Revision notes

Make a new first slide giving motivation for AD and my work in particular.
Slides 28, 29: streamline.
Maybe use Monoidal/(***) rather than Cartesian/(&&&). I'd have to define (&&&) and (|||).

Done:

Slide 6: drop "i.e."
Slide 7: drop product subscript (not used elsewhere).
Slide 8: side-by-side homomorphisms
Slide 13: add CCC expression.
Slides 8, 16, ...: Drop extra parens? Or move them to around the second fork argument.
Slide 24: use superscript and subscript (both as in paper)
Slide 26: simplify.
Slide 28: Replace r by s.
Slide 31: break slide in two, with specification and solution.
Slide 32: drop "Double". Other slides, too?
Slide 37: correct picture? [yes]
The functorial specification. Somewhere: point out that all of the algorithms are calculated from simple specifications as homomorphisms, referring to the paper.

To do

CoproductPCat for GD k. The "cocartesian rule", a peer to the chain and cartesian rules.

AddFun
Abstract
Use infix (~>) in place of k.
Rework Incremental.
Resolve whether to give the talk at PEPM. Yes.
AD example cosSinProd
Extracting a data representation: if we use AddFun, we have an expensive extraction step e.g., to get the gradient.
RAD examples with derivatives as dual functions and as dual vectors: add, fst, sqr, magSqr, cosSinProd.
Get the talk scheduled at work. Wed 3pm.
Add Incremental to talk.
Remarks on symbolic vs automatic differentiation
Maybe show CPS-like category (ConCat.Continuation, in progress).
Conclusions: FAD & RAD ...
Linear maps via representable functors.
Perhaps material from second set of notes