A λ-Calculus for Resource Separation

  • Robert Atkey
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3142)

Abstract

We present a typed λ-calculus for recording resource separation constraints between terms. The calculus contains a novel way of manipulating nested multi-place contexts augmented with constraints, allowing a concise presentation of the typing rules. It is an extension of the affine αλ-calculus. We give a semantics based on sets indexed by resources, and show how the calculus may be extended to handle non-symmetric relations with application to allowable information flow. Finally, we mention some future directions and questions we have about the calculus.

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References

  1. 1.
    Areces, C., Blackburn, P.: Bringing them all together. Logic and Computation 11(5) (2001); Editorial of special issue on Hybrid LogicsGoogle Scholar
  2. 2.
    Bechet, D., de Groote, P., Retoré, C.: A complete axiomatisation for the inclusion of series-parallel partial orders. In: Comon, H. (ed.) RTA 1997. LNCS, vol. 1232, pp. 230–240. Springer, Heidelberg (1997)Google Scholar
  3. 3.
    da, M., Corrêa, S., Haeusler, E.H., de Paiva, V.C.V.: A dialectica model of state. In: CATS 1996, Computing: The Australian Theory Symposium Proceedings (January 1996)Google Scholar
  4. 4.
    Day, B.J.: On closed categories of functors. In: Mac Lane, S. (ed.) Reports of the Midwest Category Seminar. Lecture Notes in Mathematics, vol. 137, pp. 1–38. Springer, Heidelberg (1970)CrossRefGoogle Scholar
  5. 5.
    Hofmann, M.: A type system for bounded space and functional in-place update. Nordic Journal of Computing 7(4), 258–289 (2000)MATHMathSciNetGoogle Scholar
  6. 6.
    Hofmann, M., Jost, S.: Static prediction of heap space usage for firstorder functional programs. In: Proceedings of the 30th ACM SIGPLAN-SIGACT symposium on Principles of Programming Languages, pp. 185–197. ACM Press, New York (2003)CrossRefGoogle Scholar
  7. 7.
    Konečný, M.: Functional in-place update with layered datatype sharing. In: Hofmann, M.O. (ed.) TLCA 2003. LNCS, vol. 2701, pp. 195–210. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Lane, S.M.: Categories for the Working Mathematician, 2nd edn. Springer, Heidelberg (1998)MATHGoogle Scholar
  9. 9.
    O’Hearn, P.W.: On bunched typing. Journal of Functional Programming 13(4), 747–796 (2003)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    O’Hearn, P.W., Power, A.J., Takeyama, M., Tennent, R.D.: Syntactic control of interference revisited. Theoretical Computer Science 228, 211–252 (1999)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Petersen, L., Harper, R., Crary, K., Pfenning, F.: A type theory for memory allocation and data layout. In: Morrisett, G. (ed.) Conference Record of the 30th Annual Symposium on Principles of Programming Languages (POPL 2003), January 2003, pp. 172–184. ACM Press, New York (2003)Google Scholar
  12. 12.
    Pym, D.J.: The Semantics and Proof Theory of the Logic of Bunched Implications. Applied Logic Series, vol. 26. Kluwer Academic Publishers, Dordrecht (2002)MATHGoogle Scholar
  13. 13.
    Reddy, U.: A linear logic model of state (October 1993), Electronic manuscript http://www.cs.bham.ac.uk/~udr/
  14. 14.
    Retoré, C.: Pomset logic: a non-commutative extension of classical linear logic. In: de Groote, P., Hindley, J.R. (eds.) TLCA 1997. LNCS, vol. 1210, pp. 300–318. Springer, Heidelberg (1997)Google Scholar
  15. 15.
    Reynolds, J.C.: Syntactic control of interference. In: Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of Programming Languages, pp. 39–46. ACM Press, New York (1978)CrossRefGoogle Scholar
  16. 16.
    Reynolds, J.C.: Syntactic control of interference, part 2. In: Ronchi Della Rocca, S., Ausiello, G., Dezani-Ciancaglini, M. (eds.) ICALP 1989. LNCS, vol. 372, pp. 704–722. Springer, Heidelberg (1989)CrossRefGoogle Scholar
  17. 17.
    Sabelfeld, A., Myers, A.C.: Language-based information-flow security. IEEE Journal on Selected Areas in Communications 21(1), 5–19 (2003); Special issue on Formal Methods for SecurityCrossRefGoogle Scholar
  18. 18.
    Valdes, J., Tarjan, R.E., Lawler, E.L.: The recognition of series-parallel digraphs. SIAM Journal of Computing 11(2), 298–313 (1982)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Robert Atkey
    • 1
  1. 1.LFCS, School of InformaticsUniversity of EdinburghEdinburghUK

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