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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.
Functional interpretations of feasibly constructive arithmetic
 Annals of Pure and Applied Logic
, 1993
"... i ..."
StepIndexed Syntactic Logical Relations for Recursive and Quantified Types
 of Lecture Notes in Computer Science
, 2006
"... We present a sound and complete proof technique, based on syntactic logical relations, for showing contextual equivalence of expressions in a #calculus with recursive types and impredicative universal and existential types. Our development builds on the stepindexed PER model of recursive types ..."
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Cited by 72 (10 self)
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We present a sound and complete proof technique, based on syntactic logical relations, for showing contextual equivalence of expressions in a #calculus with recursive types and impredicative universal and existential types. Our development builds on the stepindexed PER model of recursive types presented by Appel and McAllester. We have discovered that a direct proof of transitivity of that model does not go through, leaving the "PER" status of the model in question. We show how to extend the AppelMcAllester model to obtain a logical relation that we can prove is transitive, as well as sound and complete with respect to contextual equivalence. We then augment this model to support relational reasoning in the presence of quantified types.
A Categorical Programming Language
, 1987
"... A theory of data types and a programming language based on category theory are presented. Data types play a crucial role in programming. They enable us to write programs easily and elegantly. Various programming languages have been developed, each of which may use different kinds of data types. Ther ..."
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Cited by 67 (0 self)
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A theory of data types and a programming language based on category theory are presented. Data types play a crucial role in programming. They enable us to write programs easily and elegantly. Various programming languages have been developed, each of which may use different kinds of data types. Therefore, it becomes important to organize data types systematically so that we can understand the relationship between one data type and another and investigate future directions which lead us to discover exciting new data types. There have been several approaches to systematically organize data types: algebraic specification methods using algebras, domain theory using complete partially ordered sets and type theory using the connection between logics and data types. Here, we use category theory. Category theory has proved to be remarkably good at revealing the nature of mathematical objects, and we use it to understand the true nature of data types in programming.
An intuitionistic theory of types
"... An earlier, not yet conclusive, attempt at formulating a theory of this kind was made by Scott 1970. Also related, although less closely, are the type and logic free theories of constructions of Kreisel 1962 and 1965 and Goodman 1970. In its first version, the present theory was based on the strongl ..."
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Cited by 66 (0 self)
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An earlier, not yet conclusive, attempt at formulating a theory of this kind was made by Scott 1970. Also related, although less closely, are the type and logic free theories of constructions of Kreisel 1962 and 1965 and Goodman 1970. In its first version, the present theory was based on the strongly impredicative axiom that there is a type of all types whatsoever, which is at the same time a type and an object of that type. This axiom had to be abandoned, however, after it was shown to lead to a contradiction by Jean Yves Girard. I am very grateful to him for showing me his paradox. The change that it necessitated is so drastic that my theory no longer contains intuitionistic simple type theory as it originally did. Instead, its proof theoretic strength should be close to that of predicative analysis.
Intersection Type Assignment Systems
 THEORETICAL COMPUTER SCIENCE
, 1995
"... This paper gives an overview of intersection type assignment for the Lambda Calculus, as well as compare in detail variants that have been defined in the past. It presents the essential intersection type assignment system, that will prove to be as powerful as the wellknown BCDsystem. It is essenti ..."
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Cited by 61 (33 self)
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This paper gives an overview of intersection type assignment for the Lambda Calculus, as well as compare in detail variants that have been defined in the past. It presents the essential intersection type assignment system, that will prove to be as powerful as the wellknown BCDsystem. It is essential in the following sense: it is an almost syntax directed system that satisfies all major properties of the BCDsystem, and the types used are the representatives of equivalence classes of types in the BCDsystem. The set of typeable terms can be characterized in the same way, the system is complete with respect to the simple type semantics, and it has the principal type property.
Computational types from a logical perspective
 Journal of Functional Programming
, 1998
"... Moggi’s computational lambda calculus is a metalanguage for denotational semantics which arose from the observation that many different notions of computation have the categorical structure of a strong monad on a cartesian closed category. In this paper we show that the computational lambda calculus ..."
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Cited by 54 (6 self)
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Moggi’s computational lambda calculus is a metalanguage for denotational semantics which arose from the observation that many different notions of computation have the categorical structure of a strong monad on a cartesian closed category. In this paper we show that the computational lambda calculus also arises naturally as the term calculus corresponding (by the CurryHoward correspondence) to a novel intuitionistic modal propositional logic. We give natural deduction, sequent calculus and Hilbertstyle presentations of this logic and prove strong normalisation and confluence results. 1
Inductive Data Type Systems
 THEORETICAL COMPUTER SCIENCE
, 1997
"... In a previous work (“Abstract Data Type Systems”, TCS 173(2), 1997), the last two authors presented a combined language made of a (strongly normalizing) algebraic rewrite system and a typed λcalculus enriched by patternmatching definitions following a certain format, called the “General Schema”, w ..."
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Cited by 44 (10 self)
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In a previous work (“Abstract Data Type Systems”, TCS 173(2), 1997), the last two authors presented a combined language made of a (strongly normalizing) algebraic rewrite system and a typed λcalculus enriched by patternmatching definitions following a certain format, called the “General Schema”, which generalizes the usual recursor definitions for natural numbers and similar “basic inductive types”. This combined language was shown to be strongly normalizing. The purpose of this paper is to reformulate and extend the General Schema in order to make it easily extensible, to capture a more general class of inductive types, called “strictly positive”, and to ease the strong normalization proof of the resulting system. This result provides a computation model for the combination of an algebraic specification language based on abstract data types and of a strongly typed functional language with strictly positive inductive types.