Lightweight linear types in System F°

We present Fo, an extension of System F that uses kinds to distinguish between linear and unrestricted types, simplifying the use of linearity for general-purpose programming. We demonstrate through examples how Fo can elegantly express many useful protocols, and we prove that any protocol representable as a DFA can be encoded as an Fo type. We supply mechanized proofs of Fo's soundness and parametricity properties, along with a nonstandard operational semantics that formalizes common intuitions about linearity and aids in reasoning about protocols. We compare Fo to other linear systems, noting that the simplicity of our kind-based approach leads to a more explicit account of what linearity is meant to capture, allowing otherwise-conflicting interpretations of linearity (in particular, restrictions on aliasing versus restrictions on resource usage) to coexist peacefully. We also discuss extensions to Fo aimed at making the core language more practical, including the additive fragment of linear logic, algebraic datatypes, and recursion.