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Complete restrictions of the intersection type discipline
 Theoretical Computer Science
, 1992
"... In this paper the intersection type discipline as defined in [Barendregt et al. ’83] is studied. We will present two different and independent complete restrictions of the intersection type discipline. The first restricted system, the strict type assignment system, is presented in section two. Its m ..."
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Cited by 112 (44 self)
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In this paper the intersection type discipline as defined in [Barendregt et al. ’83] is studied. We will present two different and independent complete restrictions of the intersection type discipline. The first restricted system, the strict type assignment system, is presented in section two. Its major feature is the absence of the derivation rule (≤) and it is based on a set of strict types. We will show that these together give rise to a strict filter lambda model that is essentially different from the one presented in [Barendregt et al. ’83]. We will show that the strict type assignment system is the nucleus of the full system, i.e. for every derivation in the intersection type discipline there is a derivation in which (≤) is used only at the very end. Finally we will prove that strict type assignment is complete for inference semantics. The second restricted system is presented in section three. Its major feature is the absence of the type ω. We will show that this system gives rise to a filter λImodel and that type assignment without ω is complete for the λIcalculus. Finally we will prove that a lambda term is typeable in this system if and only if it is strongly normalizable.
Intersection Type Assignment Systems
 THEORETICAL COMPUTER SCIENCE
, 1995
"... This paper gives an overview of intersection type assignment for the Lambda Calculus, as well as compare in detail variants that have been defined in the past. It presents the essential intersection type assignment system, that will prove to be as powerful as the wellknown BCDsystem. It is essenti ..."
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Cited by 71 (37 self)
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This paper gives an overview of intersection type assignment for the Lambda Calculus, as well as compare in detail variants that have been defined in the past. It presents the essential intersection type assignment system, that will prove to be as powerful as the wellknown BCDsystem. It is essential in the following sense: it is an almost syntax directed system that satisfies all major properties of the BCDsystem, and the types used are the representatives of equivalence classes of types in the BCDsystem. The set of typeable terms can be characterized in the same way, the system is complete with respect to the simple type semantics, and it has the principal type property.
Filter Models for ConjunctiveDisjunctive λcalculi
, 1996
"... The distinction between the conjunctive nature of nondeterminism as opposed to the disjunctive character of parallelism constitutes the motivation and the starting point of the present work. λcalculus is extended with both a nondeterministic choice and a parallel operator; a notion of reduction i ..."
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Cited by 11 (6 self)
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The distinction between the conjunctive nature of nondeterminism as opposed to the disjunctive character of parallelism constitutes the motivation and the starting point of the present work. λcalculus is extended with both a nondeterministic choice and a parallel operator; a notion of reduction is introduced, extending fireduction of the classical calculus. We study type assignment systems for this calculus, together with a denotational semantics which is initially defined constructing a set semimodel via simple types. We enrich the type system with intersection and union types, dually reflecting the disjunctive and conjunctive behaviour of the operators, and we build a filter model. The theory of this model is compared both with a Morrisstyle operational semantics and with a semantics based on a notion of capabilities.
Essential intersection type assignment
 Proceedings of FST&TCS '93. 13 th Conference on Foundations of Software Technology and Theoretical Computer Science
, 1993
"... This paper introduces a notion of intersection type assignment on the Lambda Calculus that is a restriction of the BCDsystem as presented in [4]. This restricted system is essential in the following sense: it is an almost syntax directed system that satisfies all major properties of the BCDsystem. ..."
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Cited by 10 (6 self)
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This paper introduces a notion of intersection type assignment on the Lambda Calculus that is a restriction of the BCDsystem as presented in [4]. This restricted system is essential in the following sense: it is an almost syntax directed system that satisfies all major properties of the BCDsystem. The set of typeable terms can be characterized in the same way, the system is complete with respect to the simple type semantics, and it has the principal type property.
Strict Intersection Types for the Lambda Calculus
, 2010
"... This paper will show the usefulness and elegance of strict intersection types for the Lambda Calculus; these are strict in the sense that they are the representatives of equivalence classes of types in the BCDsystem [15]. We will focus on the essential intersection type assignment; this system is a ..."
