The language X: circuits, computations and classical logic

  • Authors:
  • Steffen van Bakel;Stéphane Lengrand;Pierre Lescanne

  • Affiliations:
  • Department of Computing, Imperial College London, London, U.K.;School of Computer Science, University of St Andrews, North Haugh, St Andrews, Fife, Scotland;École Normale Supérieure de Lyon, Lyon 07, France

  • Venue:
  • ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
  • Year:
  • 2005

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Abstract

We present the syntax and reduction rules for χ, an untyped language that is well suited to describe structures which we call “circuits” and which are made of parts that are connected by wires. To demonstrate that χ gives an expressive platform, we will show how, even in an untyped setting, that we can faithfully embed algebraic objects and elaborate calculi, like the naturals, the λ-calculus, Bloe and Rose’s calculus of explicit substitutions λx, and Parigot’s λμ.