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SemiExplicit FirstClass Polymorphism for ML
 Information and Computation
, 1999
"... We propose a modest conservative extension to ML that allows semiexplicit firstclass polymorphism while preserving the essential properties of type inference. In our proposal, the introduction of polymorphic types is fully explicit, that is, both introduction points and exact polymorphic types ..."
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Cited by 20 (1 self)
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We propose a modest conservative extension to ML that allows semiexplicit firstclass polymorphism while preserving the essential properties of type inference. In our proposal, the introduction of polymorphic types is fully explicit, that is, both introduction points and exact polymorphic types are to be specified. However, the elimination of polymorphic types is semiimplicit: only elimination points are to be specified as polymorphic types themselves are inferred. This extension is particularly useful in Objective ML where polymorphism replaces subtyping. Introduction The success of the ML language is due to its combination of several attractive features. Undoubtedly, the polymorphism of ML [Damas and Milner, 1982] or polymorphism `a la ML with the type inference it allows, is a major advantage. The ML type system stays in close correspondence with the rules of logic, following the CurryHoward isomorphism between types and formulas, which provides a simple intuition, ...
Extending ML with SemiExplicit HigherOrder Polymorphism
, 1997
"... . We propose a modest conservative extension to ML that allows semiexplicit higherorder polymorphism while preserving the essential properties of ML. In our proposal, the introduction of polymorphic types remains fully explicit, that is, both the introduction and the exact polymorphic type must be ..."
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Cited by 18 (8 self)
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. We propose a modest conservative extension to ML that allows semiexplicit higherorder polymorphism while preserving the essential properties of ML. In our proposal, the introduction of polymorphic types remains fully explicit, that is, both the introduction and the exact polymorphic type must be specified. However, the elimination of polymorphic types is now semiimplicit: only the elimination itself must be specified as the polymorphic type is inferred. This extension is particularly useful in Objective ML where polymorphism replaces subtyping. Introduction The success of the ML language is due to its combination of several attractive features. Undoubtedly, the polymorphism of ML [2] or polymorphism `a la ML with the type inference it allows, is a major advantage. The ML type system stays in close correspondence with the rules of logic, following the CurryHoward isomorphism between types and formulas, which provides a simple intuition, and a strong type discipline. Simult...
Calculi of Generalised βReduction and Explicit Substitutions: The TypeFree and Simply Typed Versions
, 1998
"... Extending the λcalculus with either explicit substitution or generalized reduction has been the subject of extensive research recently, and still has many open problems. This paper is the first investigation into the properties of a calculus combining both generalized reduction and explicit substit ..."
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Cited by 14 (7 self)
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Extending the λcalculus with either explicit substitution or generalized reduction has been the subject of extensive research recently, and still has many open problems. This paper is the first investigation into the properties of a calculus combining both generalized reduction and explicit substitutions. We present a calculus, gs, that combines a calculus of explicit substitution, s, and a calculus with generalized reduction, g. We believe that gs is a useful extension of the  calculus, because it allows postponement of work in two different but complementary ways. Moreover, gs (and also s) satisfies properties desirable for calculi of explicit substitutions and generalized reductions. In particular, we show that gs preserves strong normalization, is a conservative extension of g, and simulates fireduction of g and the classical calculus. Furthermore, we study the simply typed versions of s and gs, and show that welltyped terms are strongly normalizing and that other properties,...
Typability and Type Checking in the SecondOrder lambdaCalculus Are Equivalent and Undecidable
, 1993
"... We consider the problems of typability and type checking in the Girard/Reynolds secondorder polymorphic typedcalculus, for which we use the short name "System F" and which we use in the "Curry style" where types are assigned to pureterms. These problems have been considered and proven to be d ..."
