dI-Domains as prime information systems
Information and Computation
Handbook of logic in computer science (vol. 3)
The largest cartesian closed category of stable domains
Theoretical Computer Science
Domains and lambda-calculi
Stable Models of Typed lambda-Calculi
Proceedings of the Fifth Colloquium on Automata, Languages and Programming
Proceedings of the 4th International Conference on Category Theory and Computer Science
Sequential algorithms and strongly stable functions
Theoretical Computer Science - Game theory meets theoretical computer science
A logical approach to stable domains
Theoretical Computer Science
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In the seventies, G. Plotkin noticed that T^@w, the cartesian product of @w copies of the 3 elements flat domain of Boolean, is a universal domain, where ''universal'' means that the retracts of T^@w in Scott's continuous semantics are exactly all the @wCC-domains, which with Scott continuous functions form a cartesian closed category. As usual ''@w'' is for ''countably based'', and here ''CC'' is for ''conditionally complete'', which essentially means that any subset which is pairwise bounded has an upper bound. Since T^@w is also an @wDI-domain (an important structure in the stable domain theory), a problem arises naturally: Is T^@w a universal domain for Berry's stable semantics? The aim of this paper is to answer this question. We investigate the properties of stable retracts and introduce a new domain named a conditionally complete DI-domain (a CCDI-domain for short). We show that, (1) a dcpo is a stable retract of T^@w if and only if it is an @wCCDI-domain; (2) the category of @wCCDI-domain (resp. CCDI-domains) with stable functions is cartesian closed. So, the problem above has an affirmative answer.