Skip to main content

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

ZĂ©rics said…
there is an error in the code :

K17 >:x

should be :

K17 >::x

otherwise, it won't compile
cialis generic said…
Thanks mate... just dropped by. Will look for BIKE STN when we get to Seattle. Still in Buenos Airies.
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.

Popular Content

Unit Testing C++ Templates and Mock Injection Using Traits

Unit testing your template code comes up from time to time. (You test your templates, right?) Some templates are easy to test. No others. Sometimes it's not clear how to about injecting mock code into the template code that's under test. I've seen several reasons why code injection becomes challenging. Here I've outlined some examples below with roughly increasing code injection difficulty. Template accepts a type argument and an object of the same type by reference in constructor Template accepts a type argument. Makes a copy of the constructor argument or simply does not take one Template accepts a type argument and instantiates multiple interrelated templates without virtual functions Lets start with the easy ones. Template accepts a type argument and an object of the same type by reference in constructor This one appears straight-forward because the unit test simply instantiates the template under test with a mock type. Some assertion might be tested in

Multi-dimensional arrays in C++11

What new can be said about multi-dimensional arrays in C++? As it turns out, quite a bit! With the advent of C++11, we get new standard library class std::array. We also get new language features, such as template aliases and variadic templates. So I'll talk about interesting ways in which they come together. It all started with a simple question of how to define a multi-dimensional std::array. It is a great example of deceptively simple things. Are the following the two arrays identical except that one is native and the other one is std::array? int native[3][4]; std::array<std::array<int, 3>, 4> arr; No! They are not. In fact, arr is more like an int[4][3]. Note the difference in the array subscripts. The native array is an array of 3 elements where every element is itself an array of 4 integers. 3 rows and 4 columns. If you want a std::array with the same layout, what you really need is: std::array<std::array<int, 4>, 3> arr; That's quite annoying for

Covariance and Contravariance in C++ Standard Library

Covariance and Contravariance are concepts that come up often as you go deeper into generic programming. While designing a language that supports parametric polymorphism (e.g., templates in C++, generics in Java, C#), the language designer has a choice between Invariance, Covariance, and Contravariance when dealing with generic types. C++'s choice is "invariance". Let's look at an example. struct Vehicle {}; struct Car : Vehicle {}; std::vector<Vehicle *> vehicles; std::vector<Car *> cars; vehicles = cars; // Does not compile The above program does not compile because C++ templates are invariant. Of course, each time a C++ template is instantiated, the compiler creates a brand new type that uniquely represents that instantiation. Any other type to the same template creates another unique type that has nothing to do with the earlier one. Any two unrelated user-defined types in C++ can't be assigned to each-other by default. You have to provide a