Author

# Delia Kesner

Other affiliations: University of Paris

Bio: Delia Kesner is an academic researcher from University of Paris-Sud. The author has contributed to research in topics: Normalization (statistics) & Normalisation by evaluation. The author has an hindex of 6, co-authored 7 publications receiving 175 citations. Previous affiliations of Delia Kesner include University of Paris.

##### Papers

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TL;DR: The operational behaviour of the calculus and some of its fundamental properties such as confluence, preservation of strongnormalisation, strong normalisation of simply typed terms, step by step simulation of @b-reduction and full composition are shown.

Abstract: We present a simple term calculus with an explicit control of erasure and duplication of substitutions, enjoying a sound and complete correspondence with the intuitionistic fragment of Linear Logic's proof-nets. We show the operational behaviour of the calculus and some of its fundamental properties such as confluence, preservation of strong normalisation, strong normalisation of simply typed terms, step by step simulation of @b-reduction and full composition.

51 citations

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TL;DR: This work presents a typed functional calculus that emphasizes the strong connection between the structures of whole pattern definitions and their types, and proves the basic properties connecting typing and evaluation: subject reduction and strong normalization.

Abstract: The theory of programming with pattern-matching function definitions has been studied mainly in the framework of first-order rewrite systems. We present a typed functional calculus that emphasizes the strong connection between the structures of whole pattern definitions and their types. In this calculus, type-checking guarantees the absence of runtime errors caused by non-exhaustive pattern-matching definitions. Its operational semantics is deterministic in a natural way, without the imposition of ad hoc solutions such as clause order or “best fit”. In the spirit of the Curry?Howard isomorphism, we design the calculus as a computational interpretation of the Gentzen sequent proofs for the intuitionistic propositional logic. We prove the basic properties connecting typing and evaluation: subject reduction and strong normalization. We believe that this calculus offers a rational reconstruction of the pattern-matching features found in successful functional languages.

35 citations

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TL;DR: This special issue of Mathematical Structures in Computer Science is dedicated to the theory and applications of explicit substitutions, which have attracted a growing community of researchers in the last decade, especially in the study of explicit substitution as a means of bridging the gap between theory and practice in the implementation of programming languages.

Abstract: This special issue of Mathematical Structures in Computer Science is dedicated to the theory and applications of explicit substitutions, which have attracted a growing community of researchers in the last decade, especially in the study of explicit substitutions as a means of bridging the gap between theory and practice in the implementation of programming languages, as well as theorem provers and proof checkers.Such implementations typically rely on formal calculi defined using implicit substitution operations that are left at the meta-level, so that they need to turn these meta-level operations into efficient executable code, and this is often fairly intricate and distant from the formal calculi. This causes a significant gap between theory and practice.Explicit substitutions considerably reduce this gap by bringing the meta-level operations down to the object-level calculus – where they are represented explicitly – allowing us in this way to give formal and robust models for the techniques actually used in implementations, and providing at the same time a more flexible tool for controlling the intermediate steps of evaluation.All the papers in this issue were invited on the basis of their quality and relevance to the domain, and subjected to the refereeing process of MSCS. Most of them are substantially expanded and revised versions of work originally presented at Westapp'98 and Westapp'99, the first and second ‘Workshop on Explicit Substitutions: Theory and Applications to Programs and Proofs’, which were held in conjunction with RTA'98 in Tsukuba, Japan, and with Floc'99 in Trento, Italy, respectively.As guest editor, I would like to express my warm thanks both to the authors, for their high-quality contributions to this special issue, and to the referees, whose scientific role was essential in improving the presentation of these contributions.

33 citations

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27 Jul 1996TL;DR: A general scheme for explicit substitutions is proposed which describes those abstract properties that are sufficient to guarantee confluence in λ-calculi, and makes it possible to treat at the same time many well-known calculi, or some other new calculi that are proposed in this paper.

Abstract: This paper studies confluence properties of extensional and non-extensional λ-calculi with explicit substitutions, where extensionality is interpreted by η-expansion. For that, we propose a general scheme for explicit substitutions which describes those abstract properties that are sufficient to guarantee confluence. Our general scheme makes it possible to treat at the same time many well-known calculi such as λσ, λσ⇑ and λv, or some other new calculi that we propose in this paper. We also show for those calculi not fitting in the general scheme that can be translated to another one fining the scheme, such as λs, how to reason about confluence properties of their extensional and non-extensional versions.

