The language X: circuits, computations and Classical Logic

Abstract : 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 $`l$-calculus, Bloe and Rose's calculus of explicit substitutions lambda-x, Parigot's lambda-mu and Curien and Herbelin's lambda-mu-mu~.
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Steffen van Bakel, Stéphane Lengrand, Pierre Lescanne. The language X: circuits, computations and Classical Logic. [Research Report] LIP RR-2005-11, Laboratoire de l'informatique du parallélisme. 2005, 2+25p. ⟨hal-02101957⟩

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