Introduction to combinators and &lgr;-calculus
Introduction to combinators and &lgr;-calculus
Recursion over realizability structures
Information and Computation
New foundations for fixpoint computations: FIX-hyperdoctrines and the FIX-logic
Information and Computation - Special issue: Selections from 1990 IEEE symposium on logic in computer science
Full abstraction in the lazy lambda calculus
Information and Computation
Information and Computation - Special conference issue: international conference on theoretical aspects of computer software
Category theory for computing science, 2nd ed.
Category theory for computing science, 2nd ed.
Information and Computation
Algebraic set theory
CTCS '95 Proceedings of the 6th International Conference on Category Theory and Computer Science
CTCS '95 Proceedings of the 6th International Conference on Category Theory and Computer Science
Complete Cuboidal Sets in Axiomatic Domain Theory
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Effective models of polymorphism, subtyping and recursion
Effective models of polymorphism, subtyping and recursion
Theoretical Computer Science - Domains
Formalizing Synthetic Domain Theory
Journal of Automated Reasoning
Complete Axioms for Categorical Fixed-Point Operators
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
General synthetic domain theory – a logical approach
Mathematical Structures in Computer Science
Compactly generated domain theory
Mathematical Structures in Computer Science
A Convenient Category of Domains
Electronic Notes in Theoretical Computer Science (ENTCS)
Synthetic Domain Theory and Models of Linear Abadi & Plotkin Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
Comparing free algebras in Topological and Classical Domain Theory
Theoretical Computer Science
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
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We propose a uniform way of isolating a subcategory of predomains within the category of modest sets determined by a partial combinatory algebra (PCA). Given a divergence on a PCA (which determines a notion of partiality), we identify a candidate category of predomains, the well-complete objects. We show that, whenever a single strong completeness axiom holds, the category satisfies appropriate closure properties. We consider a range of examples of PCAs with associated divergences and show that in each case the axiom does hold. These examples encompass models allowing a ‘parallel’ style of computation (for example, by interleaving), as well as models that seemingly allow only ‘sequential’ computation, such as those based on term-models for the lambda-calculus. Thus, our approach provides a uniform approach to domain theory across a wide class of realizability models. We compare our treatment with previous approaches to domain theory in realizability models. It appears that no other approach applies across such a wide range of models.