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164
An introduction to substructural logics
, 2000
"... Abstract: This is a history of relevant and substructural logics, written for the Handbook of the History and Philosophy of Logic, edited by Dov Gabbay and John Woods. 1 1 ..."
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Cited by 138 (16 self)
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Abstract: This is a history of relevant and substructural logics, written for the Handbook of the History and Philosophy of Logic, edited by Dov Gabbay and John Woods. 1 1
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 103 (40 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.
A Nominal Theory of Objects with Dependent Types
 In Proc. ECOOP’03, Springer LNCS
, 2002
"... We design and study νObj, a calculus and dependent type system for objects and classes which can have types as members. Type members can be aliases, abstract types, or new types. The type system can model the essential concepts of Java's inner classes as well as virtual types and family polymorph ..."
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Cited by 96 (17 self)
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We design and study νObj, a calculus and dependent type system for objects and classes which can have types as members. Type members can be aliases, abstract types, or new types. The type system can model the essential concepts of Java's inner classes as well as virtual types and family polymorphism found in BETA or gbeta. It can also model most concepts of SMLstyle module systems, including sharing constraints and higherorder functors, but excluding applicative functors. The type system can thus...
What Are Principal Typings and What Are They Good For?
, 1995
"... We demonstrate the pragmatic value of the principal typing property, a property more general than ML's principal type property, by studying a type system with principal typings. The type system is based on rank 2 intersection types and is closely related to ML. Its principal typing property prov ..."
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Cited by 93 (0 self)
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We demonstrate the pragmatic value of the principal typing property, a property more general than ML's principal type property, by studying a type system with principal typings. The type system is based on rank 2 intersection types and is closely related to ML. Its principal typing property provides elegant support for separate compilation, including "smartest recompilation" and incremental type inference, and for accurate type error messages. Moreover, it motivates a novel rule for typing recursive definitions that can type many examples of polymorphic recursion.
Programming with Intersection Types and Bounded Polymorphism
, 1991
"... representing the official policies, either expressed or implied, of the U.S. Government. ..."
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Cited by 66 (4 self)
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representing the official policies, either expressed or implied, of the U.S. Government.
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 61 (33 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.
The Relevance of Semantic Subtyping
 In IEEE Symposium on Logic in Computer Science (LICS
, 2002
"... We compare Meyer and Routley's minimal relevant logic B+ with the recent semanticsbased approach to subtyping introduced by Frisch, Castagna and Benzaken in the definition of a type system with intersection and union. We show that  for the functional core of the system  such notion of subtyping, ..."
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Cited by 52 (9 self)
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We compare Meyer and Routley's minimal relevant logic B+ with the recent semanticsbased approach to subtyping introduced by Frisch, Castagna and Benzaken in the definition of a type system with intersection and union. We show that  for the functional core of the system  such notion of subtyping, which is defined in purely settheoretical terms, coincides with the relevant entailment of the logic B+ . 1
Programming With Intersection Types, Union Types, and Polymorphism
, 1991
"... Type systems based on intersection types have been studied extensively in recent years, both as tools for the analysis of the pure calculus and, more recently, as the basis for practical programming languages. The dual notion, union types, also appears to have practical interest. For example, by re ..."
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Cited by 50 (3 self)
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Type systems based on intersection types have been studied extensively in recent years, both as tools for the analysis of the pure calculus and, more recently, as the basis for practical programming languages. The dual notion, union types, also appears to have practical interest. For example, by refining types ordinarily considered as atomic, union types allow a restricted form of abstract interpretation to be performed during typechecking. The addition of secondorder polymorphic types further increases the power of the type system, allowing interesting variants of many common datatypes to be encoded in the "pure" fragment with no type or term constants. This report summarizes a preliminary investigation of the expressiveness of a programming language combining intersection types, union types, and polymorphism.
Decidability of HigherOrder Subtyping with Intersection Types
 University of Edinburgh, LFCS
, 1994
"... The combination of higherorder subtyping with intersection types yields a typed model of objectoriented programming with multiple inheritance [11]. The target calculus, F ! , a natural generalization of Girard's system F ! with intersection types and bounded polymorphism, is of independent i ..."
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Cited by 40 (11 self)
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The combination of higherorder subtyping with intersection types yields a typed model of objectoriented programming with multiple inheritance [11]. The target calculus, F ! , a natural generalization of Girard's system F ! with intersection types and bounded polymorphism, is of independent interest, and is our subject of study. Our main contribution is the proof that subtyping in F ! is decidable. This yields as a corollary the decidability of subtyping in F ! , its intersection free fragment, because the F ! subtyping system is a conservative extension of that of F ! . The calculus presented in [8] has no reductions on types. In the F ! subtyping system the presence of ficonversion  an extension of ficonversion with distributivity laws  drastically increases the complexity of proving the decidability of the subtyping relation. Our proof consists of, firstly, defining an algorithmic presentation of the subtyping system of F ! , secondly, proving that th...