Concepts and the related notion of axioms were an extension to C++'s template system proposed for C++11. They were designed to improve compiler diagnostics and to allow programmers to codify in the program some formal properties of templates that they write. Incorporating these limited formal specifications into the program (in addition to improving code clarity) can guide some compiler optimizations, and can potentially help improve program reliability through the use of formal verification tools to check that the implementation and specification actually match.