We study the interaction of structural subtyping with parametric polymorphism and recursively defined type constructors. Although structural subtyping is undecidable in this setting, we describe a notion of parametricity for type constructors and then exploit it to define
parametric subtyping
, a conceptually simple, decidable, and expressive fragment of structural subtyping that strictly generalizes
rigid subtyping
. We present and prove correct an effective saturation-based decision procedure for parametric subtyping, demonstrating its applicability using a variety of examples. We also provide an implementation of this decision procedure as an artifact.