Ben, could you go a little into detail on what you had in mind with the term rewriting system? The sin/cos example seems a little underwhelming, since these should be evaluated at compile-time in the first place.

They seem like a variant on C macros, but without the restriction on function syntax. Maybe one could implement Python's with statement in userland, which is very nice.

It also seems to me that you could replace C++ templates, yet you do have generics. How come? What's the difference?

My intuition is that ambiguities are at least possible, so what about precedence, which AST term is evaluated first? I'm thinking of some situation where two subtrees match the rule, but you end up with different results depending on which is transformed first. E. g. if you were to define a cross product rule, and apply it to a × b × c.

What about infinite loops in rule sets? What about recursion?

What about a situation where multiple rules could be applied? Is there any way to debug the transformations? Is that what the `using` scopes are for? If the compiler was to detect ambiguities, that seems pretty expensive, because it would need to match every rule to every subtree, right?

This thing seems very, very powerful, I just find it a bit hard to grasp what you can do with it in practice, and what the limitations are. I would be very interested to hear what you ran into so far.