[ivansavz]

This is a theory paper so no immediate practical applications. Potential applications would be generalizing derivative calculations used in currently ML libraries, see https://en.wikipedia.org/wiki/Automatic_differentiation and http://www.cs.nuim.ie/~gunes/files/Baydin-MSR-Slides-2016020...

Useful quote from paper: "We have been inspired by the development of differentiable programming to formalize a theoretical model, that encompasses the ideas underlying differentiable programming and provides a more general setting for investigations of differentiable programs. The presented theoretical model enables analytic investigations of differentiable programs through algebraic tools, that are closer to the field of programming; i.e. the presented operators can take the same role as higher order functions in functional programming."