Typing and computational properties of lambda expressions
Theoretical Computer Science
Type theories, normal forms, and D∞-lambda-models
Information and Computation
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
Lambda-calculus, types and models
Lambda-calculus, types and models
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
Information and Computation
Foundations of programming languages
Foundations of programming languages
Semantical analysis of perpetual strategies in &lgr;-calculus
Theoretical Computer Science - Special issue: Gentzen
Domains and lambda-calculi
Lambda-terms as total or partial functions on normal forms
Proceedings of the Symposium on Lambda-Calculus and Computer Science Theory
Infinite Intersection and Union Types for the Lazy Lambda Calculus
TACS '01 Proceedings of the 4th International Symposium on Theoretical Aspects of Computer Software
ICTCS '01 Proceedings of the 7th Italian Conference on Theoretical Computer Science
Characterising Strong Normalisation for Explicit Substitutions
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Complexity of strongly normalising λ-terms via non-idempotent intersection types
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
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We show how to characterize compositionally a number of evaluation properties of λ-terms using Intersection Type assignment systems. In particular, we focus on termination properties, such as strong normalization, normalization, head normalization, and weak head normalization. We consider also the persistent versions of such notions. By way of example, we consider also another evaluation property, unrelated to termination, namely reducibility to a closed term. Many of these characterization results are new, to our knowledge, or else they streamline, strengthen, or generalize earlier results in the literature. The completeness parts of the characterizations are proved uniformly for all the properties, using a set-theoretical semantics of intersection types over suitable kinds of stable sets. This technique generalizes Krivine's and Mitchell's methods for strong normalization to other evaluation properties.