Domain Theory, Logic and Computation

Domains are mathematical structures for information and approximation; they combine order-theoretic, logical, and topological ideas and provide a natural framework for modelling and reasoning about computation. The theory of domains has proved to be a useful tool for programming languages and other areas of computer science, and for applications in mathematics.
Included in this proceedings volume are selected papers of original research presented at the 2nd International Symposium on Domain Theory in Chengdu, China. With authors from France, Germany, Great Britain, Ireland, Mexico, and China, the papers cover the latest research in these sub-areas: domains and computation, topology and convergence, domains, lattices, and continuity, and representations of domains as event and logical structures.
Researchers and students in theoretical computer science should find this a valuable source of reference. The survey papers at the beginning should be of particular interest to those who wish to gain an understanding of some general ideas and techniques in this area.

Contenu

Preface. Contributing authors. 1: Playful, streamlike computation; P.-L. Curien. 1. Prologue: playing with Böhm trees. 2. Introduction. 3. Symmetric algorithms, sequential algorithms. 4. Related works. 5. Control. 6. A few more remarks. 2: Universal types and what they are good for; J.R. Longley. 1. Universal objects. 2. lambda-algebras. 3. Denotational semantics. 4. Universal types. 5. Syntax and semantics of PCF. 6. Examples of universal types. 7. Conclusions and further directions. 3: Relational representations of hyper-continuous lattices; Xiao-Quan Xu, Ying-Ming Liu. 1. Preliminaries. 2. Regular representations of completely distributive lattices. 3. Finitely regular representations of hyper-continuous lattices. 4: Convergence classes and spaces of partial functions; A.K. Seda, R. Heinze, P. Hitzler. 1. Introduction. 2. Convergence spaces and convergence classes. 3. Convergence classes and VDM. 4. Compactness of (X --> Y). 5. Conclusions and further work. 5: On meet-continuous dcpos; Hui Kou, Ying-Ming Liu, Mao-Kang Luo. 1. Introduction. 2. Basic properties of meet-continuous dcpos. 3. Dcpos with the Hausdorff Lawson topology. 4. Adjunctions between quasicontinuous domains and continuous domains. 5. Scott-open filters. 6. Concluding remarks. 6: External characterizations of continuous sL-domains; LuoshanXu. 1. Introduction. 2. Preliminaries. 3. Continuous sL-domains and their characterizations by function spaces. 4. External characterizations by posets of ideals. 7: Projectives and injectives in the category of quantales; Yong-Ming Li, Meng Zhou. 1. Introduction. 2. Regular projectives in the category of quantales. 3. Injective objects in the category of quantales. 8: On minimal event and concrete data structures; F. Bracho, M. Droste, I. Meinecke. 1. Introduction. 2. Event structures, concrete data structures and their domains. 3. Congruences on prime intervals and associated structures. 4. Maximal and minimal structures. 5. Conclusion. 9: A note on strongly finite sequent structures; D. Spreen, R. Greb. 1. Introduction. 2. Basic definitions and results. 3. Domain constructions. 4. Strongly finite sequent structures. 5. Sequent structures and preorders. 6. Constructions on preorders. 7. Conclusion.