The simultaneous inference of underlying representations (URs) and a phonological grammar from alternating surface representations (SRs) in a morphological paradigm is a core problem in phonological learning. This problem only recently has seen progress (Tesar 2014, Berger et al. 2018). We propose a solution based on the hypothesis that phonology is subregular (Heinz, 2018). We give a procedure that, given sequences of morphemes paired with SRs, learns URs and a phonological grammar that is an Input Strictly Local (ISL; Chandlee 2014, Chandlee & Heinz 2018) function. ISL functions make changes in the output with respect to the local information in the input. The upshot is that restrictive computational principles, combined with major principles in phonological analysis, allow for significant progress in understanding how phonological grammar and URs are learned. This method is general enough to be extended to other classes of functions that capture iterative processes, long-distance processes, and featural representations.