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C++ templates are turing complete

Here you will find a short C++ program that takes more than 24 hrs to compile on a dedicated dual processor, 1GB memory machine!! Here we go...

template<int Depth, int A, typename B>
struct K17 {
static const int x =
K17 <Depth+1, 0, K17<Depth,A,B> >::x
+ K17 <Depth+1, 1, K17<Depth,A,B> >::x
+ K17 <Depth+1, 2, K17<Depth,A,B> >::x
+ K17 <Depth+1, 3, K17<Depth,A,B> >::x
+ K17 <Depth+1, 4, K17<Depth,A,B> >::x;
};
template <int A, typename B>
struct K17 <16,A,B> { static const int x = 1;
};
static const int z = K17 <0,0,int>::x;
int main(void) { }

Source: C++ Templates are Turing Complete by Todd L. Veldhuizen

This program is taken from the above paper which takes unreasonably long to compile. I belive, a simple dynamic programming solution will reduce the exponential time required by this program to compile to polynomial time. I also believe, it might be quite difficult to apply dynamic programming solution, in general, to all C++ programs of this nature. You need to have a good understanding of template meta-programming to make sense of this program. One good article by the same author is here:

This post is motivated by a anonymous comment I received on an earlier post. I am quoting him here:

"It is ___provably___ impossible to write a correct C++ parser which will complete compilation with either success or failure because the C++ template system is Turing complete. This means that code generation is based on a turing complete program. Code generation in C++ isn't based on a program description, but an actual turing complete program. As such, it is subject to the halting problem. Therefore, it is unknowable whether a compilation will complete, and unknowable if you are looking at a valid C++ program."

Comments

Zérics said…
there is an error in the code :

K17 >:x

should be :

K17 >::x

otherwise, it won't compile
Wed Mar 30, 01:17:00 PM PDT
cialis generic said…
Thanks mate... just dropped by. Will look for BIKE STN when we get to Seattle. Still in Buenos Airies.
Fri Jul 08, 11:58:00 AM PDT
David Stone said…
The only reason it takes so long to compile is because it adds in unused template arguments A and B. Once those are deleted, you give addition of the same thing 5 times, so you just replace that with multiplication.

There is also a compile-time error caused by integer overflow in a constant expression. The type of x and z need to be able to hold a 38-bit integer. Something like std::int64_t should be good enough.

Once you make the changes to get rid of useless code and allow it to compile, it finishes in about .2 seconds on my machine.
Sat Oct 04, 06:56:00 PM PDT
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