Abstract
Perhaps the most important and striking fact of domain theory is that important categories of domains are cartesian closed. This means that the category has a terminal object, finite products, and exponents. The only problematic part for domains is the exponent, which in this setting means the space of continuous functions. Cartesian closed categories of domains are well understood and the understanding is in some sense essentially complete by the work of Jung [5], Smyth [11], and others.
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References
S. Abramsky, Domain theory in logical form, Annals of Pure and Applied Logic 51 (1991), 1 - 77.
S. Abramsky and A. Jung, Domain theory, in Handbook of Logic in Computer Science, volume 3, (S. Abramsky, D. Gabbay, and T. S. E. Maibaum, editors), Oxford University Press, Oxford, 1995, 1 - 168.
J. Blanck, Effective domain representation of ???(X), the space of compact subsets, Theoretical Computer Science 219 (1999), 19 - 48.
M. Escardó, PCF extended with real numbers, Theoretical Computer Science 162 (1996), 79 - 115.
A. Jung, Cartesian closed categories of algebraic cpo’s, Theoretical Computer Science 70 (1990), 233–250.
D. Normann, Computability of the partial continuous functionals, Journal of Symbolic Logic 65 (2000), 1133 - 1142.
G. Plotkin, A power domain construction, SIAM Journal on Computing 5 (1976), 452 - 488.
G. Plotkin, LCF considered as a programming language, Theoretical Computer Science 5 (1977), 223 - 255.
G. Plotkin, Full abstraction, totality and PCF, Mathematical Structures in Computer Science 9 (1999), 1 - 20.
M. B. Smyth, Effectively given domains, Theoretical Computer Science 5 (1977), 257 - 274.
M. B. Smyth, The largest cartesian closed category of domains, Theoretical Computer Science 27 (1983), 109 - 119.
V. Stoltenberg-Hansen Effective domains and concrete computability: a survey, in F. L. Bauer and R. Steinbrüggen (editors) Foundations of Secure Computation, IOS Press, 2000.
V. Stoltenberg-Hansen, I. Lindström and E. R. Griffor, Mathematical Theory of Domains, Cambridge University Press, 1994.
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Hamrin, G., Stoltenberg-Hansen, V. (2002). Cartesian Closed Categories of Effective Domains. In: Schwichtenberg, H., Steinbrüggen, R. (eds) Proof and System-Reliability. NATO Science Series, vol 62. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0413-8_1
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DOI: https://doi.org/10.1007/978-94-010-0413-8_1
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