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CutElimination in the Strict Intersection Type Assignment System is Strongly Normalising
 NOTRE DAME J. OF FORMAL LOGIC
, 2004
"... This paper defines reduction on derivations (cutelimination) in the Strict Intersection Type Assignment System of [1] and shows a strong normalisation result for this reduction. Using this result, new proofs are given for the approximation theorem and the characterisation of normalisability of term ..."
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Cited by 16 (12 self)
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This paper defines reduction on derivations (cutelimination) in the Strict Intersection Type Assignment System of [1] and shows a strong normalisation result for this reduction. Using this result, new proofs are given for the approximation theorem and the characterisation of normalisability of terms, using intersection types.
Normalisation, Approximation, and Semantics for Combinator Systems
 Theoretical Computer Science
, 2003
"... This paper studies normalization of typeable terms and the relation between approximation semantics and filter models for Combinator Systems. It presents notions of approximants for terms, intersection type assignment, and reduction on type derivations; the last will be proved to be strongly normali ..."
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Cited by 13 (11 self)
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This paper studies normalization of typeable terms and the relation between approximation semantics and filter models for Combinator Systems. It presents notions of approximants for terms, intersection type assignment, and reduction on type derivations; the last will be proved to be strongly normalizable. With this result, it is shown that, for every typeable term, there exists an approximant with the same type, and a characterization of the normalization behaviour of terms using their assignable types is given. Then the two semantics are defined and compared, and it is shown that the approximants semantics is fully abstract but the filter semantics is not.
The heart of intersection type assignment; normalisation proofs revisited
, 2006
"... Abstract. This paper gives a new proof for the approximation theorem and the characterisation of normalisability using intersection types. The technique applied is to define reduction on derivations and to show a strong normalisation result for this reduction. From this result, the characterisation ..."
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Cited by 4 (4 self)
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Abstract. This paper gives a new proof for the approximation theorem and the characterisation of normalisability using intersection types. The technique applied is to define reduction on derivations and to show a strong normalisation result for this reduction. From this result, the characterisation of strong normalisation and the approximation result will follow easily; the latter, in its turn, will lead to the characterisation of (head)normalisability.
Strongly Normalising CutElimination with Strict Intersection Types
, 2003
"... This paper defines reduction on derivations in the strict intersection type assignment system of [2], by generalising cutelimination, and shows a strong normalisation result for this reduction. Using this result, new proofs are given for the approximation theorem and the characterisation of normali ..."
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Cited by 2 (2 self)
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This paper defines reduction on derivations in the strict intersection type assignment system of [2], by generalising cutelimination, and shows a strong normalisation result for this reduction. Using this result, new proofs are given for the approximation theorem and the characterisation of normalisability using intersection types.
Approximation and Filter Semantics for Combinator Systems (Extended Abstract)
"... Steffen van Bakel 1 and Maribel Fernandez 2 1 Department of Computing, Imperial College, 180 Queens Gate, London SW7 2BZ. svb@doc.ic.ac.uk 2 LIENS (CNRS UMR 8548), Ecole Normale Superieure, 45, rue d'Ulm, 75005 Paris, France. maribel@ens.fr Abstract. This paper studies the relation betwee ..."
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Steffen van Bakel 1 and Maribel Fernandez 2 1 Department of Computing, Imperial College, 180 Queens Gate, London SW7 2BZ. svb@doc.ic.ac.uk 2 LIENS (CNRS UMR 8548), Ecole Normale Superieure, 45, rue d'Ulm, 75005 Paris, France. maribel@ens.fr Abstract. This paper studies the relation between approximation semantics and filter models for Combinator Systems. It presents notions of approximants for terms, intersection type assignment, and using a strong normalization result of [4], it is proved that, for every typeable term, there exists an approximant of that term with the same type. Also a characterization of the normalization behaviour of terms using their assignable types is given. Then the two semantics are defined and compared, and it is shown that the approximants semantics is fully abstract but the filter semantics is not. Introduction In this paper we focus on the relation between two approaches for semantics of Combinator Systems (CS), being the filter semantics, obtained b...
Approximation and Normalization Results for Typeable Combinator Systems
, 1995
"... This paper studies the relation between types and normalization in the context of Combinator Systems. It presents notions of approximants for terms, intersection type assignment, and reduction on derivations; the last will be proved to be strongly normalizable. With this result, it is proved that, f ..."
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This paper studies the relation between types and normalization in the context of Combinator Systems. It presents notions of approximants for terms, intersection type assignment, and reduction on derivations; the last will be proved to be strongly normalizable. With this result, it is proved that, for every typeable term, there exists an approximant of that term with the same type, and a characterization of the normalization behaviour of terms using their assignable types is given. Introduction In this paper we will focus on the relation between assignable intersection types for terms and, respectively, types for their approximants and normalization in the framework of Combinator Systems (CS). This topic has been studied extensively in the setting of Lambda Calculus (LC) [6] (see [9, 7, 1, 3]), but, perhaps surprisingly, to our knowledge it has never been studied for CS. Moreover, in systems without explicit abstraction, these results are harder to obtain; in fact, in order to prove t...
The Heart of Intersection Type Assignment Normalisation
"... This paper gives a new proof for the approximation theorem and the characterisation of normalisability using intersection types for a system with ω and a ≤relation that is contravariant over arrow types. The technique applied is to define reduction on derivations and to show a strong normalisation ..."
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This paper gives a new proof for the approximation theorem and the characterisation of normalisability using intersection types for a system with ω and a ≤relation that is contravariant over arrow types. The technique applied is to define reduction on derivations and to show a strong normalisation result for this reduction. From this result, the characterisation of strong normalisation and the approximation result will follow easily; the latter, in its turn, will lead to the characterisation of (head) normalisability.
Normalisation and Approximation results for typeable Term Rewriting Systems (with abstraction and βrule) Summary
"... This paper gives an overview of results presented in (in order of appearance) [3], [8], [9] (that together will appear as [11]), and [10], [7]. 1 ..."
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This paper gives an overview of results presented in (in order of appearance) [3], [8], [9] (that together will appear as [11]), and [10], [7]. 1