The system F of variable types, fifteen years later
Theoretical Computer Science
Algebraic data type and process specifications based on projection spaces
Lecture notes in Computer Science on Recent trends in data type specification
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Domain theoretic models of polymorphism
Information and Computation
The semantics of second-order lambda calculus
Information and Computation
Parameterized data type and process specifications using projection algebras
Categorical methods in computer science with aspects from topology
The construct PRO of projection spaces: its internal structure
Categorical methods in computer science with aspects from topology
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PER models of subtyping, recursive types and higher-order polymorphism
POPL '92 Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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Proceedings of the 3rd Workshop on Mathematical Foundations of Programming Language Semantics
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Programming Symposium, Proceedings Colloque sur la Programmation
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Category Theory and Computer Science
An investigation of a programming language with a polymorphic type structure.
An investigation of a programming language with a polymorphic type structure.
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Various models for the Girard-Reynolds second-order lambda calculus have been presented in the literature. Except for the term model they are either realizability or domain models. In this paper a further model construction is introduced. Types are interpreted as inverse limits of ω-cochains of finite sets. The corresponding morphisms are sequences of maps acting locally on the finite sets in the ω-cochains. The model can easily be turned into an effectively given one. Moreover, it can be arranged in such a way that the universally quantified type ∀t.t representing absurdity in the higher-order logic defined by the type structure is interpreted by the empty set, which means that it is also a model of this logic.