Deadlock Sensitive Types for Lambda Calculus with Resources

  • Carolina Lavatelli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1530)


We define a new type system for lambda calculi with resources which characterizes the flat operational semantics that distinguishes deadlock from divergence. The system follows the intersection style but with a special management of structural rules. The novel feature in comparison with previous works is the introduction of a controlled form of weakening that allows to deal with deadlock. To show the adequacy result we apply the realizability technique on a decorated calculus where the resources to be consumed are explicitly indicated.


Type System Operational Semantic Structural Rule Sequent Calculus Convergence Testing 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abramsky, S., Ong, L.: Full Abstraction in the lazy lambda calculus. Information and Computation 105(2) (1993)Google Scholar
  2. 2.
    Boudol, G.: The lambda calculus with multiplicities. Rapport de Recherche 2025, INRIA Sophia-Antipolis (1993)Google Scholar
  3. 3.
    Boudol, G.: Typing the use of resources in a Concurrent Calculus. In: Shyamasundar, R.K. (ed.) ASIAN 1997. LNCS, vol. 1345, Springer, Heidelberg (1997)Google Scholar
  4. 4.
    Boudol, G., Laneve, C.: The discriminating power of multiplicities in the λ-calculus. Information and Computation 126(1) (1996)Google Scholar
  5. 5.
    Boudol, G., Laneve, C.: Termination, deadlock and divergence in the λ-calculus with multiplicities. In: Proc. 11th Mathematical Foundations of Programming Semantics Conference. Electronic Notes in Computer Science (1995)Google Scholar
  6. 6.
    Boudol, G., Laneve, C.: λ-Calculus, Multiplicities and the π-Calculus. Rapport de Recherche 2581, INRIA Sophia-Antipolis (1995)Google Scholar
  7. 7.
    Boudol, G., Lavatelli, C.: Full Abstraction for lambda-calculus with resources and convergence testing. In: Kirchner, H. (ed.) CAAP 1996. LNCS, vol. 1059. Springer, Heidelberg (1996)Google Scholar
  8. 8.
    Kobayashi, N.: A partially deadlock-free types process calculus. In: Proceedings of LICS 1997 (1997)Google Scholar
  9. 9.
    Lavatelli, C.: Sémantique du Lambda Calcul avec Ressources. Thèse de Doctorat. Université Paris VII, France (1996)Google Scholar
  10. 10.
    Lavatelli, C.: Algebraic Interpretation of the Lambda Calculus with Resources. In: Sassone, V., Montanari, U. (eds.) CONCUR 1996. LNCS, vol. 1119. Springer, Heidelberg (1996)Google Scholar
  11. 11.
    Lévy, J.-J.: An algebraic interpretation of the λβK-calculus; and an application of a labeled λ-calculus. Theoretical Computer Science 2(1) (1976)Google Scholar
  12. 12.
    Longo, G.: Set Theoretical Models of Lambda Calculus: Theories, expansions and isomorphisms. Annals of Pure and Applied Logic 24 (1983)Google Scholar
  13. 13.
    Milner, R., Parrow, J., Walker, D.: A Calculus of Mobile Processes, Parts I and II. Information and Computation 100(1) (1992)Google Scholar
  14. 14.
    Milner, R.: Functions as Processes. Mathematical Structures in Computer Science 2 (1992)Google Scholar
  15. 15.
    Luke Ong, C.-H.: Fully Abstract Models of the Lazy Lambda Calculus. In: Proceedings of the 29th Conference on Foundations of Computer Science. The Computer Science Press, Rockville (1988)Google Scholar
  16. 16.
    Sangiorgi, D.: The Lazy Lambda Calculus in a Concurrency Scenario. Information and Computation 120(1) (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Carolina Lavatelli
    • 1
  1. 1.INRIA Domaine de Voluceau-RocquencourtLe ChesnayFrance

Personalised recommendations