Axiomatizing permutation equivalence

摘要

We axiomatize permutation equivalence in term rewriting systems and Klop's orthogonal Combinatory Reduction Systems (Klop 1980). The axioms for the former are provided by the general approach proposed by Meseguer (Meseguer 1992). The latter need extra axioms modelling the interplay between reductions and the operation of substitution. As a consequence of this work, the definition of permutation equivalence is rid of residual calculi, which are heavy in general.