  With the increased interest in machine learning, and deep learning in
particular, the use of automatic differentiation has become more wide-spread in
computation. There have been two recent developments to provide the theoretical
support for this types of structure. One approach, due to Abadi and Plotkin,
provides a simple differential programming language. Another approach is the
notion of a reverse differential category. In the present paper we bring these
two approaches together. In particular, we show how an extension of reverse
derivative categories models Abadi and Plotkin's language, and describe how
this categorical model allows one to consider potential improvements to the
operational semantics of the language.
