Is C Template Metaprogramming Turing-Complete, and Why Does It Matter?

Turing Completeness of C Templates

C templates are considered Turing-complete because they allow constructing arbitrary computations at compilation time. This is due to the use of Template Metaprogramming (TMP), which enables the creation of metaprograms that generate executable code.

Nontrivial Example

A classic example of a nontrivial computation using C templates is a Turing Machine. In the provided code, a Turing Machine is defined using a set of states, inputs, rewrite rules, and the initial configuration. By simulating the transitions of the Turing Machine at compile time, the computation is performed and a valid output is produced.

Practical Usefulness

Whether this property is practically useful is debatable. While TMP provides vast possibilities for constructing complex computations, it can also lead to code that is challenging to read and debug. However, in certain scenarios, such as compile-time performance optimizations or automatic code generation, Turing-complete templates can offer advantages.

Code Explanation

The code implements a Turing Machine using C templates and metaprogramming. It includes:

• Definitions for input symbols (Input), states (State), and rewrite rules (Rule).
• A Configuration struct to represent the current state of the machine.
• A Controller struct to perform the transition of the Turing Machine, based on the current configuration and the defined rules.
• A TuringMachine struct to encapsulate the entire machine, including the initial configuration and transition rules.
• The main function defines the input symbols, states, and rewrite rules, and demonstrates the use of the Turing Machine by simulating the computation.

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