In this paper, we generalise the notion of explicit substitution from the -calculus to higher order rewriting, realised by combinatory reduction systems (CRSs). For every con uent CRS, R, we construct an explicit substitution variant, Rx, which we prove con uent. 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 signi cant rst step towards providing a

more »

... y for reasoning about the operational properties of higher-order rewriting in general, and higher-order program transformations in particular, since con uence 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.