Domain Theory and its Applications

Stephen Brookes, Manfred Droste, Michael Mislove
This Dagstuhl seminar focused on Domain Theory and Its Applications. Domains were first discovered by Dana Scott in the mid-1960s, and quickly became of central importance in the area of programming language semantics, which remains the primary area of their application. Recently, more diverse applications of domain theory to other areas have been discovered, and this has led to a flourishing of activity in the area. The seminar focused on this diverse range of applications, as well as on the
more » ... le of domain theory in its more established areas of application. The Dagstuhl Seminar also was coordinated with the Spring, 1998 meeting of the series , the Mathematical Foundations of Programming Semantics. This series meets annually, mainly in the U.S., and is among the most popular meetings for researchers working in programming semantics and its mathematical underpinnings. Coordinating the Dagstuhl Seminar on Domain Theory with the MFPS meeting allowed us to attract some of the most active researchers in domain theory to both meetings. More importantly, the Dagstuhl meeting was used to assess the state of domain theory, and important insights were gained through the seminar into the status and future possibilities for domain theory and its applications. Among the various areas within domain theory, we mention a few that were highlighted during the Dagstuhl Seminar: • Structure theory of domains: This "basic" area of domains has had recent impetus through the work of Achim Jung (Birmingham) in which the approach of abstract bases, originally proposed by M. B. Smyth (Imperial), was used to devise a uniform approach to the theory of continuous domains in analogy to the traditional approach to algebraic domains.