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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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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...
Coherence for Qualified Types
, 1993
"... The meaning of programs in a language with implicit overloading can be described by translating them into a second language that makes the use of overloading explicit. A single program may have many distinct translations and it is important to show that any two translations are semantically equivale ..."
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Cited by 98 (9 self)
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The meaning of programs in a language with implicit overloading can be described by translating them into a second language that makes the use of overloading explicit. A single program may have many distinct translations and it is important to show that any two translations are semantically equivalent to ensure that the meaning of the original program is welldefined. This property is commonly known as coherence. This paper deals with an implicitly typed language that includes support for parametric polymorphism and overloading based on a system of qualified types. Typical applications include Haskell type classes, extensible records and subtyping. In the general case, it is possible to find examples for which the coherence property does not hold. Extending the development of a type inference algorithm for this language to include the calculation of translations, we give a simple syntactic condition on the principal type scheme of a term that is sufficient to guarantee coherence for a large class of programs. One of the most interesting aspects of this work is the use of terms in the target language to provide a semantic interpretation for the ordering relation between types that is used to establish the existence of principal types. On a practical level, our results explain the importance of unambiguous type schemes in Haskell.
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 80 (4 self)
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representing the official policies, either expressed or implied, of the U.S. Government.
Refinement Types for Logical Frameworks
 Informal Proceedings of the Workshop on Types for Proofs and Programs
, 1993
"... We propose a refinement of the type theory underlying the LF logical framework by a form of subtypes and intersection types. This refinement preserves desirable features of LF, such as decidability of typechecking, and at the same time considerably simplifies the representations of many deductive s ..."
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Cited by 41 (8 self)
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We propose a refinement of the type theory underlying the LF logical framework by a form of subtypes and intersection types. This refinement preserves desirable features of LF, such as decidability of typechecking, and at the same time considerably simplifies the representations of many deductive systems. A subtheory can be applied directly to hereditary Harrop formulas which form the basis of Prolog and Isabelle. 1 Introduction Over the past two years we have carried out extensive experiments in the application of the LF Logical Framework [HHP93] to represent and implement deductive systems and their metatheory. Such systems arise naturally in the study of logic and the theory of programming languages. For example, we have formalized the operational semantics and type system of MiniML and implemented a proof of type preservation [MP91] and the correctness of a compiler to a variant of the Categorical Abstract Machine [HP92]. LF is based on a predicative type theory with dependent t...
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 polymorph ..."
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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
Practical RefinementType Checking
, 1997
"... Refinement types allow many more properties of programs to be expressed and statically checked than conventional type systems. We present a practical algorithm for refinementtype checking in a calculus enriched with refinementtype annotations. We prove that our basic algorithm is sound and comple ..."
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Cited by 37 (1 self)
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Refinement types allow many more properties of programs to be expressed and statically checked than conventional type systems. We present a practical algorithm for refinementtype checking in a calculus enriched with refinementtype annotations. We prove that our basic algorithm is sound and complete, and show that every term which has a refinement type can be annotated as required by our algorithm. Our positive experience with an implementation of an extension of this algorithm to the full core language of Standard ML demonstrates that refinement types can be a practical program development tool in a realistic programming language. The required refinement type definitions and annotations are not much of a burden and serve as formal, machinechecked explanations of code invariants which otherwise would remain implicit. 1 Introduction The advantages of staticallytyped programming languages are well known, and have been described many times (e.g. see [Car97]). However, conventional ty...
Characterizing Convergent Terms in Object Calculi via Intersection Types
"... We give a simple characterization of convergent terms in Abadi and Cardelli untyped Object Calculus (&calculus) via intersection types. We consider a calculus with records and its intersection type assignment system. We prove that convergent terms are characterized by their types. The cha ..."
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Cited by 14 (4 self)
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We give a simple characterization of convergent terms in Abadi and Cardelli untyped Object Calculus (&calculus) via intersection types. We consider a calculus with records and its intersection type assignment system. We prove that convergent terms are characterized by their types. The characterization is then inherited by the object calculus via selfapplication interpretation.
Advanced Languages for Systems Software The Fox Project in 1994
, 1994
"... It has been amply demonstrated in recent years that careful attention to the structure of systems software can lead to greater flexibility, reliability, and ease of implementation, without incurring an undue penalty in performance. It is our contention that advanced programming languages particul ..."
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Cited by 14 (0 self)
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It has been amply demonstrated in recent years that careful attention to the structure of systems software can lead to greater flexibility, reliability, and ease of implementation, without incurring an undue penalty in performance. It is our contention that advanced programming languages particularly languages with a mathematically rigorous semantics, and featuring higherorder functions, polymorphic types, firstclass continuations, and a useful and powerful module systemare ideally suited to expressing such structure. Indeed, our previous research has shown that the use of an advanced programming language can have a fundamental effect on system design, leading naturally to system architectures that are highly modular, efficient, and allow reuse of code. We are thus working to demonstrate the viability and benefits of advanced languages for programming realworld systems. To achieve this, we have organized our research into the three areas of language design, compiler technolo...
ML typing, explicit polymorphism and qualified types
 In TACS '94: Conference on theoretical aspects of computer software
, 1994
"... Abstract. The ML type system was originally introduced as a means of identifying a class of terms in a simple untyped language, often referred to as coreML, whose evaluation could be guaranteed not to “go wrong”. In subsequent work, the terms of coreML have also been viewed as a ‘convenient shorth ..."
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Cited by 11 (1 self)
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Abstract. The ML type system was originally introduced as a means of identifying a class of terms in a simple untyped language, often referred to as coreML, whose evaluation could be guaranteed not to “go wrong”. In subsequent work, the terms of coreML have also been viewed as a ‘convenient shorthand ’ for programs in typed languages. Notable examples include studies of ML polymorphism and investigations of overloading, motivated by the use of type classes in Haskell. In this paper, we show how qualified types, originally developed to study type class overloading, can be used to explore the relationship between coreML programs and their translations in an explicitly typed language. Viewing these two distinct applications as instances of a single framework has obvious advantages; many of the results that have been established for one can also be applied to the other. We concentrate particularly on the issue of coherence, establishing sufficient conditions to guarantee that all possible translations of a given coreML term are equivalent. One of the key features of this work is the use of conversions, similar to Mitchell’s retyping functions, to provide an interpretation of the ordering between type schemes in the target language. 1
A Formal Foundation for Concurrent Object Oriented Programming
 PROGRAMMING, DISSERTATION, TECHNISCHE UNIVERSITAT MUNCHEN
, 1995
"... In this thesis we develop a novel, implicitly typed lambdacalculus for objects, by viewing these as extendible casefunctions rather than as extendible records. This ..."
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In this thesis we develop a novel, implicitly typed lambdacalculus for objects, by viewing these as extendible casefunctions rather than as extendible records. This