LNCS, vol. 5505, pp. 352–367. Springer, Heidelberg (2009). Scholar
  9. 9.
    Felleisen, M.: On the expressive power of programming languages. In: Jones, N. (ed.) ESOP 1990. LNCS, vol. 432, pp. 134–151. Springer, Heidelberg (1990). Scholar
  10. 10.
    Férey, G., Shankar, N.: Code Generation using a formal model of reference counting. In: Rayadurgam, S., Tkachuk, O. (eds.) NFM 2016. LNCS, vol. 9690, pp. 150–165. Springer, Cham (2016). Scholar
  11. 11.
    Flanagan, C., Sabry, A., Duba, B.F., Felleisen, M.: The essence of compiling with continuations (with retrospective). In: McKinley, K.S. (ed.) Best of PLDI, pp. 502–514. ACM (1993)Google Scholar
  12. 12.
    Gopinath, K., Hennessy, J.L.: Copy elimination in functional languages. In: 16th ACM Symposium on Principles of Programming Languages. Association for Computing Machinery, January 1989Google Scholar
  13. 13.
    Hudak, P.: A semantic model of reference counting and its abstraction (detailed summary). In: Proceedings 1986 ACM Conference on LISP and Functional Programming, pp. 351–363. ACM, August 1986Google Scholar
  14. 14.
    Hudak, P., Bloss, A.: The aggregate update problem in functional programming systems. In: Proceedings of the 12th ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages, POPL 1985, pp. 300–314. ACM, New York (1985)Google Scholar
  15. 15.
    Kanade, A., Sanyal, A., Khedker, U.: A PVS based framework for validating compiler optimizations. In: Fourth IEEE International Conference on Software Engineering and Formal Methods (SEFM 2006) (2006)Google Scholar
  16. 16.
    Kumar, R., Myreen, M.O., Norrish, M., Owens, S.: CakeML: a verified implementation of ML. In: Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2014, pp. 179–191. ACM, New York (2014)Google Scholar
  17. 17.
    Leroy, X.: Formal verification of a realistic compiler. Commun. ACM 52(7), 107–115 (2009)CrossRefGoogle Scholar
  18. 18.
    Harold McBeth, J.: On the reference counter method. Commun. ACM 6(9), 575 (1963)CrossRefGoogle Scholar
  19. 19.
    Moreau, L., Duprat, J.: A construction of distributed reference counting. Acta Inf. 37(8), 563–595 (2001)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Polak, W.: Compiler Specification and Verification. Springer, Berlin (1981)CrossRefGoogle Scholar
  21. 21.
    Schulte, W.: Deriving residual reference count garbage collectors. In: Hermenegildo, M., Penjam, J. (eds.) PLILP 1994. LNCS, vol. 844, pp. 102–116. Springer, Heidelberg (1994). Scholar
  22. 22.
    Shankar, N.: Static analysis for safe destructive updates in a functional language. In: Pettorossi, A. (ed.) LOPSTR 2001. LNCS, vol. 2372, pp. 1–24. Springer, Heidelberg (2002). Scholar
  23. 23.
    Shankar, N.: A brief introduction to the PVS2C code generator. In: Dutertre, B., Shankar, N. (eds.) AFM@NFM, EasyChair, vol. 5, pp. 109–116. Kalpa Publications in Computing (2017)Google Scholar
  24. 24.
    David W.J.: Stringer-Calvert. Mechanical Verification of Compiler Correctness. Ph.D. thesis, University of York, Department of Computer Science, York, England, March 1998Google Scholar
  25. 25.
    Ullrich, S., de Moura, L.: Counting immutable beans: Reference counting optimized for purely functional programming. CoRR, abs/1908.05647, 2019. Appears in pre-conference proceedings of IFL2019:
  26. 26.
    Wand, M., Clinger, W.D.: Set constraints for destructive array update optimization. In: Proceedings of the IEEE Conference on Computer Languages 1998, pp. 184–193. IEEE, April 1998Google Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Nathanaël Courant
    • 1
  • Antoine Séré
    • 2
  • Natarajan Shankar
    • 3
    Email author
  1. 1.Inria Paris and Université Paris DiderotParisFrance
  2. 2.École PolytechniquePalaiseauFrance
  3. 3.Computer Science Laboratory, SRI InternationalMenlo ParkUSA

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