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A New Paradox in Type Theory
 Logic, Methodology and Philosophy of Science IX : Proceedings of the Ninth International Congress of Logic, Methodology, and Philosophy of Science
, 1994
"... this paper is to present a new paradox for Type Theory, which is a typetheoretic refinement of Reynolds' result [24] that there is no settheoretic model of polymorphism. We discuss then one application of this paradox, which shows unexpected connections between the principle of excluded middl ..."
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this paper is to present a new paradox for Type Theory, which is a typetheoretic refinement of Reynolds' result [24] that there is no settheoretic model of polymorphism. We discuss then one application of this paradox, which shows unexpected connections between the principle of excluded middle and the axiom of description in impredicative Type Theories. 1 Minimal and Polymorphic HigherOrder Logic
A Semantics of ObjectOriented Sets
, 1991
"... An account is given of extending the wellknown objectoriented type system of Luca Cardelli with set constructs and logical formalism. The system is based on typed notation, employing a subtyping relation and a powertype construct. Sets in this system are value expressions and are typed as some po ..."
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An account is given of extending the wellknown objectoriented type system of Luca Cardelli with set constructs and logical formalism. The system is based on typed notation, employing a subtyping relation and a powertype construct. Sets in this system are value expressions and are typed as some powertype. Sets are built up in a very general manner; in particular, sets can be described by (firstorder) predicates. The resulting system, called LPT, is statically typecheckable (in a context of multiple inheritance) and is provided with a settheoretic semantics. LPT can be used as a mathematical foundation for an objectoriented data model employing sets and constraints. 1 Introduction and results In objectoriented database systems, objectoriented programming is merged with objectoriented datastructuring, enabling the designer of a database to have all the advantages of a clean conceptual design, as well as the possibility of enforcing better software engineering. Cardelli [1] argue...