Typing a Core Binary-Field Arithmetic in a Light Logic

  • Emanuele Cesena
  • Marco Pedicini
  • Luca Roversi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7177)

Abstract

We design a library for binary-field arithmetic and we supply a core application programming interface (API) completely developed in a formal system we introduce: Typeable Functional Assembly (TFA) which essentially is the system Dual Light Affine Logic (DLAL) introduced by Baillot and Terui and extended with a fix-point formula. TFA is a light type assignment system, in the sense that substructural rules on types of linear logic allow just to type functional programs with polynomial evaluation cost. As a consequence, we show the core of a functional programming setting for binary-field arithmetic with built-in polynomial complexity.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Asperti, A., Roversi, L.: Intuitionistic light affine logic. ACM ToCL 3(1), 1–39 (2002)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Atassi, V., Baillot, P., Terui, K.: Verification of PTIME reducibility for System F terms: Type inference in dual light affine logic. Logical Methods in Computer Science 3(4) (2007)Google Scholar
  3. 3.
    Avanzi, R.M., Cohen, H., Doche, C., Frey, G., Lange, T., Nguyen, K., Vercauteren, F.: Handbook of Elliptic and Hyperelliptic Curve Cryptography. CRC Press (2005)Google Scholar
  4. 4.
    Baillot, P., Gaboardi, M., Mogbil, V.: A PolyTime Functional Language from Light Linear Logic. In: Gordon, A.D. (ed.) ESOP 2010. LNCS, vol. 6012, pp. 104–124. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Baillot, P., Mogbil, V.: Soft lambda-Calculus: A Language for Polynomial Time Computation. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 27–41. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    Baillot, P., Terui, K.: Light types for polynomial time computation in lambda calculus. I&C 207(1), 41–62 (2009)MathSciNetMATHGoogle Scholar
  7. 7.
    Burrell, J.M., Cockett, R., Redmond, F.B.: POLA: a language for PTIME programming (2009); accepted for presentation at LCC 2009Google Scholar
  8. 8.
    Dean, J., Ghemawat, S.: MapReduce: simplified data processing on large clusters. Commun. ACM 51, 107–113 (2008)CrossRefGoogle Scholar
  9. 9.
    Fong, K., Hankerson, D., Lopez, J., Menezes, A.: Field inversion and point halving revisited. IEEE Trans. Comput. 53(8), 1047–1059 (2004)CrossRefGoogle Scholar
  10. 10.
    Hofmann, M.: The strength of non-size increasing computation. In: POPL, pp. 260–269 (2002)Google Scholar
  11. 11.
    Hofmann, M.: Linear types and non-size-increasing polynomial time computation. I&C 183(1), 57–85 (2003)MATHGoogle Scholar
  12. 12.
    Hutton, G.: A tutorial on the universality and expressiveness of fold. JFP 9(4), 355–372 (1999)MathSciNetMATHGoogle Scholar
  13. 13.
    Lafont, Y.: Soft linear logic and polynomial time. TCS 318(1-2), 163–180 (2004)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Pedicini, M., Quaglia, F.: PELCR: parallel environment for optimal lambda-calculus reduction. ACM Trans. Comput. Log. 8(3) (2007), http://dx.doi.org/10.1145/1243996.1243997

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Emanuele Cesena
    • 1
  • Marco Pedicini
    • 2
    • 3
  • Luca Roversi
    • 4
    • 2
  1. 1.Dip. di Automatica e InformaticaPolitecnico di TorinoTorinoItaly
  2. 2.Istituto per le Applicazioni del Calcolo “Mauro Picone”, CNRRomaItaly
  3. 3.LIPN – UMR CNRS 7030, Institut GaliléeUniversité Paris-NordFrance
  4. 4.Dip. di InformaticaUniversità degli Studi di TorinoTorinoItaly

Personalised recommendations