I believe the only way to keep code and requirements (any documentation about the code really) is, well, to keep documentation part of the code. This is where TDD comes in. Your requirements are codified into test cases. It's a lot harder for your code to go out of sync with the requirements when the corresponding test cases blow up in your face during CI. :-D
I believe what I am looking for is for the middle ground between TDD and BDD with the option for free txt for these businesses guys...
That’s absolutely true and I agree with that. As long as we’re only talking about coding/technical requirements which only developers need to understand.
As soon as a third party needs to understand the same documentation your solution becomes useless as they don’t understand tests....
Well, maybe not completely useless. I believe we have gotten to a point technology wise where it's relatively easy to express test cases in DSLs or DSL-like APIs. In almost all modern programming languages, we can write test cases in a way that almost all technical details are hidden, and they can be comprehensible to non-programmers. On top of that we also have tools (e.g. Cucumber) that support near-natural-language test case composition directly.
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