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Categorical Logic of Names and Abstraction in Action Calculi
, 1993
"... ion elimination Definition 3.1. A monoidal category where every object has a commutative comonoid structure is said to be semicartesian. An action category is a K\Omega category with a distinguished admissible commutative comonoid structure on every object. A semicartesian category is cartesi ..."
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Cited by 21 (9 self)
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ion elimination Definition 3.1. A monoidal category where every object has a commutative comonoid structure is said to be semicartesian. An action category is a K\Omega category with a distinguished admissible commutative comonoid structure on every object. A semicartesian category is cartesian if and only if each object carries a unique comonoid structure, and such structures form two natural families, \Delta and !. The naturality means that all morphisms of the category must be comonoid homomorphisms. In action categories, the property of semicartesianness is fixed as structure: on each object, a particular comonoid structure is chosen. This choice may be constrained by some given graphic operations, with respect to which the structures must be admissible. The proof of proposition 2.6 shows that such structures determine the abstraction operators, and are determined by them. This is the essence of the equivalence of action categories and action calculi. As the embodiment of 2...
Definability and full abstraction
 GDP FESTSCHRIFT
"... Game semantics has renewed denotational semantics. It offers among other things an attractive classification of programming features, and has brought a bunch of new definability results. In parallel, in the denotational semantics of proof theory, several full completeness results have been shown sin ..."
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Cited by 17 (2 self)
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Game semantics has renewed denotational semantics. It offers among other things an attractive classification of programming features, and has brought a bunch of new definability results. In parallel, in the denotational semantics of proof theory, several full completeness results have been shown since the early nineties. In this note, we review the relation between definability and full abstraction, and we put a few old and recent results of this kind in perspective.
Confluence of Extensional and NonExtensional λcalculi with Explicit Substitutions
 Theoretical Computer Science
"... This paper studies confluence of extensional and nonextensional calculi with explicit substitutions, where extensionality is interpreted by jexpansion. For that, we propose a scheme for explicit substitutions which describes those abstract properties that are sufficient to guarantee confluence. O ..."
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Cited by 12 (2 self)
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This paper studies confluence of extensional and nonextensional calculi with explicit substitutions, where extensionality is interpreted by jexpansion. For that, we propose a scheme for explicit substitutions which describes those abstract properties that are sufficient to guarantee confluence. Our method makes it possible to treat at the same time many wellknown calculi such as oe , oe * , OE , s , AE , f , d and dn . Keywords: functional programming, calculi, explicit substitutions, confluence, extensionality. 1 Introduction The calculus is a convenient framework to study functional programming, where the evaluation process is modeled by fireduction. The main mechanism used to perform fireduction is substitution, which consists of the replacement of formal parameters by actual arguments. The correctness of substitution is guaranteed by a systematic renaming of bound variables, inconvenient which can be simply avoided in the calculus `a la de Bruijn by using natur...
Notes on game semantics
, 2006
"... The subject called game semantics grew out as a coherent body of work from two seminal works of the early 1990’s, with forerunners in logic, recursion theory, and semantics. Game semantics allows to provide precise and also natural, interactive semantics to most of the classical features of programm ..."
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The subject called game semantics grew out as a coherent body of work from two seminal works of the early 1990’s, with forerunners in logic, recursion theory, and semantics. Game semantics allows to provide precise and also natural, interactive semantics to most of the classical features of programming such as functions, control, references. The precision is measured by definability and in some cases by full interpretation are being developed, which opens the way for connecting the uses of games in semantics and in verification. 1
This document in subdirectoryRS/96/56/ Modeling Sharing and Recursion for Weak Reduction Strategies using Explicit Substitution
, 1996
"... Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS ..."
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Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS
Modeling Sharing and Recursion for Weak Reduction Strategies using Explicit Substitution
 In Proc. PLILP'96, the 8 th International Symposium on Programming Languages, Implementations, Logics, and Programs, volume 1140 of LNCS
, 1996
"... We present the oe w calculus, a formal synthesis of the concepts of sharing and explicit substitution for weak reduction. We show how w can be used as a foundation of implementations of functional programming languages by modeling the essential ingredients of such implementations, namely wea ..."
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We present the oe w calculus, a formal synthesis of the concepts of sharing and explicit substitution for weak reduction. We show how w can be used as a foundation of implementations of functional programming languages by modeling the essential ingredients of such implementations, namely weak reduction strategies, recursion, space leaks, recursive data structures, and parallel evaluation, in a uniform way.