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X.R.S: Explicit reduction systems — A first-order calculus for higher-order calculi

  • Bruno Pagano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1421)

Abstract

The λ-calculus is a confluent first-order term rewriting system which contains the λ-calculus written in de Bruijn's notation. The substitution is defined explicitly in λ by a subsystem, called the σ-calculus. In this paper, we use the σ⇑-calculus as the substitution mechanism of general higher-order systems which we will name Explicit Reduction Systems. We give general conditions to define a confluent XRS. Particularly, we restrict the general condition of orthogonality of the classical higher-order rewriting systems to the orthogonality of the rules initiating substitutions.

Keywords

Free Algebra Computation Rule Binding Operator Left Member Unary Symbol 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Bruno Pagano
    • 1
  1. 1.LIP6 - Université Pierre et Marie CurieParisFrance

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