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Communication Dans Un Congrès Année : 1998

X.R.S : explicit Reduction Systems, a first-order calculus for higher-order calculi

Bruno Pagano
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Résumé

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.

Dates et versions

hal-01622292 , version 1 (24-10-2017)

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Citer

Bruno Pagano. X.R.S : explicit Reduction Systems, a first-order calculus for higher-order calculi. Conference on Automated Deduction (CADE), Jul 1998, Lindau, Germany. pp.72-87, ⟨10.1007/BFb0054249⟩. ⟨hal-01622292⟩
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