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Computation with classical sequents
 MATHEMATICAL STRUCTURES OF COMPUTER SCIENCE
, 2008
"... X is an untyped continuationstyle formal language with a typed subset which provides a CurryHoward isomorphism for a sequent calculus for implicative classical logic. X can also be viewed as a language for describing nets by composition of basic components connected by wires. These features make X ..."
Abstract

Cited by 16 (16 self)
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X is an untyped continuationstyle formal language with a typed subset which provides a CurryHoward isomorphism for a sequent calculus for implicative classical logic. X can also be viewed as a language for describing nets by composition of basic components connected by wires. These features make X an expressive platform on which algebraic objects and many different (applicative) programming paradigms can be mapped. In this paper we will present the syntax and reduction rules for X and in order to demonstrate the expressive power of X, we will show how elaborate calculi can be embedded, like the λcalculus, Bloo and Rose’s calculus of explicit substitutions λx, Parigot’s λµ and Curien and Herbelin’s λµ ˜µ.
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, 2004
"... We prove the confluence of λµ˜µT and λµ˜µQ, two wellbehaved subcalculi of the λµ˜µ calculus, closed under callbyname and callbyvalue reduction, respectively. ..."
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We prove the confluence of λµ˜µT and λµ˜µQ, two wellbehaved subcalculi of the λµ˜µ calculus, closed under callbyname and callbyvalue reduction, respectively.
circuits, computations and Classical Logic
, 2005
"... X is an untyped language for describing circuits by composition of basic components. This language is well suited to describe structures which we call “circuits ” and which are made of parts that are connected by wires. Moreover X gives an expressive platform on which algebraic objects and many diff ..."
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X is an untyped language for describing circuits by composition of basic components. This language is well suited to describe structures which we call “circuits ” and which are made of parts that are connected by wires. Moreover X gives an expressive platform on which algebraic objects and many different (applicative) programming paradigms can be mapped. In this paper we will present the syntax and reduction rules for X and some its potential uses. To demonstrate the expressive power of X, we will show how, even in an untyped setting, elaborate calculi can be embedded, like the naturals, the λcalculus, Bloe and Rose’s calculus of explicit substitutions λx, Parigot’s λµ and Curien and Herbelin’s λµ˜µ. Keywords: Language design, mobility, circuits, classical logic, CurryHoward correspondance Résumé X est un langage non typ é conçu pour d écrire les circuits par composition de «briques » de base. Ce langage s’adapte parfaitement à la description des structures que nous appelons «circuits » et qui sont faites de composants connect és par des fils. De plus, X fournit une plateforme expressive sur laquelle des objets alg ébriques et de nombreux paradigmes de programmation (applicative) de toutes sortes peuvent être appliqu és. Dans ce rapport, nous pr ésenterons la syntaxe de X, ses règles de r éduction et certaines de ses utilisations potentielles. Pour mettre en lumière le pouvoir expressif de X, nous montrerons comment, même dans un cadre non typ é, on peut y plonger des calculs relativement sophistiqu és, comme les entiers naturels, le λcalcul, le calcul de substitutions explicites λx de Bloe et Rose, le calcul λµ de Parigot et le calcul λµ˜µ de Curien et Herbelin. Motsclés: Conception de langage, mobilit é, circuits, logique classique,