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Thomas Ehrhard

Bio: Thomas Ehrhard is an academic researcher from University of Paris. The author has contributed to research in topics: Linear logic & Probabilistic logic. The author has an hindex of 20, co-authored 44 publications receiving 1478 citations. Previous affiliations of Thomas Ehrhard include Pierre-and-Marie-Curie University & Centre national de la recherche scientifique.

Papers
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Journal ArticleDOI
TL;DR: This work presents an extension of the lambda-calculus with differential constructions, and state and prove some basic results (confluence, strong normalization in the typed case), and also a theorem relating the usual Taylor series of analysis to the linear head reduction of lambda-Calculus.

307 citations

Journal ArticleDOI
06 Nov 2006
TL;DR: This work introduces interaction nets for a fragment of the differential lambda-calculus and exhibits in this framework a new symmetry between the of course and the why not modalities of linear logic, which is completely similar to the symmetries between the tensor and par connectives oflinear logic.
Abstract: We introduce interaction nets for a fragment of the differential lambda-calculus and exhibit in this framework a new symmetry between the of course and the why not modalities of linear logic, which is completely similar to the symmetry between the tensor and par connectives of linear logic. We use algebraic intuitions for introducing these nets and their reduction rules, and then we develop two correctness criteria (weak typability and acyclicity) and show that they guarantee strong normalization. Finally, we outline the correspondence between this interaction nets formalism and the resource lambda-calculus.

157 citations

Journal ArticleDOI
TL;DR: The collective behaviour of the beta-reducts of the terms occurring in the Taylor expansion of any ordinary lambda-term is studied, using, in a surprisingly crucial way, a uniformity property that they enjoy.

102 citations

Journal ArticleDOI
TL;DR: This work provides a simple setting in which typed λ-calculus and differential calculus can be combined and gives a few examples of computations.
Abstract: We present a category of locally convex topological vector spaces that is a model of propositional classical linear logic and is based on the standard concept of Kothe sequence spaces In this setting, the ‘of course’ connective of linear logic has a quite simple structure of a commutative Hopf algebra The co-Kleisli category of this linear category is a cartesian closed category of entire mappings This work provides a simple setting in which typed λ-calculus and differential calculus can be combined; we give a few examples of computations

101 citations

Journal ArticleDOI
TL;DR: A new coherence space model of linear logic is obtained, which is non-uniform in the sense that the interpretation of a proof of !

81 citations


Cited by
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Proceedings Article
15 Jan 1995
TL;DR: In this paper, the authors define abstract bases as the bases of compact elements of algebraic domains and define the notion of ideal completion as the relation with which a basis can be equipped.
Abstract: bases were introduced in [Smy77] where they are called “R-structures”. Examples of abstract bases are concrete bases of continuous domains, of course, where the relation≺ is the restriction of the order of approximation. Axiom (INT) is satisfied because of Lemma 2.2.15 and because we have required bases in domains to have directed sets of approximants for each element. Other examples are partially ordered sets, where (INT) is satisfied because of reflexivity. We will shortly identify posets as being exactly the bases of compact elements of algebraic domains. In what follows we will use the terminology developed at the beginning of this chapter, even though the relation ≺ on an abstract basis need neither be reflexive nor antisymmetric. This is convenient but in some instances looks more innocent than it is. An idealA in a basis, for example, has the property (following from directedness) that for everyx ∈ A there is another element y ∈ A with x ≺ y. In posets this doesn’t mean anything but here it becomes an important feature. Sometimes this is stressed by using the expression ‘ A is a round ideal’. Note that a set of the form↓x is always an ideal because of (INT) but that it need not contain x itself. We will refrain from calling ↓x ‘principal’ in these circumstances. Definition 2.2.21. For a basis〈B,≺〉 let Idl(B) be the set of all ideals ordered by inclusion. It is called theideal completionof B. Furthermore, leti : B → Idl(B) denote the function which maps x ∈ B to ↓x. If we want to stress the relation with whichB is equipped then we write Idl(B,≺) for the ideal completion. Proposition 2.2.22.Let 〈B,≺〉 be an abstract basis.

1,210 citations

Journal ArticleDOI

784 citations

Journal ArticleDOI
TL;DR: An order-extensional, order (or inequationally) fully abstract model for Scott's language pcf, based on a kind of game in which each play consists of a dialogue of questions and answers between two players who observe the following principles of civil conversation.
Abstract: We present an order-extensional, order (or inequationally) fully abstract model for Scott's language pcf. The approach we have taken is very concrete and in nature goes back to S. C Kleene (1978, in “General Recursion Theory II, Proceedings of the 1977 Oslo Symposium,” North-Holland, Amsterdam) and R. O. Gandy (1993, “Dialogues, Blass Games, Sequentiality for Objects of Finite Type,” unpublished manuscript) in one tradition, and to G. Kahn and G. D. Plotkin (1993, Theoret. Comput. Sci.121, 187?278) and G. Berry and P.-L. Curien (1982, Theoret. Comput. Sci.20, 265?321) in another. Our model of computation is based on a kind of game in which each play consists of a dialogue of questions and answers between two players who observe the following principles of civil conversation: 1.Justification. A question is asked only if the dialogue at that point warrants it. An answer is proffered only if a question expecting it has already been asked. 2.Priority. Questions pending in a dialogue are answered on a last-asked-first-answered basis. This is equivalent to Gandy's no-dangling-question-mark condition. We analyze pcf-style computations directly in terms of partial strategies based on the information available to each player when he or she is about to move. Our players are required to play an innocent strategy: they play on the basis of their view which is that part of the history that interests them currently. Views are continually updated as the play unfolds. Hence our games are neither history-sensitive nor history-free. Rather they are view-dependent. These considerations give expression to what seems to us to be the nub of pcf-style higher-type sequentiality in a (dialogue) game-semantical setting.

679 citations

Book ChapterDOI
01 Jan 2002
TL;DR: This chapter presents the basic concepts of term rewriting that are needed in this book and suggests several survey articles that can be consulted.
Abstract: In this chapter we will present the basic concepts of term rewriting that are needed in this book. More details on term rewriting, its applications, and related subjects can be found in the textbook of Baader and Nipkow [BN98]. Readers versed in German are also referred to the textbooks of Avenhaus [Ave95], Bundgen [Bun98], and Drosten [Dro89]. Moreover, there are several survey articles [HO80, DJ90, Klo92, Pla93] that can also be consulted.

501 citations

Proceedings Article
19 Apr 1994
TL;DR: An intensional model for the programming language PCF is described, in which the types of PCF are interpreted by games, and the terms by certain "history-free" strategies are interpreted.

469 citations