Abstract
We give a simple order-theoretic construction of a cartesian closed category of sequential functions. It is based on biordered sets analogous to Berry’s bidomains, except that the stable order is replaced with a new notion, the bistable order, and instead of preserving stably bounded greatest lower bounds, functions are required to preserve bistably bounded least upper bounds and greatest lower bounds. We show that bistable cpos and bistable and continuous functions form a CCC, yielding models of functional languages such as the simply-typed λ-calculus and SPCF. We show that these models are strongly sequential and use this fact to prove universality and full abstraction results.
This is a preview of subscription content, log in via an institution to check access.
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
Berry, G.: Stable models of typed λ-calculi. In: Ausiello, G., Böhm, C. (eds.) ICALP 1978. LNCS, vol. 62, pp. 72–89. Springer, Heidelberg (1978)
Bucciarelli, A., Ehrhard, T.: A theory of sequentiality. Theoretical Computer Science 113, 273–292 (1993)
Cartwright, R., Felleisen, M.: Observable sequentiality and full abstraction. In: Proceedings of POPL 1992 (1992)
Cartwright, R., Curien, P.-L., Felleisen, M.: Fully abstract semantics for observably sequential languages. Information and Computation (1994)
Curien, P.-L.: On the symmetry of sequentiality. In: Main, M.G., Melton, A.C., Mislove, M.W., Schmidt, D., Brookes, S.D. (eds.) MFPS 1993. LNCS, vol. 802, Springer, Heidelberg (1994)
Curien, P.-L.: Sequential algorithms as bistable maps (2002) (unpublished note)
Hyland, M., Schalk, A.: Games on graphs and sequentially realizable functionals. In: Proceedings of LICS 2002, IEEE, Los Alamitos (2002)
Kahn, G., Plotkin, G.: Concrete domains. Theoretical Computer Science, Böhm Festschrift special issue (1993); First appeared as technical report 338 of INRIALABORIA (1978)
Laird, J.: A fully abstract and effectively presentable model of unary FPC. To appear in the Proceedings of TLCA 2003 (2003)
Lamarche, F.: Sequentiality, games and linear logic. In: Proceedings, CLICS workshop, Aarhus University. DAIMI-397–II (1992)
Loader, R.: Finitary PCF is undecidable. Annals of Pure and Applied Logic (2000)
Longley, J.: The sequentially realizable functionals. Technical Report ECS-LFCS- 98-402, LFCS, Univ. of Edinburgh (1998)
Padovani, V.: Decidability of all minimal models. In: Berardi, S., Coppo, M. (eds.) TYPES 1995. LNCS, vol. 1158, Springer, Heidelberg (1996)
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
Laird, J. (2003). Bistability: An Extensional Characterization of Sequentiality. 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_30
Download citation
DOI: https://doi.org/10.1007/978-3-540-45220-1_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40801-7
Online ISBN: 978-3-540-45220-1
eBook Packages: Springer Book Archive