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Erschienen in:
2007 | OriginalPaper | Buchkapitel
The Rewriting Calculus as a Combinatory Reduction System
verfasst von : Clara Bertolissi, Claude Kirchner
Erschienen in: Foundations of Software Science and Computational Structures
Verlag: Springer Berlin Heidelberg
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The last few years have seen the development of the
rewriting calculus
(also called rho-calculus or
ρ
-calculus) that uniformly integrates first-order term rewriting and
λ
-calculus. The combination of these two latter formalisms has been already handled either by enriching first-order rewriting with higher-order capabilities, like in the
Combinatory Reduction Systems
(CRS), or by adding to
λ
-calculus algebraic features.
In a previous work, the authors showed how the semantics of CRS can be expressed in terms of the
ρ
-calculus. The converse issue is adressed here: rewriting calculus derivations are simulated by Combinatory Reduction Systems derivations. As a consequence of this result, important properties, like standardisation, are deduced for the rewriting calculus.