This work presents a computational rule learner tasked with inferring underlying forms and ordered rules from phonological paradigms akin to those found in traditional pen and paper analyses. The scheme being proposed is a batch learner capable of analysing surface alternations and hypothesising ordered derivations compatible with them in order to create an explicit mapping from UR to SR. We shall refer to both the competence of an idealised speaker-hearer (in keeping with traditional generative linguistic theory) and the conscious methods employed by the phonologist in the course of analysing data sets. The fundamental axiom of this model is that the child has memorised the relevant surface forms (as they appear in the paradigm) alongside the appropriate semantic information in order to allow them to set up paradigmatic structures for the purpose of inferring both underlying forms and phonological rules simultaneously. The mapping from minimal pairs to underlying forms is the primary conduit to inferring the rules themselves.