Skip to main content
SpringerLink
Log in

A Substructural Type System for Delimited Continuations

  • Conference paper
Book cover Typed Lambda Calculi and Applications (TLCA 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4583))

Included in the following conference series:

Abstract

We propose type systems that abstractly interpret small-step rather than big-step operational semantics. We treat an expression or evaluation context as a structure in a linear logic with hypothetical reasoning. Evaluation order is not only regulated by familiar focusing rules in the operational semantics, but also expressed by structural rules in the type system, so the types track control flow more closely. Binding and evaluation contexts are related, but the latter are linear.

We use these ideas to build a type system for delimited continuations. It lets control operators change the answer type or act beyond the nearest dynamically-enclosing delimiter, yet needs no extra fields in judgments and arrow types to record answer types. The typing derivation of a direct-style program desugars it into continuation-passing style.

Thanks to Olivier Danvy, Andrzej Filinski, Michael Stone, Philip Wadler, and the anonymous referees. The appendices to this paper are online at http://okmij.org/ftp/papers/delim-control-logic.pdf

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Ager, M.S., Biernacki, D., Danvy, O., Midtgaard, J.: A functional correspondence between evaluators and abstract machines. In: Proc. 5th intl. conf. principles & practice of declarative prog. pp. 8–19 (2003)

    Google Scholar 

  2. Ager, M.S., Danvy, O., Midtgaard, J.: A functional correspondence between call-by-need evaluators and lazy abstract machines. Info. Proc. Lett. 90(5), 223–232 (2004)

    Article  MathSciNet  Google Scholar 

  3. Ager, M.S., Danvy, O., Midtgaard, J.: A functional correspondence between monadic evaluators and abstract machines for languages with computational effects. Theor. Comp. Sci. 342(1), 149–172 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  4. Ariola, Z.M., Herbelin, H., Sabry, A.: A type-theoretic foundation of continuations and prompts. In: ICFP, pp. 40–53 (2004)

    Google Scholar 

  5. Atkey, R.: Parameterised notions of computation. In: MSFP 2006. Conor McBride and Tarmo Uustalu. Electronic Workshops in Computing. Electronic Workshops in Computing, British Computer Society, Vancouver (2006)

    Google Scholar 

  6. Balat, V., Danvy, O.: Memoization in type-directed partial evaluation. In: Batory, D., Consel, C., Taha, W. (eds.) GPCE 2002. LNCS, vol. 2487, pp. 78–92. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  7. Balat, V., Di Cosmo, R., Fiore, M.: Extensional normalisation and type-directed partial evaluation for typed lambda calculus with sums. In: POPL, pp. 64–76 (2004)

    Google Scholar 

  8. Barker, C.: Direct compositionality on demand. In: Barker, C., Jacobson, P. (eds.) Direct compositionality, pp. 102–131. Oxford University Press, New York (2007)

    Google Scholar 

  9. Barker, C., Shan, C.-c.: Types as graphs: Continuations in type logical grammar. J. Logic, Lang. & Info. 15(4), 331–370 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  10. Biernacka, M., Biernacki, D., Danvy, O.: An operational foundation for delimited continuations in the CPS hierarchy. Logical Methods in Comp. Sci. 1(2:5) (2005)

    Google Scholar 

  11. Biernacka, M., Danvy, O.: A syntactic correspondence between context-sensitive calculi and abstract machines. Theor. Comp. Sci. 375(1-3), 76–108 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  12. Biernacki, D., Danvy, O.: From interpreter to logic engine by defunctionalization. In: Bruynooghe, M. (ed.) LOPSTR 2003. LNCS, vol. 3018, pp. 143–159. Springer, Heidelberg (2004)

    Google Scholar 

  13. Cousot, P.: Types as abstract interpretations. In POPL, pp. 316–331 (1997)

    Google Scholar 

  14. Cousot, P., Cousot, R.: Abstract interpretation: A unified lattice model for static analysis of programs by construction or approximation of fixpoints. In POPL, pp. 238–252 (1977)

    Google Scholar 

  15. Curien, P.-L., Herbelin, H.: The duality of computation. In: ICFP, pp. 233–243 (2000)

    Google Scholar 

  16. Danvy, O.: Type-directed partial evaluation. In: POPL, pp. 242–257 (1996)

    Google Scholar 

  17. Danvy, O., Filinski, A.: A functional abstraction of typed contexts. Tech. Rep. 89/12, DIKU (1989) http://www.daimi.au.dk/~danvy/Papers/fatc.ps.gz

  18. Danvy, O.: Abstracting control. In: Proc. conf. Lisp & funct. prog. pp. 151–160 (1990)

    Google Scholar 

  19. Danvy, O.: Representing control: A study of the CPS transformation. Math. Structures Comp. Sci. 2(4), 361–391 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  20. Danvy, O., Nielsen, L.R.: Syntactic theories in practice. In: van den Brand, M., Verma, R. (eds.) RULE 2001: 2nd intl. workshop on rule-based prog. Electron. Notes in Theor. Comp. Sci, vol. 59(4), pp. 358–374. Elsevier, Amsterdam (2001)

