2. type erasure: I looked this term up but it seems as if it is similar to interface/device independent/ programming. In the past we built homemade Function and used it in combination with OO specialisation with virtual functions, Now boost Function is so much better. Mathematicians and engineers are used to functions and we adopt

3. Ideally, we would like TR1 and boost to be as seamless as possible. Check out: http://www.boost.org/doc/libs/1_42_0/doc/html/boost_tr1.html Just remember that boost::tr1 is intended to be used only if the vendor hasn't

Daniel: As a caveat, I am far from an expert. just a library user focused on scientific computing in economics... but here are a few more comments that I hope the experts can correct. the same approach (e.g. using namespaces) boost::function certainly beats any home-spun solution. But type erasure is a way to bridge generic programming to give a common *runtime* interface. I think of it as akin to getting the benefits of dynamic polymorphism with arbitrary generic types - effectively creating a virtual function without inheritance. However, just as with dynamic polymorphism it is not without cost: The boost::function infrastructure puts in a dispatch which could drastically hurt performance if called in an inner loop (or have virtually no effect if the function itself is time consuming). The compiler can't inline the functions, etc. Also, the term "type erasure" should be taken literally. The functions which operate on the boost::function are not able to get any information on the type. For example, a common way to deal with a function and derivatives is to have a single function object with an operator() and a gradient() defined. But if you stuff this in a boost::function you lose the information and can only call a specific overload/template of operator(). You can see some old, stupid questions I had asked on this mailing list a while back about this topic: http://lists.boost.org/boost-users/2009/01/44253.php What I learned eventually was that I was trying to use type erasure when I didn't need it, and I was better off sticking with generic programming... So boost::function is very useful, but you run into the same tradeoffs and questions as static vs. dynamic polymorphism: If you don't need dynamic polymorphism, then consider sticking with compile time templates, etc. for better performance and genericity at the potential cost of code complexity. In the case of scientific computing, I find that almost everything is known at compile time and you are better off keeping the types generic/not using type erasure. If you are just using boost::function because the types of the function objects are complicated, consider the alternatives. See my comments in the previous post on the use of "auto" and "decltype" to make this manageable. put in a tr1 library.

4. Fusion: I think this is useful, especially with Any?

7. Numerical integration: I saw this extensive library in Vault. What is

While I have never used "any", I believe these are two different ways to deal with the problem. Using something like std::vector<boost::any> is another example of type erasure (just as std::vector<boost::function<double (double)> > would be). boost::fusion allows you to have a tuple-like vector of different types, but while retaining type information. The same types of tradeoffs apply as before... and fusion is only usable if you know the types at design-time. If you end up converting some of your code away from boost::function, you may need something like this. On the other hand, it can be pretty advanced so be careful... std::tr1::tuple is enough unless you need to apply an operation on the vector of types. For example, I have often had the case where I had a vector of functions I needed to evaluate. I was unable to use boost::function since I needed genericity so I had a boost::fusion::vector with the various function types. Then to evaluate the functions at the same point, I used a fusion::for_each, transform, or fold depending on what I was trying to do. Note that this should have very high performance: The fusion::for_each ends up doing something akin to loop unrolling at compiletime, and since I didn't lose any type information everything could be inlined. the status? These don't seem to be in active development. I have used http://www.coin-or.org/CppAD/ myself. When using AD you will find it extremely difficult to use boost::function because the function stops being generic when the type is removed (play with these libraries and you will understand quickly). This is a perfect example of why you should be wary of removing type information if you don't need to. I think that Robert is correct that you should make sure you study and work with type erasure/generic programming before writing those chapters, especially if you are intended this to be used for numeric computing. Efficiency is critical for these applications and dynamic polymorphism is often unnecessary. And don't be fooled by the name boost::function: Its primary purpose is to bridge dynamic polymorphism for generic callable types, and not to be a placeholder for mathematical functions. While using it can sometimes simplify code (when auto/decltype are not available), the cost should be considered. boost::phoenix, lambda, and bind do not erase type information and I believe all overhead of function adaptation could be optimized away with these. While a lot of the Template Metaprogramming book was beyond my needs, I found careful study essential reading(especially Chapter 9 which covers these topics) .... and that about exhausts my knowledge. Good luck with the book!