Kotlin∇ is a framework for type-safe automatic differentiation in Kotlin. It allows users to express differentiable programs with higher-dimensional data structures and operators. We attempt to restrict syntactically valid constructions to those which are algebraically valid and can be checked at compile-time. By enforcing these constraints in the type system, it eliminates certain classes of runtime errors that may occur during the execution of a differentiable program. Due to type-inference in the language, most types may be safely omitted by the end user. Kotlin∇ strives to be expressive, safe, and notationally similar to mathematics. It is currently pre-release and offers no stability guarantees at this time.