Handbook of theoretical computer science (vol. B)
Semantics of programming languages: structures and techniques
Semantics of programming languages: structures and techniques
Mathematical theory of domains
Mathematical theory of domains
Handbook of logic in computer science (vol. 3)
The largest cartesian closed category of stable domains
Theoretical Computer Science
Domains and lambda-calculi
New Results on Hierarchies of Domains
Proceedings of the 3rd Workshop on Mathematical Foundations of Programming Language Semantics
Proceedings of the 7th Colloquium on Automata, Languages and Programming
Proceedings of the 4th International Conference on Category Theory and Computer Science
Strongly algebraic = SFP (topically)
Mathematical Structures in Computer Science
On an open problem of Amadio and Curien: the finite antichain condition
Information and Computation
On an open problem of Amadio and Curien: The finite antichain condition
Information and Computation
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This paper addresses a conjecture of Smyth that says that if $D$ and $[D \rightarrow D]$ are effectively algebraic directed-complete partial orders with least element (cpo's), then $D$ is an effectively strongly algebraic cpo, though what is meant by an effectively algebraic and an effectively strongly algebraic cpo was not made precise.Notions of an effectively strongly algebraic cpo and an effective SFP domain are introduced and shown to be (effectively) equivalent. Moreover, the conjecture is shown to hold if instead of being effectively algebraic, $[D \rightarrow D]$ is only required to be $\omega$-algebraic and $D$ is forced to have a completeness test, that is a procedure that decides for any two finite sets $X$ and $Y$ of compact cpo elements whether $X$ is a complete set of upper bounds of $Y$. As a consequence, the category of effective SFP objects and continuous maps turns out to be the largest Cartesian closed full subcategory of the category of $\omega$-algebraic cpo's that have a completeness test.We then consider whether such a result also holds in a constructive framework, where one considers categories with constructive domains as objects, that is, domains consisting only of the constructive (computable) elements of an indexed $\omega$-algebraic cpo, and computable maps as morphisms. This is indeed the case: the category of constructive SFP domains is the largest constructively Cartesian closed weakly indexed effectively full subcategory of the category of constructive domains that have a completeness test and satisfy a further effectivity requirement.