Hi Bruno, thank you for your interesting, I will try to use proto, I never use it before.
yes, It's technically feasible. but the type of all the symbol in the expression can not be the build-in type. and gamma function should be a special version. integral is more difficult than derivative, else, to calculate the volume will be more easier. to simplify the expression is a interesting work. especially in compile time. BTW: I do not know how to upload source to this system, do you know how to do that?
Dongfei.
From my point of view, the main interest would be to compute expressions containing some compile-time values provided by the user. For example I want to calculate the volume of a hypersphere which is: (pi^(N/2)*r^N) / gamma(N/2 + 1), with dimension N known at compile-time. If the user happens to work only with N=2, that is circles, I want the resulting expression to be as effective as a hand-written pi*r^2 (the volume of a hypersphere<2> is the area of a circle). It's technically feasible.
While not strictly the same, there are all sorts of C++ based packages out there for doing this kind of thing. The approach taken is 'automatic differentiation', and it basically works by applying the chain rule to every individual step in a sequence of operations. One approach to doing this is through operator overloading, and replacing the underlying 'double' class with something that maintains the appropriate state. There are already some nice open source packages out there for doing this. More info: http://en.wikipedia.org/wiki/Automatic_differentiation http://www.autodiff.org/ http://www.coin-or.org/CppAD/ Cheers, Chris