I was looking into pattern matching in C++, and among things like Mach7, which seems to be a functional approach to the problem, and the more general Visitor Pattern, which seems to be the lowest common denominator: it can do everything but excels at only specific cases.
I would like to manipulate mathematical expressions (simplify, evaluate, and also perform calculations like differential equation solving, and integration, symbollically). Yes, I'm looking to end up with a Computer Algebra System. For the input, I'm looking at using Boost.Spirit (X3) to parse some form of input (currently playing with getting basic LaTeX support in there, although index vs sub/superscript is a problem for this...).
I then came to the crazy idea of using Boost.Spirit to not only parse the input "text", but also use the non-parser components of the library to actually perform the mathematical manipulations on a resulting AST. Is this versatile enough for the pattern matching my goal requires or should I look at other solutions? I have tried to find documentation on how other CAS work internally, but short of going through the undoubtetly brilliant code of things like Maxima, I can't seem to find any information on anything but very simple implementations of mathematical ASTs. So I have little input info to determine if Boost.Spirit can do what I eventually will need to do.
I'm not qualified to advise on the subject of symbolic algebra and the requirements there.
I do however know a thing or two about Boost Spirit.
All I can say is: don't do it!
You do not want to burden the parser with such complex responsibilities that are just going to be more difficult to design right inside the "warped" reality that is EDSLs and Phoenix actors.
In fact, I have oft repeated this advice (see e.g. Boost Spirit: "Semantic actions are evil"?, is the most linked to for this, but I've deepened it out in several chat rooms and on occasion in answers where the problem seemed to arise from conflating parsing with processing).