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A Calculus for Overload Functions with Subtyping

, 1992
"... We present a simple extension of typed calculus where functions can be overloaded by putting different "branches of code" together. When the function is applied, the branch to execute is chosen according to a particular selection rule which depends on the type of the argument. The cru ..."
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Cited by 139 (28 self)
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We present a simple extension of typed calculus where functions can be overloaded by putting different "branches of code" together. When the function is applied, the branch to execute is chosen according to a particular selection rule which depends on the type of the argument. The crucial feature of the present approach is that the branch selection depends on the "runtime type" of the argument, which may differ from its compiletime type, because of the existence of a subtyping relation among types. Hence overloading cannot be eliminated by a static analysis of code, but is an essential feature to be dealt with during computation. We obtain in this way a typedependent calculus, which differs from the various calculi where types do not play any role during computation. We prove Confluence and a generalized SubjectReduction theorem for this calculus. We prove Strong Normalization for a "stratified" subcalculus. The definition of this calculus is guided by the understand...
Typeful programming
, 1989
"... There exists an identifiable programming style based on the widespread use of type information handled through mechanical typechecking techniques. This typeful programming style is in a sense independent of the language it is embedded in; it adapts equally well to functional, imperative, objectorie ..."
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Cited by 139 (2 self)
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There exists an identifiable programming style based on the widespread use of type information handled through mechanical typechecking techniques. This typeful programming style is in a sense independent of the language it is embedded in; it adapts equally well to functional, imperative, objectoriented, and algebraic programming, and it is not incompatible with relational and concurrent programming. The main purpose of this paper is to show how typeful programming is best supported by sophisticated type systems, and how these systems can help in clarifying programming issues and in adding power and regularity to languages. We start with an introduction to the notions of types, subtypes and polymorphism. Then we introduce a general framework, derived in part from constructive logic, into which most of the known type systems can be accommodated and extended. The main part of the paper shows how this framework can be adapted systematically to cope with actual programming constructs. For concreteness we describe a particular programming language with advanced features; the emphasis here is on the combination of subtyping and polymorphism. We then discuss how typing concepts apply to large programs, made of collections of modules, and very large programs, made of collections of large programs. We also sketch how typing applies to system programming; an area which by nature escapes rigid typing. In summary, we compare the most common programming styles, suggesting that many of them are compatible with, and benefit from, a typeful discipline.
A runtime assertion checker for the Java Modeling Language (JML)
 PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON SOFTWARE ENGINEERING RESEARCH AND PRACTICE (SERP ’02), LAS VEGAS
, 2002
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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],
A Paradigmatic ObjectOriented Programming Language: Design, Static Typing and Semantics
 Journal of Functional Programming
, 1993
"... In order to illuminate the fundamental concepts involved in objectoriented programming languages, we describe the design of TOOPL, a paradigmatic, staticallytyped, functional, objectoriented programming language which supports classes, objects, methods, hidden instance variables, subtypes, and in ..."
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Cited by 117 (9 self)
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In order to illuminate the fundamental concepts involved in objectoriented programming languages, we describe the design of TOOPL, a paradigmatic, staticallytyped, functional, objectoriented programming language which supports classes, objects, methods, hidden instance variables, subtypes, and inheritance. It has proven to be quite difficult to design such a language which has a secure type system. A particular problem with statically type checking objectoriented languages is designing typechecking rules which ensure that methods provided in a superclass will continue to be type correct when inherited in a subclass. The typechecking rules for TOOPL have this feature, enabling library suppliers to provide only the interfaces of classes with actual executable code, while still allowing users to safely create subclasses. In order to achieve greater expressibility while retaining typesafety, we choose to separate the inheritance and subtyping hierarchy in the language. The design of...
An extension of system F with subtyping
 Information and Computation
, 1991
"... System F is a wellknown typed lcalculus with polymorphic types, which provides a basis for polymorphic programming languages. We study an extension of F, called F <: (pronounced efsub) that combines parametric polymorphism with subtyping. The main focus of the paper is the equational theory of ..."
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Cited by 114 (11 self)
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System F is a wellknown typed lcalculus with polymorphic types, which provides a basis for polymorphic programming languages. We study an extension of F, called F <: (pronounced efsub) that combines parametric polymorphism with subtyping. The main focus of the paper is the equational theory of F <: , which is related to PER models and the notion of parametricity. We study some categorical properties of the theory when restricted to closed terms, including interesting categorical isomorphisms. We also investigate prooftheoretical properties, such as the conservativity of typing judgments with respect to F. We demonstrate by a set of examples how a range of constructs may be encoded in F <: . These include record operations and subtyping hierarchies that are related to features of objectoriented languages. Appears in: International Conference on Theoretical Aspects of Computer Software, T.Ito, A.R.Meyer Eds., Lecture Notes in Computer Science n. 526, pp 750770, Springer Verlag, 19...
Type Inference for Records in a Natural Extension of ML
 Theoretical Aspects of ObjectOriented Programming: Types, Semantics, and Language Design
, 1994
"... We describe an extension of ML with records where inheritance is given by ML generic polymorphism. All common operations on records but concatenation are supported, in particular the free extension of records. Other operations such as renaming of fields are added. The solution relies on an extension ..."
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Cited by 77 (7 self)
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We describe an extension of ML with records where inheritance is given by ML generic polymorphism. All common operations on records but concatenation are supported, in particular the free extension of records. Other operations such as renaming of fields are added. The solution relies on an extension of ML, where the language of types is sorted and considered modulo equations, and on a record extension of types. The solution is simple and modular and the type inference algorithm is efficient in practice.
Types for Modules
, 1998
"... The programming language Standard ML is an amalgam of two, largely orthogonal, languages. The Core language expresses details of algorithms and data structures. The Modules language expresses the modular architecture of a software system. Both languages are statically typed, with their static and dy ..."
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Cited by 68 (9 self)
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The programming language Standard ML is an amalgam of two, largely orthogonal, languages. The Core language expresses details of algorithms and data structures. The Modules language expresses the modular architecture of a software system. Both languages are statically typed, with their static and dynamic semantics specified by a formal definition.
A Per Model of Polymorphism and Recursive Types
 In Logic in Computer Science. IEEE
, 1990
"... A model of Reynolds' polymorphic lambda calculus is provided, which also allows the recursive definition of elements and types. The technique is to use a good class of partial equivalence relations over a certain cpo. This allows the combination of inverselimits for recursion and intersection ..."
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Cited by 62 (4 self)
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A model of Reynolds' polymorphic lambda calculus is provided, which also allows the recursive definition of elements and types. The technique is to use a good class of partial equivalence relations over a certain cpo. This allows the combination of inverselimits for recursion and intersection for polymorphism.
Positive Subtyping
 Information and Computation
, 1994
"... The statement S T in a calculus with subtyping is traditionally interpreted as a semantic coercion function of type [[S]]![[T ]] that extracts the "T part" of an element of S. If the subtyping relation is restricted to covariant positions, this interpretation may be enriched to includ ..."
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Cited by 51 (8 self)
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The statement S T in a calculus with subtyping is traditionally interpreted as a semantic coercion function of type [[S]]![[T ]] that extracts the "T part" of an element of S. If the subtyping relation is restricted to covariant positions, this interpretation may be enriched to include both the coercion and an overwriting function put[S; T ] 2 [[S]]![[T ]]![[S]] that updates the T part of an element of S.