In this paper we describe an improved formalisation of slicing in WSL (Wide Spectrum Language) transformation theory and apply the result to give syntactic and semantic slices for some challenging slicing problems. Although there is no algorithm for constructing a minimal syntactic slice, we show that it is possible, in the WSL language, to derive a minimal semantic slice for any program and any slicing criteria. We describe the Representation Theorem and show how it is (partially) implemented in the FermaT transformation system. The theorem has applications to semantic (or conditioned) slicing, and we use a combination of abstraction (via the representation theorem), simplification and refinement plus other program transformations to develop a powerful conditioned slicing algorithm.