×

The bicategory-theoretic solution of recursive domain equations. (English) Zbl 1277.68117

Cardelli, Luca (ed.) et al., Computation, meaning, and logic. Articles dedicated to Gordon Plotkin. Amsterdam: Elsevier. Electronic Notes in Theoretical Computer Science 172, 203-222 (2007).
Summary: We generalise the traditional approach of Smyth and Plotkin to the solution of recursive domain equations from order-enriched structures to bicategorical ones and thereby develop a bicategorical theory for recursively defined domains in accordance with axiomatic domain theory.
For the entire collection see [Zbl 1273.68018].

MSC:

68Q55 Semantics in the theory of computing
06B35 Continuous lattices and posets, applications
18E05 Preadditive, additive categories
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Abramsky, S., On semantic foundations for applicative multiprogramming, (Proceedings of the ICALP’83 Conf.. Proceedings of the ICALP’83 Conf., Lecture Notes in Computer Science, 154 (1983)), 1-14 · Zbl 0538.68064
[2] Adámek, J., A categorical generalisation of Scott domains, Mathematical Structures in Computer Science, 7, 419-443 (1997) · Zbl 0884.18006
[3] Bénabou, J., Introduction to bicategories, (Reports of the Midwest Category Seminar. Reports of the Midwest Category Seminar, Lecture Notes in Mathematics, 47 (1967)), 1-77 · Zbl 1375.18001
[4] Blackwell, R.; Kelly, G. M.; Power, A. J., Two-dimensional monad theory, Journal of Pure and Applied Algebra, 59, 1-41 (1989) · Zbl 0675.18006
[5] Borceux, F., Handbook of categorical algebra I, Encyclopedia of Mathematics and its Applications, 50 (1994), Cambridge University Press
[6] Cattani, G.L., “Presheaf Models for Concurrency,” Ph.D. thesis, Department of Computer Science, University of Aarhus (1999); Cattani, G.L., “Presheaf Models for Concurrency,” Ph.D. thesis, Department of Computer Science, University of Aarhus (1999) · Zbl 0881.18013
[7] Cattani, G.L., M. Fiore and G. Winskel, A theory of recursive domains with applications to concurrency\(13^{th} \); Cattani, G.L., M. Fiore and G. Winskel, A theory of recursive domains with applications to concurrency\(13^{th} \) · Zbl 0945.68521
[8] Fiore, M., Axiomatic Domain Theory in Categories of Partial Maps, Distinguished Dissertations in Computer Science (1996), Cambridge University Press · Zbl 0979.68549
[9] Fiore, M.; Plotkin, G., On compactness and Cpo-enriched categories, (Winskel, G., Proceedings of the CLICS Workshop (23-27 March 1992). Proceedings of the CLICS Workshop (23-27 March 1992), DAIMI PB, volume 397-II (May 1992), Computer Science Department: Computer Science Department Aarhus University), 571-584
[10] Fiore, M. and G. Plotkin, An axiomatisation of computationally adequate domain theoretic models of FPC\(9^{th} \); Fiore, M. and G. Plotkin, An axiomatisation of computationally adequate domain theoretic models of FPC\(9^{th} \)
[11] Freyd, P., Recursive types reduced to inductive types\(5^{th} \); Freyd, P., Recursive types reduced to inductive types\(5^{th} \)
[12] Freyd, P., Algebraically complete categories, (Carboni, A.; Pedicchio, M.; Rosolini, G., Category Theory. Category Theory, Lecture Notes in Mathematics, 1488 (1991)), 131-156
[13] Freyd, P., Remarks on algebraically compact categories, (Fourman, M.; Johnstone, P.; Pitts, A., Applications of Categories in Computer Science. Applications of Categories in Computer Science, London Mathematical Society Lecture Note Series, 177 (1992)), 95-106 · Zbl 0803.18002
[14] Karazeris, P., Categorical domain theory: Scott topology, powercategories, coherent categories, Theory and Applications of Categories, 9, 106-120 (2001) · Zbl 1002.18005
[15] Kelly, G. M.; Street, R., Review of the elements of 2-categories, (Proceedings Sydney Category Theory Seminar 1972/1973. Proceedings Sydney Category Theory Seminar 1972/1973, Lecture Notes in Mathematics, 420 (1974)), 75-103
[16] Lambek, J., A fixpoint theorem for complete categories, Math. Zeitschr., 151-161 (1968) · Zbl 0149.26105
[17] Lehmann, D., “Categories for fixpoint semantics,” Ph.D. thesis, University of Warwick (1976); Lehmann, D., “Categories for fixpoint semantics,” Ph.D. thesis, University of Warwick (1976)
[18] Lehmann, D.; Smyth, M., Algebraic specification of data types: A synthetic approach, Math. Systems Theory, 14, 97-139 (1981) · Zbl 0457.68035
[19] Leinster, T., Higher operads, higher categories (2004), Cambridge University Press · Zbl 1160.18001
[20] Plotkin, G., Algebraic completeness and compactness in an enriched setting; Plotkin, G., Algebraic completeness and compactness in an enriched setting
[21] Scott, D., Outline of a mathematical theory of computation; Scott, D., Outline of a mathematical theory of computation
[22] Scott, D., Continuous lattices, (Lawvere, F., Toposes, Algebraic Geometry and Logic. Toposes, Algebraic Geometry and Logic, Lecture Notes in Mathematics, 274 (1972)), 97-136
[23] Smyth, M.; Plotkin, G., The category-theoretic solution of recursive domain equations, SIAM Journal of Computing, 11, 761-783 (1982) · Zbl 0493.68022
[24] Street, R., Cauchy characterization of enriched categories, Rend. Sem. Mat. Fis. Milano, 51, 217-233 (1981) · Zbl 0538.18005
[25] Taylor, P., The limit-colimit coincidence for categories; Taylor, P., The limit-colimit coincidence for categories
[26] Trnkova, V.; Velebil, J., On categories generalizing universal domains, Mathematical Structures in Computer Science, 9, 159-175 (1999) · Zbl 0933.18005
[27] Vickers, S., Topical categories of domains, Mathematical Structures in Computer Science, 9, 569-616 (1999) · Zbl 0946.18001
[28] Wand, M., Fixed point constructions in order-enriched categories, Theoretical Computer Science, 8, 13-30 (1979) · Zbl 0401.18005
[29] Wood, R. J., Proarrows II, Cahiers Topologie Géom. Différentielle Catégoriques, 26, 135-168 (1985) · Zbl 0583.18003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.