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Regular Object Types
 In European Conference on ObjectOriented Programming (ECOOP
, 2003
"... Regular expression types have been proposed as a foundation for statically typed processing of XML and similar forms of treestructured data. To date, however, regular expression types have been explored in specialpurpose languages (e.g., XDuce, CDuce, and XQuery) with type systems designed around ..."
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Cited by 68 (8 self)
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Regular expression types have been proposed as a foundation for statically typed processing of XML and similar forms of treestructured data. To date, however, regular expression types have been explored in specialpurpose languages (e.g., XDuce, CDuce, and XQuery) with type systems designed around regular expression types "from the ground up." The goal of the Xtatic language is to bring regular expression types to a broad audience by offering them as a lightweight extension of a popular objectoriented language, C#. We develop...
Metapredicative And Explicit Mahlo: A ProofTheoretic Perspective
"... After briefly discussing the concepts of predicativity, metapredicativity and impredicativity, we turn to the notion of Mahloness as it is treated in various contexts. Afterwards the ..."
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Cited by 5 (2 self)
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After briefly discussing the concepts of predicativity, metapredicativity and impredicativity, we turn to the notion of Mahloness as it is treated in various contexts. Afterwards the
Formalizing NonTermination of Recursive Programs
 J. OF LOGIC AND ALGEBRAIC PROGRAMMING
, 2001
"... In applicative theories the recursion theorem provides a term rec which solves recursive equations. However, it is not provable that a solution obtained by rec is minimal. In the present paper we introduce an applicative theory in which it is possible to dene a least xed point operator. Still, o ..."
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Cited by 1 (0 self)
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In applicative theories the recursion theorem provides a term rec which solves recursive equations. However, it is not provable that a solution obtained by rec is minimal. In the present paper we introduce an applicative theory in which it is possible to dene a least xed point operator. Still, our theory has a standard recursion theoretic interpretation.
Impredicative Overloading in Explicit Mathematics
, 2000
"... In this article we introduce the system OTN of explicit mathematics based on elementary separation, product, join and weak power types. We present a settheoretical model for OTN, and we develop in OTN a theory of impredicative overloading. Together this yields a solution to the problem of impredica ..."
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In this article we introduce the system OTN of explicit mathematics based on elementary separation, product, join and weak power types. We present a settheoretical model for OTN, and we develop in OTN a theory of impredicative overloading. Together this yields a solution to the problem of impredicativity encountered in denotational semantics for overloading and latebinding. Further, our work provides a first example of an application of power types in explicit mathematics. Keywords: Objectoriented constructs, type structure, proof theory. 1 Introduction Overloading is an important concept in objectoriented programming. For example, it occurs when a method is redefined in a subclass or when a class provides several methods with the same name but with di#erent argument types. Theoretically speaking, overloading denotes the possibility that several functions f i with respective types S i # T i may be combined to a new overloaded function f of type {S i # T i } i#I . We then ...
Explicit Mathematics: Power Types and Overloading
"... Systems of explicit mathematics provide an axiomatic framework to represent programs and to prove properties of them. We introduce such a system with a new form of power types using a monotone power type generator. These power types allow us to model impredicative overloading. This is a very general ..."
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Systems of explicit mathematics provide an axiomatic framework to represent programs and to prove properties of them. We introduce such a system with a new form of power types using a monotone power type generator. These power types allow us to model impredicative overloading. This is a very general form of type dependent computation which occurs in the study of objectoriented programming languages. We also present a settheoretic interpretation for monotone power types. Thus establishing the concistency our system of explicit mathematics.
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"... Abstract Regular expression types have been proposed as a foundation for statically typed processing of XML and similar forms of treestructured data. To date, however, regular expression types have been explored in specialpurpose languages (e.g., XDuce, CDuce, and XQuery) with type systems designe ..."
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Abstract Regular expression types have been proposed as a foundation for statically typed processing of XML and similar forms of treestructured data. To date, however, regular expression types have been explored in specialpurpose languages (e.g., XDuce, CDuce, and XQuery) with type systems designed around regular expression types &quot;from the ground up. &quot; The goal of the Xtatic language is to bring regular expression types to a broad audience by offering them as a lightweight extension of a popular objectoriented language, C
Semantic Types and Approximation for Featherweight Java
"... We consider semantics for the classbased objectoriented calculus Featherweight Java based upon approximation. We also define an intersection type assignment systems for this calculus and show that it is sound and complete, i.e. types are preserved under conversion. We establish the link with betwe ..."
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We consider semantics for the classbased objectoriented calculus Featherweight Java based upon approximation. We also define an intersection type assignment systems for this calculus and show that it is sound and complete, i.e. types are preserved under conversion. We establish the link with between type assignment and the approximation semantics by showing an approximation result, which leads to a sufficient condition for headnormalisation and termination. We show the expressivity of our predicate system by defining an encoding of Combinatory Logic into our calculus. We show that this encoding preserves predicateability and also that our system characterises the normalising and strongly normalising terms for this encoding. We thus demonstrate that the great analytic capabilities of intersection types can be applied to the context of classbased object orientation.
Semantic Types for Classbased Objects
, 2012
"... We investigate semanticsbased type assignment for classbased objectoriented programming. Our motivation is developing a theoretical basis for practical, expressive, typebased analysis of the functional behaviour of objectoriented programs. We focus our research using Featherweight Java, studyi ..."
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We investigate semanticsbased type assignment for classbased objectoriented programming. Our motivation is developing a theoretical basis for practical, expressive, typebased analysis of the functional behaviour of objectoriented programs. We focus our research using Featherweight Java, studying two notions of type assignment: one using intersection types, the other a ‘logical ’ restriction of recursive types. We extend to the objectoriented setting some existing results for intersection type systems. In doing so, we contribute to the study of denotational semantics for objectoriented languages. We define a model for Featherweight Java based on approximation, which we relate to our intersection type system via an Approximation Result, proved using a notion of reduction on typing derivations that we show to be strongly normalising. We consider restrictions of our system for which type assignment is decidable, observing that the implicit recursion present in the class mechanism is a limiting factor in making practical use of the expressive power of intersection types. To overcome this, we consider type assignment based on recursive types. Such types traditionally suffer from the inability to characterise convergence, a key element of our approach. To obtain a se