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37
A New Presentation of the Intersection Type Discipline Through Principal Typings of Normal Forms
, 1996
"... We introduce an intersection type system which is a restriction of the intersection type discipline. This restriction leads to a principal type property for normal forms in the classical sense, while retaining the expressivity of the classical discipline. We characterize the structure of principal ..."
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Cited by 8 (0 self)
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We introduce an intersection type system which is a restriction of the intersection type discipline. This restriction leads to a principal type property for normal forms in the classical sense, while retaining the expressivity of the classical discipline. We characterize the structure of principal types of normal forms and give an algorithm that reconstructs normal forms from types. Having shown the equivalence between principal types and normal forms, we define an expansion operation on types which allows us to recover all possible types for any normalizable term. The contribution of this work is a new and simpler presentation of the intersection type discipline through a purely syntactic and completely characterized notion of principal types.
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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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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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.
Polymorphic Intersection Type Assignment for Rewite Systems with Intersection and betarule (Extended Abstract)
 IN TYPES’99. LNCS
, 2000
"... We define two type assignment systems for firstorder rewriting extended with application,abstraction, andreduction (TRS). The types used in these systems are a combination of (free) intersection and polymorphic types. The first system is the general one, for which we prove a subject reduction t ..."
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We define two type assignment systems for firstorder rewriting extended with application,abstraction, andreduction (TRS). The types used in these systems are a combination of (free) intersection and polymorphic types. The first system is the general one, for which we prove a subject reduction theorem and show that all typeable terms are strongly normalisable. The second is a decidable subsystem of the first, by restricting types to Rank 2. For this system we define, using an extended notion of unification, a notion of principal type, and show that type assignment is decidable.
Sequence Types for the πcalculus
, 2004
"... We introduce channel sequence types to study finitary polymorphism in the context of mobile processes modelled in the #calculus. We associate to each channel a set of exchange types, and we require that output processes send values of one of those types, and input processes accept values of all the ..."
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We introduce channel sequence types to study finitary polymorphism in the context of mobile processes modelled in the #calculus. We associate to each channel a set of exchange types, and we require that output processes send values of one of those types, and input processes accept values of all the types in the set. Our type assignment system enjoys subject reduction and guarantees the absence of communication errors. We give several examples of polymorphism, and we encode the #calculus with the strict intersection type discipline.
Sequence Types for the πcalculus
 ITRS 2004 PRELIMINARY VERSION
, 2004
"... We introduce channel sequence types to study finitary polymorphism in the context of mobile processes modelled in the πcalculus. We associate to each channel a set of exchange types, and we require that output processes send values of one of those types, and input processes accept values of any typ ..."
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We introduce channel sequence types to study finitary polymorphism in the context of mobile processes modelled in the πcalculus. We associate to each channel a set of exchange types, and we require that output processes send values of one of those types, and input processes accept values of any type in the set. Our type assignment system enjoys subject reduction and guarantees the absence of communication errors. We give several examples of polymorphism, and we encode the λcalculus with the strict intersection type discipline.
Strong Normalization of Typeable Rewrite Systems Afdeling Informatica, Universiteit Nijmegen,
"... This paper studies termination properties of rewrite systems that are typeable using intersection types. It introduces a notion of partial type assignment on Curryfied Term Rewrite Systems, that consists of assigning intersection types to function symbols, and specifying the way in which types can b ..."
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This paper studies termination properties of rewrite systems that are typeable using intersection types. It introduces a notion of partial type assignment on Curryfied Term Rewrite Systems, that consists of assigning intersection types to function symbols, and specifying the way in which types can be assigned to nodes and edges between nodes in the tree representation of terms. Two operations on types are specified that are used to define type assignment on terms and rewrite rules, and are proven to be sound on both terms and rewrite rules. Using a more liberal approach to recursion, a general scheme for recursive definitions is presented, that generalizes primitive recursion, but has full Turingmachine computational power. It will be proved that, for all systems that satisfy this scheme, every typeable term is strongly normalizable.
Resolving of Intersection Types in Java
"... Abstract. In the past we analyzed typeless Java programs. One of our results was, that there may be different correct typings for one method. This means that the principal types of such methods are intersection types. We presented a typeinference algorithm. For typeless Java methods the algorithm i ..."
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Abstract. In the past we analyzed typeless Java programs. One of our results was, that there may be different correct typings for one method. This means that the principal types of such methods are intersection types. We presented a typeinference algorithm. For typeless Java methods the algorithm infers its principal intersection type. Unfortunately, like Java bytecode, Java does not allow intersection types. In this paper we present an algorithm, which resolves intersection types of Java methods, such that Java programs with standard typings are generated. Additionally, we will refine the definition of Java method principal types. 1
Principal Typing for Parallel and nonDeterministic lambdacalculus
, 1997
"... Parallelism and nondeterminism are fundamental concepts in the process algebra theory. Combining them with calculus can enlighten the theory of higherorder process algebras. In recent papers an analysis of a calculus containing parallel and nondeterministic operators was carried on by means of ..."
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Parallelism and nondeterminism are fundamental concepts in the process algebra theory. Combining them with calculus can enlighten the theory of higherorder process algebras. In recent papers an analysis of a calculus containing parallel and nondeterministic operators was carried on by means of a type assignment system with intersection and union types. The present paper answers the problem of determining principal types for this system. For correspondence contact Franco Barbanera Dipartimento di Informatica, Universit'a di Torino Corso Svizzera 185, 10149 Torino Italy email: barba@di.unito.it tel: +39 11 7429111 Fax: +39 11 751603 1 Principal Typing for Parallel and nonDeterministic calculus Abstract Parallelism and nondeterminism are fundamental concepts in the process algebra theory. Combining them with calculus can enlighten the theory of higherorder process algebras. In recent papers an analysis of a calculus containing parallel and nondeterministic operators ...
Intersection Types for λTrees
"... We introduce a type assignment system which is parametric with respect to five families of trees obtained by evaluating λterms (Böhm trees, LévyLongo trees,...). Then we prove, in an (almost) uniform way, that each type assignment system fully describes the observational equivalences induced by th ..."
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We introduce a type assignment system which is parametric with respect to five families of trees obtained by evaluating λterms (Böhm trees, LévyLongo trees,...). Then we prove, in an (almost) uniform way, that each type assignment system fully describes the observational equivalences induced by the corresponding tree representation of terms. More precisely, for each family of trees, two terms have the same tree if and only if they get assigned the same types in the corresponding type assignment system.