Abstract
Pitts and Stark’s nu-calculus is a typed lambda-calculus which forms a basis for the study of interaction between higher-order functions and dynamically created names. A similar approach has received renewed attention recently through Sumii and Pierce’s cryptographic lambda-calculus, which deals with security protocols. Logical relations are a powerful tool to prove properties of such a calculus, notably observational equivalence. While Pitts and Stark construct a logical relation for the nu-calculus, it rests heavily on operational aspects of the calculus and is hard to be extended. We propose an alternative Kripke logical relation for the nu-calculus, which is derived naturally from the categorical model of the nu-calculus and the general notion of Kripke logical relation. This is also related to the Kripke logical relation for the name creation monad by Goubault-Larrecq et al. (CSL’2002), which the authors claimed had similarities with Pitts and Stark’s logical relation. We show that their Kripke logical relation for names is strictly weaker than Pitts and Stark’s. We also show that our Kripke logical relation, which extends the definition of Goubault-Larrecq et al., is equivalent to Pitts and Stark’s up to first-order types; our definition rests on purely semantic constituents, and dispenses with the detours through operational semantics that Pitts and Stark use.
Keywords
Partially supported by the RNTL project EVA, the ACI jeunes chercheurs “Sécurité informatique, protocoles cryptographiques et détection d’intrusions” and the ACI Cryptologie “PSI-Robuste”.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alimohamed, M.: A characterization of lambda definability in categorical models of implicit polymorphism. Theoretical Computer Science 146(1–2), 5–23 (1995)
Beck, J.: Distributive laws. In: Seminar on Triples and Categorical Homology Theory. Lecture Notes in Mathematics, vol. 80, pp. 119–140. Springer, Heidelberg (1969)
Goubault-Larrecq, J., Lasota, S., Nowak, D.: Logical relations for monadic types. In: Bradfield, J.C. (ed.) CSL 2002 and EACSL 2002. LNCS, vol. 2471, pp. 553–568. Springer, Heidelberg (2002)
Lambek, J., Scott, P.J.: Introduction to Higher Order Categorical Logic. Cambridge studies in advanced mathematics. Cambridge University Press, Cambridge (1986)
Mitchell, J.C.: Foundations of Programming Languages. MIT Press, Cambridge (1996)
Mitchell, J.C., Moggi, E.: Kripke-style models for typed lambda calculus. In: LICS 1987, pp. 303–314. IEEE Computer Society Press, Los Alamitos (1987)
Mitchell, J.C., Scedrov, A.: Notes on sconing and relators. In: Martini, S., Börger, E., Kleine Büning, H., Jäger, G., Richter, M.M. (eds.) CSL 1992. LNCS, vol. 702, pp. 352–378. Springer, Heidelberg (1993)
Moggi, E.: Computational lambda-calculus and monads. In: LICS 1989, pp. 14–23. IEEE Computer Society Press, Los Alamitos (1989)
Moggi, E.: An abstract view of programming languages. Technical Report ECS-LFCS-90-113, LFCS, Department of Computer Science, University of Edinburgh (1990)
Moggi, E.: Notions of computation and monads. Information and Computation 93, 55–92 (1991)
Pitts, A., Stark, I.: Observable properties of higher order functions that dynamically create local names, or: What’s new? In: Borzyszkowski, A.M., Sokolowski, S. (eds.) MFCS 1993. LNCS, vol. 711, pp. 122–141. Springer, Heidelberg (1993)
Stark, I.: Names and Higher-Order Functions. PhD thesis, University of Cambridge (1994)
Stark, I.: Categorical models for local names. Lisp and Symbolic Computation 9(1), 77–107 (1996)
Stark, I.: Names, equations, relations: Practical ways to reason about new. Fundamenta Informaticae 33(4), 369–396 (1998)
Sumii, E., Pierce, B.: Logical relations for encryption. In: CSFW 2001, pp. 256–272. IEEE Computer Society Press, Los Alamitos (2001)
Zhang, Y.: Logical relations for names. Master’s thesis, University of Paris 7 (2002), http://www.lsv.ens-cachan.fr/Publis/PAPERS/ZY-dea02.ps
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhang, Y., Nowak, D. (2003). Logical Relations for Dynamic Name Creation. In: Baaz, M., Makowsky, J.A. (eds) Computer Science Logic. CSL 2003. Lecture Notes in Computer Science, vol 2803. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45220-1_48
Download citation
DOI: https://doi.org/10.1007/978-3-540-45220-1_48
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40801-7
Online ISBN: 978-3-540-45220-1
eBook Packages: Springer Book Archive