25 citations

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25 Sep 1996

TL;DR: In this article, the authors studied the preservation of β-strong normalization by λ d and λ n, two confluent λ-calculi with explicit substitutions defined in [10].

Abstract: We study preservation of β-strong normalization by λ d and λ dn , two confluent λ-calculi with explicit substitutions defined in [10]; the particularity of these calculi is that both have a composition operator for substitutions We develop an abstract simulation technique allowing to reduce preservation of β-strong normalization of one calculus to that of another one, and apply said technique to reduce preservation of β-strong normalization of λ d and λ dn to that of λ f , another calculus having no composition operator Then, preservation of β-strong normalization of λ f is shown using the same technique as in [2] As a consequence, λ d and λ dn become the first λ-calculi with explicit substitutions having composition and preserving β- strong normalization We also apply our technique to reduce preservation of β-strong normalization of the calculus λ v in [14] to that of λ f

18 citations

##### Cited by

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04 Apr 2013TL;DR: The Curry-Howard isomorphism as discussed by the authors is a type-free lambda-calculus, which is a variant of the Lambda-cube, and it can be expressed as follows:

Abstract: Preface Outline Acknowledgements 1. Typefree lambda-calculus 2. Intuitionistic logic 3. Simply typed lambdacalculus 4. The Curry-Howard isomorphism 5. Proofs as combinators 6. Classical logic and control operators 7. Sequent calculus 8. Firstorder logic 9. Firstorder arithmetic 10. Godel's system T 11. Secondorder logic and polymorphism 12. Secondorder arithmetic 13. Dependent types 14. Pure type systems and the lambda-cube 15. Solutions and hints to selected exercises 16. Solutions for chapter 6 Appendix A Mathematical Background Appendix B Solutions to Selected Exercises Bibliography Index

401 citations

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01 Sep 2000

TL;DR: The μ -calculus is presented, a syntax for λ-calculus + control operators exhibiting symmetries such as program/context and call-by-name/call- by-value, derived from implicational Gentzen's sequent calculus LK.

Abstract: We present the μ -calculus, a syntax for λ-calculus + control operators exhibiting symmetries such as program/context and call-by-name/call-by-value. This calculus is derived from implicational Gentzen's sequent calculus LK, a key classical logical system in proof theory. Under the Curry-Howard correspondence between proofs and programs, we can see LK, or more precisely a formulation called LKμ , as a syntax-directed system of simple types for μ -calculus. For μ -calculus, choosing a call-by-name or call-by-value discipline for reduction amounts to choosing one of the two possible symmetric orientations of a critical pair. Our analysis leads us to revisit the question of what is a natural syntax for call-by-value functional computation. We define a translation of λμ-calculus into μ -calculus and two dual translations back to λ-calculus, and we recover known CPS translations by composing these translations.

379 citations

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TL;DR: A methodology of abstract consistency methods is developed by providing the necessary model existence theorems needed to analyze completeness of (machine-oriented) higher-order calculi with respect to these model classes.

Abstract: In this paper we re-examine the semantics of classical higher-order logic with the purpose of clarifying the role of extensionality. To reach this goal, we distinguish nine classes of higher-order models with respect to various combinations of Boolean extensionality and three forms of functional extensionality. Furthermore, we develop a methodology of abstract consistency methods (by providing the necessary model existence theorems) needed to analyze completeness of (machine-oriented) higher-order calculi with respect to these model classes.

124 citations

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26 Jun 2007TL;DR: It is shown that all functional Pure Type Systems, such as the system F, or the Calculus of Constructions, can be embedded in the lambda-Pi-calculus modulo, and that this embedding is conservative under termination hypothesis.

Abstract: The lambda-Pi-calculus allows to express proofs of minimal predicate logic. It can be extended, in a very simple way, by adding computation rules. This leads to the lambda-Pi-calculus modulo. We show in this paper that this simple extension is surprisingly expressive and, in particular, that all functional Pure Type Systems, such as the system F, or the Calculus of Constructions, can be embedded in it. And, moreover, that this embedding is conservative under termination hypothesis.

115 citations

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01 Jan 2001114 citations