    Google Scholar 

  21. Danvy, O., Nielsen, L.R.: Refocusing in reduction semantics. Report RS-04-26, BRICS (2004)

    Google Scholar 

  22. Dunfield, J., Pfenning, F.: Tridirectional typechecking. In: POPL, pp. 281–292 (2004)

    Google Scholar 

  23. Dybjer, P., Filinski, A.: Normalization and partial evaluation. In: Barthe, G., Dybjer, P., Pinto, L., Saraiva, J. (eds.) APPSEM 2000. LNCS, vol. 2395, pp. 137–192. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  24. Dybvig, R.K., Peyton Jones, S.L., Sabry, A.: A monadic framework for delimited continuations. Tech. Rep. 615, Indiana U (2005)

    Google Scholar 

  25. Felleisen, M.: The calculi of λ υ -CS conversion: A syntactic theory of control and state in imperative higher-order programming languages. Ph.D. thesis, Indiana U. (1987)

    Google Scholar 

  26. Felleisen, M.: The theory and practice of first-class prompts. In: POPL, pp. 180–190 (1988)

    Google Scholar 

  27. Felleisen, M., Flatt, M.: Programming languages and lambda calculi (2006), http://www.cs.utah.edu/plt/publications/pllc.pdf

  28. Felleisen, M., Friedman, D.P.: Control operators, the SECD machine, and the λ-calculus. In: Wirsing, M. (ed.) Formal description of prog. concepts III, pp. 193–217. Elsevier, Amsterdam (1987)

    Google Scholar 

  29. Filinski, A.: Declarative continuations: An investigation of duality in programming language semantics. In: Pitt, D.H., Rydeheard, D.E., Dybjer, P., Pitts, A.M., Poigné, A. (eds.) Category Theory and Computer Science. LNCS, vol. 389, pp. 224–249. Springer, Heidelberg (1989)

    Chapter  Google Scholar 

  30. Filinski, A.: Representing monads. In: POPL, pp. 446–457 (1994)

    Google Scholar 

  31. Filinski, A.: Controlling effects. Ph.D. thesis, CMU (1996)

    Google Scholar 

  32. Filinski, A.: Representing layered monads. In: POPL, pp. 175–188 (1999)

    Google Scholar 

  33. Filinski, A.: Normalization by evaluation for the computational lambda-calculus. In: Abramsky, S. (ed.) TLCA 2001. LNCS, vol. 2044, pp. 151–165. Springer, Heidelberg (2001)

    Google Scholar 

  34. Gifford, D.K., Lucassen, J.M.: Integrating functional and imperative programming. In: Proc. conf. Lisp & funct. prog. pp. 28–38 (1986)

    Google Scholar 

  35. Graunke, P.T.: Web interactions. Ph.D. thesis, Northeastern U (2003)

    Google Scholar 

  36. Griffin, T.G.: A formulae-as-types notion of control. In: POPL, pp. 47–58 (1990)

    Google Scholar 

  37. Grobauer, B., Yang, Z.: The second Futamura projection for type-directed partial evaluation. Higher-Order & Symbolic Comp. 14(2-3), 173–219 (2001)

    Article  MATH  Google Scholar 

  38. Gunter, C.A., Rémy, D., Riecke, J.G.: A generalization of exceptions and control in ML-like languages. In: Peyton Jones, S.L. (ed.) Funct. prog. lang. & comp. architecture: 7th conf. pp. 12–23 (1995)

    Google Scholar 

  39. Gunter, C.A., Rémy, D., Riecke, J.G.: Return types for functional continuations (1998), http://pauillac.inria.fr/~remy/work/ cupto/

  40. Hieb, R., Dybvig, R.K.: Continuations and concurrency. In: Proc. 2nd symposium on principles & practice of parallel prog. pp. 128–136 (1990)

    Google Scholar 

  41. Huet, G.: The zipper. J. Funct. Prog. 7(5), 549–554 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  42. Kameyama, Y.: Towards logical understanding of delimited continuations. In: Amr, S. (ed.) Proc. 3rd workshop on continuations, pp. 27–33. Tech. Rep. 545, Indiana U (2001)

    Google Scholar 

  43. Kiselyov, O.: How to remove a dynamic prompt: Static and dynamic delimited continuation operators are equally expressible. Tech. Rep. 611, Indiana U (2005)

    Google Scholar 

  44. Kiselyov, O., Shan, C.-c., Friedman, D.P., Sabry, A.: Backtracking, interleaving, and terminating monad transformers (functional pearl). In: ICFP, pp. 192–203 (2005)

