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37
Domain Theory
 Handbook of Logic in Computer Science
, 1994
"... Least fixpoints as meanings of recursive definitions. ..."
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Cited by 461 (20 self)
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Least fixpoints as meanings of recursive definitions.
Theorems for free!
 FUNCTIONAL PROGRAMMING LANGUAGES AND COMPUTER ARCHITECTURE
, 1989
"... From the type of a polymorphic function we can derive a theorem that it satisfies. Every function of the same type satisfies the same theorem. This provides a free source of useful theorems, courtesy of Reynolds' abstraction theorem for the polymorphic lambda calculus. ..."
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Cited by 326 (6 self)
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From the type of a polymorphic function we can derive a theorem that it satisfies. Every function of the same type satisfies the same theorem. This provides a free source of useful theorems, courtesy of Reynolds' abstraction theorem for the polymorphic lambda calculus.
Games and Full Completeness for Multiplicative Linear Logic
 JOURNAL OF SYMBOLIC LOGIC
, 1994
"... We present a game semantics for Linear Logic, in which formulas denote games and proofs denote winning strategies. We show that our semantics yields a categorical model of Linear Logic and prove full completeness for Multiplicative Linear Logic with the MIX rule: every winning strategy is the den ..."
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Cited by 210 (26 self)
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We present a game semantics for Linear Logic, in which formulas denote games and proofs denote winning strategies. We show that our semantics yields a categorical model of Linear Logic and prove full completeness for Multiplicative Linear Logic with the MIX rule: every winning strategy is the denotation of a unique cutfree proof net. A key role is played by the notion of historyfree strategy; strong connections are made between historyfree strategies and the Geometry of Interaction. Our semantics incorporates a natural notion of polarity, leading to a refined treatment of the additives. We make comparisons with related work by Joyal, Blass et al.
Inheritance As Implicit Coercion
 Information and Computation
, 1991
"... . We present a method for providing semantic interpretations for languages with a type system featuring inheritance polymorphism. Our approach is illustrated on an extension of the language Fun of Cardelli and Wegner, which we interpret via a translation into an extended polymorphic lambda calculus. ..."
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Cited by 116 (3 self)
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. We present a method for providing semantic interpretations for languages with a type system featuring inheritance polymorphism. Our approach is illustrated on an extension of the language Fun of Cardelli and Wegner, which we interpret via a translation into an extended polymorphic lambda calculus. Our goal is to interpret inheritances in Fun via coercion functions which are definable in the target of the translation. Existing techniques in the theory of semantic domains can be then used to interpret the extended polymorphic lambda calculus, thus providing many models for the original language. This technique makes it possible to model a rich type discipline which includes parametric polymorphism and recursive types as well as inheritance. A central difficulty in providing interpretations for explicit type disciplines featuring inheritance in the sense discussed in this paper arises from the fact that programs can typecheck in more than one way. Since interpretations follow the type...
Parametric Polymorphism and Operational Equivalence
 MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE
, 2000
"... Studies of the mathematical properties of impredicative polymorphic types have for the most part focused on the polymorphic lambda calculus of Girard–Reynolds, which is a calculus of total polymorphic functions. This paper considers polymorphic types from a functional programming perspective, where ..."
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Cited by 75 (2 self)
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Studies of the mathematical properties of impredicative polymorphic types have for the most part focused on the polymorphic lambda calculus of Girard–Reynolds, which is a calculus of total polymorphic functions. This paper considers polymorphic types from a functional programming perspective, where the partialness arising from the presence of fixpoint recursion complicates the nature of potentially infinite (‘lazy’) data types. An approach to Reynolds' notion of relational parametricity is developed that works directly on the syntax of a programming language, using a novel closure operator to relate operational behaviour to parametricity properties of types. Working with an extension of Plotkin's PCF with ∀types, lazy lists and existential types, we show by example how the resulting logical relation can be used to prove properties of polymorphic types up to operational equivalence.
A Polymorphic Record Calculus and Its Compilation
 ACM Transactions on Programming Languages and Systems
, 1995
"... this article appeared in Proceedings of ACM Symposium on Principles of Programming Languages, 1992, under the title \A compilation method for MLstyle polymorphic record calculi." This work was partly supported by the Japanese Ministry of Education under scienti c research grant no. 06680319. Author ..."
