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Kotlin∇ is a type-safe automatic differentiation framework written 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, most type declarations may be safely omitted by the end-user. ...