Abstract
The purpose of this paper is twofold: First, we show in which way the initial solution of a domain equation for cpo's and the unique solution of a corresponding domain equation for metric spaces are related. Second, we present a technique to lift a given domain equation for cpo's to a corresponding domain equation for metric spaces.
Similar content being viewed by others
References
Abramsky, S.: A Domain Equation for Bisimulation,Information and Computation 92, pp 161–218, 1991.
Abramsky, S. and Jung, A.: Domain Theory, in S. Abramsky, D.M. Gabbay and T.S.E. Maibaum, editors,Handbook of Logic in Computer Science, Vol. 3, pp 1–168, Clarendon Press, 1994.
America, P. and Bakker, J. W. de: Designing Equivalent Semantic Models for Process Creation,Theoretical Computer Science 60, pp 109–176, 1988.
America, P., Bakker, J. W. de, Kok, J. N. and Rutten, J. J. M. M.: Denotational Semantics of a Parallel Object-Oriented Language,Information and Computation 83 (2), pp 152–205, 1989.
America, P. and Rutten, J. J. M. M.: Solving Recursive Domain Equations in a Category of Complete Metric Spaces,Journal of Computer and System Sciences 39 (3), pp 343–375, 1989.
Baier, C. and Majster-Cederbaum, M. E.: Denotational Semantics in the CPO and Metric Approach,Theoretical Computer Science 35, pp 171–220, 1994.
Baier, C. and Majster-Cederbaum, M. E.: How to Interpret and Establish Consistency Results for Semantics of Concurrent Programming Languages,Fundamanta Informaticae 29 (3), pp 225–256, 1997.
Baier, C. and Majster-Cederbaum, M. E.: Metric Semantics from Partial Order Semantics, to appear inActa Informatica, Vol. 34, 1997.
Bakker, J. W. de and Zucker, J. I.: Processes and the Denotational Semantics of Concurrency,Information and Control 54, No. 1/2, pp 70–120, 1982.
Bruce, K. and Mitchell, J. C.: PER Models of Subtyping, Recursive Types and Higherorder Polymorphism, Proc. POPL'92, pp 316–327, 1992.
Dugundji, J.: Topology, Allyn and Bacon, inc., Boston, 1966.
Edalat, A. and Smyth, M. B.: Compact Metric Information Systems, Proc. REX Workshop'92, Lecture Notes in Computer Science 666, pp 154–173, 1993.
Ehrig, H., Parisi-Presicce, F., Boehm, P., Rieckhoff, C., Dimitrovici, C. and GroßeRohde, M.: Combining Data Type Specifications using Projection Algebras,Theoretical Computer Science 71, pp 347–380, 1990.
Majster-Cederbaum, M. and Zetzsche, F.: Towards a Foundation for Semantics in Complete Metric Spaces,Information and Computation 90 (2), pp 217–243, 1991.
Rutten, J. J. M. M. and Turi, D.: On the Foundations of Final Semantics: NonStandard Sets, Metric Spaces and Partial Orders, Proc. REX Workshop'92, Lecture Notes in Computer Science 666, pp 477–530, 1993.
Rutten, J. J. M. M.: Elements of generalized ultrametric domain theory, Techn. Report, CS-R9507, CWI, 1995.
Scott, D. S.: Continuous lattices, in E. Lawvere, editor, Toposes, Algebraic Geometry and Logic, Lecture Notes in Mathematics 274, pp 97–136, 1972.
Smyth, M. B. and Plotkin, G. D.: The Category-Theoretic Solution of Recursive Equations, SIAMJ. Comput. 11, pp 761–783, 1982.
Stoltenberg-Hansen, V., Lindström, I. and Griffor, E. R.: Mathematical Theory of Domains, Cambridge University Press, 1994.
Stoltenberg-Hansen, V. and Tucker, J.: Algebraic and Fixed Point Equations over Inverse Limits of Algebras,Theoretical Computer Science 87, pp 1–24, 1991.
Wagner, K. R.: Solving Recursive Domain Equations with Enriched Categories, Ph. D. Thesis, Carnegie Mellon University, Techn. Report CMU-94-159, 1994.
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Baier, C., Majster-Cederbaum, M. The connection between initial and unique solutions of domain equations in the partial order and metric approach. Formal Aspects of Computing 9, 425–445 (1997). https://doi.org/10.1007/BF01211300
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01211300