Introduction to combinators and &lgr;-calculus
Introduction to combinators and &lgr;-calculus
A characterization of F-complete assignments
Theoretical Computer Science
Type theories, normal forms, and D∞-lambda-models
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Polymorphic type inference and containment
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Topology via logic
Complete restrictions of the intersection type discipline
Theoretical Computer Science
Operational, denotational and logical descriptions: a case study
Fundamenta Informaticae - Special issue on mathematical foundations of computer science '91
Set-theoretical and other elementary models of the &lgr;-calculus
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
Journal of Computer and System Sciences
Full abstraction in the lazy lambda calculus
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F-semantics for type assignment systems
Theoretical Computer Science
Semantical analysis of perpetual strategies in &lgr;-calculus
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The simple semantics for Coppe-Dezani-Sallé types
Proceedings of the 5th Colloquium on International Symposium on Programming
The Y-combinator in Scott''s Lambda-calculus Models
The Y-combinator in Scott''s Lambda-calculus Models
Intersection types and lambda models
Theoretical Computer Science - Logic, language, information and computation
Compositional characterisations of λ-terms using intersection types
Theoretical Computer Science - Mathematical foundations of computer science 2000
Calculi, types and applications
Theoretical Computer Science
Theoretical Computer Science
A type assignment system for game semantics
Theoretical Computer Science
Recursive domain equations of filter models
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
A filter model for the λµ-calculus
TLCA'11 Proceedings of the 10th international conference on Typed lambda calculi and applications
On Realisability Semantics for Intersection Types with Expansion Variables
Fundamenta Informaticae - Intersection Types and Related Systems ITRS
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We characterize those type preorders which yield complete intersection-type assignment systems for λ-calculi, with respect to the three canonical set-theoretical semantics for intersection-types: the inference semantics, the simple semantics, and the F-semantics. These semantics arise by taking as interpretation of types subsets of applicative structures, as interpretation of the preorder relation, ≤, set-theoretic inclusion, as interpretation of the intersection constructor, ∩, set-theoretic intersection, and by taking the interpretation of the arrow constructor, → à la Scott, with respect to either any possible functionality set, or the largest one, or the least one.These results strengthen and generalize significantly all earlier results in the literature, to our knowledge, in at least three respects. First of all the inference semantics had not been considered before. Second, the characterizations are all given just in terms of simple closure conditions on the preorder relation, ≤, on the types, rather than on the typing judgments themselves. The task of checking the condition is made therefore considerably more tractable. Last, we do not restrict attention just to λ-models, but to arbitrary applicative structures which admit an interpretation function. Thus we allow also for the treatment of models of restricted λ-calculi. Nevertheless the characterizations we give can be tailored just to the case of λ-models.