[noelwelsh]

Thanks for answering. This clears up some things for me.

I've made a first pass through the Pearlmutter-Siskind system (the Lambda the Ultimate Back-propagator paper) and the main idea, IIUC, is to implement backward-mode AD over reals in a compositional manner. So I generally agree with your characterisation of it. Forward-mode AD is usually presented in terms of infinitesimals (dual numbers) but backward-mode is not, but this is a minor point.