Domains and Processes

Domain theory is a rich interdisciplinary area at the intersection of logic, computer science, and mathematics. This volume contains selected papers presented at the International Symposium on Domain Theory which took place in Shanghai in October 1999. Topics of papers range from the encounters between topology and domain theory, sober spaces, Lawson topology, real number computability and continuous functionals to fuzzy modelling, logic programming, and pi-calculi. This book is a valuable reference for researchers and students interested in this rapidly developing area of theoretical computer science.

Preface	p. ix
Contributing Authors	p. xiii
Encounters Between Topology and Domain Theory	p. 1
Introduction	p. 1
Introductory Domain Theory	p. 3
The Scott Topology	p. 7
Locally Compact Spaces	p. 10
Spectral Theory	p. 11
Round Ideal Completions	p. 14
Ordered Spaces	p. 17
Compact Pospaces	p. 18
Spaces of Maximal Points	p. 19
The Domain of Closed Formal Balls	p. 23
Fixed Point Theory	p. 25
The Probabilistic Power Domain	p. 26
Open Problems and Research Directions	p. 28
Topological Appendix	p. 29
The Lawson Topology on Quasicontinuous Domains	p. 33
Introduction	p. 33
Quasicontiuous domains	p. 34
Strictly complete regularity of the Lawson topology	p. 36
U[subscript k]-admitting dcpos need not be sober	p. 41
Introduction	p. 41
U[subscript k]-admitting for locally compact dcpo's	p. 42
U[subscript k]-admitting does not always imply sober	p. 45
The Largest Topologically Cartesian Closed Categories of Domains as Topological Spaces	p. 51
Introduction and Preliminaries	p. 51
Relations between tcc and ccc categories	p. 53
FS is the largest tcc full subcategory of CONT[subscript [perpendicular, bottom]	p. 55
F-FS is the largest tcc full subcategory of CONT	p. 59
On the Equivalence of Some Approaches to Computability on the Real Line	p. 67
Introduction	p. 68
The TTE approach to real number computations	p. 71
The domain-theoretic approach to real number computability	p. 76
The language Real PCF	p. 84
The equivalence results	p. 91
Concluding remarks	p. 98
Appendix	p. 99
The continuous functionals of finite types over the reals	p. 103
Introduction	p. 103
The types	p. 105
The hereditarily total objects	p. 110
Density and co-density	p. 111
Limit spaces	p. 117
The traditional approach	p. 118
Compact Semantics on Bc-domains	p. 125
Introduction	p. 125
Preliminaries and Characterizations for Semantics Continuity	p. 127
The Compactness Theorem And Applications	p. 132
Conclusion	p. 136
Normal Subsets in Abstract Bases	p. 137
Introduction	p. 137
Prerequisites	p. 139
Normal subsets and sub-domains	p. 140
The dcpo class of abstract bases and a fixed point theorem	p. 145
Semantics of Logic Programs and Representation of Smyth Powerdomain	p. 151
Introduction	p. 152
Domains and information systems	p. 154
Main representation theorem	p. 158
Proofs	p. 160
Examples	p. 166
Semantics of disjunctive logic programs	p. 169
Clausal logic over sequent structures	p. 174
Conclusion	p. 179
Domains of view: a foundation for specification and analysis	p. 183
Introduction	p. 183
Kripke modal transition systems	p. 185
Fuzzy Kripke modal transition systems	p. 195
Modal Markov chains	p. 206
Modal relations	p. 209
Related work	p. 213
Semantic Theory and Proof System of Open Bisimulation for the [pi]-Calculus with Mismatching	p. 219
Introduction	p. 220
Operational Semantics of the [pi superscript [not equal]-Calculus	p. 222
Open Bisimulation and Its Symbolic Characterization	p. 225
Proof System for Open Bisimulation	p. 232
The Weak Case	p. 237
Conclusions	p. 241
Axiomatization without Prefix Combinator	p. 245
Introduction	p. 245
Preliminaries	p. 250
Polyadic X-Calculus	p. 252
A Process Calculus without Precedence	p. 256
Ground Bisimilarity for Atomic X-Calculus	p. 262
Axiomatization in the Absence of Prefix, Summation and Match Combinators	p. 264
Final Remarks	p. 271
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