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The Rewriting Calculus - Part I

Horatiu Cirstea 1 Claude Kirchner 1
1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : The rho-calculus integrates in a uniform and simple setting first-order rewriting, lambda-calculus and non-deterministic computations. Its abstraction mechanism is based on the rewrite rule formation and its main evaluation rule is based on matching modulo a theory T. In this first part, the calculus is motivated and its syntax and evaluation rules for any theory T are presented. In the syntactic case, i.e. when T is the empty theory, we study its basic properties for the untyped case. We first show how it uniformly encodes lambda-calculus as well as first-order rewriting derivations. Then we provide sufficient conditions for ensuring confluence of the calculus.
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Submitted on : Tuesday, September 26, 2006 - 2:46:31 PM
Last modification on : Friday, February 4, 2022 - 3:22:00 AM

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Horatiu Cirstea, Claude Kirchner. The Rewriting Calculus - Part I. Logic Journal of the IGPL, Oxford University Press (OUP), 2001, 9 (3), pp.339-375. ⟨10.1093/jigpal/9.3.339⟩. ⟨inria-00100531⟩

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