My hind-brain memory is that he’s identified something to do with AD that you can nearly-but-not-quite Do Right in Haskell. I never quite got my brain around what that Thing was, but I’m sure he could tell you. It may be that some implementation hack would let you do it Right, but I’m not quite sure what the hack is. It’s cool stuff anyway.

Simon

http://en.wikipedia.org/wiki/Automatic_differentiation

and found it not bad. in particular i thought the following really explained AD well vs. the other 2 options:

“AD exploits the fact that any computer program that implements a vector function y = F(x) (generally) can be decomposed into a sequence of elementary assignments, any one of which may be trivially differentiated by a simple table lookup. These elemental partial derivatives, evaluated at a particular argument, are combined in accordance with the chain rule from derivative calculus to form some derivative information for F (such as gradients, tangents, the Jacobian matrix, etc.). This process yields exact (to numerical accuracy) derivatives. Because the symbolic transformation occurs only at the most basic level, AD avoids the computational problems inherent in complex symbolic computation.”