Skip to main content
Springer Nature Link
Log in

Quasi-interpretation Synthesis by Decomposition

An Application to Higher-Order Programs

  • Conference paper
Theoretical Aspects of Computing – ICTAC 2007 (ICTAC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4711))

Included in the following conference series:

Abstract

Quasi-interpretation analysis belongs to the field of implicit computational complexity (ICC) and has shown its interest to deal with resource analysis of first-order functional programs, which are terminating or not. In this paper, we tackle the issue of program decomposition wrt quasi-interpretations analysis. For that purpose, we use the notion of modularity. Firstly, modularity decreases the complexity of the quasi-interpretation search algorithms. Secondly, modularity increases the intentionality of the quasi-interpretation method, that is the number of captured programs. Finally, we take advantage of modularity conditions to extend smoothly quasi-interpretations to higher-order programs.

We study the modularity of quasi-interpretations through the notions of constructor-sharing and hierarchical unions of programs. We show that, in both cases, the existence of quasi-interpretations is no longer a modular property. However, we can still certify the complexity of programs by showing, under some restrictions, that the size of the values computed by a program remains polynomially bounded by the inputs size.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Amadio, R.: Max-plus quasi-interpretations. In: Hofmann, M.O. (ed.) TLCA 2003. LNCS, vol. 2701, pp. 31–45. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  2. Amadio, R., Coupet-Grimal, S., Dal-Zilio, S., Jakubiec, L.: A functional scenario for bytecode verification of resource bounds. In: Marcinkowski, J., Tarlecki, A. (eds.) CSL 2004. LNCS, vol. 3210, pp. 265–279. Springer, Heidelberg (2004)

    Google Scholar 

  3. Amadio, R., Dal-Zilio, S.: Resource control for synchronous cooperative threads. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 68–82. Springer, Heidelberg (2004)

    Google Scholar 

  4. Baillot, P., Terui, K.: A feasible algorithm for typing in elementary affine logic. In: Urzyczyn, P. (ed.) TLCA 2005. LNCS, vol. 3461, pp. 55–70. Springer, Heidelberg (2005)

    Google Scholar 

  5. Bonfante, G., Marion, J.-Y., Moyen, J.-Y.: On lexicographic termination ordering with space bound certifications. In: Bjørner, D., Broy, M., Zamulin, A.V. (eds.) PSI 2001. LNCS, vol. 2244, Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  6. Bonfante, G., Marion, J.-Y., Moyen, J.-Y.: Quasi-interpretation a way to control resources. Theoretical Computer Science (2005) (submitted), http://www.loria.fr/~marionjy

  7. Bonfante, G., Marion, J.-Y., Moyen, J.-Y., Péchoux, R.: Synthesis of quasi-interpretations. In: LCC2005, LICS affiliated Workshop (2005), http://hal.inria.fr/

  8. Coppola, P., Rocca, S.R.D.: Principal typing for lambda calculus in elementary affine logic. Fundamenta Informaticae 65(1-2), 87–112 (2005)

    MATH  MathSciNet  Google Scholar 

  9. Dal-Zilio, S., Gascon, R.: Resource bound certification for a tail-recursive virtual machine. In: Yi, K. (ed.) APLAS 2005. LNCS, vol. 3780, pp. 247–263. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  10. Danvy, O.: An analytical approach to programs as data objects, Doctor Scientarum degree in Computer Science. BRICS. Departement of Computer Science. University of Aarhus (2006)

    Google Scholar 

  11. Dershowitz, N.: Orderings for term-rewriting systems. Theoretical Computer Science 17(3), 279–301 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  12. Dershowitz, N.: Hierachical termination. In: Lindenstrauss, N., Dershowitz, N. (eds.) CTRS 1994. LNCS, vol. 968, Springer, Heidelberg (1995)

