## Combinatory Reduction Systems: introduction and survey (1993)

Venue: | THEORETICAL COMPUTER SCIENCE |

Citations: | 84 - 9 self |

### BibTeX

@ARTICLE{Klop93combinatoryreduction,

author = {Jan Willem Klop and Vincent van Oostrom and Femke van Raamsdonk},

title = {Combinatory Reduction Systems: introduction and survey},

journal = {THEORETICAL COMPUTER SCIENCE},

year = {1993},

volume = {121},

pages = {279--308}

}

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### Abstract

Combinatory Reduction Systems, or CRSs for short, were designed to combine the usual first-order format of term rewriting with the presence of bound variables as in pure λ-calculus and various typed -calculi. Bound variables are also present in many other rewrite systems, such as systems with simplification rules for proof normalization. The original idea of CRSs is due to Aczel, who introduced a restricted class of CRSs and, under the assumption of orthogonality, proved confluence. Orthogonality means that the rules are non-ambiguous (no overlap leading to a critical pair) and left-linear (no global comparison of terms necessary). We introduce the class of orthogonal CRSs, illustrated with many examples, discuss its expressive power, and give an outline of a short proof of confluence. This proof is a direct generalization of Aczel's original proof, which is close to the well-known confluence proof for λ-calculus by Tait and Martin-Lof. There is a well-known connection between the para...