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Cited by 12 (1 self)
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We consider the problems of typability and type checking in the Girard/Reynolds secondorder polymorphic typedcalculus, for which we use the short name "System F" and which we use in the "Curry style" where types are assigned to pureterms. These problems have been considered and proven to be decidable or undecidable for various restrictions and extensions of System F and other related systems, and lowerbound complexity results for System F have been achieved, but they have remained "embarrassing open problems" 3 for System F itself. We first prove that type checking in System F is undecidable by a reduction from semiunification. We then prove typability in System F is undecidable by a reduction from type checking. Since the reverse reduction is already known, this implies the two problems are equivalent. The second reduction uses a novel method of constructingterms such that in all type derivations, specific bound variables must always be assigned a specific type. Using this technique, we can require that specif subterms must be typable using a specific, fixed type assignment in order for the entire term to be typable at all. Any desired type assignment maybe simulated. We develop this method, which we call \constants for free", for both the K and I calculi.
ML^F  Raising ML to the Power of System F
 In ICFP ’03: Proceedings of the eighth ACM SIGPLAN international conference on Functional programming
, 2003
"... We propose a type system ML F that generalizes ML with firstclass polymorphism as in System F. We perform partial type reconstruction. As in ML and in opposition to System F, each typable expression admits a principal type, which can be inferred. Furthermore, all expressions of ML are welltyped, ..."
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Cited by 12 (0 self)
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We propose a type system ML F that generalizes ML with firstclass polymorphism as in System F. We perform partial type reconstruction. As in ML and in opposition to System F, each typable expression admits a principal type, which can be inferred. Furthermore, all expressions of ML are welltyped, with a possibly more general type than in ML, without any need for type annotation. Only arguments of functions that are used polymorphically must be annotated, which allows to type all expressions of System F as well.
Branching Types
, 2002
"... Although systems with intersection types have many unique capabilities, there has never been a fully satisfactory explicitly typed system with intersection types. We introduce and prove the basic properties of # , a typed #calculus with branching types and types with quantification over type ..."
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Cited by 11 (5 self)
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Although systems with intersection types have many unique capabilities, there has never been a fully satisfactory explicitly typed system with intersection types. We introduce and prove the basic properties of # , a typed #calculus with branching types and types with quantification over type selection parameters. The new system # an explicitly typed system with the same expressiveness as a system with intersection types. Typing derivations in # use branching types to squash together what would be separate parallel derivations in earlier systems with intersection types.
Raising ML to the Power of System F
 In ICFP ’03: Proceedings of the eighth ACM SIGPLAN international conference on Functional programming
, 2003
"... We propose a type system MLF that generalizes ML with firstclass polymorphism as in System F. We perform partial type reconstruction. As in ML and in opposition to System F, each typable expression admits a principal type, which can be inferred. Furthermore, all expressions of ML are welltyped, wi ..."
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Cited by 10 (0 self)
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We propose a type system MLF that generalizes ML with firstclass polymorphism as in System F. We perform partial type reconstruction. As in ML and in opposition to System F, each typable expression admits a principal type, which can be inferred. Furthermore, all expressions of ML are welltyped, with a possibly more general type than in ML, without any need for type annotation. Only arguments of functions that are used polymorphically must be annotated, which allows to type all expressions of System F as well.
Type Checking Meta Programs
 In Workshop on Logical Frameworks and MetaLanguages
, 1999
"... We report on preliminary experiments with inferring types for meta programs: programs that manipulate programs. For this purpose we provide a twolevel type system in a fragment of a higherorder system of dependent types. The system is formulated with automatic type inference in mind. In particular ..."
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Cited by 7 (0 self)
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We report on preliminary experiments with inferring types for meta programs: programs that manipulate programs. For this purpose we provide a twolevel type system in a fragment of a higherorder system of dependent types. The system is formulated with automatic type inference in mind. In particular, we give a type system for dependent types and a constraint generation procedure which generates semiunification constraints from untyped terms that have a solution if and only if the terms have a type annotation in the type system. More interestingly, typability is preserved under reflection, i.e. when object level programs are reflected to the metalevel. 1 Introduction We would like to have a way to infer that the operations meta programs perform on their objects preserve typability of the objects. Here, we develop type rules and constraint solving techniques for inferring types of such programs. On the surface this may seem as an innocent exercise in extending for instance the Hindley...