Question

In this article, the writer asserts:

…the program did show that the template instantiation mechanism is a primitive recursive language that can perform nontrivial computations at compile time.

I found this rather interesting, as I help to teach a class in Theory of Computation which delves into the theory of primitive recursive functions. However, I was under the impression that Template Metaprogramming was Turing-complete, which is a strictly stronger statement than to say that it is primitive recursive…And after all, it is not very difficult to create a template metaprogram which fails to halt.

Am I missing something? Is Template Metaprogramming a strictly primitive recursive language, or am I correct in believing it to cover a wider range of programs?

Answer 1

I believe you just read too much into the text, and the “primitive” is not meant as “primitive recursive”, but rather it is a “recursive language” (which sounds odd, I’d call describe that as a functional language, but never mind), which is primitive.

If you look at TMP as a functional language, it is not a very sophisticated one; thus, it is a primitive one.

But you are correct, TMP certainly is Turing-complete.

I doubt many people have heard of primitive recursive languages, and so this is just an unfortunate choice of words.