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Compiling polymorphism using intensional type analysis
 In Symposium on Principles of Programming Languages
, 1995
"... The views and conclusions contained in this document are those of the authors and should not be interpreted as ..."
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Cited by 260 (18 self)
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The views and conclusions contained in this document are those of the authors and should not be interpreted as
Typed closure conversion
 In Proceedings of the 23th Symposium on Principles of Programming Languages (POPL
, 1996
"... The views and conclusions contained in this document are those of the authors and should not be interpreted as representing o cial policies, either expressed or implied, of the Advanced Research Projects Agency or the U.S. Government. Any opinions, ndings, and conclusions or recommendations expresse ..."
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Cited by 154 (22 self)
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The views and conclusions contained in this document are those of the authors and should not be interpreted as representing o cial policies, either expressed or implied, of the Advanced Research Projects Agency or the U.S. Government. Any opinions, ndings, and conclusions or recommendations expressed in this material are those of the We study the typing properties of closure conversion for simplytyped and polymorphiccalculi. Unlike most accounts of closure conversion, which only treat the untypedcalculus, we translate welltyped source programs to welltyped target programs. This allows later compiler phases to take advantage of types for representation analysis and tagfree garbage collection, and it facilitates correctness proofs. Our account of closure conversion for the simplytyped language takes advantage of a simple model of objects by mapping closures to existentials. Closure conversion for the polymorphic language requires additional type machinery, namely translucency in the style of Harper and Lillibridge's module calculus, to express the type of a closure.
Types, Abstraction, and Parametric Polymorphism, Part 2
, 1991
"... The concept of relations over sets is generalized to relations over an arbitrary category, and used to investigate the abstraction (or logicalrelations) theorem, the identity extension lemma, and parametric polymorphism, for Cartesianclosedcategory models of the simply typed lambda calculus and P ..."
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Cited by 53 (1 self)
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The concept of relations over sets is generalized to relations over an arbitrary category, and used to investigate the abstraction (or logicalrelations) theorem, the identity extension lemma, and parametric polymorphism, for Cartesianclosedcategory models of the simply typed lambda calculus and PLcategory models of the polymorphic typed lambda calculus. Treatments of Kripke relations and of complete relations on domains are included.
Relational interpretations of recursive types in an operational setting
 Information and Computation
, 1997
"... Submitted for publication to Information and Computation. A summary of this paper appeared in TACS '97. ..."
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Cited by 34 (3 self)
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Submitted for publication to Information and Computation. A summary of this paper appeared in TACS '97.
On Girard’s “Candidats de Réductibilité
 Logic and Computer Science
, 1990
"... Abstract: We attempt to elucidate the conditions required on Girard’s candidates of reducibility (in French, “candidats de reductibilité”) in order to establish certain properties of various typed lambda calculi, such as strong normalization and ChurchRosser property. We present two generalizations ..."
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Cited by 33 (5 self)
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Abstract: We attempt to elucidate the conditions required on Girard’s candidates of reducibility (in French, “candidats de reductibilité”) in order to establish certain properties of various typed lambda calculi, such as strong normalization and ChurchRosser property. We present two generalizations of the candidates of reducibility, an untyped version in the line of Tait and Mitchell, and a typed version which is an adaptation of Girard’s original method. As an application of this general result, we give two proofs of strong normalization for the secondorder polymorphic lambda calculus under ⌘reduction (and thus underreduction). We present two sets of conditions for the typed version of the candidates. The first set consists of conditions similar to those used by Stenlund (basically the typed version of Tait’s conditions), and the second set consists of Girard’s original conditions. We also compare these conditions, and prove that Girard’s conditions are stronger than Tait’s conditions. We give a new proof of the ChurchRosser theorem for bothreduction and ⌘reduction, using the modified version of Girard’s method. We also compare various proofs that have appeared in the literature (see section 11). We conclude by sketching the extension of the above results to Girard’s higherorder polymorphic calculus F!, and in appendix 1, to F! with product types. i 1
From semantics to rules: A machine assisted analysis
 Proceedings of CSL '93, LNCS 832
, 1999
"... this paper is similar to the one in [2]. In this paper they define a normalization function for simply typed ..."
