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The language X: circuits, computations and classical logic

Steffen van Bakel, Lengrand, Pierre Lescanne

Conference or Workshop Paper
9th Italian Conference on Theoretical Computer Science (ICTCS'05), Siena, Italy
October, 2005
Lecture Notes in Computer Science
Volume 3701
DOI 10.1007/11560586_8

We present the syntax and reduction rules for X, 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 X 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 lambda-calculus, Bloe and Rose's calculus of explicit substitutions lambda-x, and Parigot's lambda-mu.

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