Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
Cancel
×
×
Home
  • Home
Article
  • Cited by 10
  • Cited by
    Crossref Citations
    Crossref logo
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Kammar, Ohad Levy, Paul B. Moss, Sean K. and Staton, Sam 2017. A monad for full ground reference cells. p. 1.
    Birkedal, Lars Jaber, Guilhem Sieczkowski, Filip and Thamsborg, Jacob 2016. A Kripke logical relation for effect-based program transformations. Information and Computation, Vol. 249, Issue. , p. 160.
    Brunel, Aloïs and Gaboardi, Marco 2015. Realizability models for a linear dependent PCF. Theoretical Computer Science, Vol. 585, Issue. , p. 55.
    POTTIER, FRANÇOIS 2013. Syntactic soundness proof of a type-and-capability system with hidden state. Journal of Functional Programming, Vol. 23, Issue. 01, p. 38.
    Charlton, Nathaniel and Reus, Bernhard 2013. Specification patterns for reasoning about recursion through the store. Information and Computation, Vol. 231, Issue. , p. 167.
    Tzevelekos, Nikos 2012. Program equivalence in a simple language with state. Computer Languages, Systems & Structures, Vol. 38, Issue. 2, p. 181.
    Murawski, Andrzej S. and Tzevelekos, Nikos 2011. Game Semantics for Good General References. p. 75.
    Birkedal, Lars Mogelberg, Rasmus Ejlers Schwinghammer, Jan and Stovring, Kristian 2011. First Steps in Synthetic Guarded Domain Theory: Step-Indexing in the Topos of Trees. p. 55.
    Buisse, Alexandre Birkedal, Lars and Støvring, Kristian 2011. Step-Indexed Kripke Model of Separation Logic for Storable Locks. Electronic Notes in Theoretical Computer Science, Vol. 276, Issue. , p. 121.
    Svendsen, Kasper Birkedal, Lars and Nanevski, Aleksandar 2011. Typed Lambda Calculi and Applications. Vol. 6690, Issue. , p. 198.
    ×

  • Get access
    Add to cart USD35.00
    Check if you have access via personal or institutional login
    Log in Register

Realisability semantics of parametric polymorphism, general references and recursive types

  • LARS BIRKEDAL (a1), KRISTIAN STØVRING (a1) and JACOB THAMSBORG (a1)
Abstract

We present a realisability model for a call-by-value, higher-order programming language with parametric polymorphism, general first-class references, and recursive types. The main novelty is a relational interpretation of open types that include general reference types. The interpretation uses a new approach to modelling references.

The universe of semantic types consists of world-indexed families of logical relations over a universal predomain. In order to model general reference types, worlds are finite maps from locations to semantic types: this introduces a circularity between semantic types and worlds that precludes a direct definition of either. Our solution is to solve a recursive equation in an appropriate category of metric spaces. In effect, types are interpreted using a Kripke logical relation over a recursively defined set of worlds.

We illustrate how the model can be used to prove simple equivalences between different implementations of imperative abstract data types.

