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Mechanized metatheory for the masses: The POPLmark challenge
 In Theorem Proving in Higher Order Logics: 18th International Conference, number 3603 in LNCS
, 2005
"... Abstract. How close are we to a world where every paper on programming languages is accompanied by an electronic appendix with machinechecked proofs? We propose an initial set of benchmarks for measuring progress in this area. Based on the metatheory of System F<:, a typed lambdacalculus with secon ..."
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Cited by 140 (14 self)
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Abstract. How close are we to a world where every paper on programming languages is accompanied by an electronic appendix with machinechecked proofs? We propose an initial set of benchmarks for measuring progress in this area. Based on the metatheory of System F<:, a typed lambdacalculus with secondorder polymorphism, subtyping, and records, these benchmarks embody many aspects of programming languages that are challenging to formalize: variable binding at both the term and type levels, syntactic forms with variable numbers of components (including binders), and proofs demanding complex induction principles. We hope that these benchmarks will help clarify the current state of the art, provide a basis for comparing competing technologies, and motivate further research. 1
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.
A Unifying TypeTheoretic Framework for Objects
, 1993
"... We give a direct typetheoretic characterization of the basic mechanisms of objectoriented programming, including objects, methods, message passing, and subtyping, by introducing an explicit constructor for object types and suitable introduction, elimination, and equality rules. The resulting abst ..."
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Cited by 37 (9 self)
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We give a direct typetheoretic characterization of the basic mechanisms of objectoriented programming, including objects, methods, message passing, and subtyping, by introducing an explicit constructor for object types and suitable introduction, elimination, and equality rules. The resulting abstract framework provides a basis for justifying and comparing previous encodings of objects based on recursive record types (Cardelli, 1984; Cardelli, 1992; Bruce, 1994; Cook et al., 1990; Mitchell, 1990a) and encodings based on existential types (Pierce & Turner, 1994).
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 36 (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
ObjectOriented Programming Without Recursive Types
 In Proc 20th ACM Symp. Principles of Programming Languages
"... It is widely agreed that recursive types are inherent in the static typing of the essential mechanisms of objectoriented programming: encapsulation, message passing, subtyping, and inheritance. We demonstrate here that modeling object encapsulation in terms of existential types yields a substantiall ..."
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Cited by 35 (1 self)
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It is widely agreed that recursive types are inherent in the static typing of the essential mechanisms of objectoriented programming: encapsulation, message passing, subtyping, and inheritance. We demonstrate here that modeling object encapsulation in terms of existential types yields a substantially more straightforward explanation of these features in a simpler calculus without recursive types. 1 Introduction Static type systems for objectoriented programming languages have progressed significantly in the past decade. The line of research begun by Cardelli [11] and continued by Cardelli [18, 17, 14, 13], Mitchell [32, 10, 33], Bruce [8, 5, 7], and others [31, 39, 21, 10, 23, 20, 19, 26, 29, 44, 45, 46] has culminated in typetheoretic accounts [6, 14] of many of the features of languages like Smalltalk [28]. Our goal here is to reformulate the essential mechanisms of these accounts using a simpler type theory: we give a complete model of encapsulation, message passing, subtyping, ...
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.
Statically Typed Friendly Functions via Partially Abstract Types
, 1993
"... A wellknown shortcoming of the object model of Simula and Smalltalk is the inability to deal cleanly with methods that require access to the internal state of more than one object at a time. Recent language designs have therefore extended the basic object model with notions such as friends' me ..."
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Cited by 26 (1 self)
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A wellknown shortcoming of the object model of Simula and Smalltalk is the inability to deal cleanly with methods that require access to the internal state of more than one object at a time. Recent language designs have therefore extended the basic object model with notions such as friends' methods and protected features, which allow external access to the internal state of objects but limit the scope in which such access can be used. We show that a variant of this idea can be added to any typetheoretic model of the basic objectoriented mechanisms (encapsulation, message passing, and inheritance), using a construction based on Cardelli and Wegner's partially abstract types, a refinement of Mitchell and Plotkin's typetheoretic treatment of abstract types.
Decidable Bounded Quantification
 IN 21ST ACM SYMP. ON PRINCIPLES OF PROGRAMMING LANGUAGES
, 1994
"... The standard formulation of bounded quantification, system F , is difficult to work with and lacks important syntactic properties, such as decidability. More tractable variants have been studied, but those studied so far either exclude significant classes of useful programs or lack a compelling ..."
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Cited by 26 (3 self)
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The standard formulation of bounded quantification, system F , is difficult to work with and lacks important syntactic properties, such as decidability. More tractable variants have been studied, but those studied so far either exclude significant classes of useful programs or lack a compelling semantics. We propose
Multiple Inheritance via Intersection Types
 UNIVERSITY OF EDINBURGH
, 1993
"... Combining intersection types with higherorder subtyping yields a typed model of objectoriented programming with multiple inheritance. Objects, message passing, subtyping, and inheritance appear as programming idioms in a typed calculus, a modelling technique that facilitates experimentation and h ..."
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Cited by 12 (4 self)
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Combining intersection types with higherorder subtyping yields a typed model of objectoriented programming with multiple inheritance. Objects, message passing, subtyping, and inheritance appear as programming idioms in a typed calculus, a modelling technique that facilitates experimentation and helps in distinguishing between essential aspects of the objectoriented style encapsulation and subtype polymorphism, which are directly reflected in the lowlevel type system  and useful but inessential programming idioms such as inheritance. The target calculus, a natural generalization of system F ! with intersection types, is of independent interest. We establish basic structural properties and give a proof of type soundness using a simple semantics based on partial equivalence relations.
Type Destructors
, 1998
"... We study a variant of System F that integrates and generalizes several existing proposals for calculi with structural typing rules. To the usual type constructors (!, \Theta, All, Some, Rec) we add a number of type destructors, each internalizing a useful fact about the subtyping relation. For exa ..."
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Cited by 7 (0 self)
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We study a variant of System F that integrates and generalizes several existing proposals for calculi with structural typing rules. To the usual type constructors (!, \Theta, All, Some, Rec) we add a number of type destructors, each internalizing a useful fact about the subtyping relation. For example, in F with products every closed subtype of a product S\ThetaT must itself be a product S 0 \ThetaT 0 with S 0 !:S and T 0 !:T. We internalise this observation by introducing type destructors .1 and .2 and postulating an equivalence T = j T.1\ThetaT.2 whenever T !: U\ThetaV (including, for example, when T is a variable). In other words, every subtype of a product type literally is a product type, modulo jconversion. Adding type destructors provides a clean solution to the problem of polymorphic update without introducing new term formers, new forms of polymorphism, or quantification over type operators. We illustrate this by giving elementary presentations of two wellknown e...