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...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. Kotlin∇ strives to be expressive, safe, and notationally similar to mathematics.