Copyright
COPYRIGHT: © Cambridge University Press 2010
References
Hide All
Abadi, M. (2000) Top-top-closed relations and admissibility. Mathematical Structures in Computer Science 10 (3)313–320.
Abadi, M. and Plotkin, G. D. (1990) A per model of polymorphism and recursive types. In: Proceedings of LICS 355–365.
Abramsky, S., Honda, K. and McCusker, G. (1998) A fully abstract game semantics for general references. In: Proceedings of LICS 334–344.
Abramsky, S. and Jagadeesan, R. (2005) A game semantics for generic polymorphism. Annals of Pure and Applied Logic 133 (1–3)3–37.
Ahmed, A. (2004) Semantics of Types for Mutable State, Ph.D. thesis, Princeton University.
Ahmed, A., Dreyer, D. and Rossberg, A. (2009) State-dependent representation independence. In: Proceedings of POPL 340–353.
Amadio, R. M. (1991) Recursion over realizability structures. Information and Computation 91 (1)55–85.
Amadio, R. M. and Curien, P.-L. (1998) Domains and Lambda-Calculi, Cambridge University Press.
America, P. and Rutten, J. J. M. M. (1989) Solving reflexive domain equations in a category of complete metric spaces. J. Comput. Syst. Sci. 39 (3)343–375.
Baier, C. and Majster-Cederbaum, M. E. (1997) The connection between initial and unique solutions of domain equations in the partial order and metric approach. Formal Aspects of Computing 9 (4)425–445.
Benton, N. and Hur, C.-K. (2009) Biorthogonality, step-indexing and compiler correctness. In: Proceedings of ICFP 97–108.
Benton, N. and Leperchey, B. (2005) Relational reasoning in a nominal semantics for storage. In: Proceedings of TLCA. Springer-Verlag Lecture Notes in Computer Science 3461 86–101.
Birkedal, L., Reus, B., Schwinghammer, J., Støvring, K., Thamsborg, J. and Yang, H. (2010a) Step-indexed kripke models over recursive worlds. Submitted for publication. Available at http://www.itu.dk/people/birkedal/papers/step-recworld-conf.pdf.
Birkedal, L., Støvring, K. and Thamsborg, J. (2009) Relational parametricity for references and recursive types. In: Proceedings of TLDI 91–104.
Birkedal, L., Støvring, K. and Thamsborg, J. (2010b) A relational realizability model for higher-order stateful ADTs. Submitted for publication. Available at http://www.itu.dk/people/birkedal/papers/relrmhoadt.pdf.
Bohr, N. and Birkedal, L. (2006) Relational reasoning for recursive types and references. In: Proceedings of APLAS. Springer-Verlag Lecture Notes in Computer Science 4279 79–96.
Cardone, F. (1989) Relational semantics for recursive types and bounded quantification. In: Proceedings of ICALP. Springer-Verlag Lecture Notes in Computer Science 372 164–178.
Crary, K. and Harper, R. (2007) Syntactic logical relations for polymorphic and recursive types. Electronic Notes in Theoretical Computer Science 172 259–299.
Laird, J. (2007) A fully abstract trace semantics for general references. In: Proceedings of ICALP. Springer-Verlag Lecture Notes in Computer Science 4596 667–679.
Levy, P. B. (2006) Call-by-push-value: Decomposing call-by-value and call-by-name. Higher-Order and Symbolic Computation 19 (4)377–414.
MacQueen, D. B., Plotkin, G. D. and Sethi, R. (1986) An ideal model for recursive polymorphic types. Information and Control 71 (1/2)95–130.
McCusker, G. (2000) Games and full abstraction for FPC. Information and Computation 160 (1–2)1–61.
Moggi, E. (1991) Notions of computation and monads. Information and Computation 93 55–92.
Petersen, R. L., Birkedal, L., Nanevski, A. and Morrisett, G. (2008) A realizability model for impredicative Hoare type theory. In: Proceedings of ESOP. Springer-Verlag Lecture Notes in Computer Science 4960 337–352.
Pierce, B. C. (2002) Types and Programming Languages, The MIT Press.
Pitts, A. M. (1996) Relational properties of domains. Information and Computation 127 66–90.
Pitts, A. M. (1998) Existential types: Logical relations and operational equivalence. In: Proceedings of ICALP. Springer-Verlag Lecture Notes in Computer Science 1443 309–326.
Plotkin, G. D. and Power, J. (2004) Computational effects and operations: An overview. Electronic Notes in Theoretical Computer Science 73 149–163.
Schwinghammer, J., Birkedal, L., Reus, B. and Yang, H. (2009) Nested Hoare triples and frame rules for higher-order store. In: Proceedings of CSL. Springer-Verlag Lecture Notes in Computer Science 5771 440–454.
Schwinghammer, J., Yang, H., Birkedal, L., Pottier, F. and Reus, B. (2010) A semantic foundation for hidden state. In: Proceedings of FOSSACS. Springer-Verlag Lecture Notes in Computer Science 6014 2–17.
Smyth, M. B. (1992) Topology. In: Abramsky, S., Gabbay, D. and Maibaum, T. S. E. (eds.) Handbook of Logic in Computer Science, Oxford University Press.
Smyth, M. B. and Plotkin, G. D. (1982) The category-theoretic solution of recursive domain equations. SIAM Journal on Computing 11 (4)761–783.
Wagner, K. R. (1994) Solving Recursive Domain Equations with Enriched Categories, Ph.D. thesis, Carnegie Mellon University.
Winskel, G. (1993) The Formal Semantics of Programming Languages, Foundation of Computing Series, The MIT Press.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

CAPTCHA *

Skip to the audio challenge
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed

Cancel
Confirm
×