The clausal theory of types
Combinatory reduction systems: introduction and survey
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
Theoretical Computer Science - Special issue: algebraic development techniques
POPL '03 Proceedings of the 30th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Higher-Order Logic Programming
Proceedings of the Third International Conference on Logic Programming
Orthogonal Higher-Order Rewrite Systems are Confluent
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
Linear Unification of Higher-Order Patterns
TAPSOFT '93 Proceedings of the International Joint Conference CAAP/FASE on Theory and Practice of Software Development
Exceptions in the Rewriting Calculus
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
Comparing Combinatory Reduction Systems and Higher-order Rewrite Systems
HOA '93 Selected Papers from the First International Workshop on Higher-Order Algebra, Logic, and Term Rewriting
Definitions by Rewriting in the Calculus of Constructions
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Modularity of strong normalization in the algebraic-λ-cube
Journal of Functional Programming
The rewriting calculus as a combinatory reduction system
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
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The last few years have seen the development of the rewriting calculus (also called rho-calculus or 驴-calculus) that uniformly integrates first-order term rewriting and the 驴-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 the 驴-calculus algebraic features. The various higher-order rewriting systems and the rewriting calculus share similar concepts and have similar applications, and thus, it is important to compare these formalisms to better understand their respective strengths and differences.We show in this paper that we can express Combinatory Reduction Systems derivations in terms of rewriting calculus derivations. The approach we present is based on a translation of each possible CRS-reduction into a corresponding 驴-reduction. Since for this purpose we need to make precise the matching used when evaluating CRS, the second contribution of the paper is to present an original matching algorithm for CRS terms that uses a simple term translation and the classical matching of lambda terms.