Transducers are also familiar from automata theory. There’s a recent line of research into automata and transducers with symbolic representations for transitions. I’ve studied using them to apply fusion to pipelines of stream transformations [1]. Here’s talk I have for a related paper [2] and this talk by Loris d’Antoni gives a general overview of symbolic automata and transducers [3]. In a few weeks I’ll have a talk up that summarizes the last three papers I have on the subject.
[1] http://dx.doi.org/10.1145/3062341.3062362