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Journal of the ACM (JACM)
Journal of Computer and System Sciences
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Proceedings of the 9th Colloquium on Automata, Languages and Programming
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LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
βη-complete models for System F
Mathematical Structures in Computer Science
Graph models of $\lambda$-calculus at work, and variations
Mathematical Structures in Computer Science
On the completeness of order-theoretic models of the λ-calculus
Information and Computation
Effective λ-models versus recursively enumerable λ-theories
Mathematical Structures in Computer Science
Bidomains and full abstraction for countable nondeterminism
FOSSACS'06 Proceedings of the 9th European joint conference on Foundations of Software Science and Computation Structures
Separation logic for higher-order store
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
Lambda theories of effective lambda models
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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In this paper we address the problem of solving recursive domain equations using uncountable limits of domains. These arise for instance, when dealing with the ω1-continuous function-space constructor and are used in the denotational semantics of programming languages which feature unbounded choice constructs. Surprisingly, the category of cpo's and ω1-continuous embeddings is not ω0-cocomplete. Hence the standard technique for solving reflexive domain equations fails. We give two alternative methods. We discuss also the issue of completeness of the λβηcalculus w.r.t reflexive domain models. We show that among the reflexive domain models in the category of cpo's and ω0-continuous functions there is one which has a minimal theory. We give a reflexive domain model in the category of cpo's and ω1-continuous functions whose theory is precisely the λβη theory. So ω1-continuous λ-models are complete for the λβη-calculus.