Computing Interpolating Sequences

Naftalevi's Theorem states that, given a Blaschke sequence, it is possible to modify the arguments of its terms so as to obtain an interpolating sequence. We prove a computable version of this theorem in that it possible, given a Blaschke sequence, to computably modify the arguments of its terms so as to obtain an interpolating sequence. Using this result, we produce a computable, interpolating Blaschke sequence that does not define a computable Blaschke product. This answers a question posed by Matheson and McNicholl in a recent paper. We use Type-Two Effectivity as our foundation.