I believe this is called literate programming (LP), which focuses on real documentation (in the broader sense, including specs, etc) rather than mere API docs. There are quite a lot of LP tools, many of them being independent from the language.

However, LP is not about tools. I've written LP programs that don't need any extra tool[1]. Rather, LP is about putting the documentation (spec, requirements, etc) at the highest level, and make the code a sublevel of that. This is very different from the traditional approaches where code is the highest level, or where documentation and code are separate.

[1] This worked because the build script was part of the literate program, too. Many "problems" with LP solve themselves if you just apply LP consequently.