Abstract
In [8] J. Laird has shown that an infinitary sequential extension of PCF has a fully abstract model in his category of locally boolean domains (introduced in [10] ). In this paper we introduce an extension SPCF ∞ of his language by recursive types and show that it is universal for its model in locally boolean domains.
Finally we consider an infinitary target language CPS ∞ for (the) CPS translation (of[18] ) and show that it is universal for a model in locally boolean domains which is constructed like Dana Scott’s D ∞ where \(D = \{\bot,\top\}\).
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
Abramsky, S., Jagadeesan, R., Malacaria, P.: Full abstraction for PCF. Inf. Comput. 163(2), 409–470 (2000)
Amadio, R.M., Curien, P.-L.: Domains and lambda-calculi. Cambridge University Press, New York (1998)
Asperti, A.: Stability and computability in coherent domains. Inf. Comput. 86(2), 115–139 (1990)
Barendregt, H.P.: The Lambda Calculus - its syntax and semantics. North-Holland, Amsterdam (1981) (1984)
Cartwright, R., Curien, P.-L., Felleisen, M.: Fully abstract models of observably sequential languages. Information and Computation 111(2), 297–401 (1994)
Harmer, R., McCusker, G.: A fully abstract game semantics for finite nondeterminism. In: LICS, pp. 422–430 (1999)
Hyland, J.M.E., Ong, C.-H.L.: On full abstraction for PCF: I. models, observables and the full abstraction problem, ii. dialogue games and innocent strategies, iii. a fully abstract and universal game model. Information and Computation 163, 285–408 (2000)
Laird, J.: Bistable biorders: a sequential domain theory (submitted, 2005)
Laird, J.: A semantic analysis of control. PhD thesis, University of Edinburgh (1998)
Laird, J.: Locally boolean domains. Theoretical Computer Science 342, 132–148 (2005)
Loader, R.: Finitary PCF is not decidable. Theor. Comput. Sci. 266(1-2), 341–364 (2001)
Longley, J.: The sequentially realizable functionals. Ann. Pure Appl. Logic 117(1-3), 1–93 (2002)
Löw, T.: Locally Boolean Domains and Curien-Lamarche Games. PhD thesis, Technical University of Darmstadt (in prepration, 2006), preliminary version available from: http://www.mathematik.tu-darmstadt.de/~loew/lbdclg.pdf
Maurel, F.: Un cadre quantitatif pour la Ludique. PhD thesis, Université Paris 7, Paris (2004)
O’Hearn, P.W., Riecke, J.G.: Kripke logical relations and PCF. Information and Computation 120(1), 107–116 (1995)
Pitts, A.M.: Relational properties of domains. Information and Computation 127(2), 66–90 (1996)
Plotkin, G.D.: Lectures on predomains and partial functions. Course notes, Center for the Study of Language and Information, Stanford (1985)
Reus, B., Streicher, T.: Classical logic, continuation semantics and abstract machines. J. Funct. Prog. 8(6), 543–572 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Löw, T., Streicher, T. (2006). Universality Results for Models in Locally Boolean Domains. In: Ésik, Z. (eds) Computer Science Logic. CSL 2006. Lecture Notes in Computer Science, vol 4207. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11874683_30
Download citation
DOI: https://doi.org/10.1007/11874683_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-45458-8
Online ISBN: 978-3-540-45459-5
eBook Packages: Computer ScienceComputer Science (R0)