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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],
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 include both the ..."
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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.
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...
Polarized HigherOrder Subtyping
, 1997
"... The calculus of higher order subtyping, known as F ω ≤ , a higherorder polymorphic λcalculus with subtyping, is expressive enough to serve as core calculus for typed objectoriented languages. The versions considered in the literature usually support only pointwise subtyping of type operators, whe ..."
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Cited by 32 (1 self)
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The calculus of higher order subtyping, known as F ω ≤ , a higherorder polymorphic λcalculus with subtyping, is expressive enough to serve as core calculus for typed objectoriented languages. The versions considered in the literature usually support only pointwise subtyping of type operators, where two types S U and T U are in subtype relation, if S and T are. In the widely cited, unpublished note [Car90], Cardelli presents F ω ≤ in a more general form going beyond pointwise subtyping of type applications in distinguishing between monotone and antimonotone operators. Thus, for instance, T U1 is a subtype of T U2, if U1 ≤ U2 and T is a monotone operator. My thesis extends F ω ≤ by polarized application, it explores its proof theory, establishing decidability of polarized F ω ≤. The inclusion of polarized application rules leads to an interdependence of the subtyping and the kinding system. This contrasts with pure F ω ≤ , where subtyping depends on kinding but not vice versa. To retain decidability of the system, the equalbounds subtyping rule for alltypes is rephrased in the polarized setting as a mutualsubtype requirement of the upper bounds.
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
Typed operational semantics for higher order subtyping
, 1997
"... Bounded operator abstraction is a language construct relevant to object oriented programming languages and to ML2000, the successor to Standard ML. In this paper, we introduce F!^, a variant of F!!: with this feature and with Cardelli and Wegner's kernel Fun rule for quantifiers. We define a typed ..."
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Cited by 13 (4 self)
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Bounded operator abstraction is a language construct relevant to object oriented programming languages and to ML2000, the successor to Standard ML. In this paper, we introduce F!^, a variant of F!!: with this feature and with Cardelli and Wegner's kernel Fun rule for quantifiers. We define a typed operational semantics with subtyping and prove that it is equivalent with F!^, using a Kripke model to prove soundness. The typed operational semantics provides a powerful tool to establish the metatheoretic properties of F!^, such as ChurchRosser, subject reduction, the admissibility of structural rules, and the equivalence with the algorithmic presentation of the system.
Programming in the picalculus: A tutorial introduction to Pict (Pict Version 3.8d)
, 1996
"... Pict is a programming language in the ML tradition, formed by adding highlevel derived forms and a powerful static type system to a tiny core language. The core, Milner's picalculus, has been used as a theoretical foundation for a broad class of concurrent computations. The goal in Pict is to iden ..."
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Cited by 7 (2 self)
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Pict is a programming language in the ML tradition, formed by adding highlevel derived forms and a powerful static type system to a tiny core language. The core, Milner's picalculus, has been used as a theoretical foundation for a broad class of concurrent computations. The goal in Pict is to identify idioms that arise naturally when these primitives are used to build working programs  idioms such as basic data structures, protocols for returning results, higherorder programming, selective communication, and concurrent objects. The type system integrates a number of features found in recent work on theoretical foundations for typed objectoriented languages: higherorder polymorphism, simple recursive types, subtyping, and a useful partial type inference algorithm. This is a tutorial introduction to Pict, with examples and exercises. Consumer Safety Warning Pict is an evolving language design and the current implementation is experimental software. You are welcome to use Pict in...