Study of the Subtyping Machine of Nominal Subtyping with Variance (full version)

This is a study of the computing power of the subtyping machine behind Kennedy and Pierce's nominal subtyping with variance. We depict the lattice of fragments of Kennedy and Pierce's type system and characterize their computing power in terms of regular, context-free, deterministic, and non-deterministic tree languages. Based on the theory, we present Treetop -- a generator of C# implementations of subtyping machines. The software artifact constitutes the first feasible (yet POC) fluent API generator to support context-free API protocols in a decidable type system fragment.