Skip to main content
SpringerLink
Log in

A λ-Calculus for Resource Separation

  • Conference paper
Automata, Languages and Programming (ICALP 2004)

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

Included in the following conference series:

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 239.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Areces, C., Blackburn, P.: Bringing them all together. Logic and Computation 11(5) (2001); Editorial of special issue on Hybrid Logics

    Google Scholar 

  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. 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. 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)

    Chapter  Google Scholar 

  5. Hofmann, M.: A type system for bounded space and functional in-place update. Nordic Journal of Computing 7(4), 258–289 (2000)

    MATH  MathSciNet  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  8. Lane, S.M.: Categories for the Working Mathematician, 2nd edn. Springer, Heidelberg (1998)

    MATH  Google Scholar 

  9. O’Hearn, P.W.: On bunched typing. Journal of Functional Programming 13(4), 747–796 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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. Pym, D.J.: The Semantics and Proof Theory of the Logic of Bunched Implications. Applied Logic Series, vol. 26. Kluwer Academic Publishers, Dordrecht (2002)

    MATH  Google Scholar 

  13. Reddy, U.: A linear logic model of state (October 1993), Electronic manuscript http://www.cs.bham.ac.uk/~udr/

  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. 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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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 Security

    Article  Google Scholar 

  18. Valdes, J., Tarjan, R.E., Lawler, E.L.: The recognition of series-parallel digraphs. SIAM Journal of Computing 11(2), 298–313 (1982)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LFCS, School of Informatics, University of Edinburgh, Mayfield Rd, Edinburgh, EH9 3JZ, UK

    Robert Atkey

Authors
  1. Robert Atkey
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Departament de Llenguatges i Sistemes Informatics, Universitat Politecnica de Catalunya, Campus Nord - Ed. Omega, 240 Jordi Girona Salgado, 1-3 E-08034, Barcelona

    Josep Díaz

  2. Department of Mathematics and Turku Centre for Computer Science TUCS, University of Turku, 20014, Turku, Finland

    Juhani Karhumäki

  3. Department of Mathematics, University of Turku, Turku, Finland

    Arto Lepistö

  4. Laboratory for Foundations of Computer Science, University of Edinburgh,  

    Donald Sannella

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Atkey, R. (2004). A λ-Calculus for Resource Separation. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds) Automata, Languages and Programming. ICALP 2004. Lecture Notes in Computer Science, vol 3142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27836-8_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-27836-8_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22849-3

  • Online ISBN: 978-3-540-27836-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation