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28
Pict: A programming language based on the picalculus
 PROOF, LANGUAGE AND INTERACTION: ESSAYS IN HONOUR OF ROBIN MILNER
, 1997
"... The πcalculus offers an attractive basis for concurrent programming. It is small, elegant, and well studied, and supports (via simple encodings) a wide range of highlevel constructs including data structures, higherorder functional programming, concurrent control structures, and objects. Moreover ..."
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Cited by 254 (8 self)
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The πcalculus offers an attractive basis for concurrent programming. It is small, elegant, and well studied, and supports (via simple encodings) a wide range of highlevel constructs including data structures, higherorder functional programming, concurrent control structures, and objects. Moreover, familiar type systems for the calculus have direct counterparts in the πcalculus, yielding strong, static typing for a highlevel language using the πcalculus as its core. This paper describes Pict, a stronglytyped concurrent programming language constructed in terms of an explicitlytypedcalculus core language.
Comparing object encodings
 Journal of Functional Programming, 16:375 – 414
, 2006
"... Recent years have seen the development of several foundational models for statically typed objectoriented programming. But despite their intuitive similarity, di erences in the technical machinery used to formulate the various proposals have made them di cult to compare. Using the typed lambdacalc ..."
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Cited by 119 (3 self)
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Recent years have seen the development of several foundational models for statically typed objectoriented programming. But despite their intuitive similarity, di erences in the technical machinery used to formulate the various proposals have made them di cult to compare. Using the typed lambdacalculus F! as a common basis, we nowo er a detailed comparison of four models: (1) a recursiverecord encoding similar to the ones used by Cardelli [Car84],
Subtyping Dependent Types
, 2000
"... The need for subtyping in typesystems with dependent types has been realized for some years. But it is hard to prove that systems combining the two features have fundamental properties such as subject reduction. Here we investigate a subtyping extension of the system *P, which is an abstract versio ..."
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Cited by 70 (6 self)
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The need for subtyping in typesystems with dependent types has been realized for some years. But it is hard to prove that systems combining the two features have fundamental properties such as subject reduction. Here we investigate a subtyping extension of the system *P, which is an abstract version of the type system of the Edinburgh Logical Framework LF. By using an equivalent formulation, we establish some important properties of the new system *P^, including subject reduction. Our analysis culminates in a complete and terminating algorithm which establishes the decidability of typechecking.
On subtyping and matching
 In Proceedings ECOOP '95
, 1995
"... Abstract. A relation between recursive object types, called matching, has been proposed as a generalization of subtyping. Unlike subtyping, matching does not support subsumption, but it does support inheritance of binary methods. We argue that matching is a good idea, but that it should not be regar ..."
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Cited by 45 (3 self)
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Abstract. A relation between recursive object types, called matching, has been proposed as a generalization of subtyping. Unlike subtyping, matching does not support subsumption, but it does support inheritance of binary methods. We argue that matching is a good idea, but that it should not be regarded as a form of Fbounded subtyping (as was originally intended). We show that a new interpretation of matching as higherorder subtyping has better properties. Matching turns out to be a thirdorder construction, possibly the only one to have been proposed for general use in programming.
An Imperative, FirstOrder Calculus with Object Extension
 In Proceedings of the European Conference on ObjectOriented Programming (ECOOP
, 1998
"... This paper presents an imperative object calculus designed to support classbased programming via a combination of extensible objects and encapsulation. This calculus simplifies the language presented in [17] in that, like C++ and Java, it chooses to support an imperative semantics instead of me ..."
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Cited by 40 (9 self)
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This paper presents an imperative object calculus designed to support classbased programming via a combination of extensible objects and encapsulation. This calculus simplifies the language presented in [17] in that, like C++ and Java, it chooses to support an imperative semantics instead of method specialization. We show how Javastyle classes and "mixins" may be coded in this calculus, prove a type soundness theorem (via a subject reduction property), and give a sound and complete typing algorithm.
Intersection Types and Bounded Polymorphism
, 1996
"... this paper (Compagnoni, Intersection Types and Bounded Polymorphism 3 1994; Compagnoni, 1995) has been used in a typetheoretic model of objectoriented multiple inheritance (Compagnoni & Pierce, 1996). Related calculi combining restricted forms of intersection types with higherorder polymorphism ..."
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Cited by 37 (0 self)
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this paper (Compagnoni, Intersection Types and Bounded Polymorphism 3 1994; Compagnoni, 1995) has been used in a typetheoretic model of objectoriented multiple inheritance (Compagnoni & Pierce, 1996). Related calculi combining restricted forms of intersection types with higherorder polymorphism and dependent types have been studied by Pfenning (Pfenning, 1993). Following a more detailed discussion of the pure systems of intersections and bounded quantification (Section 2), we describe, in Section 3, a typed calculus called F ("Fmeet ") integrating the features of both. Section 4 gives some examples illustrating this system's expressive power. Section 5 presents the main results of the paper: a prooftheoretic analysis of F 's subtyping and typechecking relations leading to algorithms for checking subtyping and for synthesizing minimal types for terms. Section 6 discusses semantic aspects of the calculus, obtaining a simple soundness proof for the typing rules by interpreting types as partial equivalence relations; however, another prooftheoretic result, the nonexistence of least upper bounds for arbitrary pairs of types, implies that typed models may be more difficult to construct. Section 7 offers concluding remarks. 2. Background
Foundations for Virtual Types
 INFORMATION AND COMPUTATION
, 1998
"... Virtual types have been proposed as a notation for generic programming in objectoriented languagesan alternative to the more familiar mechanism of parametric classes. The tradeoffs between the two mechanisms are a matter of current debate: for many examples, both appear to offer convenient (ind ..."
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Cited by 28 (2 self)
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Virtual types have been proposed as a notation for generic programming in objectoriented languagesan alternative to the more familiar mechanism of parametric classes. The tradeoffs between the two mechanisms are a matter of current debate: for many examples, both appear to offer convenient (indeed almost interchangeable) solutions; in other situations, one or the other seems to be more satisfactory. However, it has proved difficult to draw rigorous comparisons between the two approaches, partly because current proposals for virtual types vary considerably in their details, and partly because the proposals themselves are described rather informally, usually in the complicating context of fullscale language designs. Work on the foundations of objectoriented languages has already established a clear connection between parametric classes and the polymorphic functions found in familiar typed lambdacalculi. Our aim here is to explore a similar connection between virtual types and dep...
HigherOrder Intersection Types and Multiple Inheritance
, 1995
"... this paper was completed, the metatheory of this system has been studied in much greater detail by Compagnoni [ Compagnoni, 1994, Compagnoni, 1995 ] . A type system combining intersection types with a powerful form of polymorphism is of independent interest. Reynolds [ 1988 ] has argued that interse ..."
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Cited by 17 (6 self)
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this paper was completed, the metatheory of this system has been studied in much greater detail by Compagnoni [ Compagnoni, 1994, Compagnoni, 1995 ] . A type system combining intersection types with a powerful form of polymorphism is of independent interest. Reynolds [ 1988 ] has argued that intersection types can form the basis of elegant language designs. But his Forsythe language has only a firstorder type system, and thus lacks some of the expressive possibilities of polymorphic languages like ML. Our work represents a step toward a synthesis of these styles of language design. The following section shows some examples of multiple inheritance using a simple highlevel syntax. Section 3, the core of the paper, defines the calculus F
NuPRL’s class theory and its applications
 Foundations of Secure Computation, NATO ASI Series, Series F: Computer & System Sciences
, 2000
"... This article presents a theory of classes and inheritance built on top of constructive type theory. Classes are defined using dependent and very dependent function types that are found in the Nuprl constructive type theory. Inheritance is defined in terms of a general subtyping relation over the und ..."
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Cited by 15 (7 self)
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This article presents a theory of classes and inheritance built on top of constructive type theory. Classes are defined using dependent and very dependent function types that are found in the Nuprl constructive type theory. Inheritance is defined in terms of a general subtyping relation over the underlying types. Among the basic types is the intersection type which plays a critical role in the applications because it provides a method of composing program components. The class theory is applied to defining algebraic structures such as monoids, groups, rings, etc. and relating them. It is also used to define communications protocols as infinite state automata. The article illustrates the role of these formal automata in defining the services of a distributed group communications system. In both applications the inheritance mechanisms allow reuse of proofs and the statement of general properties of system composition. 1
Subtyping for Object Type Constructors
 In FOOL 6. Foundations of ObjectOriented Languages
, 1999
"... Object type constructors have been introduced as an approach to adding container object types to a language with type inference. Useful subtyping for object type constructors requires a flexible subtype rule for type constructors that is not simply the pointwise extension of subtyping for types. At ..."
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Cited by 13 (2 self)
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Object type constructors have been introduced as an approach to adding container object types to a language with type inference. Useful subtyping for object type constructors requires a flexible subtype rule for type constructors that is not simply the pointwise extension of subtyping for types. At the same time, subtyping should avoid requiring runtime type checks, as in the Java subtype rule for arrays. An extension of object type constructors is considered to allow this subtyping, extending the kinds of object type constructors with polarities that allow this subtyping without jeopardizing soundness. 1 Introduction Recent years have seen much attention paid to the foundations of typed object oriented programming languages. Less attention has been paid to the types of container objects (for example, vectors, lists and arrays). Such objects provides interfaces that are parameterized by one or more type variables (representing the element type, in the aforesaid examples). A formal ca...