    Google Scholar 

  13. Girard, J.-Y.: Light linear logic. Information and Computation 143(2), 175–204 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  14. Gramlich, B.: Generalized sufficient conditions for modular termination of rewriting. In: Kirchner, H., Levi, G. (eds.) ALP 1992. LNCS, vol. 632, pp. 53–68. Springer, Heidelberg (1992)

    Google Scholar 

  15. Hofmann, M.: A type system for bounded space and functional in-place update. Nordic Journal of Computing 7(4), 258–289 (2000)

    MATH  MathSciNet  Google Scholar 

  16. Hofmann, M.: The strength of Non-Size Increasing computation. In: POPL, pp. 260–269 (2002)

    Google Scholar 

  17. Huet, G.: Confluent reductions: Abstract properties and applications to term rewriting systems. Journal of the ACM 27(4), 797–821 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  18. Jones, N.D.: Computability and complexity, from a programming perspective. MIT Press, Cambridge (1997)

    MATH  Google Scholar 

  19. Klop, J.W.: Term rewriting systems. In: Handbook of logic in Computer Science, vol. 2, pp. 1–116. Oxford University Press, Oxford (1992)

    Google Scholar 

  20. Kristiansen, L., Jones, N.D.: The flow of data and the complexity of algorithms. In: Cooper, S.B., Löwe, B., Torenvliet, L. (eds.) CiE 2005. LNCS, vol. 3526, pp. 263–274. Springer, Heidelberg (2005)

    Google Scholar 

  21. Kurihara, M., Ohuchi, A.: Modularity of simple termination of term rewriting systems with shared constructors. Theoretical Computer Science 103, 273–282 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  22. Lafont, Y.: Soft linear logic and polynomial time. Theoretical Computer Science 318, 163–180 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  23. Marion, J.-Y., Moyen, J.-Y.: Efficient first order functional program interpreter with time bound certifications. In: Parigot, M., Voronkov, A. (eds.) LPAR 2000. LNCS (LNAI), vol. 1955, pp. 25–42. Springer, Heidelberg (2000)

    Google Scholar 

  24. Marion, J.-Y., Moyen, J.-Y.: Heap analysis for assembly programs. Technical report, Loria (2006)

    Google Scholar 

  25. Middeldorp, A.: Modular properties of term rewriting Systems. PhD thesis, Vrije Universiteit te Amsterdam (1990)

    Google Scholar 

  26. Niggl, K.-H., Wunderlich, H.: Certifying polynomial time and linear/polynomial space for imperative programs. SIAM Journal on Computing 35(5), 1122–1147 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  27. Ohlebusch, E.: Advanced Topics in Term Rewriting. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  28. Krishna Rao, M.R.K.: Modular proofs of completeness of hierarchical term rewriting systems. Theoretical Computer Science 151, 487–512 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  29. Reynolds, J.C.: Definitional interpreters for higher-order programming languages. In: ACM, pp. 717–740. ACM Press, New York (1972)

    Google Scholar 

  30. Toyama, Y.: Counterexamples for the direct sum of term rewriting systems. Information Processing Letters 25, 141–143 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  31. Toyama, Y.: On the church-rosser property for the direct sum of term rewriting systems. Journal of the ACM 34(1), 128–143 (1987)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Nancy-Université, Loria, Carte team, B.P. 239, 54506 Vandœuvre-lès-Nancy Cedex, France, and École Nationale Supérieure des Mines de Nancy, INPL, France

    Guillaume Bonfante, Jean-Yves Marion & Romain Péchoux

Authors
  1. Guillaume Bonfante
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jean-Yves Marion
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Romain Péchoux
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Cliff B. Jones Zhiming Liu Jim Woodcock

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bonfante, G., Marion, JY., Péchoux, R. (2007). Quasi-interpretation Synthesis by Decomposition. In: Jones, C.B., Liu, Z., Woodcock, J. (eds) Theoretical Aspects of Computing – ICTAC 2007. ICTAC 2007. Lecture Notes in Computer Science, vol 4711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75292-9_28

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-75292-9_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75290-5

  • Online ISBN: 978-3-540-75292-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics