Skip to main content

Automatic Partial Inversion of Inductively Sequential Functions

  • Conference paper
Implementation and Application of Functional Languages (IFL 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4449))

Included in the following conference series:

Abstract

We introduce a new partial inversion technique for first-order functional programs. Our technique is simple, fully automatic, and (when it succeeds) returns a program that belongs to the same class of the original program, namely the class of inductively sequential programs (i.e., typical functional programs). To ease the definition, our method proceeds in a stepwise manner: normalization (introduction of let expressions), proper inversion, and removal of let expressions. Furthermore, it can easily be implemented. Therefore, it forms an appropriate basis for developing a practically applicable transformation tool. Preliminary experiments with a prototype implementation of the partial inverter demonstrates the usefulness and viability of our approach.

This work has been partially supported by the EU (FEDER) and the Spanish MEC under grant TIN2005-09207-C03-02 and by the ICT for EU-India Cross-Cultural Dissemination Project ALA/95/23/2003/077-054.

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

Access this chapter

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Antoy, S.: Definitional trees. In: Kirchner, H., Levi, G. (eds.) Algebraic and Logic Programming. LNCS, vol. 632, pp. 143–157. Springer, Heidelberg (1992)

    Chapter  Google Scholar 

  2. Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)

    Google Scholar 

  3. Danvy, O., Schultz, U.P.: Lambda-Lifting in Quadratic Time. Journal of Functional and Logic Programming, 2004 (2004)

    Google Scholar 

  4. Hanus, M. (ed.): Curry: An Integrated Functional Logic Language Available at: http://www.informatik.uni-kiel.de/~mh/curry/

  5. Fischbach, A., Hannan, J.: Specification and correctness of lambda lifting. J. Funct. Program. 13(3), 509–543 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  6. Glück, R., Kawabe, M.: A Program Inverter for a Functional Language with Equality and Constructors. In: Ohori, A. (ed.) APLAS 2003. LNCS, vol. 2895, pp. 246–264. Springer, Heidelberg (2003)

    Google Scholar 

  7. Glück, R., Kawabe, M.: Derivation of deterministic inverse programs based on LR parsing. In: Kameyama, Y., Stuckey, P.J. (eds.) FLOPS 2004. LNCS, vol. 2998, pp. 291–306. Springer, Heidelberg (2004)

    Google Scholar 

  8. Harrison, P.G.: Function Inversion. In: Proc. of Int’l Workshop on Partial Evaluation and Mixed Computation, pp. 153–166. North-Holland, Amsterdam (1988)

    Google Scholar 

  9. Johnsson, T.: Lambda Lifting: Transforming Programs to Recursive Equations. In: Jouannaud, J.-P. (ed.) Functional Programming Languages and Computer Architecture(Nancy,France). LNCS, vol. 201, pp. 190–203. Springer, Heidelberg (1985)

    Google Scholar 

  10. Khoshnevisan, H., Sephton, K.M.: InvX: An Automatic Function Inverter. In: Dershowitz, N. (ed.) Rewriting Techniques and Applications. LNCS, vol. 355, pp. 564–568. Springer, Heidelberg (1989)

    Google Scholar 

  11. Marchiori, M.: Unraveling and Ultraproperties. In: Hanus, M., Rodríguez-Artalejo, M. (eds.) ALP 1996. LNCS, vol. 1139, pp. 107–121. Springer, Heidelberg (1996)

    Google Scholar 

  12. Mogensen, T.Æ.: Semi-inversion of Guarded Equations. In: Glück, R., Lowry, M. (eds.) GPCE 2005. LNCS, vol. 3676, pp. 189–204. Springer, Heidelberg (2005)

    Google Scholar 

  13. Morazán, M.T., Mucha, B.: Improved Graph-Based Lambda Lifting. In: Proc. of the Int’l Conf. on Software Engineering Research and Practice (SERP 2006), pp. 896–902. CSREA Press (2006)

    Google Scholar 

  14. Mu, S.-C.: A Calculational Approach to Program Inversion. PhD thesis, Oxford University Computing Laboratory (2003)

    Google Scholar 

  15. Nishida, N., Sakai, M., Sakabe, T.: Partial Inversion of Constructor Term Rewriting Systems. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, pp. 264–278. Springer, Heidelberg (2005)

    Google Scholar 

  16. Pareja-Flores, C., Velázquez-Iturbide, J.A.: Synthesis of Functions by Transformations and Constraints. In: Proc. of the Int’l Conf. on Functional Programming (ICFP 1997), pp. 317–317. ACM Press, New York (1997)

    Google Scholar 

  17. Romanenko, A.: Inversion and metacomputation. In: Partial Evaluation and Semantics-Based Program Manipulation, Sigplan Notices, vol. 26(9), pp. 12–22. ACM, New York (1991)

    Google Scholar 

  18. Slagle, J.R.: Automated Theorem-Proving for Theories with Simplifiers, Commutativity and Associativity. Journal of the ACM 21(4), 622–642 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  19. Wadler, P.: Views: A Way for Pattern Matching to Cohabit with Data Abstraction. In: Proc. of 14th ACM Symp. on Principles of Programming Languages (POPL 1987), pp. 307–313. ACM Press, New York (1987)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Zoltán Horváth Viktória Zsók Andrew Butterfield

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Almendros-Jiménez, J.M., Vidal, G. (2007). Automatic Partial Inversion of Inductively Sequential Functions . In: Horváth, Z., Zsók, V., Butterfield, A. (eds) Implementation and Application of Functional Languages. IFL 2006. Lecture Notes in Computer Science, vol 4449. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74130-5_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-74130-5_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74129-9

  • Online ISBN: 978-3-540-74130-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics