C++ Template Metaprogramming and Polynomial-Time Functions

In this paper we investigate the relationship between template metaprogramming and implicit complexity, defining a recursive metalanguage by means of C++ templates; we show that the language captures the set of polynomial-time computable functions, that is, functions computable by a Turing machine in which the number of moves - the time complexity - is bounded by a polynomial. We also show that our approach can be extended to recursion schemes that are more general than those used in ICC; this implies that we are able to capture more natural algorithms.