Example for ast.NodeTransformer that mutates an equation

So the input and the output are Fortran code? And you want to use arbitrary Fortran expressions/statements? (Including array slices, ...?) Fortran is a pretty complex language; reading it requires pretty much a full parser.

Perhaps you want to use an program transformation tool that can already manipulate Fortran directly. Such a tool would read the Fortran code, build an AST, let you "randomize" it using a set of randomly chosen transformations, and then regenerate valid Fortran code.

Our DMS Software Reengineering Toolkit with its Fortran front end could be directly used for this.

EDIT Aug 26 2011: OP confirms he wants to "evolve" (transform) real Fortran code. It is worth noting that building a real Fortran parser (like building parsers for any other real language) is pretty hard; it took us months and our tools are really good at defining parsers (we've done some 40 languages and a variety of dialects using DMS). It is probably not a good idea for him to build his own real Fortran parser, at least not if he wants to get on with his life or his actual task.

It might be possible for OP to constrain the Fortran code to a very restricted subset, and build a parser for that.

What are you trying to do? Looking for the right permutation of an equation might be easy but time consuming (n! possibilities), but generating new ones and optimize those using a genetic algorithm is imho impossible, because it`s not an optimization problem... For example x^0.00 and x^0.01 are fundamental different. Also, you can not optimize for the right operator, that just won't work. Sorry.

Although, the situation isn't that bad. Looking for the right function is an extremely common task. I am now assuming that you do not know the function, but you know a couple of points from measurements (you would have needed that to calculate the fitness in your genetic algorithm anyway, didn't you?). You now can use Lagrange to get a polynomial which passes those given points. There are two good examples in the middle of the wikipedia article, and lagrange is quite easy to implement (<10 lines of code I guess). Also note that you have the ability to improve the accuracy of the polynomial just by adding more reference points.