Theoretical Computer Science
Cartesian closed categories of algebraic CPOs
Theoretical Computer Science
Logic of domains
The formal semantics of programming languages: an introduction
The formal semantics of programming languages: an introduction
Theoretical Computer Science - Special volume of selected papers of the Sixth Workshop on the Mathematical Foundations of Programming Semantics, Kingston, Ont., Canada, May 1990
dI-Domains as prime information systems
Information and Computation
The largest cartesian closed category of stable domains
Theoretical Computer Science
DI-Domains as a Model of Polymorphism
Proceedings of the 3rd Workshop on Mathematical Foundations of Programming Language Semantics
An introduction to event structures
Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, School/Workshop
Proceedings of the 4th International Conference on Category Theory and Computer Science
Linear types and approximation
Mathematical Structures in Computer Science
An enrichment theorem for an axiomatisation of categories of domains and continuous functions
Mathematical Structures in Computer Science
The largest Cartesian closed category of domains, considered constructively
Mathematical Structures in Computer Science
Domains and Lambda-Calculi (Cambridge Tracts in Theoretical Computer Science)
Domains and Lambda-Calculi (Cambridge Tracts in Theoretical Computer Science)
Maximality and totality of stable functions in the category of stable bifinite domains
Computers & Mathematics with Applications
TLCA'07 Proceedings of the 8th international conference on Typed lambda calculi and applications
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More than a dozen years ago, Amadio [Bifinite domains: stable case, in: Lecture Notes in Computer Science, vol. 530, 1991, pp. 16-33] (see Amadio and Curien, Domains and Lambda-Calculi, Cambridge Tracts in Theoretical Computer Science, vol. 46, Cambridge University Press, 1998 as well) raised the question of whether the category of stable bifinite domains of Amadio-Droste [R.M. Amadio, Bifinite domains: stable case, in: Lecture Notes in Computer Science, vol. 530, 1991, pp. 16-33; M. Droste, On stable domains, Theor. Comput. Sci. 111 (1993) 89-101; M. Droste, Cartesian closed categories of stable domains for polymorphism, Preprint, Universitat GHS Essen] is the largest cartesian closed full sub-category of the category of @w-algebraic meet-cpos with stable functions. An affirmative solution to this problem has two major steps: (1) Show that for any @w-algebraic meet-cpo D, if all higher-order stable function spaces built from D are @w-algebraic, then D is finitary (i.e., it satisfies the so-called axiom I); (2) Show that for any @w-algebraic meet-cpo D, if D violates MI^~, then [D-D] violates either M or I. We solve the first part of the problem in this paper, i.e., for any @w-algebraic meet-cpo D, if the stable function space [D-D] satisfies M, then D is finitary. Our notion of (mub, meet)-closed set, which is introduced for step 1, will also be used for treating some example cases in step 2.