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Compositional Characterizations of λterms using Intersection Types (Extended Abstract)
, 2000
"... We show how to characterize compositionally a number of evaluation properties of λterms 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 ..."
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Cited by 17 (6 self)
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We show how to characterize compositionally a number of evaluation properties of λterms 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 settheoretical 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.
Filter Models and Easy Terms
, 2001
"... We illustrate the use of intersection types as a tool for synthesizing models which exhibit special purpose features. We focus on semantical proofs of easiness. This allows us to prove that the class of theories induced by graph models is strictly included in the class of theories induced by n ..."
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Cited by 12 (4 self)
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We illustrate the use of intersection types as a tool for synthesizing models which exhibit special purpose features. We focus on semantical proofs of easiness. This allows us to prove that the class of theories induced by graph models is strictly included in the class of theories induced by nonextensional lter models.
Intersection Types and Lambda Models
, 2005
"... Invariance of interpretation by #conversion is one of the minimal requirements for any standard model for the #calculus. With the intersection type systems being a general framework for the study of semantic domains for the #calculus, the present paper provides a (syntactic) characterisation of t ..."
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Cited by 11 (1 self)
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Invariance of interpretation by #conversion is one of the minimal requirements for any standard model for the #calculus. With the intersection type systems being a general framework for the study of semantic domains for the #calculus, the present paper provides a (syntactic) characterisation of the above mentioned requirement in terms of characterisation results for intersection type assignment systems.
Compositional Characterisations of λterms using Intersection Types
, 2003
"... We show how to characterise compositionally a number of evaluation properties of λterms using Intersection Type assignment systems. In particular, we focus on termination properties, such as strong normalisation, normalisation, head normalisation, and weak head normalisation. We consider also the p ..."
Abstract

Cited by 1 (0 self)
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We show how to characterise compositionally a number of evaluation properties of λterms using Intersection Type assignment systems. In particular, we focus on termination properties, such as strong normalisation, normalisation, head normalisation, and weak head normalisation. 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 characterisation results are new, to our knowledge, or else they streamline, strengthen, or generalise earlier results in the literature. The completeness parts of the characterisations are proved uniformly for all the properties, using a settheoretical semantics of intersection types over suitable kinds of stable sets. This technique generalises Krivine's and Mitchell's methods for strong normalisation to other evaluation properties.
A Filter Model for the λµ Calculus
"... We introduce an intersection type assignment system for the pure λµcalculus, which is invariant under subject reduction and expansion. The system is obtained by describing Streicher and Reus’s denotational model of continuations in the category of ωalgebraic lattices via Abramsky’s domain logic ap ..."
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We introduce an intersection type assignment system for the pure λµcalculus, which is invariant under subject reduction and expansion. The system is obtained by describing Streicher and Reus’s denotational model of continuations in the category of ωalgebraic lattices via Abramsky’s domain logic approach. This provides a tool for showing the completeness of the type assignment system with respect to the continuation models via a filter model construction. We also show that typed λµterms in Parigot’s system have a nontrivial intersection typing in our system. 1
Automated Equational Reasoning in Nondeterministic λCalculi Modulo Theories H*
, 2009
"... In this thesis I study four extensions of untyped λcalculi all under the maximally coarse semantics of the theory H ∗ (observable equality), and implement a system for reasoning about and storing abstract knowledge expressible in languages with these extensions. The extensions are: (1) a semilattic ..."
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In this thesis I study four extensions of untyped λcalculi all under the maximally coarse semantics of the theory H ∗ (observable equality), and implement a system for reasoning about and storing abstract knowledge expressible in languages with these extensions. The extensions are: (1) a semilattice operation J, the join w.r.t the Scott ordering; (2) a random mixture R for stochastic λcalculus; (3) a computational comonad 〈code,apply,eval,quote, {−}〉 for Gödel codes modulo provable equality; and (4) a Π 1 1complete oracle O. I develop three languages from combinations of these extensions. The syntax of these languages is always simple: each is a finitely generated combinatory algebra. The semantics of these languages are various fragments of Dana Scott’s D ∞ models. Although the languages use ideas