I’d prefer a solution in which this reliance is made explicit at compile time; basically relying on Template Haskell or the like to enforce that the g passed to adiff is a compile-time-constant which can be safely passed to deriv.

In fact, I think TH could be useful for a lot of things if the syntax for invoking it wasn’t so ugly. I’d love for a “transparent” TH. Consider a macro application in LISP: in the source code, it looks just like a function call. Perhaps a TH function should get some form of context (the AST it is a part of) and be allowed to return parts of that context “unmodified” after picking out the data it expects, instead of needing to use the ugly splice syntax.

This would give you the same power that you get from rewrite rules but relying on the specification of the language rather than the internals of the optimizer.

… rewrite rules should not be relied on for correctness, …

That guideline is the conventional wisdom I hear. I hope that examples like the one above motivate a shift, so that rewrite rules can be counted on, considering the boost in modularity that results.