    Google Scholar 

  45. Kiselyov, O., Shan, C.-c., Sabry, A.: Delimited dynamic binding. In: ICFP, pp. 26–37 (2006)

    Google Scholar 

  46. Lambek, J.: The mathematics of sentence structure. Amer. Math. Monthly 65(3), 154–170 (1958)

    Article  MATH  MathSciNet  Google Scholar 

  47. Lawall, J.L., Danvy, O.: Continuation-based partial evaluation. In: Proc. conf. Lisp & funct. prog. pp. 227–238 (1994)

    Google Scholar 

  48. Lucassen, J.M.: Types and effects: Towards the integration of functional and imperative programming. Ph.D. thesis, MIT (1987)

    Google Scholar 

  49. Moortgat, M.: Categorial type logics. In: van Benthem, J.F.A.K., ter Meulen, A.G.B. (eds.) Handbook of logic and language, ch. 2, Elsevier, Amsterdam (1997)

    Google Scholar 

  50. Murphy, T., Crary, K., Harper, R.: Distributed control ow with classical modal logic. In: Ong, L. (ed.) CSL 2005. LNCS, vol. 3634, pp. 51–69. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  51. Murthy, C.R.: Control operators, hierarchies, and pseudo-classical type systems: A-translation at work. In: Danvy, O., Talcott, C. (eds.) Proc. workshop on continuations, pp. 49–71 (1992) Tech. Rep. STAN-CS-92-1426, Stanford U.

    Google Scholar 

  52. Polakow, J.: Ordered linear logic and applications. Ph.D. thesis, CMU (2001)

    Google Scholar 

  53. Queinnec, C.: Continuations and web servers. Higher-Order & Symbolic Comp. 17(4), 277–295 (2004)

    Article  Google Scholar 

  54. Restall, G.: An introduction to substructural logics. Routledge, London (2000)

    Google Scholar 

  55. Selinger, P.: Control categories and duality: On the categorical semantics of the lambda-mu calculus. Math. Structures Comp. Sci. 11, 207–260 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  56. Sewell, P., Leifer, J.J., Wansbrough, K., Nardelli, F.Z., Allen-Williams, M., Habouzit, P., Vafeiadis, V.: Acute: High-level programming language design for distributed computation. In: ICFP, pp. 15–26 (2005)

    Google Scholar 

  57. Shan, C.-c.: Shift to control. In: Shivers, O., Waddell, O. (eds.) Proc. Scheme workshop, pp. 99–107, Tech. Rep. 600, Indiana U. (2004)

    Google Scholar 

  58. Shan, C.-c.: Linguistic side effects. Ph.D. thesis, Harvard U. (2005)

    Google Scholar 

  59. Sitaram, D.: Handling control. In: PLDI, pp. 147–155 (1993)

    Google Scholar 

  60. Sumii, E.: An implementation of transparent migration on standard Scheme. In: Felleisen, M. (ed.) Proc. Scheme workshop, pp. 61–63, Tech. Rep. 00-368, Rice U (2000)

    Google Scholar 

  61. Talpin, J.-P., Jouvelot, P.: Polymorphic type, region and effect inference. J. Funct. Prog. 2(3), 245–271 (1992)

    MATH  MathSciNet  Google Scholar 

  62. Talpin, J.-P., Jouvelot, P.: The type and effect discipline. Info. & Comp. 111(2), 245–296 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  63. Thielecke, H.: From control effects to typed continuation passing. In: POPL, pp. 139–149 (2003)

    Google Scholar 

  64. Thiemann, P.: Combinators for program generation. J. Funct. Prog. 9(5), 483–525 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  65. Wadler, P.L.: The marriage of effects and monads. In: ICFP, pp. 63–74 (1998)

    Google Scholar 

  66. Wadler, P.L.: Call-by-value is dual to call-by-name. In: ICFP (2003)

    Google Scholar 

  67. Wand, M., Friedman, D.P.: The mystery of the tower revealed: A non-reflective description of the reflective tower. Lisp & Symbolic Comp. 1(1), 11–37 (1988)

    Article  Google Scholar 

  68. Wright, A.K., Felleisen, M.: A syntactic approach to type soundness. Info. & Comp. 115(1), 38–94 (1994)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. FNMOC,  

    Oleg Kiselyov

  2. Rutgers University,  

    Chung-chieh Shan

Authors
  1. Oleg Kiselyov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chung-chieh Shan
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Simona Ronchi Della Rocca

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer Berlin Heidelberg

About this paper

Cite this paper

Kiselyov, O., Shan, Cc. (2007). A Substructural Type System for Delimited Continuations. In: Della Rocca, S.R. (eds) Typed Lambda Calculi and Applications. TLCA 2007. Lecture Notes in Computer Science, vol 4583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73228-0_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-73228-0_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73227-3

  • Online ISBN: 978-3-540-73228-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation