Algorithm Differentiation in Lisp: ADIL

Algorithm differentiation is a technique used to take a program F computing a numerical function of one argument F(x) and transform it into another program G that returns a pair, hF0(x), F(x)i where by F0(x) the authors mean the derivative of F with respect to its argument, evaluated at x. That is, they have a program AD that takes as input a program, and returns another: G := AD(F). This task has been specialized so that F may be expressed in a subset of any of several prominent programming languages. The task is especially simple in Lisp.