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Cited by 7 (5 self)
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This paper will show the usefulness and elegance of strict intersection types for the Lambda Calculus; these are strict in the sense that they are the representatives of equivalence classes of types in the BCDsystem [15]. We will focus on the essential intersection type assignment; this system is almost syntax directed, and we will show that all major properties hold that are known to hold for other intersection systems, like the approximation theorem, the characterisation of (head/strong) normalisation, completeness of type assignment using filter semantics, strong normalisation for cutelimination and the principal pair property. In part, the proofs for these properties are new; we will briefly compare the essential system with other existing systems.
Intersection Type Assignment Systems. Theoret
 Comput. Sci
, 1995
"... This paper gives an overview of intersection type assignment for the Lambda Calculus, as well as compare in detail variants that have been defined in the past. It presents the essential intersection type assignment system, that will prove to be as powerful as the wellknown BCDsystem. It is essenti ..."
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Cited by 5 (0 self)
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This paper gives an overview of intersection type assignment for the Lambda Calculus, as well as compare in detail variants that have been defined in the past. It presents the essential intersection type assignment system, that will prove to be as powerful as the wellknown BCDsystem. It is essential in the following sense: it is an almost syntax directed system that satisfies all major properties of the BCDsystem, and the types used are the representatives of equivalence classes of types in the BCDsystem. The set of typeable terms can be characterized in the same way, the system is complete with respect to the simple type semantics, and it has the principal type property.
A Convex Powerdomain over Lattices: its Logic and λCalculus
, 1997
"... To model at the same time parallel and nondeterministic functional calculi we define a powerdomain functor P such that it is an endofunctor over the category of algebraic lattices. P is locally continuous and we study the initial solution D 1 of the domain equation D = P([D ! D]? ). We derive fro ..."
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Cited by 1 (1 self)
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To model at the same time parallel and nondeterministic functional calculi we define a powerdomain functor P such that it is an endofunctor over the category of algebraic lattices. P is locally continuous and we study the initial solution D 1 of the domain equation D = P([D ! D]? ). We derive from the algebras of P the logic of D 1 , that is the axiomatic description of its compact elements. We then define a calculus and a type assignment system using the logic of D 1 as the related type theory. We prove that the filter model of this calculus, which is isomorphic to D 1 , is fully abstract with respect to the observational preorder of the λcalculus.
IOS Press AConvex Powerdomain over Lattices: its Logic andCalculus
"... Abstract. To model at the same time parallel and nondeterministic functional calculi we de ne a powerdomain functor P such that it is an endofunctor over the category of algebraic lattices. P is locally continuous and we study the initial solution D 1 of the domain equation D = P([D! D]?). We derive ..."
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Abstract. To model at the same time parallel and nondeterministic functional calculi we de ne a powerdomain functor P such that it is an endofunctor over the category of algebraic lattices. P is locally continuous and we study the initial solution D 1 of the domain equation D = P([D! D]?). We derive from the algebras of P the logic of D 1, that is the axiomatic description of its compact elements. We then de ne acalculus and a type assignment system using the logic of D 1 as the related type theory. Weprove that the lter model of this calculus, which is isomorphic to D 1,is fully abstract with respect to the observational Preorder of thecalculus.
Intersection Type Assignment Systems Steffen
"... This paper gives an overview of intersection type assignment for the Lambda Calculus, as well as compare in detail variants that have been defined in the past. It presents the essential intersection type assignment system, that will prove to be as powerful as the wellknown BCDsystem. It is essenti ..."
Abstract
 Add to MetaCart
(Show Context)
This paper gives an overview of intersection type assignment for the Lambda Calculus, as well as compare in detail variants that have been defined in the past. It presents the essential intersection type assignment system, that will prove to be as powerful as the wellknown BCDsystem. It is essential in the following sense: it is an almost syntax directed system that satisfies all major properties of the BCDsystem, and the types used are the representatives of equivalence classes of types in the BCDsystem. The set of typeable terms can be characterized in the same way, the system is complete with respect to the simple type semantics, and it has the principal type property.