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Cited by 72 (8 self)
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this article appeared in Proceedings of ACM Symposium on Principles of Programming Languages, 1992, under the title \A compilation method for MLstyle polymorphic record calculi." This work was partly supported by the Japanese Ministry of Education under scienti c research grant no. 06680319. Author's address: Research Institute for Mathematical Sciences, Kyoto University, Sakyoku, Kyoto 60601, JAPAN; email: ohori@kurims.kyotou.ac.jp Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of ACM. To copy otherwise, or to republish, requires a fee and/or speci c permission. c 1999 ACM 01640925/99/01000111 $00.75
A Per Model of Polymorphism and Recursive Types
 In Logic in Computer Science. IEEE
, 1990
"... A model of Reynolds' polymorphic lambda calculus is provided, which also allows the recursive definition of elements and types. The technique is to use a good class of partial equivalence relations over a certain cpo. This allows the combination of inverselimits for recursion and intersection for p ..."
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Cited by 62 (4 self)
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A model of Reynolds' polymorphic lambda calculus is provided, which also allows the recursive definition of elements and types. The technique is to use a good class of partial equivalence relations over a certain cpo. This allows the combination of inverselimits for recursion and intersection for polymorphism.
Syntactic Type Abstraction
 ACM TOPLAS
, 2000
"... data types; F.3.2 [Logics and Meanings of Programs]: Semantics of Programming LanguagesOperational Semantics; F.3.3 [Logics and Meanings of Programs]: Studies of Program ConstructsType Structure General Terms: Languages, Security, Theory, Verification Additional Key Words and Phrases: Opera ..."
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Cited by 52 (1 self)
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data types; F.3.2 [Logics and Meanings of Programs]: Semantics of Programming LanguagesOperational Semantics; F.3.3 [Logics and Meanings of Programs]: Studies of Program ConstructsType Structure General Terms: Languages, Security, Theory, Verification Additional Key Words and Phrases: Operational semantics, parametricity, proof techniques, syntactic proofs, type abstraction 1.
Domain Theoretic Models Of Polymorphism
, 1989
"... We give an illustration of a construction useful in producing and describing models of Girard and Reynolds' polymorphic calculus. The key unifying ideas are that of a Grothendieck fibration and the category of continuous sections associated with it, constructions used in indexed category theory; th ..."
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Cited by 34 (2 self)
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We give an illustration of a construction useful in producing and describing models of Girard and Reynolds' polymorphic calculus. The key unifying ideas are that of a Grothendieck fibration and the category of continuous sections associated with it, constructions used in indexed category theory; the universal types of the calculus are interpreted as the category of continuous sections of the fibration. As a major example a new model for the polymorphic calculus is presented. In it a type is interpreted as a Scott domain. In fact, understanding universal types of the polymorphic calculus as categories of continuous sections appears to be useful generally. For example, the technique also applies to the finitary projection model of Bruce and Longo, and a recent model of Girard. (Indeed the work here was inspired by Girard's and arose through trying to extend the construction of his model to Scott domains.) It is hoped that by pinpointing a key construction this paper will help towards...
Notes on Sconing and Relators
, 1993
"... This paper describes a semantics of typed lambda calculi based on relations. The main mathematical tool is a categorytheoretic method of sconing, also called glueing or Freyd covers. Its correspondence to logical relations is also examined. 1 Introduction Many modern programming languages feature ..."
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Cited by 24 (0 self)
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This paper describes a semantics of typed lambda calculi based on relations. The main mathematical tool is a categorytheoretic method of sconing, also called glueing or Freyd covers. Its correspondence to logical relations is also examined. 1 Introduction Many modern programming languages feature rather sophisticated typing mechanisms. In particular, languages such as ML include polymorphic data types, which allow considerable programming flexibility. Several notions of polymorphism were introduced into computer science by Strachey [Str67], among them the important notion of parametric polymorphism. Strachey's intuitive definition is that a polymorphic function is parametric if it has a uniformly given algorithm in all types, that is, if the function's behavior is independent of the type at which the function is instantiated. Reynolds [Rey83] proposed a mathematical definition of parametric polymorphic functions by means of invariance with respect to certain relations induced by typ...