Advertisement

A Formalization of Static Analyses in System F

  • Frédéric Prost
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1632)

Abstract

In this paper, we propose a common theoretical framework for type based static analyses. The aim is the study of relationships between typing and program analysis.

We present a variant of Girard’s System F called F stackП stack≤:. We prove standard properties of F stackП stack≤:. We show how it can be used to formalize various program analyses like binding time and dead code. We relate our work to previous analyses in terms of expressivness (often only simply typed calculi are considered) and power (more information can be inferred). F stackП: features polymorphism as well as subtyping at the level of universe extending previous author work where only universe polymorphism (on a simply typed calculus) was considered

Keywords

Derivation Tree Typing Rule Type Inference Positive Type Negative Type 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [BB95]
    S. Berardi and L. Boerio. Using subtyping in program optimization. In Proceedings of TLCA’95, LNCS 902. Spinger-Verlag, 1995.Google Scholar
  2. [BBC+96]
    B. Barras, S. Boutin, C. Cornes, J. Courant, J.-C. Filliatre, H. Herbelin, G. Huet, P. Manoury, C. Muñoz, C. Murthy, C. Parent, C. Paulin-Mohring, A. Saïbi, and B. Werner. The Coq Proof Assistant ReferenceManual Version 6.1. INRIA-Rocquencourt-CNRS-ENS Lyon, December 1996.Google Scholar
  3. [Ber96]
    S. Berardi. Pruning simply typed lambda terms. Journal of Logic and Computation, 125(2):663–681, 15 March 1996.CrossRefGoogle Scholar
  4. [Boe94]
    L. Boerio. Extending pruning techniques to polymorphic second order λ-calculus. In D. Sanella, editor, Proceedings of ESOP’94, LNCS 788, pages 120–134. Springer-Verlag, April 1994.Google Scholar
  5. [CC77]
    P. Cousot and R. Cousot. Abstract interpretation: A unified lattice model for static analysis of programs by construction or approximation of fixpoints. In Conference Record of the 4th ACM Symposium on Principles of Programming Languages (POPL’ 77 ), pages 238–252, New York, 1977. ACM Press.Google Scholar
  6. [CDDK86]
    D. Clément, J. Despeyroux, T. Desperoux, and G. Kahn. A simple applicative language: Mini-ML. Technical Report 529, INRIA-Sophia Antipolis, May 1986.Google Scholar
  7. [DHM95]
    D. Dussart, F. Henglein, and C. Mossin. Polymorphic recursion and subtype qualifications: Polymorphic binding-time analysis in polynomial time. In Alan Mycroft, editor, SAS’95: 2nd Int’l Static Analysis Symposium, volume 983 of Lecture Notes in Computer Science, pages 118–135, Glasgow, Scotland, September 1995. Springer-Verlag.Google Scholar
  8. [DP98]
    F. Damiani and F. Prost. Detecting and removing dead code using rank-2 intersection. In International Workshop:“TYPES’96”, selected papers, LNCS1512. Spinger-Verlag, 1998.Google Scholar
  9. [GLT89]
    J.-Y. Girard, Y. Lafont, and P. Taylor. Proofs and Types. Cambridge University Press, 1989.Google Scholar
  10. [Hei95]
    N. Heintze. Control-flow analysis and type systems. In Alan Mycroft, editor, Proceeding of SAS 1995, LNCS 983, pages 189–206. Springer-Verlag, 1995.Google Scholar
  11. [HM94]
    C. Hankin and D. Le Métayer. A type-based framework for program analysis. In Proceedings of the Static Analysis Symposium, LNCS 864, pages 380–394. Springer-Verlag, 1994.Google Scholar
  12. [Hun91]
    S. Hunt. Abstract Interpretation of functionnal languages: from theory to Practice. PhD thesis, Department of Computing, Imperial College, London, 1991.Google Scholar
  13. [LP92]
    Z. Luo and R. Pollack. Lego proof development system: User’s manual. Technical Report ECS-LFCS-92-211, University of Edinburgh., 1992.Google Scholar
  14. [Mit90]
    J.C. Mitchell. A type inference approach to reduction properties and semantics of polymorphic expressions. In G. Huet, editor, Logical Foundations of Functionnal programming, pages 195–211. Addison-Wesley, 1990. (Chapter 9).Google Scholar
  15. [NSN94]
    H.R. Nielson, K.L. Solberg, and F. Nielson. Strictness and totality analysis. In Static Analysis, LNCS 864, pages 408–422. Springer-Verlag, 1994.Google Scholar
  16. [Pau89]
    C. Paulin. Extraction de programmes dans le calcul des constructions. PhD thesis, Université Paris 7, January 1989.Google Scholar
  17. [PM89]
    C. Paulin-Mohring. Extracting Fω’s programs from proofs in the Calculus of Constructions. In Sixteenth Annual ACM Symposium on Principles of Programming Languages, Austin, January 1989. ACM.Google Scholar
  18. [Pro97]
    F. Prost. Using ML type inference for dead code analysis. Research Report RR 97-09, LIP, ENS Lyon, France, May 1997.Google Scholar
  19. [Sol95]
    K. Lackner Solberg. Annotated Type Systems for Program Analysis. PhD thesis, Odense University, July 1995.Google Scholar
  20. [TJ92]
    J.-P. Talpin and P. Jouvelot. The type and effect discipline. In IEEE Computer Society Press, editor, Proceedings of the 1992 Conference on Logic in Computer Science, 1992.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Frédéric Prost
    • 1
  1. 1.LIP, Ecole Normale Supérieure de Lyon46 Allée d’ItalieLyon Cedex 07France

Personalised recommendations