On understanding types, data abstraction, and polymorphism
ACM Computing Surveys (CSUR) - The MIT Press scientific computation series
LFP '90 Proceedings of the 1990 ACM conference on LISP and functional programming
Research topics in functional programming
Intersection and union types: syntax and semantics
Information and Computation
Duality beyond sober spaces: topological spaces and observation frames
Selected papers of the workshop on Topology and completion in semantics
Handbook of logic in computer science (vol. 3)
Toward an infinitary logic of domains: Abramsky logic for transition systems
Information and Computation
TACS '91 Proceedings of the International Conference on Theoretical Aspects of Computer Software
Domains for Denotational Semantics
Proceedings of the 9th Colloquium on Automata, Languages and Programming
An extended type system for OCL supporting templates and transformations
FMOODS'05 Proceedings of the 7th IFIP WG 6.1 international conference on Formal Methods for Open Object-Based Distributed Systems
Untyped recursion schemes and infinite intersection types
FOSSACS'10 Proceedings of the 13th international conference on Foundations of Software Science and Computational Structures
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A type theory with infinitary intersection and union types for an extension of the λ-calculus is introduced. Types are viewed as upper closed subsets of a Scott domain and intersection and union type constructors are interpreted as the set-theoretic intersection and union, respectively, even when they are not finite. The assignment of types to λ-terms extends naturally the basic type assignment system. We prove soundness and completeness using a generalization of Abramsky's finitary logic of domains. Finally we apply the framework to applicative transition systems, obtaining a sound a complete infinitary intersection type assignment system for the lazy λ-calculus.