Program slicing provides explanations that illustrate how program outputs were produced from inputs. We build on an approach introduced in prior work, where dynamic slicing was defined for pure higher-order functional programs as a Galois connection between lattices of partial inputs and partial outputs. We extend this approach to \emph{imperative functional programs} that combine higher-order programming with references and exceptions. We present proofs of correctness and optimality of our approach and a proof-of-concept implementation and experimental evaluation.