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Cited by 29 (0 self)
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this paper is similar to the one in [2]. In this paper they define a normalization function for simply typed
A New Characterization of Lambda Definability
, 1993
"... . We give a new characterization of lambda definability in Henkin models using logical relations defined over ordered sets with varying arity. The advantage of this over earlier approaches by Plotkin and Statman is its simplicity and universality. Yet, decidability of lambda definability for heredit ..."
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Cited by 26 (1 self)
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. We give a new characterization of lambda definability in Henkin models using logical relations defined over ordered sets with varying arity. The advantage of this over earlier approaches by Plotkin and Statman is its simplicity and universality. Yet, decidability of lambda definability for hereditarily finite Henkin models remains an open problem. But if the variable set allowed in terms is also restricted to be finite then our techniques lead to a decision procedure. 1 Introduction An applicative structure consists of a family (A oe ) oe2T of sets, one for each type oe, together with a family (app oe;ø ) oe;ø 2T of application functions, where app oe;ø maps A oe!ø \Theta A oe into A ø . For an applicative structure to be a model of the simply typed lambda calculus (in which case we call it a Henkin model, following [4]), one requires two more conditions to hold. It must be extensional which means that the elements of A oe!ø are uniquely determined by their behavior under app oe;ø...
Abstract Interpretation of Functional Languages: From Theory to Practice
, 1991
"... Abstract interpretation is the name applied to a number of techniques for reasoning about programs by evaluating them over nonstandard domains whose elements denote properties over the standard domains. This thesis is concerned with higherorder functional languages and abstract interpretations with ..."
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Cited by 25 (0 self)
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Abstract interpretation is the name applied to a number of techniques for reasoning about programs by evaluating them over nonstandard domains whose elements denote properties over the standard domains. This thesis is concerned with higherorder functional languages and abstract interpretations with a formal semantic basis. It is known how abstract interpretation for the simply typed lambda calculus can be formalised by using binary logical relations. This has the advantage of making correctness and other semantic concerns straightforward to reason about. Its main disadvantage is that it enforces the identification of properties as sets. This thesis shows how the known formalism can be generalised by the use of ternary logical relations, and in particular how this allows abstract values to deno...
Finitary PCF is not decidable
 Theoretical Computer Science
, 1996
"... The question of the decidability of the observational ordering of finitary PCF was raised [5] to give mathematical content to the full abstraction problem for PCF [9, 14]. We show that the ordering is in fact undecidable. This result places limits on how explicit a representation of the fully abstra ..."
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Cited by 25 (0 self)
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The question of the decidability of the observational ordering of finitary PCF was raised [5] to give mathematical content to the full abstraction problem for PCF [9, 14]. We show that the ordering is in fact undecidable. This result places limits on how explicit a representation of the fully abstract model can be. It also gives a slight strengthening of the author’s earlier result on typed λdefinability [6].
Correspondence between Operational and Denotational Semantics
 Handbook of Logic in Computer Science
, 1995
"... This course introduces the operational and denotational semantics of PCF and examines the relationship between the two. Topics: Syntax and operational semantics of PCF, Activity Lemma, undefinability of parallel or; Context Lemma (first principles proof) and proof by logical relations Denotational ..."
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This course introduces the operational and denotational semantics of PCF and examines the relationship between the two. Topics: Syntax and operational semantics of PCF, Activity Lemma, undefinability of parallel or; Context Lemma (first principles proof) and proof by logical relations Denotational semantics of PCF induced by an interpretation; (standard) Scott model, adequacy, weak adequacy and its proof (by a computability predicate) Domain Theory up to SFP and Scott domains; non full abstraction of the standard model, definability of compact elements and full abstraction for PCFP (PCF + parallel or), properties of orderextensional (continuous) models of PCF, Milner's model and Mulmuley's construction (excluding proofs) Additional topics (time permitting): results on pure simplytyped lambda calculus, Friedman 's Completeness Theorem, minimal model, logical relations and definability, undecidability of lambda definability (excluding proof), dIdomains and stable functions Homepa...