Internal Normalization, Compilation and Decompilation for System \({\mathcal F}_{\beta\eta}\)

  • Stefano Berardi
  • Makoto Tatsuta
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6009)


This paper defines a family of terms of System F which is a decompiler-normalizer for an image of System F by some injective interpretation in System F. We clarify the relationship among these terms, normalization by evaluation, and beta-eta-complete models of F.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abel, A.: Weak beta-Normalization and Normalization by Evaluation for System F. In: Cervesato, I., Veith, H., Voronkov, A. (eds.) LPAR 2008. LNCS (LNAI), vol. 5330, pp. 497–511. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  2. 2.
    Berardi, S., Tatsuta, M.: Internal Normalization, Compilation and Decompilation for System \({\mathcal F}_{\beta\eta}\) (full paper). Draft,
  3. 3.
    Berger, U., Eberl, M., Schwichtenberg, H.: Normalisation by Evaluation. In: Prospects for Hardware Foundations, pp. 117–137 (1998)Google Scholar
  4. 4.
    Barbanera, F., Berardi, S.: A full continuous model of polymorphism. Theor. Comput. Sci. 290(1), 407–428 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Berardi, S., Berline, C.: βη-Complete Models for System F. Mathematical Structures in Computer Science 12(6), 823–874 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Berardi, S., Berline, C.: Building continuous webbed models for system F. Theor. Comput. Sci. 315(1), 3–34 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Friedman, H.: Classically and Intuitionistically Provably Recursive Functions. In: Scott, D.S., Muller, G.H. (eds.) Higher Set Theory. LNM, vol. 699, pp. 21–28. Springer, Heidelberg (1978)CrossRefGoogle Scholar
  8. 8.
    Joly, T.: Codage, Separabilite et Representation, These de doctorat, Universite de Paris VII (2000),
  9. 9.
    Garillot, F., Werner, B.: Simple Types in Type Theory: Deep and Shallow Encodings. In: Schneider, K., Brandt, J. (eds.) TPHOLs 2007. LNCS, vol. 4732, pp. 368–382. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  10. 10.
    Longo, G., Moggi, E.: Constructive Natural Deduction and its ‘Omega-Set’ Interpretation. MSCS 1(2), 215–254 (1991)zbMATHMathSciNetGoogle Scholar
  11. 11.
    Mitchell, J.C.: Semantic Models For Second-Order Lambda Calculus. In: 25th Annual Symposium on Foundations of Computer Science, pp. 289–299 (1984)Google Scholar
  12. 12.
    Moggi, E., Statman, R.: The Maximum Consistent Theory of Second Order Lambda Calculus. e-mail message to the “Types” net (July 24, 1986),
  13. 13.
    Pfenning, F., Elliott, C.: Higher-order abstract syntax. In: Wexelblat, R.L. (ed.) Proceedings of the ACM SIGPLAN 1988 PLDI. SIGPLAN Notices, vol. 23(7), pp. 199–208. ACM Press, New York (1988)Google Scholar
  14. 14.
    Pfenning, F., Lee, P.: LEAP: A language with eval and polymorphism. In: Díaz, J., Orejas, F. (eds.) TAPSOFT 1989 and CCIPL 1989. LNCS, vol. 352, pp. 345–359. Springer, Heidelberg (1989)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Stefano Berardi
    • 1
  • Makoto Tatsuta
    • 2
  1. 1.C.S. Dept.University of TurinItaly
  2. 2.National Institute of InformaticsJapan

Personalised recommendations