Abstract
In this paper we investigate the problem of “partializing” Stone spaces by “Sequence of Finite Posets” (SFP) domains. More specifically, we introduce a suitable subcategory SFP m of SFP which is naturally related to the special category of Stone spaces 2-Stone by the functor MAX, which associates to each object of SFPm the space of its maximal elements. The category SFP m is closed under limits as well as many domain constructors, such as lifting, sum, product and Plotkin powerdomain. The functor MAX preserves limits and commutes with these constructors. Thus, SFP domains which “partialize” solutions of a vast class of domain equations in 2-Stone, can be obtained by solving the corresponding equations in SFP m. Furthermore, we compare two classical partializations of the space of Milner's Synchronization Trees using SFP domains (see [3], [15]). Using the notion of “rigid” embedding projection pair, we show that the two domains are not isomorphic, thus providing a negative answer to an open problem raised in [15].
Partially supported by EC HCM project Lambda Calcul Typé, CHRX-CT92.0046.
Chapter PDF
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Samson Abramsky. Total vs. partial object and fixed points of functors. Unpublished Manuscript, 1985.
Samson Abramsky. A Cook's tour of the finitary non-well-founded sets. Talk delivered at BTCS Colloquium, 1988.
Samson Abramsky. A domain equation for bisimulation. Information and Computation, 92(2):161–218, 1991.
Samson Abramsky. Domain theory in logical form. Annals of Pure and Applied Logic, 51:1–77, 1991.
F. Alessi, P. Baldan and F. Honsell. Partializing Stone Spaces using SFP domains. Technical Report. University of Udine.
F. Alessi and M. Lenisa. Stone duality for trees of balls. Talk delivered at MASK workshop, Koblenz, 1993.
P. Baldan. A fixed point theorem for the solution of domain equations in a category of trees. Tesi di Laurea, Udine 1994.
J.W. de Bakker and E. de Vink. Control Flow Semantics. MIT Press, 1996.
J.W. de Bakker and J.I. Zucker. Processes and the denotational semantics of concurrency. Information and Control, 54(1/2):70–120, 1982.
P. Di Gianantonio. Real number computability and domain theory. Information and Computation, 127(1):11–25, 1996.
J. Dugundji. Topology. Allyn and Bacon, 1966.
A. Edalat and R. Heckmann. A computational model for metric spaces. 1996, to appear.
M. Forti, F. Honsell, and M. Lenisa. Processes and hyperuniverses. MFCS '93, LNCS 841:352–367, 1994.
M.E. Majster-Cederbaum and F. Zetzsche. Towards a foundations for semantics in complete metric spaces. Information and Computation, 90:217–243, 1991.
M.W. Mislove, L.S. Moss, and F.J. Oles. Non-well-founded sets modeled as ideal fixed points. Information and Computation, 93(1):16–54, 1991.
Gordon D. Plotkin. A powerdomain construction. SIAM Journal on Computing, 5(3):452–487, 1976.
Gordon D. Plotkin. Domains. Unpublished Course Notes. University of Edinburgh, 1983.
Marshall H. Stone. The theory of representations for Boolean algebras. Transactions of the American Mathematical Society, 40:37–111, 1936.
K Weihrauch and U. Shreiber. Embedding metric spaces into cpo's. Theoretical Computer Science, 16(1):5–24, 1981.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Alessi, F., Baldan, P., Honsell, F. (1997). Partializing stone spaces using SFP domains. In: Bidoit, M., Dauchet, M. (eds) TAPSOFT '97: Theory and Practice of Software Development. CAAP 1997. Lecture Notes in Computer Science, vol 1214. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030620
Download citation
DOI: https://doi.org/10.1007/BFb0030620
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62781-4
Online ISBN: 978-3-540-68517-3
eBook Packages: Springer Book Archive