Combinatory Reduction Systems with Explicit Substitution that Preserve Strong Nomalisation

x Abstract. We generalise the notion of explicit substitution from the-calculus to higher order rewriting, realised by combinatory reduction systems (CRSs). For every connuent CRS, R, we construct an explicit substitution variant, Rx, which we prove connuent. We identify a large subset of the CRSs, the structure-preserving CRSs, and show for any structure-preserving CRS R that Rx preserves strong normalisation of R. We believe that this is a signiicant rst step towards providing a methodology for reasoning about the operational properties of higher-order rewriting in general, and higher-order program transformations in particular, since connuence ensures correctness of such transformations and preservation of strong normalisation ensures that the transformations are always safe, in both cases independently of the used reduction strategy.