[ethan_g]

Your example of rewrite rules reminds me a lot of expression templates in C++, though there's no direct support by the language and it's done through the type system instead. Some libraries (e.g. eigen or the boost library for linear algebra) use expression templates to produce optimized code for a chain of functions or operators.

The specialization example is the same as template specialization in C++.

[mrkgnao]

I've heard a little about generics/templating/whatever-you-call-the-things-between-angle-brackets techniques in C++ from far away.

> The specialization example is the same as template specialization in C++.

This sounds very interesting to me, because you're saying it's accomplished entirely in the type system: do you have an example or a reference you can point me to?

I'm guessing there's a type-level tag for an algorithm, and the compiler is told how to combine tags corresponding to a sequence of operations on vectors that looks a certain way. Something like do_the_thing<t, DotWith<Self>, HasFastNorm<t>> = do_the_thing<Norm<t>>? (just thinking aloud in pseudo-C++, nothing to see here, move along) In that case, it would be closer to something using a function on types, which Haskell has in the form of type families.

[mrkgnao]

Oh, this is interesting!

http://www.cprogramming.com/tutorial/template_specialization...

What you have towards the end of that post is actually something like

  type family Vector a where
    type instance Vector (Ptr a) = ...
    type instance Vector a = ...

This is a closed type family. (Think of it as a pattern-match on types where the cases are tried in order.) Very cool!

I still don't know how the linear algebra/Eigen examples might work, though.