Optimizing term rewriting with creeper trace transducers

In the context of functional programming/term normalization algorithms we discuss the optimization problem of constructing the result of a sequence of rewrite steps, without computing all the intermediate terms. From a rewrite system we construct a creeper trace transducer, which reads a sequence of backwards overlapping rewrite steps while producing the desired answer. The transducer writes each symbol of the output only once, skipping overlap between each pair of subsequent rules. In some cases a part of the trace can be disregarded altogether.